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the intermolecular interactions in the title compound are investigated using self - consistent charge density functional based tight binding molecular dynamics. emphasis is put on the analysis of correlated motions of ion pairs using ideas of network theory. at equilibrium such correlations are not very pronounced on average. however, there exist sizeable local correlations for cases where two cations share the same anion via two nho - hydrogen bonds. the effect of an external perturbation, which artificially introduces a sudden local heating of an nh - bond, is investigated using nonequilibrium molecular dynamics. here, it is found that the average n - h bond vibrational relaxation time is about 5. 3 ~ ps. this energy redistribution is rather nonspecific with respect to the ion pairs and does not lead to long - range correlations spreading from the initially excited ion pair. | arxiv:1603.05985 |
space - time wave packets are diffraction - free, dispersion - free pulsed beams whose propagation - invariance stems from correlations introduced into their spatio - temporal spectrum. we demonstrate here experimentally and computationally that space - time light sheets exhibit self - healing properties upon traversing obstacles in the form of opaque obstructions. the unscattered fraction of the wave packet retains the spatio - temporal correlations and thus propagation - invariance is maintained. the scattered component does not satisfy the requisite correlation and thus undergoes diffractive spreading. these results indicate the robustness of st wave packets and their potential utility for deep illumination and imaging in scattering media such as biological tissues. | arxiv:1812.10567 |
we investigate the fundamental concept of a closed quantum subgroup of a locally compact quantum group. two definitions - one due to s. vaes and one due to s. l. woronowicz - are analyzed and relations between them discussed. among many reformulations we prove that the former definition can be phrased in terms of quasi - equivalence of representations of quantum groups while the latter can be related to an old definition of podle \ ' s from the theory of compact quantum groups. the cases of classical groups, duals of classical groups, compact and discrete quantum groups are singled out and equivalence of the two definitions is proved in the relevant context. a deep relationship with the quantum group generalization of herz restriction theorem from classical harmonic analysis is also established, in particular, in the course of our analysis we give a new proof of herz restriction theorem. | arxiv:1203.5063 |
the re - ranking approach leverages high - confidence retrieved samples to refine retrieval results, which have been widely adopted as a post - processing tool for image retrieval tasks. however, we notice one main flaw of re - ranking, i. e., high computational complexity, which leads to an unaffordable time cost for real - world applications. in this paper, we revisit re - ranking and demonstrate that re - ranking can be reformulated as a high - parallelism graph neural network ( gnn ) function. in particular, we divide the conventional re - ranking process into two phases, i. e., retrieving high - quality gallery samples and updating features. we argue that the first phase equals building the k - nearest neighbor graph, while the second phase can be viewed as spreading the message within the graph. in practice, gnn only needs to concern vertices with the connected edges. since the graph is sparse, we can efficiently update the vertex features. on the market - 1501 dataset, we accelerate the re - ranking processing from 89. 2s to 9. 4ms with one k40m gpu, facilitating the real - time post - processing. similarly, we observe that our method achieves comparable or even better retrieval results on the other four image retrieval benchmarks, i. e., veri - 776, oxford - 5k, paris - 6k and university - 1652, with limited time cost. our code is publicly available. | arxiv:2012.07620 |
in the present manuscript, we employ the feynman path integral method to derive the propagator in one - dimensional wigner - dunkl quantum mechanics. to verify our findings we calculate the propagator associated with the free particle and the harmonic oscillator in the presence of the dunkl derivative. we also deduce the energy spectra and the corresponding bound - state wave functions from the spectral decomposition of the propagator. | arxiv:2407.12644 |
velocity - squared drag forces are common in describing an object moving through a granular material. the resulting force law is a nonlinear differential equation, and closed - form solutions of the dynamics are typically obtained by making simplifying assumptions. here, we consider a generalized version of such a force law which has been used in many studies of granular impact. we show that recasting the force law into an equation for the kinetic energy versus depth, k ( z ), yields a linear differential equation, and thus general closed - form solutions for the velocity versus depth. this approach also has several advantages in fitting such models to experimental data, which we demonstrate by applying it to data from 2d impact experiments. we also present new experimental results for this model, including shape and depth dependence of the velocity - squared drag force. | arxiv:1210.6692 |
at the nucleus of a superconducting vortex is a small, circular region where superconductivity is destroyed. like an atomic nucleus, this core may become deformed, and such distortions can have important consequences in non - equilibrium situations. using ginzburg - landau theory, we have investigated this phenomenon for vortices in the presence of artificial defects. we show that when a vortex approaches the vicinity of a defect, an abrupt transition occurs in which the vortex core develops a " string " extending to the defect boundary, while simultaneously the supercurrents and associated magnetic flux spread out and engulf the defect. the energetics of stretching the string determines the pinning behavior of the vortex. experimental consequences of these strings are discussed. | arxiv:cond-mat/0111502 |
we compare axial charges of excited nucleons, as predicted by the chiral symmetry restoration picture, with the traditional, moderately successful for the ground - state baryons su ( 6 ) symmetry. the axial charges of excited nucleons can ( and will ) be measured in lattice qcd simulations, and comparison of the lattice results with the two different symmetry schemes will give an insight on the origins of the excited hadron masses as well as on interrelations of chiral symmetry and confinement. | arxiv:0801.4343 |
we describe a notion of ampleness for line bundles on orbifolds with cyclic quotient singularities that is related to embeddings in weighted projective space, and prove a global asymptotic expansion for a weighted bergman kernel associated to such a line bundle. | arxiv:0907.5215 |
we explore the relationship between the nonlinear matter power spectrum and the various lagrangian and standard perturbation theories ( lpt and spt ). we first look at it in the context of one dimensional ( 1 - d ) dynamics, where 1lpt is exact at the perturbative level and one can exactly resum the spt series into the 1lpt power spectrum. shell crossings lead to non - perturbative effects, and the pt ignorance can be quantified in terms of their ratio, which is also the transfer function squared in the absence of stochasticity. at the order of pt we work, this parametrization is equivalent to the results of effective field theory ( eft ), and can thus be expanded in terms of the same parameters. we find that its radius of convergence is larger than the spt loop expansion. the same eft parametrization applies to all spt loop terms and, if stochasticity can be ignored, to all n - point correlators. in 3 - d, the lpt structure is considerably more complicated, and we find that lpt models with parametrization motivated by the eft exhibit running with $ k $ and that spt is generally a better choice. since these transfer function expansions contain free parameters that change with cosmological model their usefulness for broadband power is unclear. for this reason we test the predictions of these models on baryonic acoustic oscillations ( bao ) and other primordial oscillations, including string monodromy models, for which we ran a series of simulations with and without oscillations. most models are successful in predicting oscillations beyond their corresponding pt versions, confirming the basic validity of the model. | arxiv:1509.02120 |
the definition of an innovative therapeutic protocol requires the fine tuning of all the involved operations in order to maximize the efficiency. in some cases, the price of the experiments, or their duration, represents a great obstacle and the full potential of the protocol risks to be reduced or even hidden by a non - optimal application. the implementation of a numerical model of the protocol may represent the solution, allowing a systematic exploration of all the different alternatives, shedding the light on the most promising combination and also identifying the key elements / parameters. in this paper, the injection of a plasmid, preceded by a hyaluronidase injection, is simulated through a mathematical model. some key elements of the administration protocol are identified by means of a mathematical optimization procedure, maximizing the efficacy of the therapy. as a side effect of the extensive investigation, robust solutions able to reduce the effects of human errors in the administration are also obtained. | arxiv:1907.11055 |
we firstly report mode - locked square - wave pulse in yb - doped fiber laser based on graded index multimode fiber of reverse suturable absorption. by adjusting the pump power, the width of the square - wave can be tuned range from 350 ps to 52. 6 ns with 3db bandwidth spectrum of 0. 73 nm. the supermode suppression ratio exceeds ~ 65 db, which indicates excellent mode - locked operation state, and we also study the characteristic of pulse by the chirp measurement system. the mode - locked square - wave pulse fiber laser can sever as high power light source for industrial applications. | arxiv:1904.06706 |
numerical software is usually shipped with built - in hyperparameters. by carefully tuning those hyperparameters, significant performance enhancements can be achieved for specific applications. we developed mindopt tuner, a new automatic tuning tool that supports a wide range of numerical software, including optimization and other solvers. mindopt tuner uses elastic cloud resources, features a web - based task management panel and integration with ipython notebook with both command - line tools and python apis. our experiments with coin - or cbc, an open - source mixed - integer optimization solver, demonstrate remarkable improvements with the tuned parameters compared to the default ones on the miplib2017 test set, resulting in over 100x acceleration on several problem instances. additionally, the results demonstrate that tuner has a higher tuning efficiency compared to the state - of - the - art automatic tuning tool smac3. | arxiv:2307.08085 |
it was discovered by gordon in 1977 that keplerian ellipses in the plane are minimizers of the lagrangian action and spectrally stable as periodic points of the associated hamiltonian flow. the aim of this paper is to give a homotopy theoretical proof of these results through a self - contained, explicit and simple computation of the conley - zehnder index. the techniques developed in this paper can be used to investigate the higher dimensional case of keplerian ellipses, where the classical variational proof no longer applies. | arxiv:1908.00075 |
the effects of magnetic fields on big bang nucleosynthesis ( bbn ) have been calculated, and the impact on the abundances of the light elements have been investigated numerically. an upper limit on the strength of primordial magnetic fields compatible with observations of light element abundances has been thus obtained. in the framework of standard bbn theory, the maximum strength of the primordial magnetic fields, on scales greater than $ 10 ^ 4 $ cm but smaller than the event horizon at the bbn epoch ( $ \ sim 1 $ min., $ \ sim 2 \ times 10 ^ { 12 } $ cm ), is $ \ le 10 ^ { 11 } $ gauss. this limit is shown to allow magnetic fields at the time of recombination no stronger than $ \ sim 0. 1 $ gauss on scales $ \ ge 10 ^ { 11 } { \ rm cm } $. our results also strongly indicate that, at the bbn epoch, and for field strengths $ b \ le10 ^ { 13 } $ gauss, the effects of magnetic fields on the primordial abundances of light elements are dominated by effects from reaction rates in the presense of primeval magnetic fields rather than by magnetic density effects on the expansion rate. | arxiv:astro-ph/9308041 |
in this paper, we define and study the new problem simultaneous pq - ordering. its input consists of a set of pq - trees, which represent sets of circular orders of their leaves, together with a set of child - parent relations between these pq - trees, such that the leaves of the child form a subset of the leaves of the parent. simultaneous pq - ordering asks whether orders of the leaves of each of the trees can be chosen simultaneously, that is, for every child - parent relation the order chosen for the parent is an extension of the order chosen for the child. we show that simultaneous pq - ordering is np - complete in general and that it is efficiently solvable for a special subset of instances, the 2 - fixed instances. we then show that several constrained embedding problems can be formulated as such 2 - fixed instances. in particular, we obtain a linear - time algorithm for partially pq - constrained planarity for biconnected graphs, a common generalization of two recently considered embedding problems, and a quadratic - time algorithm for simultaneous embedding with fixed edges for biconnected graphs with a connected intersection ; formerly only the much more restricted case that the intersection is biconnected was known to be efficiently solvable. both results can be extended to the case where the input graphs are not necessarily biconnected but have the property that each cutvertex is contained in at most two non - trivial blocks. this includes for example the case where both graphs have maximum degree 5. moreover, we give an optimal linear - time algorithm for recognition of simultaneous interval graphs, improving upon a recent o ( n ^ 2 log n ) - time algorithm due to jampani and lubiw and show that this can be used to also solve the problem of extending partial interval representations of graphs with n vertices and m edges in time o ( n + m ), improving a recent result of klav \ ' ik et al. | arxiv:1112.0245 |
an x - ray interferometer ( xri ) has recently been proposed as a theme for esa ' s voyage 2050 planning cycle, with the eventual goal to observe the x - ray sky with an unprecedented angular resolution better than 1 micro arcsec ( 5 prad ) [ 1 ]. a scientifically very interesting mission is possible on the basis of a single spacecraft [ 2 ], owing to the compact ' telephoto ' design proposed earlier by willingale [ 3 ]. between the practical demonstration of x - ray interferometry at 1 kev by cash et al. [ 4 ] with a 1 mm baseline and 0. 1 arcsec effective resolution to a mission flying an interferometer with a baseline of one or more meters, an effective collecting area of square meters and micro arcsec resolution lie many milestones. the first important steps to scale up from a laboratory experiment to a viable mission concept will have to be taken on a scalable and flexible testbed set - up. such a testbed cannot singularly focus on the optical aspects, but should simultaneously address the thermal and mechanical stability of the interferometer. a particular challenge is the coherent x - ray source, which should provide a wavefront at the entrance of the interferometer that is transversely coherent over a distance at least equal to the baseline, and bright enough. in this paper, we will explore the build - up of a testbed in several stages, with increasing requirements on optical quality and associated thermo - mechanical control and source sophistication, with the intent to guide the technological development of x - ray interferometry from the lab to space in a sequence of achievable milestones. | arxiv:2107.07857 |
sparse inverse covariance selection is a fundamental problem for analyzing dependencies in high dimensional data. however, such a problem is difficult to solve since it is np - hard. existing solutions are primarily based on convex approximation and iterative hard thresholding, which only lead to sub - optimal solutions. in this work, we propose a coordinate - wise optimization algorithm to solve this problem which is guaranteed to converge to a coordinate - wise minimum point. the algorithm iteratively and greedily selects one variable or swaps two variables to identify the support set, and then solves a reduced convex optimization problem over the support set to achieve the greatest descent. as a side contribution of this paper, we propose a newton - like algorithm to solve the reduced convex sub - problem, which is proven to always converge to the optimal solution with global linear convergence rate and local quadratic convergence rate. finally, we demonstrate the efficacy of our method on synthetic data and real - world data sets. as a result, the proposed method consistently outperforms existing solutions in terms of accuracy. | arxiv:1711.07038 |
few - shot segmentation of point cloud remains a challenging task, as there is no effective way to convert local point cloud information to global representation, which hinders the generalization ability of point features. in this study, we propose a bidirectional feature globalization ( bfg ) approach, which leverages the similarity measurement between point features and prototype vectors to embed global perception to local point features in a bidirectional fashion. with point - to - prototype globalization ( po2prg ), bfg aggregates local point features to prototypes according to similarity weights from dense point features to sparse prototypes. with prototype - to - point globalization ( pr2pog ), the global perception is embedded to local point features based on similarity weights from sparse prototypes to dense point features. the sparse prototypes of each class embedded with global perception are summarized to a single prototype for few - shot 3d segmentation based on the metric learning framework. extensive experiments on s3dis and scannet demonstrate that bfg significantly outperforms the state - of - the - art methods. | arxiv:2208.06671 |
spiking neural networks combine analog computation with event - based communication using discrete spikes. while the impressive advances of deep learning are enabled by training non - spiking artificial neural networks using the backpropagation algorithm, applying this algorithm to spiking networks was previously hindered by the existence of discrete spike events and discontinuities. for the first time, this work derives the backpropagation algorithm for a continuous - time spiking neural network and a general loss function by applying the adjoint method together with the proper partial derivative jumps, allowing for backpropagation through discrete spike events without approximations. this algorithm, eventprop, backpropagates errors at spike times in order to compute the exact gradient in an event - based, temporally and spatially sparse fashion. we use gradients computed via eventprop to train networks on the yin - yang and mnist datasets using either a spike time or voltage based loss function and report competitive performance. our work supports the rigorous study of gradient - based learning algorithms in spiking neural networks and provides insights toward their implementation in novel brain - inspired hardware. | arxiv:2009.08378 |
we study evolutionary canalization using a spin - glass model with replica theory, where spins and their interactions are dynamic variables whose configurations correspond to phenotypes and genotypes, respectively. the spins are updated under temperature t _ s, and the genotypes evolve under temperature t _ j, according to the evolutionary fitness. it is found that adaptation occurs at t _ s < t _ s ^ { rs }, and a replica symmetric phase emerges at t _ s ^ { rsb } < t _ s < t _ s ^ { rs }. the replica symmetric phase implies canalization, and replica symmetry breaking at lower temperatures indicates loss of robustness. | arxiv:1111.5770 |
we consider the problem of the evolution of a code within a structured population of agents. the agents try to maximise their information about their environment by acquiring information from the outputs of other agents in the population. a naive use of information - theoretic methods would assume that every agent knows how to " interpret " the information offered by other agents. however, this assumes that one " knows " which other agents one observes, and thus which code they use. in our model, however, we wish to preclude that : it is not clear which other agents an agent is observing, and the resulting usable information is therefore influenced by the universality of the code used and by which agents an agent is " listening " to. we further investigate whether an agent who does not directly perceive the environment can distinguish states by observing other agents ' outputs. for this purpose, we consider a population of different types of agents " talking " about different concepts, and try to extract new ones by considering their outputs only. | arxiv:1505.04142 |
two novel decoupling and matching networks ( dmns ) in microstrip technology for three - element uniform circular arrays ( ucas ) are investigated and compared to a more conventional dmn approach with simple neutralization lines. the array elements are coaxially - fed quarter - wavelength monopole antennas over a finite groundplane. three - element arrays are considered since ucas with an odd number of elements are able to provide an almost constant maximum array factor over the whole azimuthal angular range. the new designs are explained from a theoretical point of view and their implementations are compared to four - and three - elements ucas without dmn in terms of decoupling and matching bandwidth as well as beamforming capabilities. in addition to excellent decoupling and matching below - 16 db, a broader bandwidth is obtained by the two dmns. the reasons for the enhanced bandwidth are similar in both cases : by introducing several circuit elements offering additional degrees of freedom, matching of the monopole input impedances at different frequencies becomes feasible. one of the presented designs offers a larger bandwidth, while the other design is able to provide a better total efficiency. scattering parameters, radiation patterns, beamforming capabilities, and enhanced gain are all verified by measurements over the operating bandwidth. | arxiv:2105.09333 |
we study the radio - far - infrared ( fir ) correlation in a sample of faint dwarf irregular galaxies using nvss data for 1. 4 ghz radio flux, spitzer mips 70 um data for fir flux, and galex fuv data to estimate the star formation rates ( sfr ). since our target galaxies are extremely faint, we stack images of many galaxies together to estimate the average radio and fir fluxes. we find that for a given sfr both 70 um and 1. 4 ghz fluxes are low compared to the calibration for large spirals. nonetheless, the ratio of 70 um to 1. 4 ghz flux agrees within errorbars with that seen for large galaxies. the radio - fir correlation thus appears to be the result of a ' conspiracy '. we use the sfr to estimate the non - thermal fraction of the 1. 4 ghz radio emission and find it to be around 50 %, much smaller than the 90 % typical for spirals. we also estimate the equipartition magnetic field and find it to be ~ 2 microgauss, about five times smaller than that typical for spirals. | arxiv:1204.3305 |
we show how localization and smoothing techniques can be used to establish universality in the bulk of the spectrum for a fixed positive measure mu on [ - 1, 1 ]. assume that mu is a regular measure, and is absolutely continuous in an open interval containing some closed subinterval j of ( - 1, 1 ). assume that in j, the absolutely continuous component mu ' is positive and continuous. then universality in j for mu follows from universality for the classical legendre weight. we also establish universality in an l _ { p } sense under weaker assumptions on mu. | arxiv:math/0701307 |
let $ m $ and $ n $ be two positive integers such that $ m < n $. let $ q _ { n - m + 1 } $ be the symplectic quasi - projective space of rank $ n - m + 1 $. in this article, we will study the order of the samelson product $ s ^ { 4m - 1 } \ wedge q _ { n - m + 1 } \ rightarrow sp ( n ) $. | arxiv:2305.11447 |
closed timelike curves are among the most controversial features of modern physics. as legitimate solutions to einstein ' s field equations, they allow for time travel, which instinctively seems paradoxical. however, in the quantum regime these paradoxes can be resolved leaving closed timelike curves consistent with relativity. the study of these systems therefore provides valuable insight into non - linearities and the emergence of causal structures in quantum mechanics - essential for any formulation of a quantum theory of gravity. here we experimentally simulate the non - linear behaviour of a qubit interacting unitarily with an older version of itself, addressing some of the fascinating effects that arise in systems traversing a closed timelike curve. these include perfect discrimination of non - orthogonal states and, most intriguingly, the ability to distinguish nominally equivalent ways of preparing pure quantum states. finally, we examine the dependence of these effects on the initial qubit state, the form of the unitary interaction, and the influence of decoherence. | arxiv:1501.05014 |
we show that all nontrivial members of the kinoshita - terasaka and conway knot families satisfy the purely cosmetic surgery conjecture. | arxiv:2009.00522 |
in this paper, we apply the generalized integration constants method in field theory to quantize maxwell and the klein - gordon free fields. the study is performed in both position and momentum spaces, to obtain equal - time dirac brackets among the fields and their conjugate momenta. the idea is to obtain the brackets near the initial instant using the taylor polynomial expansion, and then deduce directly their expressions at any later time. in the case of the maxwell field, the interdependence of the field components ( constraints ) requires the use the helmholtz theorem to separate the transversal and longitudinal parts. keywords : singular systems, constraints, dirac brackets, ci method, taylor expansion, kg field, maxwell field, fourier transform, helmholtz decomposition. | arxiv:2304.02018 |
we extend the relativistic mean - field models with hadron masses and meson - baryon coupling constants dependent on the scalar $ \ sigma $ field, studied previously to incorporate $ \ delta ( 1232 ) $ baryons. available empirical information is analyzed to put constraints on the couplings of $ \ delta $ s with meson fields. conditions for the appearance of $ \ delta $ s are studied. we demonstrate that with inclusion of the $ \ delta $ s our equations of state continue to fulfill majority of known empirical constraints including the pressure - density constraint from heavy - ion collisions, the constraint on the maximum mass of the neutron stars, the direct urca and the gravitational - baryon mass ratio constraints. | arxiv:1610.09746 |
kinetic alfven wave turbulence in solar wind is considered and it is shown that non - maxwellian electron distribution function has a significant effect on the dynamics of the solar wind plasmas. linear landau damping leads to the formation of a plateau in the parallel electron distribution function which diminishes the landau damping rate significantly. nonlinear scattering of waves by plasma particles is generalized to short wavelengths and it is found that for the solar wind parameters this scattering is the dominant process as compared to three wave decay and coalescence in the wave vector range. incorporation of these effects lead to the steepening of the wave spectrum between the inertial and the dissipation ranges with a spectral index between 2 and 3. this region can be labeled as the scattering range. such steepening has been observed in the solar wind plasmas. | arxiv:1008.0993 |
stochastic reaction network models are widely utilized in biology and chemistry to describe the probabilistic dynamics of biochemical systems in general, and gene interaction networks in particular. most often, statistical analysis and inference of these systems is addressed by parametric approaches, where the laws governing exogenous input processes, if present, are themselves fixed in advance. motivated by reporter gene systems, widely utilized in biology to monitor gene activation at the individual cell level, we address the analysis of reaction networks with state - affine reaction rates and arbitrary input processes. we derive a generalization of the so - called moment equations where the dynamics of the network statistics are expressed as a function of the input process statistics. in stationary conditions, we provide a spectral analysis of the system and elaborate on connections with linear filtering. we then apply the theoretical results to develop a method for the reconstruction of input process statistics, namely the gene activation autocovariance function, from reporter gene population snapshot data, and demonstrate its performance on a simulated case study. | arxiv:1710.06259 |
by using the free field worldsheet realization described by gaberdiel and gopakumar recently, we construct the nontrivial lowest generators of the higher spin superalgebra $ hs ( 2, 2 | 4 ) $. they consist of cubic terms between the bilinears of ambitwistor - like fields. we also obtain the worldsheet description for the findings of sezgin and sundell twenty years ago given by the familiar oscillator construction. the first order poles of the operator product expansions ( opes ), between the conformal weight - $ 1 $ generators of lie superalgebra $ psu ( 2, 2 | 4 ) $ and the above conformal weight - $ 3 $ generators of $ hs ( 2, 2 | 4 ) $, are determined explicitly and the additional generators appear in the worldsheet theory. | arxiv:2109.09260 |
nomad camels ( short : camels ) is a configurable, open - source measurement software that records fully self - describing experimental data. it has its origins in the field of experimental physics where a wide variety of measurement instruments are used in frequently changing experimental setups and measurement protocols. camels provides a graphical user interface ( gui ) which allows the user to configure experiments without the need of programming skills or deep understanding of instrument communication. camels translates user - defined measurement protocols into stand - alone executable python code for full transparency of the actual measurement sequences. existing large - scale, distributed control systems using e. g. epics can be natively implemented. camels is designed with focus on full recording of data and metadata. when shared with others, data produced with camels allow full understanding of the measurement and the resulting data in accordance with the fair ( findable, accessible, interoperable and re - usable ) principles. | arxiv:2402.07548 |
analytical formulae for the points and weights of two fifth - order quadrature rules for c _ 3, the 3 - cube, are given. the rules, originally formulated by a. h. stroud in 1967, are discussed in greater detail in terms of both the setup of the basic equations and the method of obtaining their solutions analytically. the primary purpose of this paper is to better document what we feel is a particularly practical quadrature rule ( e. g. in finite element calculations ) and one for which we felt comprehensive information was scarce. | arxiv:0909.5106 |
we investigate the relationship between the black hole accretion rate ( bhar ) and star - formation rate ( sfr ) for milky way ( mw ) and andromeda ( m31 ) - mass progenitors from z = 0. 2 - 2. 5. we source galaxies from the ks - band selected zfourge survey, which includes multi - wavelenth data spanning 0. 3 - 160um. we use decomposition software to split the observed seds of our galaxies into their active galactic nuclei ( agn ) and star - forming components, which allows us to estimate bhars and sfrs from the infrared ( ir ). we perform tests to check the robustness of these estimates, including a comparison to bhars and sfrs derived from x - ray stacking and far - ir analysis, respectively. we find as the progenit - ors evolve, their relative black hole - galaxy growth ( i. e. their bhar / sfr ratio ) increases from low to high redshift. the mw - mass progenitors exhibit a log - log slope of 0. 64 + / - 0. 11, while the m31 - mass progenitors are 0. 39 + / - 0. 08. this result contrasts with previous studies that find an almost flat slope when adopting x - ray / agn - selected or mass - limited samples and is likely due to their use of a broad mixture of galaxies with different evolutionary histories. our use of progenitor - matched samples highlights the potential importance of carefully selecting progenitors when searching for evolutionary relationships between bhar / sfrs. additionally, our finding that bhar / sfr ratios do not track the rate at which progenitors quench casts doubts over the idea that the suppression of star - formation is predominantly driven by luminous agn feedback ( i. e. high bhars ). | arxiv:1710.04225 |
in this paper, we apply a blow - up method of schoen and yau in \ cite { sy81 } to study a large class of prescribed mean curvature ( pmc ) dirichlet problems in $ n ( n \ geq 2 ) $ - dimensional riemannian manifolds. in this process we establish curvature estimates for almost minimizing pmc hypersurfaces, using an approach of schauder estimates from simon \ cite { sim76 }. we define an nc - f domain, where $ f $ is a given function generating from the pmc equation. combining this condition with a sufficiently mean convex assumption the blow - up method yields corresponding solutions to these pmc dirichlet problems. such nc - f assumption is almost optimal by an example. an application of our result into the pmc plateau problem is also presented. | arxiv:2208.07213 |
we prove the full range of estimates for a five - linear singular integral of brascamp - lieb type. the study is methodology - oriented with the goal to develop a sufficiently general technique to estimate singular integral variants of brascamp - lieb inequalities that do not obey h \ " older scaling. the invented methodology constructs localized analysis on the entire space from local information on its subspaces of lower dimensions and combines such tensor - type arguments with the generic localized analysis. a direct consequence of the boundedness of the five - linear singular integral is a leibniz rule which captures nonlinear interactions of waves from transversal directions. | arxiv:2001.09064 |
we investigate the effects of a nearby free surface on the stability of a flexible plate in axial flow. confinement by rigid boundaries is known to affect flag flutter thresholds and fluttering dynamics significantly, and this work considers the effects of a more general confinement involving a deformable free surface. to this end, a local linear stability is proposed for a flag in axial uniform flow and parallel to a free surface, using one - dimensional beam and potential flow models to revisit this classical fluid - structure interaction problem. the physical behaviour of the confining free surface is characterized by the froude number, corresponding to the ratio of the incoming flow velocity to that of the gravity waves. after presenting the simplified limit of infinite span ( i. e. two - dimensional problem ), the results are generalized to include finite - span and lateral confinement effects. in both cases, three unstable regimes are identified for varying froude number. rigidly - confined flutter is observed for low froude number, i. e. when the free surface behaves as a rigid wall, and is equivalent to the classical problem of the confined flag. when the flow and wave velocities are comparable, a new instability is observed before the onset of flutter ( i. e. at lower reduced flow speed ) and results from the resonance of a structural bending wave and one of the fundamental modes of surface gravity waves. finally, for large froude number ( low effect of gravity ), flutter is observed with significant but passive deformation of the free surface in response of the flag ' s displacement. | arxiv:2005.08667 |
we consider supergravity configuration of d5 branes wrapped on supersymmetric 2 - cycles and use it to calculate one - point and two - point green functions of some special operators in n = 2 super yang - mills theory. we show that green functions obtained from supergravity include two very different parts. one of them corresponds to perturbative results of quantum field theory, and another is a non - perturbative effect which corresponds to contribution from instantons with fractional charge. comparing green functions obtained from supergravity and gauge theory, we obtain radial / energy - scale relation for this gauge / gravity correspondence with n = 2 supersymmetry. this relation leads right beta - function of n = 2 sym from supergravity configuration. | arxiv:hep-th/0207145 |
the distributed optimization problem is set up in a collection of nodes interconnected via a communication network. the goal is to find the minimizer of a global objective function formed by the addition of partial functions locally known at each node. a number of methods are available for addressing this problem, having different advantages. the goal of this work is to achieve the maximum possible convergence rate. as the first step towards this end, we propose a new method which we show converges faster than other available options. as with most distributed optimization methods, convergence rate depends on a step size parameter. as the second step towards our goal we complement the proposed method with a fully distributed method for estimating the optimal step size that maximizes convergence speed. we provide theoretical guarantees for the convergence of the resulting method in a neighborhood of the solution. also, for the case in which the global objective function has a single local minimum, we provide a different step size selection criterion together with theoretical guarantees for convergence. we present numerical experiments showing that, when using the same step size, our method converges significantly faster than its rivals. experiments also show that the distributed step size estimation method achieves an asymptotic convergence rate very close to the theoretical maximum. | arxiv:2102.08726 |
arising from the interplay between charge, spin and orbital of electrons, spin - orbit torque ( sot ) has attracted immense interest in the past decade. despite vast progress, the existing quantification methods of sot still have their respective restrictions on the magnetic anisotropy, the entanglement between sot effective fields, and the artifacts from the thermal gradient and the planar hall effect, etc. thus, accurately characterizing sot across diverse samples remains as a critical need. in this work, with the aim of removing the afore - mentioned restrictions, thus enabling the universal sot quantification, we report the characterization of the sign and amplitude of sot by angular measurements. we first validate the applicability of our angular characterization in a perpendicularly magnetized pt / co - ni heterostructure by showing excellent agreements to the results of conventional quantification methods. remarkably, the thermoelectric effects, i. e., the anomalous nernst effect ( ane ) arising from the temperature gradient can be self - consistently disentangled and quantified from the field dependence of the angular characterization. the superiority of this angular characterization has been further demonstrated in a cu / cotb / cu sample with large ane but negligible sot, and in a pt / co - ni sample with weak perpendicular magnetic anisotropy ( pma ), for which the conventional quantification methods are not applicable and even yield fatal error. by providing a comprehensive and versatile way to characterize sot and thermoelectric effects in diverse heterostructures, our results pave the important foundation for the spin - orbitronic study as well as the interdisciplinary research of thermal spintronic. | arxiv:1909.09012 |
we have learned recently that the inner halo of the milky way contains a kinematically coherent component ( gaia - enceladus ) from a significant merger 10 gyrs ago. by contrast the inner halo ( defined to exclude the magellanic stream ) contains no similar intruder stellar population of billion year age. the tracer we use to set the corresponding upper limit is gaia asymptotic giant branch stars, rather than gaia kinematics. the primary sample is drawn from gaia dr2 with skymapper photometry. this is supplemented with panstarrs and 2mass photometry. as the gaia mission proceeds, a star formation history in the galactic halo should emerge. | arxiv:1903.05296 |
we introduce the notion of ricci - corrected differentiation in parabolic geometry, which is a modification of covariant differentiation with better transformation properties. this enables us to simplify the explicit formulae for standard invariant operators given in work of cap, slovak and soucek, and at the same time extend these formulae from the context of ahs structures ( which include conformal and projective structures ) to the more general class of all parabolic structures ( including cr structures ). | arxiv:math/0310311 |
let $ { f } _ { n } $ be the farey sequence of order $ n $. for $ s \ subseteq { f } _ n $ we let $ \ mathcal { q } ( s ) = \ left \ { x / y : x, y \ in s, x \ le y \, \, \ textrm { and } \, \, y \ neq 0 \ right \ } $. we show that if $ \ mathcal { q } ( s ) \ subseteq f _ n $, then $ | s | \ leq n + 1 $. moreover, we prove that in any of the following cases : ( 1 ) $ \ mathcal { q } ( s ) = f _ n $ ; ( 2 ) $ \ mathcal { q } ( s ) \ subseteq f _ n $ and $ | s | = n + 1 $, we must have $ s = \ left \ { 0, 1, \ frac { 1 } { 2 }, \ ldots, \ frac { 1 } { n } \ right \ } $ or $ s = \ left \ { 0, 1, \ frac { 1 } { n }, \ ldots, \ frac { n - 1 } { n } \ right \ } $ except for $ n = 4 $, where we have an additional set $ \ { 0, 1, \ frac { 1 } { 2 }, \ frac { 1 } { 3 }, \ frac { 2 } { 3 } \ } $ for the second case. our results are based on graham ' s gcd conjectures, which have been proved by balasubramanian and soundararajan. | arxiv:2005.04429 |
based on dispersion theory, we present a formalism for a model - independent evaluation of the hadronic light - by - light contribution to the anomalous magnetic moment of the muon. in particular, we comment on the definition of the pion pole in this framework and provide a master formula that relates the effect from pi pi intermediate states to the partial waves for the process gamma ^ * gamma ^ * - - > pi pi. all contributions are expressed in terms of on - shell form factors and scattering amplitudes, and as such amenable to an experimental determination. | arxiv:1402.7081 |
in this paper we consider vacuum kasner spacetimes, focusing on those that can be parametrized as linear perturbations of the special petrov type d case. for these quasi - d kasner models we first investigate the modification to the principal null directions, then a teukolsky master equation for fields of any spin, considering in particular the quasi - d models as curvature perturbations of the type d background. considering the speciality index and the principal null directions and comparing the results for the exact solutions and those for the perturbative ones, this simple kasner example allows us to clarify that perturbed spacetime do not retain in general the speciality character of the background. there are four distinct principal null directions, although they are not necessarily first order perturbations of the background principal null directions, as our example of the quasi - d kasner models shows. for the quasi - d kasner models the use of a teukolsky master equation, a classical tool for studying black hole perturbations, allows us to show, from a completely new point of view, the well known absence of gravitational waves in kasner spacetimes. this result, used together with an explicit expression of the electric weyl tensor in terms of weyl scalars, provides an example of the fact that the presence of transverse curvature terms does not necessarily imply the presence of gravitational waves. | arxiv:gr-qc/0404075 |
we introduce and analyze a model that sheds light on the interplay between correlated insulating states, superconductivity, and flavor - symmetry breaking in magic angle twisted bilayer graphene. using a variational mean - field theory, we determine the normal - state phase diagram of our model as a function of the band filling. the model features robust insulators at even integer fillings, occasional weaker insulators at odd integer fillings, and a pattern of flavor - symmetry breaking at non - integer fillings. adding a phonon - mediated inter - valley retarded attractive interaction, we obtain strong - coupling superconducting domes, whose structure is in qualitative agreement with experiments. our model elucidates how the intricate form of the interactions and the particle - hole asymmetry of the electronic structure determine the phase diagram. it also explains how subtle differences between devices may lead to the different behaviors observed experimentally. a similar model can be applied with minor modifications to other moir \ ' { e } systems, such as twisted trilayer graphene. | arxiv:2107.08486 |
according to a standard view, quantum mechanics ( qm ) is a contextual theory and quantum probability does not satisfy kolmogorov ' s axioms. we show, by considering the macroscopic contexts associated with measurement procedures and the microscopic contexts ( mu - contexts ) underlying them, that one can interpret quantum probability as epistemic, despite its non - kolmogorovian structure. to attain this result we introduce a predicate language l ( x ), a classical probability measure on it and a family of classical probability measures on sets of mu contexts, each element of the family corresponding to a ( macroscopic ) measurement procedure. by using only kolmogorovian probability measures we can thus define mean conditional probabilities on the set of properties of any quantum system that admit an epistemic interpretation but are not bound to satisfy kolmogorov ' s axioms. the generalized probability measures associated with states in qm can then be seen as special cases of these mean probabilities, which explains how they can be non - classical and provides them with an epistemic interpretation. moreover, the distinction between compatible and incompatible properties is explained in a natural way, and purely theoretical classical conditional probabilities coexist with empirically testable quantum conditional probabilities. | arxiv:1806.09125 |
most thermal infrared ( tir ) tracking methods are discriminative, treating the tracking problem as a classification task. however, the objective of the classifier ( label prediction ) is not coupled to the objective of the tracker ( location estimation ). the classification task focuses on the between - class difference of the arbitrary objects, while the tracking task mainly deals with the within - class difference of the same objects. in this paper, we cast the tir tracking problem as a similarity verification task, which is coupled well to the objective of the tracking task. we propose a tir tracker via a hierarchical spatial - aware siamese convolutional neural network ( cnn ), named hssnet. to obtain both spatial and semantic features of the tir object, we design a siamese cnn that coalesces the multiple hierarchical convolutional layers. then, we propose a spatial - aware network to enhance the discriminative ability of the coalesced hierarchical feature. subsequently, we train this network end to end on a large visible video detection dataset to learn the similarity between paired objects before we transfer the network into the tir domain. next, this pre - trained siamese network is used to evaluate the similarity between the target template and target candidates. finally, we locate the candidate that is most similar to the tracked target. extensive experimental results on the benchmarks vot - tir 2015 and vot - tir 2016 show that our proposed method achieves favourable performance compared to the state - of - the - art methods. | arxiv:1711.09539 |
maxi j1421 - 613 is an x - ray burster discovered by monitor of all - sky x - ray image ( maxi ) on 9 january 2014 and is considered to be a low - mass x - ray binary. a previous study analyzing follow - up observation data obtained by suzaku on 31 january to 3 february 2014 reported that an annular emission of ~ 3 ' - 9 ' radius was found around the transient source. the most plausible origin of the annular emission is a dust scattering echo by the outburst of maxi j1421 - 613. in this paper, we confirm the annular emission by analyzing the data of the swift follow - up observation which was conducted by the photon counting mode on 18 january 2014. in a radial profile, we found an annular emission at ~ 2 '. 5 - 4 '. 5. its spectrum was well explained by an absorbed power law, and the photon index was higher than that of maxi j1421 - 613 itself by delta gamma ~ 2. the flux and radius of the annular emission observed by swift are explained by dust scattering of the same outburst as is responsible for the annular emission observed by suzaku. assuming that the dust layer causing the annular emission found by swift is located at the same position as the co cloud in front of maxi j1421 - 613, the distance to the transient source was estimated to be ~ 3 kpc, which is consistent with the value estimated by the previous study of suzaku. | arxiv:2209.07755 |
extremely large - scale massive multiple - input multiple - output ( mimo ) has shown considerable potential in future mobile communications. however, the use of extremely large aperture arrays has led to near - field and spatial non - stationary channel conditions, which result in changes to transceiver design and channel state information that should be acquired. this letter focuses on the channel estimation problem and describes the non - stationary channel through mapping between subarrays and scatterers. we propose subarray - wise and scatterer - wise channel estimation methods to estimate the near - field non - stationary channel from the view of subarray and scatterer, respectively. numerical results demonstrate that subarray - wise method can derive accurate channel estimation results with low complexity, whereas the scatterer - wise method can accurately position the scatterers and identify almost all the mappings between subarrays and scatterers. | arxiv:1910.05432 |
let $ x _ 1, x _ 2, \ ldots, x _ n $ be chosen independently and uniformly at random from the unit $ d $ - dimensional cube $ [ 0, 1 ] ^ d $. let $ r $ be given and let $ \ cal x = \ { x _ 1, x _ 2, \ ldots, x _ n \ } $. the random geometric graph $ g = g _ { \ cal x, r } $ has vertex set $ \ cal x $ and an edge $ x _ ix _ j $ whenever $ \ | x _ i - x _ j \ | \ leq r $. we show that if each edge of $ g $ is colored independently from one of $ n + o ( n ) $ colors and $ r $ has the smallest value such that $ g $ has minimum degree at least two, then $ g $ contains a rainbow hamilton cycle a. a. s. | arxiv:2003.02998 |
in this paper, we consider the semi - classical setting constructed on nilpotent graded lie groups by means of representation theory. we analyze the effects of the pull - back by diffeomorphisms on pseudodifferential operators. we restrict to diffeomorphisms that preserve the filtration and prove that they are pansu differentiable. we show that the pull - back of a semi - classical pseudodifferential operator by such a diffeomorphism has a semi - classical symbol that is expressed at leading order in terms of the pansu differential. we interpret the geometric meaning of this invariance in the setting of filtered manifolds. | arxiv:2112.11509 |
we describe calabi - yau objects in the regular block of the ( parabolic ) bgg category $ \ mathcal { o } $ associated to a semi - simple finite dimensional complex lie algebra. each such object comes with a natural transformation from the serre functor to a shifted identity whose evaluation at that object is an isomorphism. | arxiv:2403.05258 |
we report a novel bell - state synthesizer in which an interferometric entanglement concentration scheme is used. an initially mixed polarization state from type - ii spontaneous parametric down - conversion becomes entangled after the interferometric entanglement concentrator. this bell - state synthesizer is universal in the sense that the output polarization state is not affected by spectral filtering, crystal thickness, and, most importantly, the choice of pump source. it is also robust against environmental disturbance and a more general state, partially mixed $ - $ partially entangled state, can be readily generated as well. | arxiv:quant-ph/0209041 |
we report on the discovery of a new correlation between global parameters of the hot interstellar gas in elliptical galaxies. we reanalyze archival chandra data for 30 normal early - type systems, removing the contributions of resolved and unresolved point sources to reveal the x - ray morphology of the hot gas. we determine the half - light radius, r _ x, and the mean surface brightness, i _ x, from the gas surface brightness profiles. a spectral analysis determines the temperature, t _ x, of the gas within 3 optical effective radii. we find that the galaxies lie on an x - ray gas fundamental plane ( xgfp ) of the form t _ x ~ r _ x ^ { 0. 28 } i _ x ^ { 0. 22 }. this is close to, but distinct from, a simple luminosity - temperature relation. the intrinsic width of the xgfp is only 0. 07dex, nearly identical to that of the stellar ( optical ) fundamental plane ( sfp ). this is surprising since x - ray gas masses are typically ~ 10 ^ { - 2 } of the stellar masses. we show that the xgfp is not a simple consequence of the virial theorem or hydrostatic equilibrium, and that it is essentially independent of the sfp. the xgfp thus represents a genuinely new constraint on the hydrodynamical evolution of elliptical galaxies. | arxiv:astro-ph/0509599 |
federated learning ( fl ) typically aggregates client model parameters using a weighting approach determined by sample proportions. however, this naive weighting method may lead to unfairness and degradation in model performance due to statistical heterogeneity and the inclusion of noisy data among clients. theoretically, distributional robustness analysis has shown that the generalization performance of a learning model with respect to any shifted distribution is bounded. this motivates us to reconsider the weighting approach in federated learning. in this paper, we replace the aforementioned weighting method with a new strategy that considers the generalization bounds of each local model. specifically, we estimate the upper and lower bounds of the second - order origin moment of the shifted distribution for the current local model, and then use these bounds disagreements as the aggregation proportions for weightings in each communication round. experiments demonstrate that the proposed weighting strategy significantly improves the performance of several representative fl algorithms on benchmark datasets. | arxiv:2311.05936 |
the mean - square relative displacements ( msrd ) of atomic pair motions in crystals are studied as a function of pair distance and temperature using the atomic pair distribution function ( pdf ). the effects of the lattice vibrations on the pdf peak widths are modelled using both a multi - parameter born von - karman ( bvk ) force model and a single - parameter debye model. these results are compared to experimentally determined pdfs. we find that the near - neighbor atomic motions are strongly correlated, and that the extent of this correlation depends both on the interatomic interactions and crystal structure. these results suggest that proper account of the lattice vibrational effects on the pdf peak width is important in extracting information on static disorder in a disordered system such as an alloy. good agreement is obtained between the bvk model calculations of pdf peak widths and the experimentally determined peak widths. the debye model successfully explains the average, though not detailed, natures of the msrd of atomic pair motion with just one parameter. also the temperature dependence of the debye model largely agrees with the bvk model predictions. therefore, the debye model provides a simple description of the effects of lattice vibrations on the pdf peak widths. | arxiv:cond-mat/0209603 |
we propose the hamiltonian model of $ { \ cal n } = 8 $ supersymmetric mechanics on $ n - $ dimensional special k \ " ahler manifolds ( of the rigid type ). | arxiv:hep-th/0410029 |
we consider the main factors which cause the variation of the value of the local slope of the elastic pp cross section b ( t ) = d [ \ ln ( d \ sigma _ el ( pp ) / dt ] / dt with t. namely, we discuss the role of the pion - loop insertion in the pomeron trajectory, the t - dependence of the pomeron - nucleon coupling and the role of the eikonalization of the proton - proton amplitude in both the one - and two - channel eikonal models. | arxiv:1410.0508 |
noisy labels, which are common in real - world datasets, can significantly impair the training of deep learning models. however, recent adversarial noise - combating methods overlook the long - tailed distribution of real data, which can significantly harm the effect of denoising strategies. meanwhile, the mismanagement of noisy labels further compromises the model ' s ability to handle long - tailed data. to tackle this issue, we propose a novel approach to manage data characterized by both long - tailed distributions and noisy labels. first, we introduce a loss - distance cross - selection module, which integrates class predictions and feature distributions to filter clean samples, effectively addressing uncertainties introduced by noisy labels and long - tailed distributions. subsequently, we employ optimal transport strategies to generate pseudo - labels for the noise set in a semi - supervised training manner, enhancing pseudo - label quality while mitigating the effects of sample scarcity caused by the long - tailed distribution. we conduct experiments on both synthetic and real - world datasets, and the comprehensive experimental results demonstrate that our method surpasses current state - of - the - art methods. our code will be available in the future. | arxiv:2408.03977 |
in this work, the cpt - violating ( cptv ) interactions on neutrons ' gravitational bound state are studied. with simple analytical solutions, we provide a preliminary investigation on the lorentz - violation ( lv ) induced spin precession due to the $ \ vec { \ sigma } \ cdot \ vec { \ tilde { b } } ( 1 + gz ) $ and $ \ bar { b } / m _ { _ i } \ vec { \ sigma } \ cdot \ hat { \ vec { p } } $ couplings, where $ \ vec { \ tilde { b } } $ and $ \ bar { b } $ represent lv coefficients. the helicity - dependent couplings can induce unusual phase evolutions with position and momentum dependence. as $ \ vec { \ tilde { b } } $ varies with time due to the earth ' s motion, the spin polarization also shows a sidereal time dependence, and it may be enhanced with time for ultra - stable polarized state of neutrons. the inseparability of the spin - momentum coupling of the $ \ bar { b } $ - term can also lead to motional dependent polarization state. with the precisely measured transition frequency between different gravitational bound states, we get a rough bound $ | \ vec { \ tilde { b } } | < 3. 9 \ times10 ^ { - 3 } $ gev for unpolarized neutrons. if the spin - flip transition frequency can reach comparable precision in the future, the bound can be improved to the level of $ 10 ^ { - 24 } $ gev. the test of weak equivalence principle with polarized atom may also improve it significantly. | arxiv:1906.00146 |
we show that for any locally compact second countable group $ g $ and any continuous positive definite function $ \ phi : g \ rightarrow \ mathbb { c } $, there exists an ergodic measure preserving system $ ( x, \ mathscr { b }, \ mu, \ { t _ g \ } _ { g \ in g } ) $ and a function $ f \ in l ^ 2 ( x, \ mu ) $ for which $ \ phi ( g ) = \ langle t _ gf, f \ rangle $. we also show that if $ g $ is a countably infinite abelian group, then there exists a ( not necessarily ergodic ) measure preserving system $ ( x, \ mathscr { b }, \ mu, \ { t _ g \ } _ { g \ in g } ) $ and a function $ f \ in l ^ 2 ( x, \ mu ) $ with $ | f | = \ phi ( 0 ) $ and $ \ phi ( g ) = \ langle t _ gf, f \ rangle $. | arxiv:2310.19386 |
transformer has been widely - used in many natural language processing ( nlp ) tasks and the scaled dot - product attention between tokens is a core module of transformer. this attention is a token - wise design and its complexity is quadratic to the length of sequence, limiting its application potential for long sequence tasks. in this paper, we propose a dimension - wise attention mechanism based on which a novel language modeling approach ( namely tensorcoder ) can be developed. the dimension - wise attention can reduce the attention complexity from the original $ o ( n ^ 2d ) $ to $ o ( nd ^ 2 ) $, where $ n $ is the length of the sequence and $ d $ is the dimensionality of head. we verify tensorcoder on two tasks including masked language modeling and neural machine translation. compared with the original transformer, tensorcoder not only greatly reduces the calculation of the original model but also obtains improved performance on masked language modeling task ( in ptb dataset ) and comparable performance on machine translation tasks. | arxiv:2008.01547 |
for a finite abelian group $ g $ and a positive integer $ h $, the unrestricted ( resp. ~ restricted ) $ h $ - critical number $ \ chi ( g, h ) $ ( resp. ~ $ \ chi \ hat { \ ; } ( g, h ) $ ) of $ g $ is defined to be the minimum value of $ m $, if exists, for which the $ h $ - fold unrestricted ( resp. ~ restricted ) sumset of every $ m $ - subset of $ g $ equals $ g $ itself. here we determine $ \ chi ( g, h ) $ for all $ g $ and $ h $ ; and prove several results for $ \ chi \ hat { \ ; } ( g, h ) $, including the cases of any $ g $ and $ h = 2 $, any $ g $ and large $ h $, and any $ h $ for the cyclic group $ \ mathbb { z } _ n $ of even order. we also provide a lower bound for $ \ chi \ hat { \ ; } ( \ mathbb { z } _ n, 3 ) $ that we believe is exact for every $ n $ - - - this conjecture is a generalization of the one made by gallardo, grekos, et al. ~ that was proved ( for large $ n $ ) by lev. | arxiv:1412.4058 |
neutron reflectometry is a powerful tool used for studies of surfaces and interfaces. in general the absorption in the typical studied materials can be neglected and this technique is limited to the measurement of the reflectivity only. in the case of strongly absorbing nuclei the number of neutrons is not conserved and the absorption can be directly measured by using the neutron - induced fluorescence technique which exploits the prompt particle emission of absorbing isotopes. this technique is emerging from soft matter and biology where highly absorbing nuclei, generally in very small quantities, are used as a label for buried layers. nowadays the importance of highly absorbing layers is rapidly increasing, partially because of their application in neutron detection ; a field that has become more and more active also due to the 3he - shortage. in this manuscript we extend the neutron - induced fluorescence technique to the study of thick layers of highly absorbing materials ; in particular 10b4c. the theory of neutron reflectometry is a commonly studied topic, however the subtle relationship between the reflection and the absorption of neutrons is not widely known, in particular when a strong absorption is present. the theory for a general stack of absorbing layers has been developed and compared to measurements. this new technique has potential as a tool for characterization of highly absorbing layers. we also report on the requirements that a 10b4c layer must fulfill in order to be employed as a converter in neutron detection. | arxiv:1510.01085 |
mechanical engineering is the study of physical machines and mechanisms that may involve force and movement. it is an engineering branch that combines engineering physics and mathematics principles with materials science, to design, analyze, manufacture, and maintain mechanical systems. it is one of the oldest and broadest of the engineering branches. mechanical engineering requires an understanding of core areas including mechanics, dynamics, thermodynamics, materials science, design, structural analysis, and electricity. in addition to these core principles, mechanical engineers use tools such as computer - aided design ( cad ), computer - aided manufacturing ( cam ), computer - aided engineering ( cae ), and product lifecycle management to design and analyze manufacturing plants, industrial equipment and machinery, heating and cooling systems, transport systems, motor vehicles, aircraft, watercraft, robotics, medical devices, weapons, and others. mechanical engineering emerged as a field during the industrial revolution in europe in the 18th century ; however, its development can be traced back several thousand years around the world. in the 19th century, developments in physics led to the development of mechanical engineering science. the field has continually evolved to incorporate advancements ; today mechanical engineers are pursuing developments in such areas as composites, mechatronics, and nanotechnology. it also overlaps with aerospace engineering, metallurgical engineering, civil engineering, structural engineering, electrical engineering, manufacturing engineering, chemical engineering, industrial engineering, and other engineering disciplines to varying amounts. mechanical engineers may also work in the field of biomedical engineering, specifically with biomechanics, transport phenomena, biomechatronics, bionanotechnology, and modelling of biological systems. = = history = = the application of mechanical engineering can be seen in the archives of various ancient and medieval societies. the six classic simple machines were known in the ancient near east. the wedge and the inclined plane ( ramp ) were known since prehistoric times. mesopotamian civilization is credited with the invention of the wheel by several, mainly old sources. however, some recent sources either suggest that it was invented independently in both mesopotamia and eastern europe or credit prehistoric eastern europeans with the invention of the wheel the lever mechanism first appeared around 5, 000 years ago in the near east, where it was used in a simple balance scale, and to move large objects in ancient egyptian technology. the lever was also used in the shadoof water - lifting device, the first crane machine, which appeared in mesopotamia circa 3000 bc. the earliest evidence of pulleys date back to mesopotamia in the early 2nd millennium bc. | https://en.wikipedia.org/wiki/Mechanical_engineering |
the problem of diffraction of an electromagnetic plane wave by a perfectly conducting circular disk and its complementary problem, diffraction by a circular hole in an infinite conducting plate, are rigorously solved using the method of the kobayashi potential. the mathematical formulation involved dual integral equation derived from the potential integral and boundary condition on the plane where a disk or hole is located. the weighting function in the potential integral are determined by applying the properties of the weber - schafheitlin ' s discontinuous integral and the solution are obtained in the form of a matrix equation. the matrix elements of the equations for the expansion coefficients are given by three kinds of infinite integral and the series solution for these infinite integral are derived. for the verification of these series solution, the numerical integral are derived and the results are computed numerically using the method of gaussian quadrature for conformation. the numerical results are given for the far - field pattern diffraction by a perfectly conducting disk and the results are compared with those obtained from physical optics method ( po ), which is fairly good. | arxiv:1004.5365 |
federated learning ( fl ) has emerged as an effective learning paradigm for distributed computation owing to its strong potential in capturing underlying data statistics while preserving data privacy. however, in cases of practical data heterogeneity among fl clients, existing fl frameworks still exhibit deficiency in capturing the overall feature properties of local client data that exhibit disparate distributions. in response, generative adversarial networks ( gans ) have recently been exploited in fl to address data heterogeneity since gans can be integrated for data regeneration without exposing original raw data. despite some successes, existing gan - related fl frameworks often incur heavy communication cost and also elicit other privacy concerns, which limit their applications in real scenarios. to this end, this work proposes a novel fl framework that requires only partial gan model sharing. named as ps - fedgan, this new framework enhances the gan releasing and training mechanism to address heterogeneous data distributions across clients and to strengthen privacy preservation at reduced communication cost, especially over wireless networks. our analysis demonstrates the convergence and privacy benefits of the proposed ps - fedgan framework. through experimental results based on several well - known benchmark datasets, our proposed ps - fedgan shows great promise to tackle fl under non - iid client data distributions, while securing data privacy and lowering communication overhead. | arxiv:2305.11437 |
we consider the sample of weakly active galaxies situated in ' local universe ' collected in the paper of pellegrini ( 2005 ) with inferred accretion efficiencies from $ 10 ^ { - 2 } $ to $ 10 ^ { - 7 } $. we apply a model of spherically symmetrical bondi accretion for given parameters ( $ m _ { bh } $, $ t _ { \ infty } $, $ \ rho _ { \ infty } $, ) taken from observation. we calculate spectra emitted by the gas accreting onto its central objects using monte carlo method including synchrotron and bremsstrahlung photons as seed photons. we compare our results with observed nuclear x - ray luminosities $ l _ { x, nuc } $ ( 0. 3 - 10 kev ) of the sample. model is also tested for different external medium parameters ( $ \ rho _ { \ infty } $ and $ t _ { \ infty } $ ) and different free parameters of the model. our model is able to explain most of the observed nuclear luminosities $ l _ x $ under an assumption that half of the compresion energy is transfered directly to the electrons. | arxiv:astro-ph/0512527 |
we investigate the homology of a congruence subgroup gamma of sl _ 3 ( z ) with coefficients in the steinberg modules st ( q ^ 3 ) and st ( e ^ 3 ), where e is a real quadratic field and the coefficients are q. by borel - serre duality, h _ 0 ( gamma, st ( q ^ 3 ) ) is isomorphic to h ^ 3 ( gamma, q ). taking the image of the connecting homomorphism h _ 1 ( gamma, st ( e ^ 3 ) / st ( q ^ 3 ) ) \ to h _ 0 ( gamma, st ( q ^ 3 ) ), followed by the borel - serre isomorphism, we obtain a naturally defined hecke - stable subspace h ( gamma, e ) of h ^ 3 ( gamma, q ). we conjecture that h ( gamma, e ) is independent of e and consists of the cuspidal cohomology h _ cusp ^ 3 ( gamma, q ) plus a certain subspace of h ^ 3 ( gamma, q ) $ that is isomorphic to the sum of the cuspidal cohomologies of the maximal faces of the borel - serre boundary. we report on computer calculations of h ( gamma, e ) for various gamma, e which provide evidence for the conjecture. we give a partial heuristic for the conjecture. | arxiv:2107.10918 |
we perform the first simultaneous extraction of unpolarized parton distributions and fragmentation functions from a monte carlo analysis of inclusive and semi - inclusive deep - inelastic scattering, drell - yan lepton - pair production, and single - inclusive $ e ^ + e ^ - $ annihilation data. we use data resampling techniques to thoroughly explore the bayesian posterior distribution of the extracted functions, and use $ k $ - means clustering on the parameter samples to identify the configurations that give the best description across all reactions. inclusion of the semi - inclusive data reveals a strong suppression of the strange quark distribution at parton momentum fractions $ x \ gtrsim 0. 01 $, in contrast with the atlas observation of enhanced strangeness in $ w ^ \ pm $ and $ z $ production at the lhc. our study reveals significant correlations between the strange quark density and the strange $ \ to $ kaon fragmentation function needed to simultaneously describe semi - inclusive $ k ^ \ pm $ production data from compass and inclusive $ k ^ \ pm $ spectra in $ e ^ + e ^ - $ annihilation from aleph and sld, as well as between the strange and light antiquark densities in the proton. | arxiv:1905.03788 |
we study the avalanche statistics observed in a minimal random growth model. the growth is governed by a reproduction rate obeying a probability distribution with finite mean a and variance va. these two control parameters determine if the avalanche size tends to a stationary distribution, ( finite scale statistics with finite mean and variance or power - law tailed statistics with exponent in ( 1, 3 ] ), or instead to a non - stationary regime with log - normal statistics. numerical results and their statistical analysis are presented for a uniformly distributed growth rate, which are corroborated and generalized by analytical results. the latter show that the numerically observed avalanche regimes exist for a wide family of growth rate distributions and provide a precise definition of the boundaries between the three regimes. | arxiv:2107.08002 |
the differential structure of operator bases used in various forms of the weyl - wigner - groenewold - moyal ( wwgm ) quantization is analyzed and a derivative - based approach, alternative to the conventional integral - based one is developed. thus the fundamental quantum relations follow in a simpler and unified manner. an explicit formula for the ordered products of the heisenberg - weyl algebra is obtained. the w ( infty ) - covariance of the wwgm - quantization in its most general form is established. it is shown that the group action of w ( infty ) that is realized in the classical phase space induces on bases operators in the corresponding hilbert space a similarity transformation generated by the corresponding quantum w ( infty ) which provides a projective representation of the former $ w _ { \ infty } $. explicit expressions for the algebra generators in the classical phase space and in the hilbert space are given. it is made manifest that this w ( infty ) - covariance of the wwgm - quantization is a genuine property of the operator bases. | arxiv:quant-ph/9707040 |
we discuss the bose - fermi equivalence in the quantum brownian motion ( qbm ) on a triangular lattice, mapping the action for the qbm into a string theory action with a periodic boundary tachyon potential. we construct new klein factors which are more appropriate than the conventional ones to deal with the quantum field theories defined on a two dimensioanl space - time with boundaries. using the fermi - bose equivalence with the new klein factors, we show that the model for the quantum bownian motion on a triangular lattice is equivalent to the thirring model with boundary terms, which are quadratic in fermion field operators, in the off - critical regions and to a $ su ( 3 ) \ times su ( 3 ) $ free fermion theory with quadratic boundary terms at the critical point. | arxiv:1508.01649 |
frequency estimation is a fundamental problem in many areas. the well - known a & m and its variant estimators have established an estimation framework by iteratively interpolating the discrete fourier transform ( dft ) coefficients. in general, those estimators require two dft interpolations per iteration, have uneven initial estimation performance against frequencies, and are incompetent for small sample numbers due to low - order approximations involved. exploiting the iterative estimation framework of a & m, we unprecedentedly introduce the pad \ ' e approximation to frequency estimation, unveil some features about the updating function used for refining the estimation in each iteration, and develop a simple closed - form solution to solving the residual estimation error. extensive simulation results are provided, validating the superiority of the new estimator over the state - the - art estimators in wide ranges of key parameters. | arxiv:2105.13567 |
maximum likelihood constraint inference is a powerful technique for identifying unmodeled constraints that affect the behavior of a demonstrator acting under a known objective function. however, it was originally formulated only for discrete state - action spaces. continuous dynamics are more useful for modeling many real - world systems of interest, including the movements of humans and robots. we present a method to generate a tabular state - action space that approximates continuous dynamics and can be used for constraint inference on demonstrations that obey the true system dynamics. we then demonstrate accurate constraint inference on nonlinear pendulum systems with 2 - and 4 - dimensional state spaces, and show that performance is robust to a range of hyperparameters. the demonstrations are not required to be fully optimal with respect to the objective, and the most likely constraints can be identified even when demonstrations cover only a small portion of the state space. for these reasons, the proposed approach may be especially useful for inferring constraints on human demonstrators, which has important applications in human - robot interaction and biomechanical medicine. | arxiv:2109.04874 |
this note contains some observations on abelian convexity theorems. convexity along an orbit is established in a very general setting using kempf - ness functions. this is applied to give short proofs of the atiyah - guillemin - sternberg theorem and of abelian convexity for the gradient map in the case of a real analytic submanifold of complex projective space. finally we give an application to the action on the probability measures. | arxiv:1801.01778 |
we implement a double - pixel, compressive sensing camera to efficiently characterize, at high resolution, the spatially entangled fields produced by spontaneous parametric downconversion. this technique leverages sparsity in spatial correlations between entangled photons to improve acquisition times over raster - scanning by a scaling factor up to n ^ 2 / log ( n ) for n - dimensional images. we image at resolutions up to 1024 dimensions per detector and demonstrate a channel capacity of 8. 4 bits per photon. by comparing the classical mutual information in conjugate bases, we violate an entropic einstein - podolsky - rosen separability criterion for all measured resolutions. more broadly, our result indicates compressive sensing can be especially effective for higher - order measurements on correlated systems. | arxiv:1212.5530 |
we present the first semi - streaming ptas for the minimum feedback arc set problem on directed tournaments in a small number of passes. namely, we obtain a $ ( 1 + \ varepsilon ) $ - approximation in polynomial time $ o \ left ( \ text { poly } ( n ) 2 ^ { \ text { poly } ( 1 / \ varepsilon ) } \ right ) $, with $ p $ passes in $ n ^ { 1 + 1 / p } \ cdot \ text { poly } \ left ( \ frac { \ log n } { \ varepsilon } \ right ) $ space. the only previous algorithm with this pass / space trade - off gave a $ 3 $ - approximation ( soda, 2020 ), and other polynomial - time algorithms which achieved a $ ( 1 + \ varepsilon ) $ - approximation did so with quadratic memory or with a linear number of passes. we also present a new time / space trade - off for $ 1 $ - pass algorithms that solve the tournament feedback arc set problem. this problem has several applications in machine learning such as creating linear classifiers and doing bayesian inference. we also provide several additional algorithms and lower bounds for related streaming problems on directed graphs, which is a mostly unexplored territory. | arxiv:2107.07141 |
a subset $ a $ of an additive abelian group is an $ h $ - sidon set if every element in the $ h $ - fold sumset $ ha $ has a unique representation as the sum of $ h $ not necessarily distinct elements of $ a $. let $ \ mathbf { f } $ be a field of characteristic 0 with a nontrivial absolute value, and let $ a = \ { a _ i : i \ in \ mathbf { n } \ } $ and $ b = \ { b _ i : i \ in \ mathbf { n } \ } $ be subsets of $ \ mathbf { f } $. let $ \ varepsilon = \ { \ varepsilon _ i : i \ in \ mathbf { n } \ } $, where $ \ varepsilon _ i > 0 $ for all $ i \ in \ mathbf { n } $. the set $ b $ is an $ \ varepsilon $ - perturbation of $ a $ if $ | b _ i - a _ i | < \ varepsilon _ i $ for all $ i \ in \ mathbf { n } $. it is proved that, for every $ \ varepsilon = \ { \ varepsilon _ i : i \ in \ mathbf { n } \ } $ with $ \ varepsilon _ i > 0 $, every set $ a = \ { a _ i : i \ in \ mathbf { n } \ } $ has an $ \ varepsilon $ - perturbation $ b $ that is an $ h $ - sidon set. this result extends to sets of vectors in $ \ mathbf { f } ^ n $. | arxiv:1707.04522 |
we report the electronic structure of ybb6, a recently predicted moderately correlated topological insulator, measured by angle - resolved photoemission spectroscopy. we directly observed linearly dispersive bands around the time - reversal invariant momenta { \ gamma } and x with negligible kz dependence, consistent with odd number of surface states crossing the fermi level in a z2 topological insulator. circular dichroism photoemission spectra suggest that these in - gap states possess chirality of orbital angular momentum, which is related to the chiral spin texture, further indicative of their topological nature. the observed insulating gap of ybb6 is about 100 mev, larger than that reported by theoretical calculations. our results present strong evidence that ybb6 is a correlated topological insulator and provide a foundation for further studies of this promising material. | arxiv:1404.6217 |
in this work we study the electronic structure and magnetism of a tio2 film grown on another non - magnetic oxide such as a laalo3 ( 001 ) substrate, concentrating on the role played by structural relaxation and oxygen vacancies. using density functional theory ab - initio methods, we study the free - standing anatase film as well as the interfaces with either the lao or alo2 planes of laalo3, focusing on the possibility of magnetic solutions. our results show that the interface lao / tio2 is favored against the alo2 / tio2 one if no oxygen vacancies are present in the interface whereas the contrary happens when there are oxygen vacancies. in both cases, the cohesive energy is of the same order of magnitude but only the alo2 / tio2 interface presents an stable magnetic solution. | arxiv:0811.2172 |
we study a non - linear modification to general relativity in which the standard einstein - hilbert action is replaced by a born - infeld type action. also study us stability issues to judge about viability of this modification. we establish the conditions that this modification must satisfy for to avoid the problems associated with the dolgov - kawasaki instability, tachyon instability and negative effective gravitational coupling. the particle content of gravitational spectrum of the linearized born - infeld theory shows the existence of massless gravitons plus new degree of freedom of 0 - spin associated with $ r ^ 2 $ term. for a toy model we proved that for appropriate values of the background curvature, this theory is free of ghost, dolgov - kawasaki instability and tachyon instability also it has a positive effective gravitational coupling. we find the scalar - tensor theory equivalent at this $ f ( r ) $ - theory in the einstein frame, and we study some properties of the scalar potential. | arxiv:1209.6559 |
the aim of this paper is to present a unified theory of many kato type representation theorems in terms of solvable forms on hilbert spaces. in particular, for some sesquilinear forms $ \ omega $ on a dense domain $ \ mathcal { d } $ one looks for an expression $ $ \ omega ( \ xi, \ eta ) = \ langle t \ xi, \ eta \ rangle, \ qquad \ forall \ xi \ in d ( t ), \ eta \ in \ mathcal { d }, $ $ where $ t $ is a densely defined closed operator with domain $ d ( t ) \ subseteq \ mathcal { d } $. there are two characteristic aspects of solvable forms. namely, one is that the domain of the form can be turned into a reflexive banach space need not be a hilbert space. the second one is the existence of a perturbation with a bounded form which is not necessarily a multiple of the inner product. | arxiv:1710.09911 |
we consider a classical spin model, of two - dimensional spins, with continuous symmetry, and investigate the effect of a symmetry breaking unidirectional quenched disorder on the magnetization of the system. we work in the mean field regime. we show, by numerical simulations and by perturbative calculations in the low as well as in the high temperature limits, that although the continuous symmetry of the magnetization is lost, the system still magnetizes, albeit with a lower value as compared to the case without disorder. the critical temperature at which the system starts magnetizing, also decreases with the introduction of disorder. however, with the introduction of an additional constant magnetic field, the component of magnetization in the direction that is transverse to the disorder field increases with the introduction of the quenched disorder. we discuss the same effects also for three - dimensional spins. | arxiv:0712.0829 |
we study the problem of measuring errors in non - trace - preserving quantum operations, with a focus on their impact on quantum computing. we propose an error metric that efficiently provides an upper bound on the trace distance between the normalized output states from imperfect and ideal operations, while remaining compatible with the diamond distance. as a demonstration of its application, we apply our metric in the analysis of a lossy beam splitter and a nondeterministic conditional sign - flip gate, two primary non - trace - preserving operations in the knill - laflamme - milburn protocol. we then turn to the leakage errors of neutral - atom quantum computers, finding that these errors scale worse than previously anticipated, implying a more stringent fault - tolerant threshold. we also assess the quantum zeno gate ' s error using our metric. in a broader context, we discuss the potential of our metric to analyze general postselected protocols, where it can be employed to study error propagation and estimate thresholds in fault - tolerant quantum computing. the results highlight the critical role of our proposed error metric in understanding and addressing challenges in practical quantum information processing. | arxiv:2110.02290 |
alignment with human preference prevents large language models ( llms ) from generating misleading or toxic content while requiring high - cost human feedback. assuming resources of human annotation are limited, there are two different ways of allocating considered : more diverse prompts or more diverse responses to be labeled. nonetheless, a straightforward comparison between their impact is absent. in this work, we first control the diversity of both sides according to the number of samples for fine - tuning, which can directly reflect their influence. we find that instead of numerous prompts, more responses but fewer prompts better trigger llms for human alignment. additionally, the concept of diversity for prompts can be more complex than responses that are typically quantified by single digits. consequently, a new formulation of prompt diversity is proposed, further implying a linear correlation with the final performance of llms after fine - tuning. we also leverage it on data augmentation and conduct experiments to show its effect on different algorithms. | arxiv:2403.11124 |
the intersection of electronic topology and strong correlations offers a rich platform to discover exotic quantum phases of matter and unusual materials. an overarching challenge that impedes the discovery is how to diagnose topology in strongly correlated settings, as exemplified by mott insulators. here, we develop a general framework to address this outstanding question and illustrate its power in the case of mott insulators. the concept of green ' s function berry curvature - - which is frequency dependent - - is introduced. we apply this notion in a system that contains symmetry - protected nodes in its noninteracting bandstructure ; strong correlations drive the system into a mott insulating state, creating contours in frequency - momentum space where the green ' s function vanishes. the green ' s function berry flux of such zeros is found to be quantized, and is as such direct probe of the system ' s topology. our framework allows for a comprehensive search of strongly correlated topological materials with green ' s function topology. | arxiv:2311.12031 |
we prove that the image of the lifted period map on the universal cover lies in a complex euclidean space. we also prove that the teichm \ " uller spaces of a class of polarized manifolds have complex affine structures. | arxiv:1910.06767 |
resolution of cosmological singularities is an important problem in any full theory of quantum gravity. the milne orbifold is a cosmology with a big - bang / big - crunch singularity, but being a quotient of flat space it holds potential for resolution in string theory. it is known however, that some perturbative string amplitudes diverge in the milne geometry. here we show that flat space higher spin theories can effect a simple resolution of the milne singularity when one embeds the latter in 2 + 1 dimensions. we explain how to reconcile this with the expectation that non - perturbative string effects are required for resolving milne. along the way, we introduce a grassmann realization of the \. { i } n \ " on \ " u - wigner contraction to export much of the ads technology to our flat space computation. | arxiv:1311.7315 |
we consider the problem of securely and robustly embedding covert messages into an image - based diffusion model ' s output. the sender and receiver want to exchange the maximum amount of information possible per diffusion sampled image while remaining undetected. the adversary wants to detect that such communication is taking place by identifying those diffusion samples that contain covert messages. to maximize robustness to transformations of the diffusion sample, a strategy is for the sender and the receiver to embed the message in the initial latents. we first show that prior work that attempted this is easily broken because their embedding technique alters the latents ' distribution. we then propose a straightforward method to embed covert messages in the initial latent { \ em without } altering the distribution. we prove that our construction achieves indistinguishability to any probabilistic polynomial time adversary. finally, we discuss and analyze empirically the tradeoffs between embedding capacity, message recovery rates, and robustness. we find that optimizing the inversion method for error correction is crucial for reliability. | arxiv:2503.10063 |
this paper addresses the challenge of decentralized task allocation within heterogeneous multi - agent systems operating under communication constraints. we introduce a novel framework that integrates graph neural networks ( gnns ) with a centralized training and decentralized execution ( ctde ) paradigm, further enhanced by a tailored proximal policy optimization ( ppo ) algorithm for multi - agent deep reinforcement learning ( marl ). our approach enables unmanned aerial vehicles ( uavs ) and unmanned ground vehicles ( ugvs ) to dynamically allocate tasks efficiently without necessitating central coordination in a 3d grid environment. the framework minimizes total travel time while simultaneously avoiding conflicts in task assignments. for the cost calculation and routing, we employ reservation - based a * and r * path planners. experimental results revealed that our method achieves a high 92. 5 % conflict - free success rate, with only a 7. 49 % performance gap compared to the centralized hungarian method, while outperforming the heuristic decentralized baseline based on greedy approach. additionally, the framework exhibits scalability with up to 20 agents with allocation processing of 2. 8 s and robustness in responding to dynamically generated tasks, underscoring its potential for real - world applications in complex multi - agent scenarios. | arxiv:2502.02311 |
we study a family of reachability problems under waiting - time restrictions in temporal and vertex - colored temporal graphs. given a temporal graph and a set of source vertices, we find the set of vertices that are reachable from a source via a time - respecting path, where the difference in timestamps between consecutive edges is at most a resting time. given a vertex - colored temporal graph and a multiset query of colors, we find the set of vertices reachable from a source via a time - respecting path such that the vertex colors of the path agree with the multiset query and the difference in timestamps between consecutive edges is at most a resting time. these kind of problems have applications in understanding the spread of a disease in a network, tracing contacts in epidemic outbreaks, finding signaling pathways in the brain network, and recommending tours for tourists, among other. we present an algebraic algorithmic framework based on constrained multi \ - linear sieving for solving the restless reachability problems we propose. in particular, parameterized by the length $ k $ of a path sought, we show that the proposed problems can be solved in $ o ( 2 ^ k k m \ delta ) $ time and $ o ( n \ delta ) $ space, where $ n $ is the number of vertices, $ m $ the number of edges, and $ \ delta $ the maximum resting time of an input temporal graph. in addition, we prove that our algorithms for the restless reachability problems in vertex - colored temporal graphs are optimal under plausible complexity - theoretic assumptions. finally, with an open - source implementation, we demonstrate that our algorithm scales to large graphs with up to one billion temporal edges, despite the problems being np - hard. specifically, we present extensive experiments to evaluate our scalability claims both on synthetic and real - world graphs. our implementation is efficiently engineered and highly optimized. | arxiv:2010.08423 |
the cusp anomalous dimension is a ubiquitous quantity in four - dimensional gauge theories, ranging from qcd to maximally supersymmetric n = 4 yang - mills theory, and it is one of the best investigated observables in the ads / cft correspondence. in planar n = 4 sym theory, its perturbative expansion at weak coupling has a finite radius of convergence while at strong coupling it admits an expansion in inverse powers of the ' t hooft coupling which is given by a non - borel summable asymptotic series. we study the cusp anomalous dimension in the transition regime from strong to weak coupling and argue that the transition is driven by nonperturbative, exponentially suppressed corrections. to compute these corrections, we revisit the calculation of the cusp anomalous dimension in planar n = 4 sym theory and extend the previous analysis by taking into account nonperturbative effects. we demonstrate that the scale parameterizing nonperturbative corrections coincides with the mass gap of the two - dimensional bosonic o ( 6 ) sigma model embedded into the ads _ 5xs ^ 5 string theory. this result is in agreement with the prediction coming from the string theory consideration. | arxiv:0901.4945 |
let $ q $ be a pisot or salem number. let $ f _ j ( x ) $ $ ( j = 1, 2, \ dots ) $ be integer - valued polynomials of degree $ \ ge2 $ with positive leading coefficients, and let $ \ { a _ j ( n ) \ } _ { n \ ge1 } $ $ ( j = 1, 2, \ dots ) $ be sequences of algebraic integers in the field $ \ mathbb { q } ( q ) $ with suitable growth conditions. in this paper, we investigate linear independence over $ \ mathbb { q } ( q ) $ of the numbers \ begin { equation * } 1, \ qquad \ sum _ { n = 1 } ^ { \ infty } \ frac { a _ j ( n ) } { q ^ { f _ j ( n ) } } \ quad ( j = 1, 2, \ dots ). \ end { equation * } in particular, when $ a _ j ( n ) $ $ ( j = 1, 2, \ dots ) $ are polynomials of $ n $, we give a linear independence criterion for the above numbers. | arxiv:2412.04801 |
each round in differential private stochastic gradient descent ( dpsgd ) transmits a sum of clipped gradients obfuscated with gaussian noise to a central server which uses this to update a global model which often represents a deep neural network. since the clipped gradients are computed separately, which we call individual clipping ( ic ), deep neural networks like resnet - 18 cannot use batch normalization layers ( bnl ) which is a crucial component in deep neural networks for achieving a high accuracy. to utilize bnl, we introduce batch clipping ( bc ) where, instead of clipping single gradients as in the orginal dpsgd, we average and clip batches of gradients. moreover, the model entries of different layers have different sensitivities to the added gaussian noise. therefore, adaptive layerwise clipping methods ( alc ), where each layer has its own adaptively finetuned clipping constant, have been introduced and studied, but so far without rigorous dp proofs. in this paper, we propose { \ em a new alc and provide rigorous dp proofs for both bc and alc }. experiments show that our modified dpsgd with bc and alc for cifar - $ 10 $ with resnet - $ 18 $ converges while dpsgd with ic and alc does not. | arxiv:2307.11939 |
clustering is a well - known unsupervised machine learning approach capable of automatically grouping discrete sets of instances with similar characteristics. constrained clustering is a semi - supervised extension to this process that can be used when expert knowledge is available to indicate constraints that can be exploited. well - known examples of such constraints are must - link ( indicating that two instances belong to the same group ) and cannot - link ( two instances definitely do not belong together ). the research area of constrained clustering has grown significantly over the years with a large variety of new algorithms and more advanced types of constraints being proposed. however, no unifying overview is available to easily understand the wide variety of available methods, constraints and benchmarks. to remedy this, this study presents in - detail the background of constrained clustering and provides a novel ranked taxonomy of the types of constraints that can be used in constrained clustering. in addition, it focuses on the instance - level pairwise constraints, and gives an overview of its applications and its historical context. finally, it presents a statistical analysis covering 307 constrained clustering methods, categorizes them according to their features, and provides a ranking score indicating which methods have the most potential based on their popularity and validation quality. finally, based upon this analysis, potential pitfalls and future research directions are provided. | arxiv:2303.00522 |
this paper describes the espnet unsupervised asr open - source toolkit ( euro ), an end - to - end open - source toolkit for unsupervised automatic speech recognition ( uasr ). euro adopts the state - of - the - art uasr learning method introduced by the wav2vec - u, originally implemented at fairseq, which leverages self - supervised speech representations and adversarial training. in addition to wav2vec2, euro extends the functionality and promotes reproducibility for uasr tasks by integrating s3prl and k2, resulting in flexible frontends from 27 self - supervised models and various graph - based decoding strategies. euro is implemented in espnet and follows its unified pipeline to provide uasr recipes with a complete setup. this improves the pipeline ' s efficiency and allows euro to be easily applied to existing datasets in espnet. extensive experiments on three mainstream self - supervised models demonstrate the toolkit ' s effectiveness and achieve state - of - the - art uasr performance on timit and librispeech datasets. euro will be publicly available at https : / / github. com / espnet / espnet, aiming to promote this exciting and emerging research area based on uasr through open - source activity. | arxiv:2211.17196 |
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