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we construct the einstein equation for an invariant riemannian metric on the exceptional full flag manifold $ m = g _ 2 / t $. by computing a gr \ " obner basis for a system of polynomials of multi - variables we prove that this manifold admits exactly two non - k \ " ahler invariant einstein metrics. thus $ g _ 2 / t $ turns out to be the first known example of an exceptional full flag manifold which admits at least one non - k \ " ahler and not normal homogeneous einstein metric.
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arxiv:1010.3661
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we performed multi - band deep imaging of the field around grb 050730 to identify the host galaxies of intervening absorbers, which consist of a damped ly { \ alpha } absorption ( dla ) system at zabs = 3. 564, a sub - dla system at zabs = 3. 022, and strong mgii absorption systems at zabs = 1. 773 and 2. 253. our observations were performed after the gamma - ray burst afterglow had disappeared. thus, our imaging survey has a higher sensitivity to the host galaxies of the intervening absorbers than the normal imaging surveys in the direction of qsos, for which the qso glare tends to hide the foreground galaxies. in this deep imaging survey, we could not detect any unambiguous candidates for the host galaxies of the intervening absorbers. using the 3sigma upper limit of the flux in the optical to mid - infrared observing bands, which corresponds to the uv to optical bands in the rest - frame of the intervening absorbers, we constrained the star - formation rates and stellar masses of the hosts. we estimated the star - formation rates for the intervening absorbers as < 2. 5 msun / yr for z > 3 dlas and < 1. 0 msun / yr for z ~ 2 mgii systems. their stellar masses are estimated to be several times 10 ^ 9 msun or smaller for all intervening galaxies. these properties are comparable to dwarf galaxies, rather than the massive star - forming galaxies commonly seen in the z > 2 galaxy surveys based on emission - line selection or color selection.
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arxiv:1207.5840
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in semiconductors, spin - orbit effective magnetic fields, i. e., the rashba and dresselhaus fields, are used to control electron - spin polarization. this operation, however, destroys the electron - spin coherence, and the spin polarization is limited to the vicinity of a ferromagnetic source electrode. in this paper, we propose the use of dilute magnetic semiconductors to improve the coherence of spatially oscillating electron - spin polarization. in dilute magnetic semiconductors, the electron - spin polarization near the source electrode dynamically induces the local spin polarization of magnetic impurities through s - d spin - flip scattering. this impurity - spin polarization improves, in turn, the coherence of the electron - spin polarization, and this improved electron - spin polarization induces impurity - spin polarization farther in the adjacent region. because of this positive feedback, the coherent and synchronized spatial oscillations of electron - and impurity - spin polarizations grow cooperatively. a numerical calculation for a cdmnte quantum well demonstrates the validity of this mechanism.
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arxiv:1106.3124
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brane configurations in a circle allow subsequent applications of the hanany - witten transitions, which are known as duality cascades. by studying the process of duality cascades corresponding to quantum curves with symmetries of weyl groups, we find a hidden structure of affine weyl groups. namely, the fundamental domain of duality cascades consisting of all the final destinations is characterized by the affine weyl chamber and the duality cascades are realized as translations of the affine weyl group, where the overall rank in the brane configuration associates to the grading operator of the affine algebra. the structure of the affine weyl group guarantees the finiteness of the processes and the uniqueness of the endpoint of the duality cascades. in addition to the original duality cascades, we can generalize to the cases with fayet - iliopoulos parameters. there we can utilize the weyl group to analyze the fundamental domain similarly and find that the fundamental domain continues to be the affine weyl chamber. we further interpret the weyl group we impose as a " half " of the hanany - witten transition.
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arxiv:2112.13616
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regularity, complete intersection and gorenstein properties of a local ring can be characterized by homological conditions on the canonical homomorphism into its residue field ( serre, avramov, auslander ). it is also known that in positive characteristic, the frobenius endomorphism can also be used for these characterizations ( kunz,... ), and more generally any contracting endomorphism. we introduce here a class of local homomorphisms, in some sense larger than all above, for which these characterizations still hold, providing an unified treatment for this class of homomorphisms.
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arxiv:1209.5051
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learning argumentative writing is challenging. besides writing fundamentals such as syntax and grammar, learners must select and arrange argument components meaningfully to create high - quality essays. to support argumentative writing computationally, one step is to mine the argumentative structure. when combined with automatic essay scoring, interactions of the argumentative structure and quality scores can be exploited for comprehensive writing support. although studies have shown the usefulness of using information about the argumentative structure for essay scoring, no argument mining corpus with ground - truth essay quality annotations has been published yet. moreover, none of the existing corpora contain essays written by school students specifically. to fill this research gap, we present a german corpus of 1, 320 essays from school students of two age groups. each essay has been manually annotated for argumentative structure and quality on multiple levels of granularity. we propose baseline approaches to argument mining and essay scoring, and we analyze interactions between both tasks, thereby laying the ground for quality - oriented argumentative writing support.
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arxiv:2404.02529
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it has been known for some time that $ w $ algebras can be realised in terms of an energy - momentum tensor together with additional free scalar fields. some recent results have shown that more general realisations are also possible. in this paper, we consider a wide class of realisations that may be obtained from the miura transformation, related to the existence of canonical subalgebras of the lie algebras on which the $ w $ algebras are based. we give explicit formulae for all realisations of this kind, and discuss their applications in $ w $ - string theory.
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arxiv:hep-th/9204038
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qed cascades play an important role in extreme astrophysical environments like magnetars. they can also be produced by passing a relativistic electron beam through an intense laser field. signatures of collective pair plasma effects in these qed cascades are shown to appear, in exquisite detail, through plasma - induced frequency upshifts in the laser spectrum. remarkably, these signatures can be detected even in small plasma volumes moving at relativistic speeds. strong - field quantum and collective pair plasma effects can thus be explored with existing technology, provided that ultra - dense electron beams are colocated with multi - pw lasers.
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arxiv:2001.02590
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we use the matching method to investigate the first - order phase transition in holographic superconductor and superfluid. we first use the simple holographic superconductor model to describe the matching method and mention how to see the first - order phase transition. next, we study the holographic superconductor with st \ " uckelberg term and see that the analytic results indicate the existence of first - order phase transition. finally, we study the holographic superfluid and show that the first - order phase transition can be found for some values of parameters. we determine the critical value analytically and compare it with the previous numerical result.
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arxiv:1307.5614
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security models have been designed to ensure data is accessed and used in proper manner according to the security policies. unfortunately, human role in designing security models has been ignored. human behavior relates to many security breaches and plays a significant part in many security situations. in this paper, we study users ' security decision making toward security and usability through the mental model approach. to elicit and depict users ' security and usability mental models, crowd sourcing techniques and cognitive map method are applied and we have performed an experiment to evaluate our findings using amazon mturk.
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arxiv:1807.06729
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we demonstrate spectroscopy of incoherent light with sub - diffraction resolution. in a proof - of - principle experiment we analyze the spectrum of a pair of incoherent point - like sources whose separation is below the diffraction limit. the two sources mimic a planetary system, with a brighter source for the star and a dimmer one for the planet. acquiring spectral information about the secondary source is hard because the two images have a substantial overlap. this limitation is solved by leveraging a structured measurement based on spatial - mode demultiplexing, where light is first sorted in its hermite - gaussian components in the transverse field, then measured by photon detection. this allows us to effectively decouple the photons coming from the two sources. an application is suggested to enhance exoplanets ' atmosphere spectroscopy. a number of experiments of super - resolution imaging based on spatial demultiplexing have been conducted in the past few years, with promising results. here, for the first time to the best of our knowledge, we extend this concept to the domain of spectroscopy.
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arxiv:2409.01190
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in this paper different types of compositions involving independent fractional brownian motions b ^ j _ { h _ j } ( t ), t > 0, j = 1, $ are examined. the partial differential equations governing the distributions of i _ f ( t ) = b ^ 1 _ { h _ 1 } ( | b ^ 2 _ { h _ 2 } ( t ) | ), t > 0 and j _ f ( t ) = b ^ 1 _ { h _ 1 } ( | b ^ 2 _ { h _ 2 } ( t ) | ^ { 1 / h _ 1 } ), t > 0 are derived by different methods and compared with those existing in the literature and with those related to b ^ 1 ( | b ^ 2 _ { h _ 2 } ( t ) | ), t > 0. the process of iterated brownian motion i ^ n _ f ( t ), t > 0 is examined in detail and its moments are calculated. furthermore for j ^ { n - 1 } _ f ( t ) = b ^ 1 _ { h } ( | b ^ 2 _ h (... | b ^ n _ h ( t ) | ^ { 1 / h }... ) | ^ { 1 / h } ), t > 0 the following factorization is proved j ^ { n - 1 } _ f ( t ) = \ prod _ { j = 1 } ^ { n } b ^ j _ { \ frac { h } { n } } ( t ), t > 0. a series of compositions involving cauchy processes and fractional brownian motions are also studied and the corresponding non - homogeneous wave equations are derived.
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arxiv:1003.5276
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the classical electromagnetic lag assocated with the aharonov - bohm phase shift is obtained by using a darwin - lagrangian analysis similar to that given by coleman and van vleck to identify the puzzling forces of the shockley - james paradox. the classical forces cause changes in particle velocities and so produce a relative lag leading to the same phase shift as predicted by aharonov and bohm and observed in experiments. an experiment is proposed to test for this lag aspect implied by the classical analysis but not present in the currently - accepted quantum topological description of the phase shift.
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arxiv:physics/0506180
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we present a novel space - efficient graph coarsening technique for $ n $ - vertex planar graphs $ g $, called cloud partition, which partitions the vertices $ v ( g ) $ into disjoint sets $ c $ of size $ o ( \ log n ) $ such that each $ c $ induces a connected subgraph of $ g $. using this partition $ p $ we construct a so - called structure - maintaining minor $ f $ of $ g $ via specific contractions within the disjoint sets such that $ f $ has $ o ( n / \ log n ) $ vertices. the combination of $ ( f, p ) $ is referred to as a cloud decomposition. for planar graphs we show that a cloud decomposition can be constructed in $ o ( n ) $ time and using $ o ( n ) $ bits. given a cloud decomposition $ ( f, p ) $ constructed for a planar graph $ g $ we are able to find a balanced separator of $ g $ in $ o ( n / \ log n ) $ time. contrary to related publications, we do not make use of an embedding of the planar input graph. we generalize our cloud decomposition from planar graphs to $ h $ - minor - free graphs for any fixed graph $ h $. this allows us to construct the succinct encoding scheme for $ h $ - minor - free graphs due to blelloch and farzan ( cpm 2010 ) in $ o ( n ) $ time and $ o ( n ) $ bits improving both runtime and space by a factor of $ \ theta ( \ log n ) $. as an additional application of our cloud decomposition we show that, for $ h $ - minor - free graphs, a tree decomposition of width $ o ( n ^ { 1 / 2 + \ epsilon } ) $ for any $ \ epsilon > 0 $ can be constructed in $ o ( n ) $ bits and a time linear in the size of the tree decomposition. finally, we implemented our cloud decomposition algorithm and experimentally verified its practical effectiveness on both randomly generated graphs and real - world graphs such as road networks. the obtained data shows that a simplified version of our algorithms suffices in a practical setting, as many of the theoretical worst - case scenarios are not present in the graphs we encountered.
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arxiv:2205.06128
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automated program repair ( apr ) techniques have drawn wide attention from both academia and industry. meanwhile, one main limitation with the current state - of - the - art apr tools is that patches passing all the original tests are not necessarily the correct ones wanted by developers, i. e., the plausible patch problem. to date, various patch - correctness checking ( pcc ) techniques have been proposed to address this important issue. however, they are only evaluated on very limited datasets as the apr tools used for generating such patches can only explore a small subset of the search space of possible patches, posing serious threats to external validity to existing pcc studies. in this paper, we construct an extensive pcc dataset ( the largest manually labeled pcc dataset to our knowledge ) to revisit all state - of - the - art pcc techniques. more specifically, our pcc dataset includes 1, 988 patches generated from the recent prapr apr tool, which leverages highly - optimized bytecode - level patch executions and can exhaustively explore all possible plausible patches within its large predefined search space ( including well - known fixing patterns from various prior apr tools ). our extensive study of representative pcc techniques on the new dataset has revealed various surprising findings and provided guidelines for future pcc research.
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arxiv:2207.06590
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search for compressed supersymmetry at multi - tev scale, in the presence of a light gravitino dark matter, can get sizable uplift while looking into the associated fat - jets with missing transverse momenta as a signature of the boson produced in the decay process of much heavier next - to - lightest sparticle. we focus on the hadronic decay of the ensuing higgs and / or $ z $ boson giving rise to at least two fat - jets and $ \ slashed { e } _ t $ in the final state. we perform a detailed background study adopting a multivariate analysis using a boosted decision tree to provide a robust investigation to explore the discovery potential for such signal at 14 tev lhc considering different benchmark points satisfying all the theoretical and experimental constraints. this channel provides the best discovery prospects with most of the benchmarks discoverable within an integrated luminosity of $ \ mathcal { l } = 200 $ fb $ ^ { - 1 } $. kinematic observables are investigated in order to distinguish between compressed and uncompressed spectra having similar event yields.
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arxiv:2007.00351
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in this sequel to the recent work ( see azizi et al., 2015 ), we investigate a subclass of analytic and bi - univalent functions in the open unit disk. we obtain bounds for initial coefficients, the fekete - szeg \ " o inequality and the second hankel determinant inequality for functions belonging to this subclass. we also discuss some new and known special cases, which can be deduced from our results.
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arxiv:1508.07462
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we describe the lattice deformation in graphene under strain effect by considering the spacial - momenta coordinates do not commute. this later can be realized by introducing the star product to end up with a generalized heisenberg algebra. within such framework, we build a new model describing dirac fermions interacting with an external source that noncommutative parameter $ \ kappa $ dependent. the solutions of the energy spectrum are showing effective landau levels in similar way to the case of a real magnetic field applied to graphene. we show that some strain configurations would be able to explicitly evaluate $ \ kappa $ and then offer a piste toward its measurement.
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arxiv:2006.04143
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this paper reviews the status of high temperature superconductors for high field magnets for future devices such as a high energy lhc or a muon collider. some of the primary challenges faced for the implementation of systems are discussed. two conductor technologies, bi $ _ 2 $ sr $ _ 2 $ cacu $ _ 2 $ o $ _ { 8 + x } $ and yba $ _ 2 $ cu $ _ 3 $ o $ _ { 7 - \ delta } $, have emerged as high field conductor options, but their relative advantages and disadvantages for high field magnets are quite different. these are reviewed from an engineering perspective, including coil manufacturing, electromechanical behaviour and quench behaviour. lastly, the important roles of " system pull " upon conductor and magnet technology development, and of interactions between the materials and magnet communities for accelerating development, are discussed.
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arxiv:1108.1634
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computer science is the study of computation, information, and automation. computer science spans theoretical disciplines ( such as algorithms, theory of computation, and information theory ) to applied disciplines ( including the design and implementation of hardware and software ). algorithms and data structures are central to computer science. the theory of computation concerns abstract models of computation and general classes of problems that can be solved using them. the fields of cryptography and computer security involve studying the means for secure communication and preventing security vulnerabilities. computer graphics and computational geometry address the generation of images. programming language theory considers different ways to describe computational processes, and database theory concerns the management of repositories of data. human – computer interaction investigates the interfaces through which humans and computers interact, and software engineering focuses on the design and principles behind developing software. areas such as operating systems, networks and embedded systems investigate the principles and design behind complex systems. computer architecture describes the construction of computer components and computer - operated equipment. artificial intelligence and machine learning aim to synthesize goal - orientated processes such as problem - solving, decision - making, environmental adaptation, planning and learning found in humans and animals. within artificial intelligence, computer vision aims to understand and process image and video data, while natural language processing aims to understand and process textual and linguistic data. the fundamental concern of computer science is determining what can and cannot be automated. the turing award is generally recognized as the highest distinction in computer science. = = history = = the earliest foundations of what would become computer science predate the invention of the modern digital computer. machines for calculating fixed numerical tasks such as the abacus have existed since antiquity, aiding in computations such as multiplication and division. algorithms for performing computations have existed since antiquity, even before the development of sophisticated computing equipment. wilhelm schickard designed and constructed the first working mechanical calculator in 1623. in 1673, gottfried leibniz demonstrated a digital mechanical calculator, called the stepped reckoner. leibniz may be considered the first computer scientist and information theorist, because of various reasons, including the fact that he documented the binary number system. in 1820, thomas de colmar launched the mechanical calculator industry when he invented his simplified arithmometer, the first calculating machine strong enough and reliable enough to be used daily in an office environment. charles babbage started the design of the first automatic mechanical calculator, his difference engine, in 1822, which eventually gave him the idea of the first programmable mechanical calculator,
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https://en.wikipedia.org/wiki/Computer_science
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graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics ( e. g., node arrival order inference ). whereas erd \ h { o } s - r \ ' enyi graphs are typically asymmetric, real networks are highly symmetric. so a natural question is whether preferential attachment graphs, where in each step a new node with $ m $ edges is added, exhibit any symmetry. in recent work it was proved that preferential attachment graphs are symmetric for $ m = 1 $, and there is some non - negligible probability of symmetry for $ m = 2 $. it was conjectured that these graphs are asymmetric when $ m \ geq 3 $. we settle this conjecture in the affirmative, then use it to estimate the structural entropy of the model. to do this, we also give bounds on the number of ways that the given graph structure could have arisen by preferential attachment. these results have further implications for information theoretic problems of interest on preferential attachment graphs.
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arxiv:1607.04102
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we consider the quadratic derivative nonlinear schr \ " odinger equation ( dnls ) on the circle. in particular, we develop an infinite iteration scheme of normal form reductions for dnls. by combining this normal form procedure with the cole - hopf transformation, we prove unconditional global well - posedness in $ l ^ 2 ( \ mathbb { t } ) $, and more generally in certain fourier - lebesgue spaces $ \ mathcal { f } l ^ { s, p } ( \ mathbb { t } ) $, under the mean - zero and smallness assumptions. as a byproduct, we construct an infinite sequence of quantities that are invariant under the dynamics. we also show the necessity of the smallness assumption by explicitly constructing a finite time blowup solution with non - small mean - zero initial data.
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arxiv:1509.08139
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theoretical aspects of transversity observables are reviewed. the main focus is on two leading twist transversity single spin asymmetries, one arising from the collins effect and one from the interference fragmentation functions. electron - positron annihilation experiments which are required to obtain these fragmentation functions are discussed, as well as the issues of factorization, evolution and sudakov factors for the relevant observables. these theoretical considerations pinpoint the most realistic scenarios towards measurements of transversity.
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arxiv:hep-ph/0109221
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a detailed study of the absorbing molecular clouds towards the radio source pks1413 + 135, at a redshift z = 0. 247, is reported. physical conditions are derived for the molecular gas in the frame work of two models : a homogeneous multicomponent model with equal filling factors, and a two - phase medium consisting of dense clumps embedded in a more diffuse component. our absorption data are consistent with the presence of a diffuse gas component, dominating the observed opacity, and a dense component, accounting for most of the mass. we show that without knowledge of the small scale structure of the absorbing molecular gas, we can only derive lower limits to the column density. we find that the opacity ratio between two absorbing components in co has varied by a factor 2. 3 \ pm 0. 3. we also discuss what can be derived from molecular absorption line observations concerning the invariance of physical constants.
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arxiv:astro-ph/9708051
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we present results of one - dimensional collisionless simulations of plasma turbulence and related anomalous electron current of the electron cyclotron drift instability ( ecdi ). our highly resolved, long - term simulations of xenon plasma in the magnetic field performed with the warpx particle - in - cell ( pic ) code show several intermediate non - linear stages before the system enters a stationary state with significantly increased electron temperature and a finite level of energy in the electrostatic fluctuations. in early and intermediate non - linear stages, the fluctuations are driven by the electron cyclotron resonances gradually shifting from higher ( $ m > 1 $ ) modes to the fundamental $ m = 1 $ resonance. enhanced resonant growth is observed from the point when the cyclotron $ m = 1 $ mode coincides with the most unstable ion - acoustic mode. in the final stage, the anomalous electron current existing in intermediate stages is quenched to zero. following this quenching, our simulations reveal a transition from ecdi - driven dynamics to saturated ion - acoustic turbulence. the modification of the electron and ion distribution functions and their roles in the non - linear developments and saturation of the instability are analyzed at different non - linear stages. the non - linear development of ecdi driven by the $ \ mathbf { e } \ times \ mathbf { b } $ electron drift from the applied current and the ecdi driven by the ion beam perpendicular to the magnetic field are compared and characterized as two perspectives of the instability, observed through different doppler - shifted frames. an extension of this work incorporating full the dynamics of magnetized ions for ecdi driven by a hydrogen ion beam is shown to develop full beam inversion, with the periodic bursts of growth - saturation cycles of ecdi.
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arxiv:2503.03015
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generalized ideas of unified dark matter and dark energy in the context of dynamical space time theories with a diffusive transfer of energy are studied. the dynamical space - time theories are introduced a vector field whose equation of motion guarantees a conservation of a certain energy momentum tensor, which may be related, but in general is not the same as the gravitational energy momentum tensor. this particular energy momentum tensor is built from a general combination of scalar fields derivatives as the kinetic terms, and possibly potentials for the scalar field. by demanding that the dynamical space vector field be the gradient of a scalar the dynamical space time theory becomes a theory for diffusive interacting dark energy and dark matter. these generalizations produce non - conserved energy momentum tensors instead of conserved energy momentum tensors which leads at the end to a formulation for interacting de - dm. we solved analytically the theories and we show that the $ \ lambda $ cdm is a fixed point of these theories at large times. a particular case has asymptotic correspondence to previously studied non - lagrangian formulations of diffusive exchange between dark energy dark matter.
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arxiv:1812.06151
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coherent state operators ( cso ) are defined as operator valued functions on g = sl ( n, c ), homogeneous with respect to right multiplication by lower triangular matrices. they act on a model space containing all holomorphic finite dimensional representations of g with multiplicity 1. cso provide an analytic tool for studying g invariant 2 - and 3 - point functions, which are written down in the case of $ su _ 3 $. the quantum group deformation of the construction gives rise to a non - commutative coset space. we introduce a " standard " polynomial basis in this space ( related to but not identical with the lusztig canonical basis ) which is appropriate for writing down $ u _ q ( sl _ 3 ) $ invariant 2 - point functions for representaions of the type $ ( \ lambda, 0 ) $ and $ ( 0, \ lambda ) $. general invariant 2 - point functions are written down in a mixed poincar \ ' e - birkhoff - witt type basis.
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arxiv:hep-th/9409027
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we introduce a new system of equations coupling k \ " ahler - einstein and hermitian - yang - mills equations. we provide a moment map interpretation of these equations. we identify a futaki type invariant as an obstruction to the existence of solutions to these equations. we also prove a matsushima - lichnerowicz type theorem. we prove a deformation result that produces nontrivial solutions of these equations under some conditions. we produce examples on some projective bundles using calabi ansatz.
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arxiv:2212.01043
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abstract. automatically generating scientific literature surveys is a valuable task that can significantly enhance research efficiency. however, the diverse and complex nature of information within a literature survey poses substantial challenges for generative models. in this paper, we design a series of prompts to systematically leverage large language models ( llms ), enabling the creation of comprehensive literature surveys through a step - by - step approach. specifically, we design prompts to guide llms to sequentially generate the title, abstract, hierarchical headings, and the main content of the literature survey. we argue that this design enables the generation of the headings from a high - level perspective. during the content generation process, this design effectively harnesses relevant information while minimizing costs by restricting the length of both input and output content in llm queries. our implementation with qwen - long achieved third place in the nlpcc 2024 scientific literature survey generation evaluation task, with an overall score only 0. 03 % lower than the second - place team. additionally, our soft heading recall is 95. 84 %, the second best among the submissions. thanks to the efficient prompt design and the low cost of the qwen - long api, our method reduces the expense for generating each literature survey to 0. 1 rmb, enhancing the practical value of our method.
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arxiv:2408.07884
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we study invariants defined by count of charged, elliptic $ j $ - holomorphic curves in locally conformally symplectic manifolds. we use this to define $ \ mathbb { q } $ - valued deformation invariants of certain complete riemann - finlser manifolds and their isometries and this is used to find some new phenomena in riemann - finlser geometry. in contact geometry this gromov - witten theory is used to study fixed reeb strings of strict contactomorphisms. along the way, we state an analogue of the weinstein conjecture in lcs geometry, directly extending the weinstein conjecture, and discuss various partial verifications. a counterexample for a stronger, also natural form of this conjecture is given.
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arxiv:2309.09848
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stroke - based rendering aims to reconstruct an input image into an oil painting style by predicting brush stroke sequences. conventional methods perform this prediction stroke - by - stroke or require multiple inference steps due to the limitations of a predictable number of strokes. this procedure leads to inefficient translation speed, limiting their practicality. in this study, we propose mambapainter, capable of predicting a sequence of over 100 brush strokes in a single inference step, resulting in rapid translation. we achieve this sequence prediction by incorporating the selective state - space model. additionally, we introduce a simple extension to patch - based rendering, which we use to translate high - resolution images, improving the visual quality with a minimal increase in computational cost. experimental results demonstrate that mambapainter can efficiently translate inputs to oil painting - style images compared to state - of - the - art methods. the codes are available at https : / / github. com / stomoya / mambapainter.
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arxiv:2410.12524
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we analyze an algorithmic question about immersion theory : for which $ m $, $ n $, and $ cat = \ mathbf { diff } $ or $ \ mathbf { pl } $ is the question of whether an $ m $ - dimensional $ cat $ - manifold is immersible in $ \ mathbb { r } ^ n $ decidable? as a corollary, we show that the smooth embeddability of an $ m $ - manifold with boundary in $ \ mathbb { r } ^ n $ is undecidable when $ n - m $ is even and $ 11m \ geq 10n + 1 $.
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arxiv:1812.09413
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a new method to construct algebro - geometric solutions of rank two schlesinger systems is presented. for an elliptic curve represented as a ramified double covering of cp ^ 1, a meromorphic differential is constructed with the following property : the common projection of its two zeros on the base of the covering, regarded as a function of the only moving branch point of the covering, is a solution of a painleve vi equation. this differential provides an invariant formulation of a classical okamoto transformation for the painleve vi equations. a generalization of this differential to hyperelliptic curves is also constructed. in this case, positions of zeros of the differential provide part of a solution of the multidimensional garnier system. the corresponding solutions of the rank two schlesinger systems associated with elliptic and hyperelliptic curves are constructed in terms of this differential. the initial data for construction of the meromorphic differential include a point in the jacobian of the curve, under the assumption that this point has nonvariable coordinates with respect to the lattice of the jacobian while the branch points vary. it appears that the cases where the coordinates of the point are rational correspond to periodic trajectories of the billiard ordered games associated with g confocal quadrics in ( g + 1 ) - dimensional space. this is a generalization of a situation studied by hitchin, who related algebraic solutions of a painleve vi equation with the poncelet polygons.
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arxiv:1506.06301
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we prove that the critical wave maps equation with target $ s ^ 2 $ and origin $ \ mathbb { r } ^ { 2 + 1 } $ admits energy class blow up solutions of the form $ $ u ( t, r ) = q ( \ lambda ( t ) r ) + \ epsilon ( t, r ) $ $ where $ q : \ mathbb { r } ^ 2 \ to s ^ 2 $ is the ground state harmonic map and $ \ lambda ( t ) = t ^ { - 1 - \ nu } $ for any $ \ nu > 0 $. this extends the work [ 13 ], where such solutions were constructed under the assumption $ \ nu > 1 / 2 $. in light of a result of struwe [ 22 ], our result is optimal for polynomial blow up rates.
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arxiv:1403.7356
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we present a jt gravity set up in the presence of projected modmax corrections in two dimensions. our starting point is the einstein ' s gravity in four dimensions accompanied by the modmax lagrangian. the 2d gravity action is obtained following a suitable dimensional reduction which contains a 2d image of the 4d modmax lagrangian. we carry out a perturbative analysis to find out the vacuum structure of the theory which asymptotes to $ ads _ 2 $ in the absence of $ u ( 1 ) $ gauge fields. we estimate the holographic central charge and obtain corrections perturbatively upto quadratic order in the modmax and the $ u ( 1 ) $ coupling. we also find out modmax corrected 2d black hole solutions and discuss their extremal limits.
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arxiv:2303.14379
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electron magnetic circular dichroism ( emcd ) is a powerful technique for estimating element - specific magnetic moments of materials on nanoscale with the potential to reach atomic resolution in transmission electron microscopes. however, the fundamentally weak emcd signal strength complicates quantification of magnetic moments, as this requires very high precision, especially in the denominator of the sum rules. here, we employ a statistical resampling technique known as bootstrapping to an experimental emcd dataset to produce an empirical estimate of the noise dependent error distribution resulting from application of emcd sum rules to bcc iron in a 3 beam orientation. we observe clear experimental evidence that noisy emcd signals preferentially bias the estimation of magnetic moments, further supporting this with error distributions produced by monte - carlo simulations. finally, we propose guidelines for the recognition and minimization of this bias in the estimation of magnetic moments.
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arxiv:2306.15866
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we propose a method for extracting hierarchical backbones from a bipartite network. our method leverages the observation that a hierarchical relationship between two nodes in a bipartite network is often manifested as an asymmetry in the conditional probability of observing the connections to them from the other node set. our method estimates both the importance and direction of the hierarchical relationship between a pair of nodes, thereby providing a flexible way to identify the essential part of the networks. using semi - synthetic benchmarks, we show that our method outperforms existing methods at identifying planted hierarchy while offering more flexibility. application of our method to empirical datasets - - - a bipartite network of skills and individuals as well as the network between gene products and gene ontology ( go ) terms - - - demonstrates the possibility of automatically extracting or augmenting ontology from data.
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arxiv:2002.07239
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the physical phase space of gauge field theories on a cylindrical spacetime with an arbitrary compact simple gauge group is shown to be the quotient $ { \ bf r } ^ { 2r } / w _ a, $ $ r $ a rank of the gauge group, $ w _ a $ the affine weyl group. the pi formula resulting from dirac ' s operator method contains a symmetrization with respect to $ w _ a $ rather than the integration domain reduction. it gives a natural solution to gribov ' s problem. some features of fermion quantum dynamics caused by the nontrivial phase space geometry are briefly discussed.
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arxiv:hep-th/9308002
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there are a multitude of emerging imaging technologies that could benefit robotics. however the need for bespoke models, calibration and low - level processing represents a key barrier to their adoption. in this work we present nocal, neural odometry and calibration using light fields, a semi - supervised learning architecture capable of interpreting previously unseen cameras without calibration. nocal learns to estimate camera parameters, relative pose, and scene appearance. it employs a scene - rendering hypernetwork pretrained on a large number of existing cameras and scenes, and adapts to previously unseen cameras using a small supervised training set to enforce metric scale. we demonstrate nocal on rendered and captured imagery using conventional cameras, demonstrating calibration - free odometry and novel view synthesis. this work represents a key step toward automating the interpretation of general camera geometries and emerging imaging technologies.
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arxiv:2210.07435
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we give a brief review of the definition of the wang - yau quasilocal mass and discuss the evaluation of which on surfaces of unit size at null infinity of an axi - symmetric spacetime in bondi - van der burg - metzner coordinates.
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arxiv:1901.06948
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we propose two kinds of distinguishing parameter regimes to induce topological su - schrieffer - heeger ( ssh ) phase in a one dimensional ( 1d ) multi - resonator cavity optomechanical system via modulating the frequencies of both cavity fields and resonators. the introduction of the frequency modulations allows us to eliminate the stokes heating process for the mapping of the tight - binding hamiltonian without usual rotating wave approximation, which is totally different from the traditional mapping of the topological tight - binding model. we find that the tight - binding hamiltonian can be mapped into a topological ssh phase via modifying the bessel function originating from the frequency modulations of cavity fields and resonators, and the induced ssh phase is independent on the effective optomechanical coupling strength. on the other hand, the insensitivity of the system to the effective optomechanical coupling provides us another new path to induce the topological ssh phase based on the present 1d cavity optomechanical system. and we show that the system can exhibit a topological ssh phase via varying the effective optomechanical coupling strength in an alternative way, which is much more easier to be achieved in experiment. furthermore, we also construct an analogous bosonic kitaev model with the trivial topology by keeping the stokes heating processes. our scheme provides a steerable platform to investigate the effects of next - nearest - neighboring interactions on the topology of the system.
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arxiv:1912.13231
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we report the discovery of a very young high - mass x - ray binary ( hmxb ) system associated with the supernova remnant ( snr ) mcsnrj0513 - 6724 in the large magellanic cloud ( lmc ), using xmm - newton x - ray observations. the hmxb is located at the geometrical centre of extended soft x - ray emission, which we confirm as an snr. the hmxb spectrum is consistent with an absorbed power law with spectral index ~ 1. 6 and a luminosity of 7x10 ^ { 33 } ergs / s ( 0. 2 - - 12 kev ). tentative x - ray pulsations are observed with a periodicity of 4. 4 s and the ogle i - band light curve of the optical counterpart from more than 17. 5 years reveals a period of 2. 2324 \ pm0. 0003 d, which we interpret as the orbital period of the binary system. the x - ray spectrum of the snr is consistent with non - equilibrium shock models as expected for young / less evolved snrs. from the derived ionisation time scale we estimate the age of the snr to be < 6 kyr. the association of the hmxb with the snr makes it the youngest hmxb, in the earliest evolutionary stage known to date. a hmxb as young as this can switch on as an accreting pulsar only when the spin period has reached a critical value. under this assumption, we obtain an upper limit to the magnetic field of < 5x10 ^ { 11 } g. this implies several interesting possibilities including magnetic field burial, possibly by an episode of post - supernova hyper - critical accretion. since these fields are expected to diffuse out on a timescale of 10 ^ { 3 } - 10 ^ { 4 } years, the discovery of a very young hmxb can provide us the unique opportunity to observe the evolution of the observable magnetic field for the first time in x - ray binaries.
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arxiv:1910.02792
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in this article, we construct some examples of noncommutative projective calabi - yau schemes by using noncommutative segre products and quantum weighted hypersurfaces. we also compare them with commutative calabi - yau varieties and examples by kanazawa. in particular, we show that some of our constructions are essentially new examples of noncommutative projective calabi - yau schemes.
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arxiv:2209.12190
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here we introduce probabilistic weighted and unweighted multilayer networks as derived from information theoretical correlation measures on large multidimensional datasets. we present the fundamentals of the formal application of probabilistic inference on problems embedded in multilayered environments, providing examples taken from the analysis of biological and social systems : cancer genomics and drug - related violence.
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arxiv:1808.07857
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physical unclonable functions ( pufs ), as hardware security primitives, exploit manufacturing randomness to extract hardware instance - specific secrets. one of most popular structures is time - delay based arbiter puf attributing to large number of challenge response pairs ( crps ) yielded and its compact realization. however, modeling building attacks threaten most variants of apufs that are usually employed for strong puf - oriented application - - - lightweight authentication - - - without reliance on the securely stored digital secrets based standard cryptographic protocols. in this paper, we investigate a reconfigurable latent obfuscation technique endowed puf construction, coined as ob - puf, to maintain the security of elementary puf crps enabled authentication where a crp is never used more than once. the obfuscation - - - determined by said random patterns - - - conceals and distorts the relationship between challenge - response pairs capable of thwarting a model building adversary needing to know the exact relationship between challenges and responses. a bit further, the obfuscation is hidden and reconfigured on demand, in other words, the patterns are not only invisible but also act as one - time pads that are only employed once per authentication around and then discarded. as a consequence, the ob - puf demonstrates significant resistance to the recent revealed powerful evaluation strategy ( es ) based modeling attacks where the direct relationship between challenge and response is even not a must. the ob - puf ' s uniqueness and reliability metrics are also systematically studied followed by formal authentication capability evaluations.
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arxiv:1706.06232
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based on the concept of a nonequilibrium steady state, we present a novel method to experimentally determine energy landscapes acting on colloidal systems. by measuring the stationary probability distribution and the current in the system, we explore potential landscapes with barriers up to several hundred $ \ kt $. as an illustration, we use this approach to measure the effective diffusion coefficient of a colloidal particle moving in a tilted potential.
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arxiv:0705.0323
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solar radio observation is a method used to study the sun. it is very important for space weather early warning and solar physics research to automatically classify solar radio spectrums in real time and judge whether there is a solar radio burst. as the number of solar radio burst spectrums is small and uneven, this paper proposes a classification method for solar radio spectrums based on the swin transformer. first, the method transfers the parameters of the pretrained model to the swin transformer model. then, the hidden layer weights of the swin transformer are frozen, and the fully connected layer of the swin transformer is trained on the target dataset. finally, pa - rameter tuning is performed. the experimental results show that the method can achieve a true positive rate of 100 %, which is more accurate than previous methods. moreover, the number of our model parameters is only 20 million, which is 80 % lower than that of the traditional vgg16 con - volutional neural network with more than 130 million parameters.
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arxiv:2502.03782
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bismuth ( 209bi ) is the deepest group v donor in silicon and possesses the most extreme characteristics such as a 9 / 2 nuclear spin and a 1. 5 ghz hyperfine coupling. these lead to several potential advantages for a si : bi donor electron spin qubit compared to the more common phosphorus donor. previous studies on si : bi have been performed using natural silicon where linewidths and electron spin coherence times are limited by the presence of 29si impurities. here we describe electron spin resonance ( esr ) and electron nuclear double resonance ( endor ) studies on 209bi in isotopically pure 28si. esr and endor linewidths, transition probabilities and coherence times are understood in terms of the spin hamiltonian parameters showing a dependence on field and mi of the 209bi nuclear spin. we explore various decoherence mechanisms applicable to the donor electron spin, measuring coherence times up to 700 ms at 1. 7 k at x - band, comparable with 28si : p. the coherence times we measure follow closely the calculated field - sensitivity of the transition frequency, providing a strong motivation to explore ' clock ' transitions where coherence lifetimes could be further enhanced.
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arxiv:1207.3776
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the study of non - local operators in gauge theory and holography, such as line - operators or interfaces, has attracted significant attention. two - dimensional symmetric product orbifolds are close cousins of higher - dimensional gauge theory. in this work, we construct a novel family of interfaces in symmetric product orbifolds. these may be regarded as two - dimensional analogues of wilson - line operators or karch - randall interfaces at the same time. the construction of the interfaces entails the choice of boundary conditions of the seed theory. for a generic seed theory, we construct the boundary states associated to the interfaces via the folding trick, compute their overlaps and extract the spectrum of interface changing operators through modular transformation. then, we specialise to the supersymmetric four - torus $ \ mathbb { t } ^ 4 $ and show that the corresponding interfaces of the symmetric product orbifold are dual to $ ads _ 2 $ branes in the tensionless limit of type iib superstring theory on $ ads _ 3 \ times s ^ 3 \ times \ mathbb { t } ^ 4 $.
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arxiv:2504.00078
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the transferable neural network ( transnet ) is a two - layer shallow neural network with pre - determined and uniformly distributed neurons in the hidden layer, and the least - squares solvers can be particularly used to compute the parameters of its output layer when applied to the solution of partial differential equations. in this paper, we integrate the transnet technique with the nonoverlapping domain decomposition and the interface conditions to develop a novel multiple transferable neural network ( multi - transnet ) method for solving elliptic interface problems, which typically contain discontinuities in both solutions and their derivatives across interfaces. we first propose an empirical formula for the transnet to characterize the relationship between the radius of the domain - covering ball, the number of hidden - layer neurons, and the optimal neuron shape. in the multi - transnet method, we assign each subdomain one distinct transnet with an adaptively determined number of hidden - layer neurons to maintain the globally uniform neuron distribution across the entire computational domain, and then unite all the subdomain transnets together by incorporating the interface condition terms into the loss function. the empirical formula is also extended to the multi - transnet and further employed to estimate appropriate neuron shapes for the subdomain transnets, greatly reducing the parameter tuning cost. additionally, we propose a normalization approach to adaptively select the weighting parameters for the terms in the loss function. ablation studies and extensive experiments with comparison tests on different types of elliptic interface problems with low to high contrast diffusion coefficients in two and three dimensions are carried out to numerically demonstrate the superior accuracy, efficiency, and robustness of the proposed multi - transnet method.
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arxiv:2502.19893
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we investigate special lcs and twisted hamiltonian torus actions on strict lcs manifolds and characterize them geometrically in terms of the minimal presentation. we prove a convexity theorem for the corresponding twisted moment map, establishing thus an analog of the symplectic convexity theorem of atiyah and guillemin - sternberg. we also prove similar results for the symplectic moment map ( defined on the minimal presentation ) whose image is then a convex cone. in the special case of a compact toric vaisman manifold, we obtain a structure theorem.
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arxiv:1805.00218
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we investigate tunneling through a short interacting wire. we identify two temperature regimes ( a ) $ t _ { kondo } < t \ le t ^ { wire } = \ hbar v _ f / k _ bd $ ( $ d $ is the length of the short wire ) and ( b ) $ t < t _ { kondo } \ ll t ^ { wire } $. in the first regime the effective ( renormalized ) electron - electron interaction is smaller than the tunneling matrix element. this is the situation at finite temperature $ t $ where the single particle spectrum of the wire is characterized by a multilevel " quantum dot " system with magnetic quantum number s = 0 which is higher in energy than the su ( 2 ) spin doublet $ s = \ pm1 / 2 $. due to the single particle energy we find that the tunneling electron into the wire must have an opposite spin to the one in the short wire giving rise to a conductance, $ g = g _ \ uparrow + g _ \ downarrow $, $ e ^ 2 / h \ le g \ ll 2e ^ 2 / h $. in the second regime, when $ t \ to0 $ we have a situation that the effective ( renormalized ) electron - electron interaction is larger than the tunneling matrix element. this problem is equivalent to a kondo problem. we find for $ t < t _ { kondo } $ that the conductance is given by $ g = 2e ^ 2 / h $. these results are in agreement with recent experiments where for $ t _ { kondo } < t < t ^ { wire } $ the conductance $ g $ obeys $ e ^ 2 / h \ le g \ ll 2e ^ 2 / h $, and for $ t < t _ { kondo } $, $ g = 2e ^ 2 / h $. in both regimes the current is not polarized and the su ( 2 ) symmetry is not broken.
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arxiv:cond-mat/0312305
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despite tremendous success of deep neural network in machine learning, the underlying reason for its superior learning capability remains unclear. here, we present a framework based on statistical physics to study dynamics of stochastic gradient descent ( sgd ) that drives learning in neural networks. by using the minibatch gradient ensemble, we construct order parameters to characterize dynamics of weight updates in sgd. without mislabeled data, we find that the sgd learning dynamics transitions from a fast learning phase to a slow exploration phase, which is associated with large changes in order parameters that characterize the alignment of sgd gradients and their mean amplitude. in the case with randomly mislabeled samples, sgd learning dynamics falls into four distinct phases. the system first finds solutions for the correctly labeled samples in phase i, it then wanders around these solutions in phase ii until it finds a direction to learn the mislabeled samples during phase iii, after which it finds solutions that satisfy all training samples during phase iv. correspondingly, the test error decreases during phase i and remains low during phase ii ; however, it increases during phase iii and reaches a high plateau during phase iv. the transitions between different phases can be understood by changes of order parameters that characterize the alignment of mean gradients for the correctly and incorrectly labeled samples and their ( relative ) strength during learning. we find that individual sample losses for the two datasets are most separated during phase ii, which leads to a cleaning process to eliminate mislabeled samples for improving generalization.
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arxiv:2101.06509
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it is well established that the hilbert space for charged particles in a plane subject to a uniform magnetic field can be described by two mutually commuting ladder algebras. we propose a similar formalism for landau level quantization involving two mutually commuting su ( 2 ) algebras.
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arxiv:1101.3943
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we study the dependence of galaxy clustering on luminosity and stellar mass at redshifts z ~ [ 0. 2 - 1 ] using the first zcosmos 10k sample. we measure the redshift - space correlation functions xi ( rp, pi ) and its projection wp ( rp ) for sub - samples covering different luminosity, mass and redshift ranges. we quantify in detail the observational selection biases and we check our covariance and error estimate techniques using ensembles of semi - analytic mock catalogues. we finally compare our measurements to the cosmological model predictions from the mock surveys. at odds with other measurements, we find a weak dependence of galaxy clustering on luminosity in all redshift bins explored. a mild dependence on stellar mass is instead observed. at z ~ 0. 7, wp ( rp ) shows strong excess power on large scales. we interpret this as produced by large - scale structure dominating the survey volume and extending preferentially in direction perpendicular to the line - of - sight. we do not see any significant evolution with redshift of the amplitude of clustering for bright and / or massive galaxies. the clustering measured in the zcosmos data at 0. 5 < z < 1 for galaxies with log ( m / m _ \ odot ) > = 10 is only marginally consistent with predictions from the mock surveys. on scales larger than ~ 2 h ^ - 1 mpc, the observed clustering amplitude is compatible only with ~ 1 % of the mocks. thus, if the power spectrum of matter is lcdm with standard normalization and the bias has no unnatural scale - dependence, this result indicates that cosmos has picked up a particularly rare, ~ 2 - 3 sigma positive fluctuation in a volume of ~ 10 ^ 6 h ^ - 1 mpc ^ 3. these findings underline the need for larger surveys of the z ~ 1 universe to appropriately characterize the level of structure at this epoch.
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arxiv:0906.1807
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quantum neuromorphic computing ( qnc ) is a sub - field of quantum machine learning ( qml ) that capitalizes on inherent system dynamics. as a result, qnc can run on contemporary, noisy quantum hardware and is poised to realize challenging algorithms in the near term. one key issue in qnc is the characterization of the requisite dynamics for ensuring expressive quantum neuromorphic computation. we address this issue by proposing a building block for qnc architectures, what we call quantum perceptrons ( qps ). our proposed qps compute based on the analog dynamics of interacting qubits with tunable coupling constants. we show that qps are, with restricted resources, a quantum equivalent to the classical perceptron, a simple mathematical model for a neuron that is the building block of various machine learning architectures. moreover, we show that qps are theoretically capable of producing any unitary operation. thus, qps are computationally more expressive than their classical counterparts. as a result, qnc architectures built our of qps are, theoretically, universal. we introduce a technique for mitigating barren plateaus in qps called entanglement thinning. we demonstrate qps ' effectiveness by applying them to numerous qml problems, including calculating the inner products between quantum states, energy measurements, and time - reversal. finally, we discuss potential implementations of qps and how they can be used to build more complex qnc architectures.
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arxiv:2211.07075
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in order to address the asynchronous interference issue for a generalized scenario with multiple primary and multiple secondary receivers, in this paper, we propose an innovative cooperative beamforming technique. in particular, the cooperative beamforming design is formulated as an optimization problem that maximizes the weighted sum achievable transmission rate of secondary destinations while it maintains the asynchronous interferences at the primary receivers below their target thresholds. in light of the intractability of the problem, we propose a two - phase suboptimal cooperative beamforming technique. first, it finds the beamforming directions corresponding to different secondary destinations. second, it allocates the power among different beamforming directions. due to the multiple interference constraints corresponding to multiple primary receivers, the power allocation scheme in the second phase is still complex. therefore, we also propose a low complex power allocation algorithm. the proposed beamforming technique is extended for the cases, when cooperating cr nodes ( ccrns ) have statistical or erroneous channel knowledge of the primary receivers. we also investigate the performance of joint ccrn selection and beamforming technique. the presented numerical results show that the proposed beamforming technique can significantly reduce the asynchronous interference signals at the primary receivers and increase the sum transmission rate of secondary destinations compared to the well known zero - forcing beamforming ( zfbf ) technique.
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arxiv:1405.1802
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we present an information - theoretic cost function for co - clustering, i. e., for simultaneous clustering of two sets based on similarities between their elements. by constructing a simple random walk on the corresponding bipartite graph, our cost function is derived from a recently proposed generalized framework for information - theoretic markov chain aggregation. the goal of our cost function is to minimize relevant information loss, hence it connects to the information bottleneck formalism. moreover, via the connection to markov aggregation, our cost function is not ad hoc, but inherits its justification from the operational qualities associated with the corresponding markov aggregation problem. we furthermore show that, for appropriate parameter settings, our cost function is identical to well - known approaches from the literature, such as information - theoretic co - clustering of dhillon et al. hence, understanding the influence of this parameter admits a deeper understanding of the relationship between previously proposed information - theoretic cost functions. we highlight some strengths and weaknesses of the cost function for different parameters. we also illustrate the performance of our cost function, optimized with a simple sequential heuristic, on several synthetic and real - world data sets, including the newsgroup20 and the movielens100k data sets.
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arxiv:1801.00584
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disorder has appeared as one of the main mechanisms to induce topologically trivial zero - energy states in superconductor - semiconductor systems, thereby challenging the detection of topological superconductivity and majorana bound states. here we demonstrate that, for disorder in any part of the system, the formation of disorder - induced trivial zero - energy states can to a large extent be mitigated by keeping the coupling between the semiconductor and superconductor weak. the only exception is strong disorder in the semiconductor, where instead the strong coupling regime is somewhat more robust against disorder. furthermore, we find that the topological phase in this weak coupling regime is robust against disorder, with a large and well - defined topological gap which is highly beneficial for topological protection. our work shows the advantages and disadvantages of weak and strong couplings under disorder, important for designing superconductor - semiconductor hybrid structures.
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arxiv:2212.06061
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we analyse the convergence of numerical schemes in the gdm - ellam ( gradient discretisation method - eulerian lagrangian localised adjoint method ) framework for a strongly coupled elliptic - parabolic pde which models miscible displacement in porous media. these schemes include, but are not limited to mixed finite element - ellam and hybrid mimetic mixed - ellam schemes. a complete convergence analysis is presented on the coupled model, using only weak regularity assumptions on the solution ( which are satisfied in practical applications ), and not relying on $ l ^ \ infty $ bounds ( which are impossible to ensure at the discrete level given the anisotropic diffusion tensors and the general grids used in applications ).
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arxiv:1710.01897
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this thesis deals with three different aspects of the combinatorics of permutations. in the first two papers, two flavours of pattern avoiding permutations are examined ; and in the third paper young tableaux, which are closely related to permutations via representation theory, are studied. in the first paper we give solutations to several interesting problems regarding pattern avoiding doubly alternating permutations, such as finding a bijection between 1234 - avoiding permutations and 1234 - avoiding doubly alternating permutations of twice the size. in the second paper partial permutations which can be extended to pattern avoiding permutations are examined. a general algorithm is presented which is subsequently used to solve many different problems. the third paper deals with involutions on young tableaux. there is a surprisingly large collection of relations among these involutions and in the paper we make the effort to study them systematically in order to create a coherent theory. the most interesting result is that for littlewood - richardson tableaux, $ a ^ 3 = 1 $, wher5e $ a $ is the composition of three different involutions : the fundamental symmetry map, the reversal and rotation involutions.
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arxiv:0908.0255
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we study ac conductivities in high - tc cuprates, which offer us significant information to reveal the true electronic ground states. based on the fluctuation - exchange ( flex ) approximation, current vertex corrections ( cvc ' s ) are correctly taken into account to satisfy the conservation laws. we find the significant role of the cvc ' s on the optical hall conductivity in the presence of strong antiferromagnetic ( af ) fluctuations. this fact leads to the failure of the relaxation time approximation ( rta ). as a result, experimental highly unusual behaviors, ( i ) prominent frequency and temperature dependences of the optical hall coefficient, and ( ii ) simple drude form of the optical hall andge for wide range of frequencies, are satisfactorily reproduced. in conclusion, both dc and ac transport phenomena in ( slightly under - doped ) high - tc cuprates can be explained comprehensively in terms of nearly af fermi liquid, if one take the cvc ' s into account.
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arxiv:cond-mat/0507664
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this paper was originally submitted to xinova as a response to a request for invention ( rfi ) on new event monitoring methods. in this paper, a new object tracking algorithm using multiple cameras for surveillance applications is proposed. the proposed system can detect sudden - appearance - changes and occlusions using a hidden markovian statistical model. the experimental results confirm that our system detect the sudden - appearance changes and occlusions reliably.
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arxiv:1610.09520
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tensor models are generalizations of matrix models, and are studied as discrete models of quantum gravity for arbitrary dimensions. among them, the canonical tensor model ( ctm for short ) is a rank - three tensor model formulated as a totally constrained system with a number of first - class constraints, which have a similar algebraic structure as the constraints of the adm formalism of general relativity. in this paper, we formulate a super - extension of ctm as an attempt to incorporate fermionic degrees of freedom. the kinematical symmetry group is extended from $ o ( n ) $ to $ osp ( n, \ tilde n ) $, and the constraints are constructed so that they form a first - class constraint super - poisson algebra. this is a straightforward super - extension, and the constraints and their algebraic structure are formally unchanged from the purely bosonic case, except for the additional signs associated to the order of the fermionic indices and dynamical variables. however, this extension of ctm leads to the existence of negative norm states in the quantized case, and requires some future improvements as quantum gravity with fermions. on the other hand, since this is a straightforward super - extension, various results obtained so far for the purely bosonic case are expected to have parallels also in the super - extended case, such as the exact physical wave functions and the connection to the dual statistical systems, i. e. randomly connected tensor networks.
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arxiv:1509.01432
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detecting non - classical light is a central requirement for photonics - based quantum technologies. unrivaled high efficiencies and low dark counts have positioned superconducting nanowire single photon detectors ( snspds ) as the leading detector technology for fiber and integrated photonic applications. however, a central challenge lies in their integration within photonic integrated circuits regardless of material platform or surface topography. here, we introduce a method based on transfer printing that overcomes these constraints and allows for the integration of snspds onto arbitrary photonic substrates. we prove this by integrating snspds and showing through - waveguide single - photon detection in commercially manufactured silicon and lithium niobate on insulator integrated photonic circuits. our method eliminates bottlenecks to the integration of high - quality single - photon detectors, turning them into a versatile and accessible building block for scalable quantum information processing.
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arxiv:2409.08412
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the monitoring of data generated by a large number of devices in internet of things ( iot ) systems is an important and complex issue. several studies have explored the use of generic rule engine, primarily based on the rete algorithm, for monitoring the flow of device data. in order to solve the performance problem of the rete algorithm in iot scenarios, some studies have also proposed improved rete algorithms. however, implementing modifications to the general rule engine remains challenges in practical applications. the thingsboard open - source platform introduces an iot - specific rule engine that does not rely on the rete algorithm. its interactive mode attracted attention from developers and researchers. however, the close integration between its rule module and the platform, as well as the difficulty in formulating rules for multiple devices, limits its flexibility. this paper presents an adaptable and user - friendly rule engine framework for monitoring and control iot device data flows. the framework is easily extensible and allows for the formulation of rules contain multiple devices. we designed a domain - specific language ( dsl ) for rule description. a prototype system of this framework was implemented to verify the validity of theoretical method. the framework has potential to be adaptable to a wide range of iot scenarios and is especially effective in where real - time control demands are not as strict.
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arxiv:2310.05493
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it was reported that, if and only if the specific heat, correlation length, and dynamical exponents $ \ alpha, \ nu $ and $ z $, fulfill the condition $ \ alpha - z \ nu > 0 $, the phase transitions can enable a quantum heat engine to approach carnot efficiency at finite power. we start our analysis via a different approach in which the effects of interaction and fluctuations on the hamiltonian of a trapped dilute bose gas belonging to the same universality as $ xy $ model. based on models of quantum otto heat engines, we find the general expression of the efficiency which includes the correction due to interaction and fluctuations at the critical point, and show that, near the bose - einstein - condensation point with $ \ alpha - z \ nu < 0 $, energy fluctuations could enable attaintment of the carnot efficiency with nonvanishing power. such quantum heat engines can also be realized by changing the shape of the trap confining the ideal and weakly interacting bose gas during the adiabatic processes of the cycle. these quantum heat engines working with the trapped bose gases, which are based on techniques of cooling bose condensates and could be realizable at present technology.
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arxiv:1803.03734
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evolution in the measured rest frame ultraviolet spectral slope and ultraviolet to optical flux ratios indicate a rapid evolution in the dust obscuration of galaxies during the first 3 billion years of cosmic time ( z > 4 ). this evolution implies a change in the average interstellar medium properties, but the measurements are systematically uncertain due to untested assumptions, and the inability to measure heavily obscured regions of the galaxies. previous attempts to directly measure the interstellar medium in normal galaxies at these redshifts have failed for a number of reasons with one notable exception. here we report measurements of the [ cii ] gas and dust emission in 9 typical ( ~ 1 - 4l * ) star - forming galaxies ~ 1 billon years after the big bang ( z ~ 5 - 6 ). we find these galaxies have > 12x less thermal emission compared with similar systems ~ 2 billion years later, and enhanced [ cii ] emission relative to the far - infrared continuum, confirming a strong evolution in the interstellar medium properties in the early universe. the gas is distributed over scales of 1 - 8 kpc, and shows diverse dynamics within the sample. these results are consistent with early galaxies having significantly less dust than typical galaxies seen at z < 3 and being comparable to local low - metallicity systems.
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arxiv:1503.07596
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phase stabilization continues to be a critical issue in hafnium oxide ( hfo $ _ 2 $ ) due to the interdependence of various contributing factors. using first - principles calculations, we analyze the effects of strain and doping on stabilizing the ferroelectric phase. we found that combining y - doping, o - vacancy, and compressive biaxial strain, particularly in the ( 111 ) orientation, offers an optimal pathway for stabilizing the ferroelectric phase of hfo $ _ 2 $. analysis of structural coordination reveals how compressive strain affects phase competition. crystallography analysis provides insights into the advantage of the ( 111 ) strain orientation compared to the ( 001 ) orientation. the impact of dopants is discussed in the context of these findings.
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arxiv:2501.00132
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we study order reconstruction ( or ) solutions in the beris - edwards framework for nematodynamics, for both passive and active nematic flows in a microfluidic channel. or solutions exhibit polydomains and domain walls, and as such, are of physical interest. we show that or solutions exist for passive flows with constant velocity and pressure, but only for specific boundary conditions. we prove the existence of unique, symmetric and non - singular nematic profiles, for boundary conditions that do not allow for or solutions. we compute asymptotic expansions for or - type solutions for passive flows with non - constant velocity and pressure, and active flows, which shed light into the internal structure of domain walls. the asymptotics are complemented by extensive numerical studies that demonstrate the universality of or - type structures in static and dynamic scenarios.
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arxiv:2204.07808
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we solve the cauchy problem of the ward model in light - cone coordinates using the inverse spectral ( scattering ) method. in particular we show that the solution can be constructed by solving a $ 2 \ times 2 $ local matrix riemann - hilbert problem which is uniquely defined in terms of the initial data. these results are also directly applicable to the 2 + 1 chiral model.
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arxiv:hep-th/9806035
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we revisit the calculation of the long - distance contribution to the muon - polarization asymmetry \ delta _ { lr }, which arises, in k ^ + \ to \ pi ^ + \ mu ^ + \ mu ^ -, from the two - photon intermediate state. the parity - violating amplitude of this process, induced by the local anomalous k ^ + \ pi ^ - \ gamma ^ * \ gamma ^ * transition, is analysed ; unfortunately, one cannot expect to predict its contribution to the asymmetry by using chiral perturbation theory alone. here we evaluate this amplitude and its contribution to \ delta _ { lr } by employing a phenomenological model called the fmv model, in which the utility of the vector and axial - vector resonances exchange is important to soften the ultraviolet behaviour of the transition. we find that the long - distance contribution is of the same order of magnitude as the standard model short - distance contribution.
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arxiv:hep-ph/0111118
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we report development of a quantum hall resistance standard accurate to a few parts in a billion at 300 mk and based on large area epitaxial graphene. the remarkable precision constitutes an improvement of four orders of magnitude over the best results obtained in exfoliated graphene and is similar to the accuracy achieved in well - established semiconductor standards. unlike the traditional resistance standards the novel graphene device is still accurately quantized at 4. 2 k, vastly simplifying practical metrology. this breakthrough was made possible by exceptional graphene quality achieved with scalable silicon carbide technology on a wafer scale and shows great promise for future large scale applications in electronics.
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arxiv:0909.1220
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noise caused by fluctuations at the molecular level is a fundamental part of intracellular processes. while the response of biological systems to noise has been studied extensively, there has been limited understanding of how to exploit it to induce a desired cell state. here we present a scalable, quantitative method based on the freidlin - wentzell action to predict and control noise - induced switching between different states in genetic networks that, conveniently, can also control transitions between stable states in the absence of noise. we apply this methodology to models of cell differentiation and show how predicted manipulations of tunable factors can induce lineage changes, and further utilize it to identify new candidate strategies for cancer therapy in a cell death pathway model. this framework offers a systems approach to identifying the key factors for rationally manipulating biophysical dynamics, and should also find use in controlling other classes of noisy complex networks.
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arxiv:1509.03349
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numerical stochastic perturbation theory was able to get three - ( and even four - ) loop results for finite lattice qcd renormalization constants. more recently, a conceptual and technical framework has been devised to tame finite size effects, which had been reported to be significant for ( logarithmically ) divergent renormalization constants. in this work we present three - loop results for fermion bilinears in the lattice qcd regularization defined by tree - level symanzik improved gauge action and n _ f = 2 wilson fermions. we discuss both finite and divergent renormalization constants in the ri ' - mom scheme. since renormalization conditions are defined in the chiral limit, our results also apply to twisted mass qcd, for which non - perturbative computations of the same quantities are available. we emphasize the importance of carefully accounting for both finite lattice space and finite volume effects. in our opinion the latter have in general not attracted the attention they would deserve.
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arxiv:1310.4981
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quantum dynamics of many - body systems is a fascinating and significant subject for both theory and experiment. the question of how an isolated many - body system evolves to its steady state after a sudden perturbation or quench still remains challenging. in this paper, using the bethe ansatz wave function, we study the quantum dynamics of an inhomogeneous gaudin magnet. we derive explicit analytical expressions for various local dynamic quantities with an arbitrary number of flipped bath spins, such as : the spin distribution function, the spin - spin correlation function, and the loschmidt echo. we also numerically study the relaxation behavior of these dynamic properties, gaining considerable insight into coherence and entanglement between the central spin and the bath. in particular, we find that the spin - spin correlations relax to their steady value via a nearly logarithmic scaling, whereas the loschmidt echo shows an exponential relaxation to its steady value. our results advance the understanding of relaxation dynamics and quantum correlations of long - range interacting models of gaudin type.
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arxiv:2201.01025
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secure multi - party computation ( mpc ) facilitates privacy - preserving computation between multiple parties without leaking private information. while most secure deep learning techniques utilize mpc operations to achieve feasible privacy - preserving machine learning on downstream tasks, the overhead of the computation and communication still hampers their practical application. this work proposes a low - latency secret - sharing - based mpc design that reduces unnecessary communication rounds during the execution of mpc protocols. we also present a method for improving the computation of commonly used nonlinear functions in deep learning by integrating multivariate multiplication and coalescing different packets into one to maximize network utilization. our experimental results indicate that our method is effective in a variety of settings, with a speedup in communication latency of $ 10 \ sim20 \ % $.
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arxiv:2407.18982
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we present progress on a comprehensive, modular, interactive modeling environment centered on overall regulation of blood pressure and body fluid homeostasis. we call the project saphir, for " a systems approach for physiological integration of renal, cardiac, and respiratory functions ". the project uses state - of - the - art multi - scale simulation methods. the basic core model will give succinct input - output ( reduced - dimension ) descriptions of all relevant organ systems and regulatory processes, and it will be modular, multi - resolution, and extensible, in the sense that detailed submodules of any process ( es ) can be " plugged - in " to the basic model in order to explore, eg. system - level implications of local perturbations. the goal is to keep the basic core model compact enough to insure fast execution time ( in view of eventual use in the clinic ) and yet to allow elaborate detailed modules of target tissues or organs in order to focus on the problem area while maintaining the system - level regulatory compensations.
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arxiv:0806.2005
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the purpose of this survey article is a comprehensive study of operator lipschitz functions. a continuous function $ f $ on the real line $ { \ bbb r } $ is called operator lipschitz if $ \ | f ( a ) - f ( b ) \ | \ le { \ rm const } \ | a - b \ | $ for arbitrary self - adjoint operators $ a $ and $ b $. we give sufficient conditions and necessary conditions for operator lipschitzness. we also study the class of operator differentiable functions on $ { \ bbb r } $. then we consider operator lipschitz functions on closed subsets of the plane as well as commutator lipschitz functions on such subsets. am important role is played by double operator integrals and schur multipliers.
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arxiv:1602.07994
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flood simulation and forecast capability have been greatly improved thanks to advances in data assimilation ( da ) strategies incorporating various types of observations ; many are derived from spatial earth observation. this paper focuses on the assimilation of 2d flood observations derived from synthetic aperture radar ( sar ) images acquired during a flood event with a dual state - parameter ensemble kalman filter ( enkf ). binary wet / dry maps are here expressed in terms of wet surface ratios ( wsr ) over a number of subdomains of the floodplain. this ratio is further assimilated jointly with in - situ water - level observations to improve the flow dynamics within the floodplain. however, the non - gaussianity of the observation errors associated with sar - derived measurements break a major hypothesis for the application of the enkf, thus jeopardizing the optimality of the filter analysis. the novelty of this paper lies in the treatment of the non - gaussianity of the sar - derived wsr observations with a gaussian anamorphosis process ( ga ). this da strategy was validated and applied over the garonne marmandaise catchment ( south - west of france ) represented with the telemac - 2d hydrodynamic model, first in a twin experiment and then for a major flood event that occurred in january - february 2021. it was shown that assimilating sar - derived wsr observations, in complement to the in - situ water - level observations significantly improves the representation of the flood dynamics. also, the ga transformation brings further improvement to the da analysis, while not being a critical component in the da strategy. this study heralds a reliable solution for flood forecasting over poorly gauged catchments thanks to available remote - sensing datasets.
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arxiv:2304.01058
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we describe the target selection procedure by which stars are selected for 2 - minute and 20 - second observations by tess. we first list the technical requirements of the tess instrument and ground systems processing that limit the total number of target slots. we then describe algorithms used by the tess payload operation center ( poc ) to merge candidate targets requested by the various tess mission elements ( the target selection working group, tess asteroseismic science consortium, and guest investigator office ). lastly, we summarize the properties of the observed tess targets over the two - year primary tess mission. we find that the poc target selection algorithm results in 2. 1 to 3. 4 times as many observed targets as target slots allocated for each mission element. we also find that the sky distribution of observed targets is different from the sky distributions of candidate targets due to technical constraints that require a relatively even distribution of targets across the tess fields of view. we caution researchers exploring statistical analyses of tess planet - host stars that the population of observed targets cannot be characterized by any simple set of criteria applied to the properties of the input candidate target lists.
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arxiv:2109.02665
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the observed iron k - alpha fluorescence lines in seyfert - 1 galaxies provide strong evidence for an accretion disk near a supermassive black hole as a source of the line emission. these lines serve as powerful probes for examining the structure of inner regions of accretion disks. previous studies of line emission have considered geometrically thin disks only, where the gas moves along geodesics in the equatorial plane of a black hole. here we extend this work to consider effects on line profiles from finite disk thickness, radial accretion flow and turbulence. we adopt the novikov and thorne ( 1973 ) solution, and find that within this framework, turbulent broadening is the dominant new effect. the most prominent change in the skewed, double - horned line profiles is a substantial reduction in the maximum flux at both red and blue peaks. the effect is most pronounced when the inclination angle is large, and when the accretion rate is high. thus, the effects discussed here may be important for future detailed modeling of high quality observational data.
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arxiv:astro-ph/9806134
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effective biosecurity practices in swine production are key in preventing the introduction and dissemination of infectious pathogens. ideally, biosecurity practices should be chosen by their impact on bio - containment and bio - exclusion, however quantitative supporting evidence is often unavailable. therefore, the development of methodologies capable of quantifying and ranking biosecurity practices according to their efficacy in reducing risk have the potential to facilitate better informed choices. using survey data on biosecurity practices, farm demographics, and previous outbreaks from 139 herds, a set of machine learning algorithms were trained to classify farms by porcine reproductive and respiratory syndrome virus status, depending on their biosecurity practices, to produce a predicted outbreak risk. a novel interpretable machine learning toolkit, mriml - biosecurity, was developed to benchmark farms and production systems by predicted risk, and quantify the impact of biosecurity practices on disease risk at individual farms. quantifying the variable impact on predicted risk 50 % of 42 variables were associated with fomite spread while 31 % were associated with local transmission. results from machine learning interpretations identified similar results, finding substantial contribution to predicted outbreak risk from biosecurity practices relating to : the turnover and number of employees ; the surrounding density of swine premises and pigs ; the sharing of trailers ; distance from the public road ; and production type. in addition, the development of individualized biosecurity assessments provides the opportunity to guide biosecurity implementation on a case - by - case basis. finally, the flexibility of the mriml - biosecurity toolkit gives it potential to be applied to wider areas of biosecurity benchmarking, to address weaknesses in other livestock systems and industry relevant diseases.
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arxiv:2106.06506
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this paper studies the space of $ l ^ 2 $ harmonic forms and $ l ^ 2 $ harmonic spinors on taub - bolt, a ricci - flat riemannian 4 - manifold of alf type. we prove that the space of harmonic square - integrable 2 - forms on taub - bolt is 2 - dimensional and construct a basis. we explicitly find a 2 - parameter family of $ l ^ 2 $ zero modes of the dirac operator twisted by an arbitrary $ l ^ 2 $ harmonic connection. we also show that the number of zero modes found is equal to the index of the dirac operator. we compare our results with those known in the case of taub - nut and euclidean schwarzschild as these manifolds present interesting similarities with taub - bolt. in doing so, we slightly generalise known results on harmonic spinors on euclidean schwarzschild.
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arxiv:1812.07512
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the young radio pulsar j1124 - 5916 is associated with a cas a like supernova remnant g292. 0 + 1. 8. it powers a compact torus - like pulsar wind nebula with a jet first detected in x - rays and then identified in the optical and mid - infrared. we carried out deep near - infrared observations of the pulsar field to identify the pulsar and its nebula in this range. the direct imaging mode of the naco adaptive optics instrument at the eso vlt in the h and ks bands was used. in both bands we detected a faint, h = 21. 30 ( 10 ) and ks = 20. 45 ( 10 ), extended elliptical object, whose center position is consistent with the x - ray position of the pulsar. the morphology of the object and the orientation of its major axis are in a good agreement with those observed for the pulsar torus - like nebula in the mid - infrared, optical, and x - rays. this suggests that it is the near - infrared counterpart of the nebula. the measured fluxes compiled with the data in other ranges show a complicated unabsorbed power law spectrum of the torus - like nebula with several steep breaks between the near - infrared and mid - infrared, the optical and x - rays, and possibly in the mid - infrared. this implies a multiple relativistic particle population responsible for the synchrotron emission of the nebula in different spectral ranges. we have not resolved the pulsar counterpart from its nebula and place only upper limits on its brightness, h > = 23. 9 $ and ks > = 22. 7. based on that, its contribution to the total near - infrared flux of the pulsar + nebula system is < = 10 %, which is comparable with the expected contribution in the optical.
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arxiv:1304.8105
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we consider a bayesian functional data analysis for observations measured as extremely long sequences. splitting the sequence into a number of small windows with manageable length, the windows may not be independent especially when they are neighboring to each other. we propose to utilize bayesian smoothing splines to estimate individual functional patterns within each window and to establish transition models for parameters involved in each window to address the dependent structure between windows. the functional difference of groups of individuals at each window can be evaluated by bayes factor based on markov chain monte carlo samples in the analysis. in this paper, we examine the proposed method through simulation studies and apply it to identify differentially methylated genetic regions in tcga lung adenocarcinoma data.
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arxiv:2112.05041
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we have previously presented the idea of how complex multimodal information could be represented in our brains in a compressed form, following mechanisms similar to those employed in machine learning tools, like autoencoders. in this short comment note we reflect, mainly with a didactical purpose, upon the basic question for a biological implementation : what could be the mechanism working as a loss function, and how it could be connected to a neuronal network providing the required feedback to build a simple training configuration. we present our initial ideas based on a basic motif that implements an xor switch, using few excitatory and inhibitory neurons. such motif is guided by a principle of homeostasis, and it implements a loss function that could provide feedback to other neuronal structures, establishing a control system. we analyse the presence of this xor motif in the connectome of c. elegans, and indicate the relationship with the well - known lateral inhibition motif. we then explore how to build a basic biological neuronal structure with learning capacity integrating this xor motif. guided by the computational analogy, we show an initial example that indicates the feasibility of this approach, applied to learning binary sequences, like it is the case for simple melodies. in summary, we provide didactical examples exploring the parallelism between biological and computational learning mechanisms, identifying basic motifs and training procedures, and how an engram encoding a melody could be built using a simple recurrent network involving both excitatory and inhibitory neurons.
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arxiv:2406.09940
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it is examined finite state automorphisms of regular rooted trees constructed to represent groups $ gl ( n, \ mathbb { z } ) $. the number of states of automorphisms that correspond to elementary matrices is computed. using the representation of $ gl ( 2, \ mathbb { z } ) $ over an alphabet of size $ 4 $ a finite state representation of the free group of rank $ 2 $ over binary alphabet is constructed.
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arxiv:2309.01241
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we study homogenization properties of the discrete laplace operator with random conductances on a large domain in $ \ mathbb { z } ^ d $. more precisely, we prove almost - sure homogenization of the discrete poisson equation and of the top of the dirichlet spectrum. we assume that the conductances are stationary, ergodic and nearest - neighbor conductances are positive. in contrast to earlier results, we do not require uniform ellipticity but certain integrability conditions on the lower and upper tails of the conductances. we further allow jumps of arbitrary length. without the long - range connections, the integrability condition on the lower tail is optimal for spectral homogenization. it coincides with a necessary condition for the validity of a local central limit theorem for the random walk among random conductances. as an application of spectral homogenization, we prove a quenched large deviation principle for the normalized and rescaled local times of the random walk in a growing box. our proofs are based on a compactness result for the laplacian ' s dirichlet energy, poincare inequalities, moser iteration and two - scale convergence.
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arxiv:1702.02860
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we propose some finite element schemes to solve a class of fourth - order nonlinear pdes, which include the vector - valued landau - - lifshitz - - baryakhtar equation, the swift - - hohenberg equation, and various cahn - - hilliard - type equations with source and convection terms, among others. the proposed numerical methods include a spatially semi - discrete scheme and two linearised fully - discrete $ c ^ 1 $ - conforming schemes utilising a semi - implicit euler method and a semi - implicit bdf method. we show that these numerical schemes are stable in $ \ mathbb { h } ^ 2 $. error analysis is performed which shows optimal convergence rates in each scheme. numerical experiments corroborate our theoretical results.
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arxiv:2309.05530
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optomechanics, which explores the fundamental coupling between light and mechanical motion, has made important advances in both exploring and manipulating macroscopic mechanical oscillators down to the quantum level. however, dynamical effects related to the vectorial nature of the optomechanical interaction remain to be investigated. here we study a nanowire with sub - wavelength dimensions strongly coupled to a tightly focused beam of light, enabling ultrasensitive readout of the nanoresonators dynamics. we experimentally determine the vectorial structure of the optomechanical interaction and demonstrate that bidimensional dynamical backaction governs the nanowire dynamics. moreover, the non - conservative topology of the optomechanical interaction is responsible for a novel canonical signature of strong coupling between the nanoresonator mechanical modes, leading to a topological instability. these results have a universal character and illustrate the increased sensitivity of nanomechanical devices towards topologically varying interactions, opening fundamental perspectives in nanomechanics, optomechanics, ultrasensitive scanning probe force microscopy and nano - optics.
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arxiv:1401.6829
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we study hypersurfaces either in the de sitter space $ \ s _ 1 ^ { n + 1 } \ subset \ r _ 1 ^ { n + 2 } $ or in the anti de sitter space $ \ h _ 1 ^ { n + 1 } \ subset \ r _ 2 ^ { n + 2 } $ whose position vector $ \ psi $ satisfies the condition $ l _ k \ psi = a \ psi + b $, where $ l _ k $ is the linearized operator of the $ ( k + 1 ) $ - th mean curvature of the hypersurface, for a fixed $ k = 0,..., n - 1 $, $ a $ is an $ ( n + 2 ) \ times ( n + 2 ) $ constant matrix and $ b $ is a constant vector in the corresponding pseudo - euclidean space. for every $ k $, we prove that when $ a $ is self - adjoint and $ b = 0 $, the only hypersurfaces satisfying that condition are hypersurfaces with zero $ ( k + 1 ) $ - th mean curvature and constant $ k $ - th mean curvature, open pieces of standard pseudo - riemannian products in $ \ s _ 1 ^ { n + 1 } $ ( $ \ s _ 1 ^ m ( r ) \ times \ s ^ { n - m } ( \ sqrt { 1 - r ^ 2 } ) $, $ \ h ^ m ( - r ) \ times \ s ^ { n - m } ( \ sqrt { 1 + r ^ 2 } ) $, $ \ s _ 1 ^ m ( \ sqrt { 1 - r ^ 2 } ) \ times \ s ^ { n - m } ( r ) $, $ \ h ^ m ( - \ sqrt { r ^ 2 - 1 } ) \ times \ s ^ { n - m } ( r ) $ ), open pieces of standard pseudo - riemannian products in $ \ h _ 1 ^ { n + 1 } $ ( $ \ h _ 1 ^ m ( - r ) \ times \ s ^ { n - m } ( \ sqrt { r ^ 2 - 1 } ) $, $ \ h ^ m ( - \ sqrt { 1 + r ^ 2 } ) \ times \ s _ 1 ^ { n - m } ( r ) $, $ \ s _ 1 ^ m ( \ sqrt { r ^ 2 - 1
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arxiv:1012.2778
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in this article, we shall study fundamental bessel functions for $ \ mathrm { gl } _ n ( \ mathbb { f } ) $ arising from the vorono \ " i summation formula for any rank $ n $ and field $ \ mathbb { f } = \ mathbb { r } $ or $ \ mathbb { c } $, with focus on developing their analytic and asymptotic theory. the main implements and subjects of our study of fundamental bessel functions are their formal integral representations and bessel differential equations. we shall prove the asymptotic formulae for fundamental bessel functions and explicit connection formulae for the bessel differential equations.
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arxiv:1612.03553
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we explore the two - dimensional extended hubbard model on the triangular lattice in the high doping regime. on - site and nearest - neighbour repulsive interactions are treated in a non - perturbative way by means of extended dynamical mean field theory. we compute the low - temperature phase diagram, displaying a metallic phase and a symmetry - broken phase for strong intersite repulsions. we describe the correlation effects on both single - particle and two - particle observables in the metallic phase. whereas single - particle spectra feature a hubbard satellite typical of strongly correlated systems, local susceptibilities remain close to their non - interacting limit, even for large on - site repulsions. we argue that this behaviour is typical of the strongly doped case. we also report a region in parameter space with negative static local screening.
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arxiv:1709.07901
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thermal infrared ( tir ) object tracking often suffers from challenges such as target occlusion, motion blur, and background clutter, which significantly degrade the performance of trackers. to address these issues, this paper pro - poses a novel siamese motion mamba tracker ( smmt ), which integrates a bidirectional state - space model and a self - attention mechanism. specifically, we introduce the motion mamba module into the siamese architecture to ex - tract motion features and recover overlooked edge details using bidirectional modeling and self - attention. we propose a siamese parameter - sharing strate - gy that allows certain convolutional layers to share weights. this approach reduces computational redundancy while preserving strong feature represen - tation. in addition, we design a motion edge - aware regression loss to improve tracking accuracy, especially for motion - blurred targets. extensive experi - ments are conducted on four tir tracking benchmarks, including lsotb - tir, ptb - tir, vot - tir2015, and vot - tir 2017. the results show that smmt achieves superior performance in tir target tracking.
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arxiv:2505.04088
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a covariantly constant dynamical two - form is exploited on a $ d _ 3 $ - brane to obtain its gravity dual action, governing an $ s ^ 3 $ deformed $ ads _ 5 $ black hole, in a type iib string theory on $ s ^ 1 \ times k3 $. we invoke the kaluza - klein compactification to work out the open / closed string duality. interestingly, the reissner - nordstrom black hole is obtained on the " non - reimannian " braneworld.
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arxiv:1002.1906
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the approach to heteroscedasticity of ref. 1 ( instruments 2022, 6 ( 1 ), 10 ) contains a sketchy application of a sub - optimal method of very easy implementation : the lucky model. the supporting proof of this method could not be inserted in ref. 1. the proof requires the analytical forms of the probability of ref. 2 for the two strip center of gravity. however, those analytical forms suggest also a completion of the lucky - model for the absence of a scaling constant, relevant for combinations of different detector types. the advanced lucky - model ( the super - lucky model ) can be directly used for track fitting in trackers composed of non - identical detectors. the construction of the weights for the fits is very simple. simulations of track fitting with this upgraded tool show resolution improvements also for combination of two types of very different detectors, near to the resolutions of the schematic model of ref. 1.
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arxiv:2205.14538
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the origin of ultra - high energy cosmic rays ( uhecrs ) is one of the most mystifying issues in astroparticle physics. it has been suggested that gamma - ray bursts ( grbs ) are excellent acceleration sites for cosmic rays. the propagation of uhecrs from the grb host galaxy to the earth should generate delayed secondary photons and neutrinos. here we present a dedicated search for delayed uhecr and neutrino emission centered around the position of nearby grb 980425 / sn 1998bw. located at a distance of 36. 9 mpc, grb 980425 / sn 1998bw is well within the greisen - zatsepin - kuzmin ( gzk ) distance horizon. we find no evidence for uhecr or neutrino clustering around the grb 980425 / sn 1998bw position between 2004 and 2020. under ideal propagation conditions, we propose that it might be possible to detect an excess from delayed uhecrs around grb 980425 / sn 1998bw within the next 100 years if the intergalactic magnetic field ( igmf ) strength is $ b \ leq 3 \ times 10 ^ { - 13 } $ g.
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arxiv:2210.10822
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most existing text - to - image synthesis tasks are static single - turn generation, based on pre - defined textual descriptions of images. to explore more practical and interactive real - life applications, we introduce a new task - interactive image editing, where users can guide an agent to edit images via multi - turn textual commands on - the - fly. in each session, the agent takes a natural language description from the user as the input and modifies the image generated in the previous turn to a new design, following the user description. the main challenges in this sequential and interactive image generation task are two - fold : 1 ) contextual consistency between a generated image and the provided textual description ; 2 ) step - by - step region - level modification to maintain visual consistency across the generated image sequence in each session. to address these challenges, we propose a novel sequential attention generative adversarial net - work ( seqattngan ), which applies a neural state tracker to encode the previous image and the textual description in each turn of the sequence, and uses a gan framework to generate a modified version of the image that is consistent with the preceding images and coherent with the description. to achieve better region - specific refinement, we also introduce a sequential attention mechanism into the model. to benchmark on the new task, we introduce two new datasets, zap - seq and deepfashion - seq, which contain multi - turn sessions with image - description sequences in the fashion domain. experiments on both datasets show that the proposed seqattnganmodel outperforms state - of - the - art approaches on the interactive image editing task across all evaluation metrics including visual quality, image sequence coherence, and text - image consistency.
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arxiv:1812.08352
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this work explores several aspects of interpolating sequences for $ \ ell ^ p _ a $, the space of analytic functions on the unit disk with $ p $ - summable maclaurin coefficients. much of this work is communicated through a carlesonian lens. we investigate various analogues of gramian matrices, for which we show boundedness conditions are necessary and sufficient for interpolation, including a characterization of universal interpolating sequences in terms of riesz systems. we also discuss weak separation, giving a characterization of such sequences using a generalization of the pseudohyperbolic metric. lastly, we consider carleson measures and embeddings.
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arxiv:2210.05823
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