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the mittag - leffler ( ml ) function plays a fundamental role in fractional calculus but very few methods are available for its numerical evaluation. in this work we present a method for the efficient computation of the ml function based on the numerical inversion of its laplace transform ( lt ) : an optimal parabolic contour is selected on the basis of the distance and the strength of the singularities of the lt, with the aim of minimizing the computational effort and reduce the propagation of errors. numerical experiments are presented to show accuracy and efficiency of the proposed approach. the application to the three parameter ml ( also known as prabhakar ) function is also presented.
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arxiv:1503.06569
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local early - type galaxies with directly - measured black hole masses, $ m _ { \ rm bh } $, have been reported to represent a biased sample relative to the population at large. such galaxies with spitzer space telescope imaging have been purported to possess velocity dispersions, $ \ sigma $, at least $ \ sim $ 0. 1 dex larger for a given galaxy stellar mass, $ m _ { \ rm *, gal } $, than is typically observed among thousands of early - type galaxies imaged by the sloan digital sky survey. this apparent offset led shankar et al. to reduce the normalisation of the observed $ m _ { \ rm bh } \ propto \ sigma ^ 5 $ relation by at least $ \ sim $ 0. 5 dex to give their " intrinsic relations ", including $ \ sigma $ - based modifications to the $ m _ { \ rm bh } $ - $ m _ { \ rm *, gal } $ relation. these modifications were based on the untested assumption that the stellar masses had been derived consistently between the two samples. here, we provide the necessary check using galaxies common to the spitzer survey of stellar structure in galaxies ( s $ ^ 4 $ g ) and the sloan digital sky survey ( sdss ). we find that the stellar masses of galaxies with and without directly measured black holes had appeared offset from each other due to the use of inconsistent stellar mass - to - light ratios, $ \ upsilon _ * $, for the optical and infrared data. we briefly discuss the " intrinsic relations " and why some of these will at times appear to have had partial success when applied to data based on similarly inconsistent values of $ \ upsilon _ * $. finally, we reiterate the importance of the $ \ upsilon $ ( lower - case $ \ upsilon $ ) term, which we previously introduced into the $ m _ { \ rm bh } $ - $ m _ { \ rm * } $ relations to help avoid $ \ upsilon _ * $ - related mismatches.
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arxiv:2210.02641
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in this paper, we study the properties of the charged black hole surrounded by the quintessence. the solution space for the horizons for various values of the mass $ m $, charge $ q $, and the quintessence parameter $ \ alpha $ are studied in detail. special focus in given to the degenerate horizons : we obtain cold, ultracold and nariai black holes which has similar topologies as for the reissner - nordstrom - de sitter black holes. we also study the lukewarm black hole with the quintessence in this paper.
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arxiv:1401.0714
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we study riemannian geometry of canonical kahler - einstein currents on projective calabi - yau varieties and canonical models of general type with crepant singularities. we prove that the metric completion of the regular part of such a canonical current is a compact metric length space homeomorphic to the original projective variety, with well - defined tangent cones. we also prove a special degeneration for kahler - einstein manifolds of general type as an approach to establish the compactification of the moduli space of kahler - einstein manifolds of general type. a number of applications are given for degeneration of calabi - yau manifolds and the kahler - ricci flow on smooth minimal models of general type.
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arxiv:1404.0445
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we study sections of a calabi - yau threefold fibered over a curve by k3 surfaces. we show that there exist infinitely many isolated sections on certain k3 fibered calabi - yau threefolds and the subgroup of the n \ ' eron - severi group generated by these sections is not finitely generated. this also gives examples of k3 surfaces over the function field f of a complex curve with zariski dense f - rational points, whose geometric model is calabi - yau.
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arxiv:1111.2545
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agents are small programs that autonomously take actions based on changes in their environment or ` ` state. ' ' over the last few years, there have been an increasing number of efforts to build agents that can interact and / or collaborate with other agents. in one of these efforts, eiter, subrahmanian amd pick ( aij, 108 ( 1 - 2 ), pages 179 - 255 ) have shown how agents may be built on top of legacy code. however, their framework assumes that agent states are completely determined, and there is no uncertainty in an agent ' s state. thus, their framework allows an agent developer to specify how his agents will react when the agent is 100 % sure about what is true / false in the world state. in this paper, we propose the concept of a \ emph { probabilistic agent program } and show how, given an arbitrary program written in any imperative language, we may build a declarative ` ` probabilistic ' ' agent program on top of it which supports decision making in the presence of uncertainty. we provide two alternative semantics for probabilistic agent programs. we show that the second semantics, though more epistemically appealing, is more complex to compute. we provide sound and complete algorithms to compute the semantics of \ emph { positive } agent programs.
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arxiv:cs/9910016
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several independent lines of evidence suggest that the stellar initial mass function ( imf ) in early - type galaxies becomes increasingly ` bottom - heavy ' with increasing galaxy mass and / or velocity dispersion, sigma. here we consider evidence for imf variation in a sample of relatively compact early - type galaxies drawn from the sloan digital sky survey. these galaxies are of sufficiently high stellar density that a dark halo likely makes a minor contribution to the total dynamical mass, mdyn, within one effective radius. we fit our detailed stellar population synthesis models to the stacked absorption line spectra of these galaxies in bins of sigma and find evidence from imf - sensitive spectral features for a bottom - heavy imf at high sigma. we also apply simple ` mass - follows - light ' dynamical models to the same data and find that mdyn is significantly higher than what would be expected if these galaxies were stellar dominated and had a universal milky way imf. adopting mdyn m _ * therefore implies that the imf is ` heavier ' at high sigma. most importantly, the quantitative amount of inferred imf variation is very similar between the two techniques, agreeing to within 0. 1 dex in mass. the agreement between two independent techniques, when applied to the same data, provides compelling evidence for systematic variation in the imf as a function of early - type galaxy velocity dispersion. any alternative explanations must reproduce both the results from dynamical and stellar population - based techniques.
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arxiv:1306.2316
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we present an original, generic, and efficient approach for computing the first and second partial derivatives of ray velocities along ray paths in general anisotropic elastic media. these derivatives are used in solving kinematic problems, like two - point ray bending methods and seismic tomography, and they are essential for evaluating the dynamic properties along the rays ( amplitudes and phases ). the traveltime is delivered through an integral over a given lagrangian defined at each point along the ray. although the lagrangian cannot be explicitly expressed in terms of the medium properties and the ray direction components, its derivatives can still be formulated analytically using the corresponding arclength - related hamiltonian that can be explicitly expressed in terms of the medium properties and the slowness vector components. this requires first to invert for the slowness vector components, given the ray direction components. computation of the slowness vector and the ray velocity derivatives is considerably simplified by using an auxiliary scaled - time - related hamiltonian obtained directly from the christoffel equation and connected to the arclength - related hamiltonian by a simple scale factor. this study consists of two parts. in part i, we consider general anisotropic ( triclinic ) media, and provide the derivatives ( gradients and hessians ) of the ray velocity, with respect to ( 1 ) the spatial / directional vectors and ( 2 ) the elastic model parameters. in part ii, we apply the theory of part i explicitly to polar anisotropic media ( transverse isotropy with tilted axis of symmetry, tti ), and obtain the explicit ray velocity derivatives for the coupled qp and qsv waves and for sh waves.
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arxiv:2106.15014
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the voiceprivacy challenge promotes the development of voice anonymisation solutions for speech technology. in this paper we present a systematic overview and analysis of the second edition held in 2022. we describe the voice anonymisation task and datasets used for system development and evaluation, present the different attack models used for evaluation, and the associated objective and subjective metrics. we describe three anonymisation baselines, provide a summary description of the anonymisation systems developed by challenge participants, and report objective and subjective evaluation results for all. in addition, we describe post - evaluation analyses and a summary of related work reported in the open literature. results show that solutions based on voice conversion better preserve utility, that an alternative which combines automatic speech recognition with synthesis achieves greater privacy, and that a privacy - utility trade - off remains inherent to current anonymisation solutions. finally, we present our ideas and priorities for future voiceprivacy challenge editions.
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arxiv:2407.11516
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the electric power system is currently experiencing radical changes stemming from the increasing share of renewable energy resources and the consequent decommissioning of conventional power plants based on synchronous generators. since the principal providers of ancillary services are being phased out, new flexibility and reserve providers are needed. the proliferation of distributed energy resources ( ders ) in modern distribution networks has opened new possibilities for distribution system operators, enabling them to fill the market gap by harnessing the der flexibility. this paper introduces a novel centralized mpc - based controller that enables the concurrent provision of voltage support, primary and secondary frequency control by adjusting the setpoints of a heterogeneous group of ders in active distribution grids. the input - multirate control framework is used to accommodate the distinct timescales and provision requirements of each ancillary service and to ensure that the available resources are properly allocated. furthermore, an efficient way for incorporating network constraints in the formulation is proposed, where network decomposition is applied to a linear power flow formulation together with network reduction. in addition, different timescale dynamics of the employed ders and their capability curves are included. the performance of the proposed controller is evaluated on several case studies via dynamic simulations of the ieee 33 - bus system.
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arxiv:2202.09403
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we investigate a way of imposing simplicity constraints in a holomorphic spin foam model that we recently introduced. rather than imposing the constraints on the boundary spin network, as is usually done, one can impose the constraints directly on the spin foam propagator. we find that the two approaches have the same leading asymptotic behaviour, with differences appearing at higher order. this allows us to obtain a model that greatly simplifies calculations, but still has regge calculus as its semi - classical limit.
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arxiv:1512.05331
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let $ g $ be a group. let $ x $ be a connected algebraic group over an algebraically closed field $ k $. denote by $ a = x ( k ) $ the set of $ k $ - points of $ x $. we study a class of endomorphisms of pro - algebraic groups, namely algebraic group cellular automata over $ ( g, x, k ) $. they are cellular automata $ \ tau \ colon a ^ g \ to a ^ g $ whose local defining map is induced by a homomorphism of algebraic groups $ x ^ m \ to x $ where $ m \ subset g $ is a finite memory set of $ \ tau $. our first result is that when $ g $ is sofic, such an algebraic group cellular automaton $ \ tau $ is invertible whenever it is injective and $ \ text { char } ( k ) = 0 $. as an application, we prove that if $ g $ is sofic and the group $ x $ is commutative then the group ring $ r [ g ] $, where $ r = \ text { end } ( x ) $ is the endomorphism ring of $ x $, is stably finite. when $ g $ is amenable, we show that an algebraic group cellular automaton $ \ tau $ is surjective if and only if it satisfies a weak form of pre - injectivity called $ ( \ bullet ) $ - pre - injectivity. this yields an analogue of the classical moore - myhill garden of eden theorem. we also introduce the near ring $ r ( k, g ) $ which is $ k [ x _ g : g \ in g ] $ as an additive group but the multiplication is induced by the group law of $ g $. the near ring $ r ( k, g ) $ contains naturally the group ring $ k [ g ] $ and we extend kaplansky ' s conjectures to this new setting. among other results, we prove that when $ g $ is an orderable group, then all one - sided invertible elements of $ r ( k, g ) $ are trivial, i. e., of the form $ ax _ g + b $ for some $ g \ in g $, $ a \ in k ^ * $, $ b \ in k $. this allows us to show that when $ g $ is locally residually finite and orderable ( e
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arxiv:1804.06631
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let $ p ( m, x, n ) $ be an $ m $ - degree polynomial in $ x \ in \ mathbb { r } $ having fixed non - negative integers $ m $ and $ n $. the polynomial $ p ( m, x, n ) $ is derived from a rearrangement of faulhaber ' s formula in the context of knuth ' s work entitled " johann faulhaber and sums of powers ". in this manuscript we discuss the approximation properties of polynomial $ p ( m, x, n ) $. in particular, the polynomial $ p ( m, x, n ) $ approximates the odd power function $ x ^ { 2m + 1 } $ in a certain neighborhood of a fixed non - negative integer $ n $ with a percentage error under $ 1 \ % $. by increasing the value of $ n $ the length of convergence interval with odd - power $ x ^ { 2m + 1 } $ also increases. furthermore, this approximation technique is generalized for arbitrary non - negative exponent $ j $ of the power function $ x ^ j $ by using splines.
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arxiv:2503.07618
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we propose a new field theoretic method for calculating renyi entropy of a sub - system of many interacting bosons without using replica methods. this method is applicable to dynamics of both open and closed quantum systems starting from arbitrary initial conditions. our method identifies the wigner characteristic of a reduced density matrix with the partition function of the whole system with a set of linear sources turned on only in the subsystem and uses this to calculate the subsystem ' s renyi entropy. we use this method to study evolution of renyi entropy in a non - interacting open quantum system starting from an initial fock state. we find a relation between the initial state and final density matrix which determines whether the entropy shows non - monotonic behaviour in time. for non - markovian dynamics, we show that the entropy approaches its steady state value as a power law with exponents governed by non - analyticities of the bath. we illustrate that this field - theoretic method can be used to study large bosonic open quantum systems.
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arxiv:1810.10545
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we develop a new analysis for portfolio optimisation with options, tackling the three fundamental issues with this problem : asymmetric options ' distributions, high dimensionality and dependence structure. to do so, we propose a new dependency matrix, built upon conditional probabilities between options ' payoffs, and show how it can be computed in closed form given a copula structure of the underlying asset prices. the empirical evidence we provide highlights that this approach is efficient, fast and easily scalable to large portfolios of ( mixed ) options.
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arxiv:2111.12658
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we use hubble space telescope near - ir grism spectroscopy to examine the h - beta line strengths of 260 star - forming galaxies in the redshift range 1. 90 < z < 2. 35. we show that at these epochs, the h - beta star formation rate ( sfr ) is a factor of ~ 1. 8 higher than what would be expected from the systems ' rest - frame uv flux density, suggesting a shift in the standard conversion between these quantities and star formation rate. we demonstrate that at least part of this shift can be attributed to metallicity, as h - beta is more greatly enhanced in systems with lower oxygen abundance. this offset must be considered when measuring the star formation rate history of the universe. we also show that the relation between stellar and nebular extinction in our z ~ 2 sample is consistent with that observed in the local universe.
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arxiv:1406.3355
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we interpret the traversable wormhole in ads / cft in the context of quantum information theory. in particular, we investigate its properties as both a quantum channel and entanglement witness. we define protocols that allow either the bounding of the channel ' s entanglement capacity or the determination of aspects of the entanglement structure between the two boundary cfts. such protocols and connections allow for the use of quantum channel techniques in the study of gravitational physics and vice versa. more generally, our results suggest a purely quantum information - theoretic criterion for recognizing when the product of two boundary theories has a classical bulk interpretation.
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arxiv:1808.05963
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defect segmentation is crucial for quality control in advanced manufacturing, yet data scarcity poses challenges for state - of - the - art supervised deep learning. synthetic defect data generation is a popular approach for mitigating data challenges. however, many current methods simply generate defects following a fixed set of rules, which may not directly relate to downstream task performance. this can lead to suboptimal performance and may even hinder the downstream task. to solve this problem, we leverage a novel bi - level optimization - based synthetic defect data generation framework. we use an online synthetic defect generation module grounded in the commonly - used cut \ & paste framework, and adopt an efficient gradient - based optimization algorithm to solve the bi - level optimization problem. we achieve simultaneous training of the defect segmentation network, and learn various parameters of the data synthesis module by maximizing the validation performance of the trained defect segmentation network. our experimental results on benchmark datasets under limited data settings show that the proposed bi - level optimization method can be used for learning the most effective locations for pasting synthetic defects thereby improving the segmentation performance by up to 18. 3 \ % when compared to pasting defects at random locations. we also demonstrate up to 2. 6 \ % performance gain by learning the importance weights for different augmentation - specific defect data sources when compared to giving equal importance to all the data sources.
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arxiv:2410.18490
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dehmelt ' s lambda - experiment for a three - level atom with simultaneously driven strong and weak transition is studied within quantum stochastic calculus approach. the statistics of the emitted photons is found by the method of generating functional of the corresponding two dimensional output counting process. in particular, the average waiting times for a count are calculated.
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arxiv:1207.1058
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for a detailed study on the semiconductor to metal transition ( smt ) in zno thin films doped with al in the concentration range from 0. 02 to 2 %, we grew these films on ( 0001 ) sapphire substrates using sequential pulsed laser deposition. it was found that the al concentration in the films increased monotonically with the ratio of ablation durations of the alumina and zno targets used during the deposition. using x - ray photo electron spectroscopy it was found that while most of the al atoms occupy the zn sites in the zno lattice, a small fraction of the al also gets into the grain boundaries present in the films. the observed smt temperature decreased from ~ 270 to ~ 50 k with increase in the al concentration from 0. 02 to 0. 25 %. in the al concentration range of ~ 0. 5 to 2 % these doped zno films showed metallic behavior at all the temperatures without undergoing any smt. a theoretical model based on thermal activation of electrons and electron scatterings due to the grain boundaries, ionic impurities and phonons has been developed to explain the observed concentration and temperature dependent smt.
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arxiv:1202.3298
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we study the cosmological dynamics of dark energy in a scalar - vector - torsion theory. the vector field is described by the cosmic triad and the scalar field is of the quintessence type with non - minimal coupling to gravity. the coupling to gravity is introduced through the interaction between the scalar field and torsion, where torsion is defined in the context of teleparallel gravity. we derive the full set of field equations for the friedmann - lema \ ^ { i } tre - robertson - walker space - time background and obtain the associated autonomous system. we obtain the critical points and their stability conditions, along with the cosmological properties of them. thus, we show that the thermal history of the universe is successfully reproduced. furthermore, new scaling solutions in which the scalar and vector field densities scale in the same way as the radiation and matter background fluids have been found. finally, we also show that there exist new attractor fixed points whose nature is mainly vectorial, and which can explain the current accelerated expansion and therefore the dark energy - domination.
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arxiv:2212.12071
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we infer supermassive black hole ( smbh ) accretion rates and eddington ratios as a function of smbh / host galaxy mass and redshift with the empirical trinity model of dark matter halo - - galaxy - - smbh connection. the galaxy - - smbh mass and growth rate connection from trinity matches galaxy observables from $ 0 < z < 13 $ and smbh observables from $ 0 < z < 6. 5 $. key findings include : 1 ) the ratio between cosmic smbh accretion rate and galaxy star formation rate stays constant at $ \ sim 2 \ times 10 ^ { - 3 } $ from $ z = 0 - 4 $, and decreases by 2 orders of magnitude from $ z = 4 - 10 $ ; 2 ) the average smbh eddington ratio $ \ overline { \ eta } $ increases towards higher redshifts, nearly reaching $ \ overline { \ eta } = 1 $ at $ z \ sim 10 $ ; 3 ) at fixed redshift for $ z < 3 $, smbhs / galaxies with higher masses have lower $ \ overline { \ eta } $, consistent with agn downsizing ; 4 ) the average ratio of specific smbh accretion rate ( $ \ overline { \ mathrm { sbhar } } $ ) to average specific star formation rate ( $ \ overline { \ mathrm { ssfr } } $ ) is nearly mass - independent, with a value $ \ overline { \ mathrm { sbhar } } / \ overline { \ mathrm { ssfr } } \ sim 1 $, which decreases slightly from $ z = 10 $ to $ z = 0 $ ; 5 ) similar to galaxies, smbhs reach their peak efficiency to convert baryons into mass when host halos reach $ 10 ^ { 12 } m _ \ odot $ ; 6 ) given galaxy and smbh growth histories from trinity, the local descendants of $ 1 < z < 11 $ overmassive jwst agns will remain outliers from the local smbh mass - - galaxy mass relation. these findings combine to give a simple explanation for massive ( $ 10 ^ 9 - 10 ^ { 10 } m _ \ odot $ ) quasars at $ z > 6 $ : at these redshifts, dark matter halos grow with an $ e $ - folding time of $ \ sim 45 $ myrs, driving similar growth rates in
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arxiv:2409.16347
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we study the distribution of several statistics of large non - crossing partitions. first, we prove the gaussian limit theorem for the number of blocks of a given fixed size. in contrast to the properties of usual set partitions, we show that the number of blocks of different sizes are negatively correlated, even for large partitions. in addition, we show that the sizes of blocks in a given large non - crossing partition are distributed according to a geometric distribution and not poisson, as in the case of usual set partitions. next, we show that the size of the largest block concentrates at $ \ log _ 2 n $, and that after an appropriate rescaling, it can be described by the double exponential distribution. finally, we show that the width of a large non - crossing partition converges to the theta - distribution which arises in the theory of brownian excursions.
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arxiv:1907.00632
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a theory of the dynamical conductance of mesoscopic conductors is presented. it is applied to mesoscopic capacitors, resonant double barriers, ballistic wires, metallic diffusive wires, and to the corbino disk and the hall bar in quantizing magnetic fields. central to this approach is a discussion of the charge and potential distribution in mesoscopic conductors. it is necessary to take into account the implications of the long - range coulomb interaction in order to obtain a charge and current conserving theory. we emphasize the low - frequency response. this has the advantage that the approach is of considerable generality. the theory can be used to discuss the self - consistency of the dc - conductance formula. the theory can also be applied to discuss the rectifying ( nonlinear ) behavior of mesoscopic conductors.
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arxiv:cond-mat/9601075
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the automated analysis of flow cytometry measurements is an active research field. we introduce a new algorithm, referred to as cytopt, using regularized optimal transport to directly estimate the different cell population proportions from a biological sample characterized with flow cytometry measurements. we rely on the regularized wasserstein metric to compare cytometry measurements from different samples, thus accounting for possible mis - alignment of a given cell population across sample ( due to technical variability from the technology of measurements ). in this work, we rely on a supervised learning technique based on the wasserstein metric that is used to estimate an optimal re - weighting of class proportions in a mixture model from a source distribution ( with known segmentation into cell sub - populations ) to fit a target distribution with unknown segmentation. due to the high - dimensionality of flow cytometry data, we use stochastic algorithms to approximate the regularized wasserstein metric to solve the optimization problem involved in the estimation of optimal weights representing the cell population proportions in the target distribution. several flow cytometry data sets are used to illustrate the performances of cytopt that are also compared to those of existing algorithms for automatic gating based on supervised learning.
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arxiv:2006.09003
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this paper explores two separate questions : can we perform natural language processing tasks without a lexicon? ; and, should we? existing natural language processing techniques are either based on words as units or use units such as grams only for basic classification tasks. how close can a machine come to reasoning about the meanings of words and phrases in a corpus without using any lexicon, based only on grams? our own motivation for posing this question is based on our efforts to find popular trends in words and phrases from online chinese social media. this form of written chinese uses so many neologisms, creative character placements, and combinations of writing systems that it has been dubbed the " martian language. " readers must often use visual queues, audible queues from reading out loud, and their knowledge and understanding of current events to understand a post. for analysis of popular trends, the specific problem is that it is difficult to build a lexicon when the invention of new ways to refer to a word or concept is easy and common. for natural language processing in general, we argue in this paper that new uses of language in social media will challenge machines ' abilities to operate with words as the basic unit of understanding, not only in chinese but potentially in other languages.
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arxiv:1212.3228
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we report measurements of the diffusion of atomic hydrogen in single crystalline vo2 micro / nanobeams by direct exposure to atomic hydrogen, without catalyst. the atomic hydrogen is generated by a hot filament, and the doping process takes place at moderate temperature ( 373 k ). undoped vo2 has a metal - to - insulator phase transition at ~ 340 k between a high - temperature, rutile, metallic phase and a low - temperature, monoclinic, insulating phase with a resistance exhibiting a semiconductor - like temperature dependence. atomic hydrogenation results in stabilization of the metallic phase of vo2 micro / nanobeams down to 2 k, the lowest point we could reach in our measurement setup. based on observing the movement of the hydrogen diffusion front in single crystalline vo2 beams, we estimate the diffusion constant for hydrogen along the c - axis of the rutile phase to be 6. 7 x 10 ^ { - 10 } cm ^ 2 / s at approximately 373 k, exceeding the value in isostructural tio2 by ~ 38x. moreover, we find that the diffusion constant along the c - axis of the rutile phase exceeds that along the equivalent a - axis of the monoclinic phase by at least three orders of magnitude. this remarkable change in kinetics must originate from the distortion of the " channels " when the unit cell doubles along this direction upon cooling into the monoclinic structure. ab initio calculation results are in good agreement with the experimental trends in the relative kinetics of the two phases. this raises the possibility of a switchable membrane for hydrogen transport.
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arxiv:1409.4661
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the relations existing between the auxiliary field ( einbein field ) formalism and the spinless salpeter equation are studied in the case of two particles with the same mass, interacting via a confining potential. the problem of non - orthogonality for radial excited states in the auxiliary field formalism is discussed and found to be non - crucial. it is shown that the classical equations of motion of the rotating string model, derived from the qcd lagrangian, reduce exactly to the classical equations of motion of the phenomenological semirelativistic flux tube model, provided all auxiliary fields are eliminated correctly from the rotating string hamiltonian.
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arxiv:hep-ph/0309256
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the easily tunable emission of halide perovskite nanocrystals throughout the visible spectrum makes them an extremely promising material for light - emitting applications. whereas high quantum yields and long - term colloidal stability have already been achieved for nanocrystals emitting in the red and green spectral range, the blue region currently lags behind, with low quantum yields, broad emission profiles and insufficient colloidal stability. in this work, we present a facile synthetic approach for obtaining two - dimensional cspbbr3 nanoplatelets with monolayer - precise control over their thickness, resulting in sharp photoluminescence and electroluminescence peaks with a tunable emission wavelength between 432 and 497 nm due to quantum confinement. subsequent addition of a pbbr2 - ligand solution repairs surface defects likely stemming from bromide and lead vacancies in a sub - ensemble of weakly emissive nanoplatelets. the overall photoluminescence quantum yield of the blue - emissive colloidal dispersions is consequently enhanced up to a value of 73 + - 2 %. transient optical spectroscopy measurements focusing on the excitonic resonances further confirm the proposed repair process. additionally, the high stability of these nanoplatelets in films and to prolonged uv light exposure is shown.
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arxiv:2010.14392
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our goal, in the context of open - domain textual question - answering ( qa ), is to explain answers by showing the line of reasoning from what is known to the answer, rather than simply showing a fragment of textual evidence ( a " rationale ' " ). if this could be done, new opportunities for understanding and debugging the system ' s reasoning become possible. our approach is to generate explanations in the form of entailment trees, namely a tree of multipremise entailment steps from facts that are known, through intermediate conclusions, to the hypothesis of interest ( namely the question + answer ). to train a model with this skill, we created entailmentbank, the first dataset to contain multistep entailment trees. given a hypothesis ( question + answer ), we define three increasingly difficult explanation tasks : generate a valid entailment tree given ( a ) all relevant sentences ( b ) all relevant and some irrelevant sentences, or ( c ) a corpus. we show that a strong language model can partially solve these tasks, in particular when the relevant sentences are included in the input ( e. g., 35 % of trees for ( a ) are perfect ), and with indications of generalization to other domains. this work is significant as it provides a new type of dataset ( multistep entailments ) and baselines, offering a new avenue for the community to generate richer, more systematic explanations.
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arxiv:2104.08661
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we discuss a simple model of thermal relic dark matter whose mass can be much larger than the so - called unitarity limit on the mass of point - like particle dark matter. the model consists of new strong dynamics with one flavor of fermions in the fundamental representation which is much heavier than the dynamical scale of the new strong dynamics. dark matter is identified with the lightest baryonic hadron of the new dynamics. the baryonic hadrons annihilate into the mesonic hadrons of the new strong dynamics when they have large radii. resultantly, thermal relic dark matter with a mass in the pev range is possible.
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arxiv:1606.00159
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we propose to create and stabilize long - lived macroscopic quantum superposition states in atomic ensembles. we show that using a fully quantum parametric amplifier can cause the simultaneous decay of two atoms and, in turn, create stabilized atomic schr \ " { o } dinger cat states. remarkably, even with modest parameters these intracavity atomic cat states can have an extremely long lifetime, up to \ emph { 4 orders of magnitude } longer than that of intracavity photonic cat states under the same parameter conditions, reaching \ emph { tens of milliseconds }. this lifetime of atomic cat states is ultimately limited to \ emph { several seconds } by extremely weak spin relaxation and thermal noise. our work opens up a new way toward the long - standing goal of generating large - size and long - lived cat states, with immediate interests both in fundamental studies and noise - immune quantum technologies.
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arxiv:2101.03662
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we study the robe ' s restricted three - body problem. such a motion was firstly studied by a. g. robe in \ cite { robe }, which is used to model small oscillations of the earth ' s inner core taking into account the moon attraction. for the linear stability of elliptic equilibrium points of the robe ' s restricted three - body problem, earlier results of such linear stability problem depend on a lot of numerical computations, while we give an analytic approach to it. the linearized hamiltonian system near the elliptic relative equilibrium point in our problem coincides with the linearized system near the euler elliptic relative equilibria in the classical three - body problem except for the rang of the mass parameter. we first establish some relations from the linear stability problem to symplectic paths and its corresponding linear operators. then using the maslov - type $ \ omega $ - index theory of symplectic paths and the theory of linear operators, we compute $ \ omega $ - indices and obtain certain properties of the linear stability of elliptic equilibrium points of the robe ' s restricted three - body problem.
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arxiv:1607.00636
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in our earlier work \ cite { dll }, we have shown the global well - posedness of strong solutions to the three - dimensional primitive equations with the magnetic field ( pem ) on a thin domain. the heart of this paper is to provide a rigorous justification of the derivation of the pem as the small aspect ratio limit of the incompressible three - dimensional scaled magnetohydrodynamics ( smhd ) equations in the anisotropic horizontal viscosity and magnetic field regime. for the case of $ h ^ 1 $ - initial data case, we prove that global leray - hopf weak solutions of the three - dimensional smhd equation strongly converge to the global strong solutions of the pem. in the $ h ^ 2 $ - initial data case, the strong solution of the smhd can be extended to be a global one for small $ \ v $. as a consequence, we observe that the global strong solutions of the smhd strong converge to the global strong solutions of the pem. as a byproduct, the convergence rate is of the same order as the aspect ratio parameter.
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arxiv:2208.01985
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dense retrieval ( dr ) has the potential to resolve the query understanding challenge in conversational search by matching in the learned embedding space. however, this adaptation is challenging due to dr models ' extra needs for supervision signals and the long - tail nature of conversational search. in this paper, we present a conversational dense retrieval system, convdr, that learns contextualized embeddings for multi - turn conversational queries and retrieves documents solely using embedding dot products. in addition, we grant convdr few - shot ability using a teacher - student framework, where we employ an ad hoc dense retriever as the teacher, inherit its document encodings, and learn a student query encoder to mimic the teacher embeddings on oracle reformulated queries. our experiments on trec cast and or - quac demonstrate convdr ' s effectiveness in both few - shot and fully - supervised settings. it outperforms previous systems that operate in the sparse word space, matches the retrieval accuracy of oracle query reformulations, and is also more efficient thanks to its simplicity. our analyses reveal that the advantages of convdr come from its ability to capture informative context while ignoring the unrelated context in previous conversation rounds. this makes convdr more effective as conversations evolve while previous systems may get confused by the increased noise from previous turns. our code is publicly available at https : / / github. com / thunlp / convdr.
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arxiv:2105.04166
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this paper addresses multi - user quantum key distribution networks, in which any two users can mutually exchange a secret key without trusting any other nodes. the same network also supports conventional classical communications by assigning two different wavelength bands to quantum and classical signals. time and code division multiple access ( cdma ) techniques, within a passive star network, are considered. in the case of cdma, it turns out that the optimal performance is achieved at a unity code weight. a listen - before - send protocol is then proposed to improve secret key generation rates in this case. finally, a hybrid setup with wavelength routers and passive optical networks, which can support a large number of users, is considered and analyzed.
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arxiv:1112.3218
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we report the first observation of multiple intercommutation ( more than two successive reconnections ) of cosmic strings at ultra - high collision speeds, and the formation of ` ` kink trains ' ' with up to four closely spaced left - or right - moving kinks. we performed a flat space numerical study of abelian higgs cosmic string intercommutation in the type - ii regime $ \ beta > 1 $ ( where $ \ beta = m ^ 2 _ { scalar } / m ^ 2 _ { gauge } $ ) up to $ \ beta = 64 $, the highest value investigated to date. our results confirm earlier claims that the minimum critical speed for double reconnection goes down with increasing $ \ beta $, from $ \ sim 0. 98 c $ at $ \ beta = 1 $ to $ \ sim 0. 86 c $ for $ \ beta = 64 $. furthermore, we observe a qualitative change in the process leading to the second intercommutation : if $ \ beta \ geq 16 $ it is mediated by a loop expanding from the collision point whereas if $ 1 < \ beta \ leq 8 $ the previously reported ` ` loop ' ' is just an expanding blob of radiation which has no topological features and is absorbed by the strings. the multiple reconnections are observed in the loop - mediated, deep type - ii regime $ \ beta \ geq 16 $. triple reconnections appear to be quite generic for collision parameters on the boundary between single and double reconnection. for $ \ beta = 16 $ we observe quadruple events. they result in clustering of small scale structure in the form of ` ` kink trains ' '. our findings suggest that, due to the core interactions, the small scale structure and stochastic gravitational wave background of abelian higgs strings in the strongly type - ii regime may be quite different from what would be expected from studies of nambu - goto strings or of abelian higgs strings in the $ \ beta \ approx 1 $ regime.
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arxiv:1006.0979
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thin films of optimally - doped ( 001 ) - oriented yba2cu3o7 - { \ delta } are epitaxially integrated on silicon ( 001 ) through growth on a single crystalline srtio3 buffer. the former is grown using pulsed - laser deposition and the latter is grown on si using oxide molecular beam epitaxy. the single crystal nature of the srtio3 buffer enables high quality yba2cu3o7 - { \ delta } films exhibiting high transition temperatures to be integrated on si. for a 30 nm thick srtio3 buffer, 50 nm thick yba2cu3o7 - { \ delta } films that exhibit a transition temperature of ~ 93 k, and a narrow transition width ( < 5 k ) are achieved. the integration of single crystalline yba2cu3o7 - { \ delta } on si ( 001 ) paves the way for the potential exploration of cuprate materials in a variety of applications.
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arxiv:1710.08600
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while most neural video codecs address p - frame coding ( predicting each frame from past ones ), in this paper we address b - frame compression ( predicting frames using both past and future reference frames ). our b - frame solution is based on the existing p - frame methods. as a result, b - frame coding capability can easily be added to an existing neural codec. the basic idea of our b - frame coding method is to interpolate the two reference frames to generate a single reference frame and then use it together with an existing p - frame codec to encode the input b - frame. our studies show that the interpolated frame is a much better reference for the p - frame codec compared to using the previous frame as is usually done. our results show that using the proposed method with an existing p - frame codec can lead to 28. 5 % saving in bit - rate on the uvg dataset compared to the p - frame codec while generating the same video quality.
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arxiv:2104.00531
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the violation of bell inequalities seems to establish an important fact about the world : that it is non - local. however, this result relies on the assumption of the statistical independence of the measurement settings with respect to potential past events that might have determined them. superdeterminism refers to the view that a local, and determinist, account of bell inequalities violations is possible, by rejecting this assumption of statistical independence. we examine and clarify various problems with superdeterminism, looking in particular at its consequences on the nature of scientific laws and scientific reasoning. we argue that the view requires a neo - humean account of at least some laws, and creates a significant problem for the use of statistical independence in other parts of physics and science more generally.
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arxiv:2009.13908
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in this paper we study the spectrum of heights of transitive models of theories extending $ v = l [ a ] $, under various definitions. in particular, we investigate the consistency strength of making those spectra as simple as possible.
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arxiv:2305.04244
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electronic - photonic computing systems offer immense potential in energy - efficient artificial intelligence ( ai ) acceleration tasks due to the superior computing speed and efficiency of optics, especially for real - time, low - energy deep neural network ( dnn ) inference tasks on resource - restricted edge platforms. however, current optical neural accelerators based on foundry - available devices and conventional system architecture still encounter a performance gap compared to highly customized electronic counterparts. to bridge the performance gap due to lack of domain specialization, we present a time - multiplexed dynamic photonic tensor accelerator, dubbed tempo, with cross - layer device / circuit / architecture customization. at the device level, we present foundry - compatible, customized photonic devices, including a slow - light electro - optic modulator with experimental demonstration, optical splitters, and phase shifters that significantly reduce the footprint and power in input encoding and dot - product calculation. at the circuit level, partial products are hierarchically accumulated via parallel photocurrent aggregation, lightweight capacitive temporal integration, and sequential digital summation, considerably relieving the analog - to - digital conversion bottleneck. we also employ a multi - tile, multi - core architecture to maximize hardware sharing for higher efficiency. across diverse edge ai workloads, tempo delivers digital - comparable task accuracy with superior quantization / noise tolerance. we achieve a 368. 6 tops peak performance, 22. 3 tops / w energy efficiency, and 1. 2 tops / mm $ ^ 2 $ compute density, pushing the pareto frontier in edge ai hardware. this work signifies the power of cross - layer co - design and domain - specific customization, paving the way for future electronic - photonic accelerators with even greater performance and efficiency.
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arxiv:2402.07393
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understanding the implicit bias of training algorithms is of crucial importance in order to explain the success of overparametrised neural networks. in this paper, we study the role of the label noise in the training dynamics of a quadratically parametrised model through its continuous time version. we explicitly characterise the solution chosen by the stochastic flow and prove that it implicitly solves a lasso program. to fully complete our analysis, we provide nonasymptotic convergence guarantees for the dynamics as well as conditions for support recovery. we also give experimental results which support our theoretical claims. our findings highlight the fact that structured noise can induce better generalisation and help explain the greater performances of stochastic dynamics as observed in practice.
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arxiv:2206.09841
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in this work, we pursue further consequences of a general formalism for non - covariant gauges developed in an earlier work ( hep - th / 0205042 ). we carry out further analysis of the additional restrictions on renormalizations noted in that work. we use the example of the axial gauge a _ 3 = 0. we find that if multiplicative renormalization together with ghost - decoupling is to hold, the ` ` prescription - term ' ' ( that defines a prescription ) cannot be chosen arbitrarily but has to satisfy certain non - trivial conditions ( over and above those implied by the validity of power counting ) arising from the wt identities associated with the residual gauge invariance. we also give a restricted class of solutions to these conditions.
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arxiv:hep-th/0209073
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in 1962, erd \ h { o } s proved a theorem on the existence of hamilton cycles in graphs with given minimum degree and number of edges. significantly strengthening in case of balanced bipartite graphs, moon and moser proved a corresponding theorem in 1963. in this paper we establish several spectral analogues of moon and moser ' s theorem on hamilton paths in balanced bipartite graphs and nearly balanced bipartite graphs. one main ingredient of our proofs is a structural result of its own interest, involving hamilton paths in balanced bipartite graphs with given minimum degree and number of edges.
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arxiv:1601.06890
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a potential framework to estimate the volume of water stored in a porous storage reservoir from seismic data is neural networks. in this study, the man - made groundwater reservoir is modeled as a coupled poroviscoelastic - viscoelastic medium, and the underlying wave propagation problem is solved using a three - dimensional discontinuous galerkin method coupled with an adams - bashforth time stepping scheme. the wave problem solver is used to generate databases for the neural network - based machine learning model to estimate the water volume. in the numerical examples, we investigate a deconvolution - based approach to normalize the effect from the source wavelet in addition to the network ' s tolerance for noise levels. we also apply the shapley additive explanations method to obtain greater insight into which part of the input data contributes the most to the water volume estimation. the numerical results demonstrate the capacity of the fully connected neural network to estimate the amount of water stored in the porous storage reservoir.
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arxiv:2211.14276
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this article introduces a metric for performance evaluation of medium access schemes in wireless ad hoc networks known as local capacity. although deriving the end - to - end capacity of wireless ad hoc networks is a difficult problem, the local capacity framework allows us to quantify the average information rate received by a receiver node randomly located in the network. in this article, the basic network model and analytical tools are first discussed and applied to a simple network to derive the local capacity of various medium access schemes. our goal is to identify the most optimal scheme and also to see how does it compare with more practical medium access schemes. we analyzed grid pattern schemes where simultaneous transmitters are positioned in a regular grid pattern, aloha schemes where simultaneous transmitters are dispatched according to a uniform poisson distribution and exclusion schemes where simultaneous transmitters are dispatched according to an exclusion rule such as node coloring and carrier sense schemes. our analysis shows that local capacity is optimal when simultaneous transmitters are positioned in a grid pattern based on equilateral triangles and our results show that this optimal local capacity is at most double the local capacity of aloha based scheme. our results also show that node coloring and carrier sense schemes approach the optimal local capacity by an almost negligible difference. at the end, we also discuss the shortcomings in our model as well as future research directions.
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arxiv:1202.4385
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motivated by the recently proposed connection between n = 2 bps black holes and topological strings, i study the attractor equations and their interplay with the holomorphic anomaly equation. the topological string partition function is interpreted as a wave - function obtained by quantizing the real cohomology of the calabi - yau. in this interpretation the apparent background dependence due to the holomorphic anomaly is caused by the choice of complex polarization. the black hole attractor equations express the moduli in terms of the electric and magnetic charges, and lead to a real polarization in which the background dependence disappears. our analysis results in a generalized formula for the relation between the microscopic density of black hole states and topological strings valid for all backgrounds.
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arxiv:hep-th/0412139
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in this work, we seek a cosmological mechanism that may define the sign of the effective gravitational coupling constant, { \ em g }. to this end, we consider general scalar - tensor gravity theories as they provide the field theory natural framework for the variation of the gravitational coupling. we find that models with a quadratic potential naturally stabilize the value of { \ em g } into the positive branch of the evolution and further, that de sitter inflation and a relaxation to general relativity is easily attained.
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arxiv:1903.07604
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terahertz ( thz ) anisotropic absorption in graphene could be significantly modified upon applying a static magnetic field on its ultra - fast 2d dirac electrons. in general, by deriving the generalized fresnel coefficients for monolayer graphene under applied magnetic field, relatively high anisotropic absorption for the incoming linearly polarized light with specific scattering angles could be achieved. we also prove that the light absorption of monolayer graphene corresponds well to its surface optical conductivity in the presence of a static magnetic field. moreover, the temperature - dependent conductivity of graphene makes it possible to show that a step by step absorption feature would emerge at very low temperatures. we believe that these properties may be considered to be used in novel graphene - based thz application.
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arxiv:2206.09776
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the beginners lab course in physics is scheduled very early in the course of studies not only for students of physics but also for students for which physics is a minor subject. we provide all partipants with several auxilliary materials for the preparation of the experiments and for writing a protocol. in our study, we enlighten the effect of the usage of these materials on the success of passing the lab course. - - - - - das anf \ " angerpraktikum physik ist eine fr \ " uh im studienverlauf stattfindende veranstaltung sowohl f \ " ur hauptfachstudierende physik, alsauch f \ " ur studierende mit nebenfach physik. die vorliegende untersuchung beleuchtet den effekt der verwendung von hilfsmitteln zur versuchsvorbereitung und protokollierung auf das erfolgreiche bestehen des praktikums.
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arxiv:1910.07871
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a proper coloring of a graph is \ emph { conflict - free } if, for every non - isolated vertex, some color is used exactly once on its neighborhood. caro, petru \ v { s } evski, and \ v { s } krekovski proved that every graph $ g $ has a proper conflict - free coloring with at most $ 5 \ delta ( g ) / 2 $ colors and conjectured that $ \ delta ( g ) + 1 $ colors suffice for every connected graph $ g $ with $ \ delta ( g ) \ ge 3 $. our first main result is that even for list - coloring, $ \ left \ lceil 1. 6550826 \ delta ( g ) + \ sqrt { \ delta ( g ) } \ right \ rceil $ colors suffice for every graph $ g $ with $ \ delta ( g ) \ ge 10 ^ { 8 } $ ; we also prove slightly weaker bounds for all graphs with $ \ delta ( g ) \ ge 750 $. these results follow from our more general framework on proper conflict - free list - coloring of a pair consisting of a graph $ g $ and a " conflict " hypergraph $ { \ mathcal h } $. as another corollary of our results in this general framework, every graph has a proper $ ( \ sqrt { 30 } + o ( 1 ) ) \ delta ( g ) ^ { 1. 5 } $ - list - coloring such that every bi - chromatic component is a path on at most three vertices, where the number of colors is optimal up to a constant factor. our proof uses a fairly new type of recursive counting argument called rosenfeld counting, which is a variant of the lov \ ' { a } sz local lemma or entropy compression. we also prove an asymptotically optimal result for a fractional analogue of our general framework for proper conflict - free coloring for pairs of a graph and a conflict hypergraph. a corollary states that every graph $ g $ has a fractional $ ( 1 + o ( 1 ) ) \ delta ( g ) $ - coloring such that every fractionally bi - chromatic component has at most two vertices. in particular, it implies that the fractional analogue of the conjecture of caro et al. \ holds asymptotically in a strong sense.
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arxiv:2211.02818
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we have performed quantum molecular - dynamics simulations for methane under shock compressions up to 80 gpa. we obtain good agreement with available experimental data for the principal hugoniot, derived from the equation of state. a systematic study of the optical conductivity spectra, one - particle density of states, and the distributions of the electronic charge over supercell at hugoniot points shows that the transition of shocked methane to a metallic state takes place close to the density at which methane dissociates significantly into molecular hydrogen and some long alkane chains. through analyzing the pair correlation function, we predict the chemical picture of the shocked methane. in contrast to usual assumptions used for high pressure modeling of methane, we find that no diamond - like configurations occurs for the whole density - temperature range studied.
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arxiv:1012.4888
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we pointed out the class of leibniz algebras such that the killing form is non degenerate implies algebra is semisimple.
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arxiv:1509.00300
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code datasets are of immense value for training neural - network - based code completion models, where companies or organizations have made substantial investments to establish and process these datasets. unluckily, these datasets, either built for proprietary or public usage, face the high risk of unauthorized exploits, resulting from data leakages, license violations, etc. even worse, the ` ` black - box ' ' nature of neural models sets a high barrier for externals to audit their training datasets, which further connives these unauthorized usages. currently, watermarking methods have been proposed to prohibit inappropriate usage of image and natural language datasets. however, due to domain specificity, they are not directly applicable to code datasets, leaving the copyright protection of this emerging and important field of code data still exposed to threats. to fill this gap, we propose a method, named codemark, to embed user - defined imperceptible watermarks into code datasets to trace their usage in training neural code completion models. codemark is based on adaptive semantic - preserving transformations, which preserve the exact functionality of the code data and keep the changes covert against rule - breakers. we implement codemark in a toolkit and conduct an extensive evaluation of code completion models. codemark is validated to fulfill all desired properties of practical watermarks, including harmlessness to model accuracy, verifiability, robustness, and imperceptibility.
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arxiv:2308.14401
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we study the behavior of a label propagation algorithm ( lpa ) on the erd \ h { o } s - r \ ' enyi random graph $ \ mathcal { g } ( n, p ) $. initially, given a network, each vertex starts with a random label in the interval $ [ 0, 1 ] $. then, in each round of lpa, every vertex switches its label to the majority label in its neighborhood ( including its own label ). at the first round, ties are broken towards smaller labels, while at each of the next rounds, ties are broken uniformly at random. the algorithm terminates once all labels stay the same in two consecutive iterations. lpa is successfully used in practice for detecting communities in networks ( corresponding to vertex sets with the same label after termination of the algorithm ). perhaps surprisingly, lpa ' s performance on dense random graphs is hard to analyze, and so far convergence to consensus was known only when $ np \ ge n ^ { 3 / 4 + \ varepsilon } $, where lpa converges in three rounds. by defining an alternative label attribution procedure which converges to the label propagation algorithm after three rounds, a careful multi - stage exposure of the edges allows us to break the $ n ^ { 3 / 4 + \ varepsilon } $ barrier and show that, when $ np \ ge n ^ { 5 / 8 + \ varepsilon } $, a. a. s. \ the algorithm terminates with a single label. moreover, we show that, if $ np \ gg n ^ { 2 / 3 } $, a. a. s. \ this label is the smallest one, whereas if $ n ^ { 5 / 8 + \ varepsilon } \ le np \ ll n ^ { 2 / 3 } $, the surviving label is a. a. s. \ not the smallest one. en passant, we show a presumably new monotonicity lemma for binomial random variables that might be of independent interest.
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arxiv:2302.03569
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we present a new method of modelling numerical systems where there are two distinct output solution classes, for example tipping points or bifurcations. gaussian process emulation is a useful tool in understanding these complex systems and provides estimates of uncertainty, but we aim to include systems where there are discontinuities between the two output solutions. due to continuity assumptions, we consider current methods of classification to split our input space into two output regions. classification and logistic regression methods currently rely on drawing from an independent bernoulli distribution, which neglects any information known in the neighbouring area. we build on this by including correlation between our input points. gaussian processes are still a vital element, but used in latent space to model the two regions. using the input values and an associated output class label, the latent variable is estimated using mcmc sampling and a unique likelihood. a threshold ( usually at zero ) defines the boundary. we apply our method to a motivating example provided by the hormones associated with the reproductive system in mammals, where the two solutions are associated with high and low rates of reproduction.
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arxiv:1901.07413
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the fano factor, an observable quantifying fluctuations of product generation by a single enzyme, can reveal information about the underlying reaction scheme. a lower bound on this fano factor that depends on the thermodynamic affinity driving the transformation from substrate to product constrains the number of intermediate states of an enzymatic cycle. so far, this bound has been proven only for a unicyclic network of states. we show that the bound can be extended to arbitrary multicyclic networks, with the fano factor constraining the largest value of the effective length, which is the ratio between the number of states and the number of products, among all cycles.
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arxiv:1505.03450
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we consider compatibility conditions between poisson and riemannian structures on smooth manifolds by means of a contravariant partially complex structure, or $ f $ - structure, introducing the notion of ( almost ) k \ " ahler - - poisson manifolds. in addition, we study some of their properties under structure preserving maps and symmetries.
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arxiv:1709.02525
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this paper provides a comprehensive study of the dimer model on infinite minimal graphs with fock ' s elliptic weights [ arxiv : 1503. 00289 ]. specific instances of such models were studied in [ arxiv : 052711, arxiv : 1612. 09082, arxiv1801. 00207 ] ; we now handle the general genus 1 case, thus proving a non - trivial extension of the genus 0 results of [ arxiv : math - ph / 0202018, arxiv : math / 0311062 ] on isoradial critical models. we give an explicit local expression for a two - parameter family of inverses of the kasteleyn operator with no periodicity assumption on the underlying graph. when the minimal graph satisfies a natural condition, we construct a family of dimer gibbs measures from these inverses, and describe the phase diagram of the model by deriving asymptotics of correlations in each phase. in the $ \ mathbb { z } ^ 2 $ - periodic case, this gives an alternative description of the full set of ergodic gibbs measures constructed in [ arxiv : math - ph / 0311005 ] by kenyon, okounkov and sheffield. we also establish a correspondence between elliptic dimer models on periodic minimal graphs and harnack curves of genus 1. finally, we show that a bipartite dimer model is invariant under the shrinking / expanding of 2 - valent vertices and spider moves if and only if the associated kasteleyn coefficients are antisymmetric and satisfy fay ' s trisecant identity.
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arxiv:2007.14699
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applying zeilberger ' s algorithm of creative telescoping to a family of certain very - well - poised hypergeometric series involving linear forms in catalan ' s constant with rational coefficients, we obtain a second - order difference equation for these forms and their coefficients. as a consequence we obtain a new way of fast calculation of catalan ' s constant as well as a new continued - fraction expansion for it. similar arguments can be put forward to indicate a second - order difference equation and a new continued fraction for $ \ zeta ( 4 ) = \ pi ^ 4 / 90 $, and we announce corresponding results at the end of this paper.
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arxiv:math/0201024
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we study nonlinear dynamics of the kicked particle whose motion is confined by square billiard. the kick source is considered as localized at the center of square with central symmetric spatial distribution. it is found that ensemble averaged energy of the particle diffusively grows as a function of time. this growth is much more extensive than that of kicked rotor energy. it is shown that momentum transfer distribution in kicked billiard is considerably different than that for kicked free particle. time - dependence of the ensemble averaged energy for different localizations of the kick source is also explored. it is found that changing of localization doesn ' t lead to crucial changes in the time - dependence of the energy. also, escape and transport of particles are studied by considering kicked open billiard with one and three holes, respectively. it is found that for the open billiard with one hole the number of ( non - interacting ) billiard particles decreases according to exponential law.
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arxiv:1106.6236
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the properties of penalized sample covariance matrices depend on the choice of the penalty function. in this paper, we introduce a class of non - smooth penalty functions for the sample covariance matrix, and demonstrate how this method results in a grouping of the estimated eigenvalues. we refer to this method as " lassoing eigenvalues " or as the " elasso ".
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arxiv:1805.08300
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the significance of transportation efficiency, safety, and related services is increasing in urban vehicular networks. within such networks, roadside units ( rsus ) serve as intermediates in facilitating communication. therefore, the deployment of rsus is of utmost importance in ensuring the quality of communication services. however, the optimization objectives, such as time delay and deployment cost, are commonly developed from diverse perspectives. as a result, it is possible that conflicts may arise among the objectives. furthermore, in urban environments, the presence of various obstacles, such as buildings, gardens, lakes, and other infrastructure, poses challenges for the deployment of rsus. hence, the deployment encounters significant difficulties due to the existence of multiple objectives, constraints imposed by obstacles, and the necessity to explore a large - scale optimization space. to address this issue, two versions of multi - objective optimization algorithms are proposed in this paper. by utilizing a multi - population strategy and an adaptive exploration technique, the methods efficiently explore a large - scale decision - variable space. in order to mitigate the issue of an overcrowded deployment of rsus, a calibrating mechanism is adopted to adjust rsu density during the optimization procedures. the proposed methods also take care of data offloading between vehicles and rsus by setting up an iterative best response sequence game ( ibrsg ). by comparing the proposed algorithms with several state - of - the - art algorithms, the results demonstrate that our strategies perform better in both high - density and low - density urban scenarios. the results also indicate that the proposed solutions substantially improve the efficiency of vehicular networks.
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arxiv:2402.18581
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we report on studies of multi - parton corrections from nonlocal operator expansion. we discuss relations between eikonal - line matrix elements and parton distributions, and present an illustration for initial - state collinear evolution.
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arxiv:0812.2873
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we present a marriage of functional and structured imperative programming that embeds in pure lambda calculus. we describe how we implement the core of this language in a monadic dsl which is structurally equivalent to our intended source language and which, when evaluated, generates pure lambda terms in continuation - passing - style.
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arxiv:1703.05227
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we investigate both linear and nonlinear stability aspects of rigid motions ( resp. m \ " obius transformations ) of $ \ mathbb { s } ^ { n - 1 } $ among sobolev maps from $ \ mathbb { s } ^ { n - 1 } $ into $ \ mathbb { r } ^ n $. unlike similar in flavour results for maps defined on domains of $ \ mathbb { r } ^ n $ and mapping into $ \ mathbb { r } ^ n $, not only an isometric ( resp. conformal ) deficit is necessary in this more flexible setting, but also a deficit measuring the distortion of $ \ mathbb { s } ^ { n - 1 } $ under the maps in consideration. the latter is defined as an associated isoperimetric type of deficit. we mostly focus on the case $ n = 3 $, where we also explain why the estimates are optimal in their corresponding settings. in the isometric case the estimate holds true also when $ n = 2 $ and generalizes in dimensions $ n \ geq 4 $ as well, if one requires apriori boundedness in a certain higher sobolev norm. we also obtain linear stability estimates for both cases in all dimensions. these can be regarded as korn - type inequalities for the combination of the quadratic form associated with the isometric ( resp. conformal ) deficit on $ \ mathbb { s } ^ { n - 1 } $ and the isoperimetric one.
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arxiv:2101.03846
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we describe a lattice calculation of the matrix elements relevant for glueball production in $ j / \ psi $ radiative decays. the techniques for such a calculation on anisotropic lattices with an improved action are outlined. we present preliminary results showing the efficacy of the computational method.
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arxiv:hep-lat/9709160
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we study the behaviour of supersymmetric ground states in a class of one - dimensional n = 2 abelian gauged linear sigma models, including theories for which the target space is a complete intersection in projective space, and more generally, models with an interaction term introduced by herbst, hori and page in which the vacua correspond to elements of hypercohomology groups of complexes of sheaves. combining physical insights from recent work by hori, kim and yi with the use of spectral sequences, we propose a way to reconcile the non - linear sigma model description, valid deep within a geometric phase, with the effective coulomb branch description, valid near a phase boundary. this leads to a physical interpretation of the hypercohomology groups from the perspective of the coulomb branch, as well as an interpretation for the spectral sequences used to compute them.
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arxiv:1511.05159
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this paper demonstrates the ability of the harmonic potential field, hpf, planning method to generate a well - behaved constrained path for a robot with second order dynamics in a cluttered environment. it is shown that hpf - based controllers may be developed for holonomic as well as nonholonomic robots to effectively suppress the effect of inertial forces on the robot trajectory while maintaining all the attractive features of a purely kinematic hpf planner. the capabilities of the suggested navigation controller are demonstrated using simulation results. comparisons are also supplied with other approaches used for converting the guidance signal from a purely kinematic hpf planner into a navigation control signal.
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arxiv:1608.05923
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this paper presents a class of event - triggering rules for dynamical control systems with guaranteed positive minimum inter - event time ( miet ). we first propose an event - based function design with guaranteed control performance under a clock - like variable for general nonlinear systems, and later specify them to general linear systems. compared to the existing static and dynamic triggering mechanisms, the proposed triggering rules hold the robust global event - separation property, and can be easily implemented on practical digital platform. namely, it is shown that the minimum inter - event time can be flexibly adapted to the various hardware limitations. finally, several numerical simulations are given to illustrate the theoretical results.
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arxiv:2002.00058
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discovering and clustering subspaces in high - dimensional data is a fundamental problem of machine learning with a wide range of applications in data mining, computer vision, and pattern recognition. earlier methods divided the problem into two separate stages of finding the similarity matrix and finding clusters. similar to some recent works, we integrate these two steps using a joint optimization approach. we make the following contributions : ( i ) we estimate the reliability of the cluster assignment for each point before assigning a point to a subspace. we group the data points into two groups of " certain " and " uncertain ", with the assignment of latter group delayed until their subspace association certainty improves. ( ii ) we demonstrate that delayed association is better suited for clustering subspaces that have ambiguities, i. e. when subspaces intersect or data are contaminated with outliers / noise. ( iii ) we demonstrate experimentally that such delayed probabilistic association leads to a more accurate self - representation and final clusters. the proposed method has higher accuracy both for points that exclusively lie in one subspace, and those that are on the intersection of subspaces. ( iv ) we show that delayed association leads to huge reduction of computational cost, since it allows for incremental spectral clustering.
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arxiv:1808.09574
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in this paper we obtain a new curious identity involving trigonometric functions. namely, for any positive odd integer $ n $ we prove that $ $ \ sum _ { k = 1 } ^ n ( - 1 ) ^ k ( \ cot kx ) \ sin k ( n - k ) x = \ frac { 1 - n } 2, $ $ which is equivalent to the identity $ $ \ sum _ { k = 1 } ^ n ( - 1 ) ^ ku _ { n - k } ( \ cos kx ) = - \ frac { n + 1 } 2, $ $ where $ u _ m ( z ) $ stands for the $ m $ th chebyshev polynomial of the second kind. as a consequence, for any positive odd integer $ n $ and positive integer $ m $ we obtain $ $ \ sum _ { k = 1 } ^ n ( - 1 ) ^ kk ^ { 2m } b _ { 2m + 1 } \ left ( \ frac { n - k } 2 \ right ) = 0, $ $ where $ b _ j ( x ) $ denotes the bernoulli polynomial of degree $ j $.
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arxiv:1907.08118
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we give an algorithm to compute inhomogeneous differential equations for definite integrals with parameters. the algorithm is based on the integration algorithm for $ d $ - modules by oaku. main tool in the algorithm is the gr \ " obner basis method in the ring of differential operators.
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arxiv:1005.3417
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for every irreducible complex representation ~ $ \ pi _ \ lambda $ of the symmetric group ~ $ \ s _ n $, we construct, in a canonical way, a so - called intrinsic hyperplane arrangement ~ $ \ a _ { \ lambda } $ in the space of ~ $ \ pi _ \ lambda $. this arrangement is a direct generalization of the classical braid arrangement ( which is the special case of our construction corresponding to the natural representation of ~ $ \ s _ n $ ), has a natural description in terms of invariant subspaces of young subgroups, and enjoys a number of remarkable properties.
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arxiv:1910.08302
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designing efficient algorithms for multi - agent reinforcement learning ( marl ) is fundamentally challenging because the size of the joint state and action spaces grows exponentially in the number of agents. these difficulties are exacerbated when balancing sequential global decision - making with local agent interactions. in this work, we propose a new algorithm $ \ texttt { subsample - mfq } $ ( $ \ textbf { subsample } $ - $ \ textbf { m } $ ean - $ \ textbf { f } $ ield - $ \ textbf { q } $ - learning ) and a decentralized randomized policy for a system with $ n $ agents. for $ k \ leq n $, our algorithm learns a policy for the system in time polynomial in $ k $. we show that this learned policy converges to the optimal policy on the order of $ \ tilde { o } ( 1 / \ sqrt { k } ) $ as the number of subsampled agents $ k $ increases. we empirically validate our method in gaussian squeeze and global exploration settings.
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arxiv:2412.00661
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we study the dirac equation of a charged massless spinor on the general charged ads black hole of conformal gravity. the equation can be solved exactly in terms of heun ' s functions. we obtain the exact green ' s function in the phase space ( \ omega, k ). this allows us to obtain fermi surfaces for both fermi and non - fermi liquids. our analytic results provide a more elegant approach of studying some strongly interacting fermionic systems not only at zero temperature, but also at any finite temperature. at zero temperature, we analyse the motion of the poles in the complex \ omega plane and obtain the leading order terms of the dispersion relation, expressed as the laurent expansion of \ omega in terms of k. we illustrate new distinguishing features arising at the finite temperature. the green ' s function with vanishing \ omega at finite temperature has a fascinating rich structure of spiked maxima in the plane of k and the fermion charge q.
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arxiv:1210.4560
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in this paper we prove, if $ u $ is a global solution to navier - stokes equations in the sobolev - gevrey spaces $ h ^ 1 _ { a, \ sigma } ( \ mathbb r ^ 3 ) $, then $ \ | u ( t ) \ | _ { h ^ 1 _ { a, \ sigma } } $ decays to zero as time goes to infinity. fourier analysis is used.
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arxiv:1502.04196
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incomplete utterance rewriting has recently raised wide attention. however, previous works do not consider the semantic structural information between incomplete utterance and rewritten utterance or model the semantic structure implicitly and insufficiently. to address this problem, we propose a query - enhanced network ( queen ). firstly, our proposed query template explicitly brings guided semantic structural knowledge between the incomplete utterance and the rewritten utterance making model perceive where to refer back to or recover omitted tokens. then, we adopt a fast and effective edit operation scoring network to model the relation between two tokens. benefiting from proposed query template and the well - designed edit operation scoring network, queen achieves state - of - the - art performance on several public datasets.
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arxiv:2307.00866
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we propose a method for hand pose estimation based on a deep regressor trained on two different kinds of input. raw depth data is fused with an intermediate representation in the form of a segmentation of the hand into parts. this intermediate representation contains important topological information and provides useful cues for reasoning about joint locations. the mapping from raw depth to segmentation maps is learned in a semi / weakly - supervised way from two different datasets : ( i ) a synthetic dataset created through a rendering pipeline including densely labeled ground truth ( pixelwise segmentations ) ; and ( ii ) a dataset with real images for which ground truth joint positions are available, but not dense segmentations. loss for training on real images is generated from a patch - wise restoration process, which aligns tentative segmentation maps with a large dictionary of synthetic poses. the underlying premise is that the domain shift between synthetic and real data is smaller in the intermediate representation, where labels carry geometric and topological meaning, than in the raw input domain. experiments on the nyu dataset show that the proposed training method decreases error on joints over direct regression of joints from depth data by 15. 7 %.
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arxiv:1511.06728
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gizis et al. ( 2001 ) reported a companion candidate of spectral type l1 near the k2 dwarf gj 1048 using the two micron all - sky survey ( 2mass ). at that time it was not possible to verify companionship astrometrically using the 2mass data alone due to the small proper motion of gj 1048. we now show that both objects share the same proper motion by using data from the uk schmidt telescope near - infrared ( ivn ) southern survey as the first epoch and data from 2mass as the second epoch. our technique of subtracting the psf of the primary from the supercosmos i scans of the southern survey enables the astrometry of the companion candidate to be measured directly.
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arxiv:astro-ph/0404252
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we investigate the robustness of { \ it virtual } topological states - - topological phases away from the fermi energy - - against the electron - electron interaction and band filling. as a case study, we employ a realistic model to investigate the properties of vacancy - driven topological phases in transition metal dichalcogenides ( tmds ) and establish a connection between the degree of localization of topological wave functions, the vacancy density, and the electron - electron interaction strength with the topological phase robustness. we demonstrate that electron - electron interactions play a crucial role in degrading topological phases thereby determining the validity of single - particle approximations for topological insulator phases. our findings can be naturally extended to { \ it virtual } topological phases of a wide range of materials.
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arxiv:2412.08607
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we consider vanishing of ext and tor, especially over artinian rings. in particular, we prove the auslander - reiten conjecture for all commutative local rings in which the cube of the maximal ideal is zero.
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arxiv:1409.1141
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we describe the geometry of an arrangement of 24 - cells inscribed in the 600 - cell. in $ \ s $ 7 we apply our results to the even unimodular lattice $ e _ 8 $ and show how the 600 - cell transforms $ e _ 8 $ / 2 $ e _ 8 $, an 8 - space over the field $ \ bf { f } $ $ _ 2 $, into a 4 - space over $ \ bf { f } $ $ _ 4 $ whose points, lines and planes are labeled by the geometric objects of the 600 - cell.
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arxiv:1912.06156
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we consider a continuous - time branching random walk on $ \ mathbb { z } $ in a random non homogeneous environment. particles can walk on the lattice points or disappear with random intensities. the process starts with one particle at initial time $ t = 0 $. it can walk on the lattice points or disappear with a random intensity until it reach the point, where initial particle can split into two offspring. this lattice point we call reproduction source. the offspring of the initial particle evolve according to the same law, independently of each other and the entire prehistory. the aim of the paper is to study the conditions for the presence of exponential growth of the average number of particle at an every lattice point. for this purpose we investigate the spectrum of the random evolution operator of the average particle numbers. we derive the condition under which there is exponential growth with probability one. we also study the process under the violation of this condition and present the lower and upper estimates for the probability of exponential growth.
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arxiv:2312.05872
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developing agents that can quickly adapt their behavior to new tasks remains a challenge. meta - learning has been applied to this problem, but previous methods require either specifying a reward function which can be tedious or providing demonstrations which can be inefficient. in this paper, we investigate if, and how, a " helper " agent can be trained to interactively adapt their behavior to maximize the reward of another agent, whom we call the " prime " agent, without observing their reward or receiving explicit demonstrations. to this end, we propose to meta - learn a helper agent along with a prime agent, who, during training, observes the reward function and serves as a surrogate for a human prime. we introduce a distribution of multi - agent cooperative foraging tasks, in which only the prime agent knows the objects that should be collected. we demonstrate that, from the emerged physical communication, the trained helper rapidly infers and collects the correct objects.
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arxiv:1906.10165
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anisotropic magnetoresistance ( amr ) of cr2ge2te6 ( cgt ), a layered ferromagnetic insulator, is investigated under an applied hydrostatic pressure up to 2 gpa. the easy axis direction of the magnetization is inferred from the amr saturation feature in the presence and absence of the applied pressure. at zero applied pressure, the easy axis is along the c - direction or perpendicular to the layer. upon application of a hydrostatic pressure > 1 gpa, the uniaxial anisotropy switches to easy - plane anisotropy which drives the equilibrium magnetization from the c - axis to the ab - plane at zero magnetic field, which amounts to a giant magnetic anisotropy energy change ( > 100 % ). as the temperature is increased across the curie temperature, the characteristic amr effect gradually decreases and disappears. our first - principles calculations confirm the giant magnetic anisotropy energy change with moderate pressure and assign its origin to the increased off - site spin - orbit interaction of te atoms due to a shorter cr - te distance. such a pressure - induced spin reorientation transition is very rare in three - dimensional ferromagnets, but it may be common to other layered ferromagnets with similar crystal structures to cgt, and therefore offers a unique way to control magnetic anisotropy.
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arxiv:1805.04937
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we introduce the branching transitive closure operator on weighted monadic second - order logic formulas where the branching corresponds in a natural way to the branching inherent in trees. for arbitrary commutative semirings, we prove that weighted monadic second order logics on trees is equivalent to the definability by formulas which start with one of the following operators : ( i ) a branching transitive closure or ( ii ) an existential second - order quantifier followed by one universal first - order quantifier ; in both cases the operator is applied to step - formulas over ( a ) boolean first - order logic enriched by modulo counting or ( b ) boolean monadic - second order logic.
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arxiv:1208.5317
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the capacity of fading channels under peak and average power constraints in the low - snr regime is investigated. we show that the capacity scales essentially as $ { c \ approx a \ \ text { snr } \ int _ { 1 - \ frac { 1 } { a } } ^ 1 f ^ { - 1 } \ left ( t \ right ) dt } $, where $ a $ is the peak to average power ratio ( papr ), and $ f ( \ cdot ) $ is the cumulative distribution function of the fading channel. we also prove that an on - off power scheme is sufficient to asymptotically achieve the capacity. furthermore, by considering the variable papr scenario, we generalize the scalability of the capacity and derive the asymptotic expression for the capacity in the low - snr regime.
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arxiv:1804.06861
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nanophosphors of ( sr0. 98 - xmgxeu0. 02 ) 2sio4 ( x = 0, 0. 18, 0. 38, 0. 58 and 0. 78 ) were prepared through low temperature solution combustion method and their luminescence properties were studied. the emission peak for eu2 + doped sr2sio4 nanophosphor is observed at ~ 490 nm and ~ 553 nm corresponding to two sr2 + sites sr ( i ) and sr ( ii ) respectively for 395 nm excitation but the addition of mg2 + dopant in sr2sio4 leads to suppression of ~ 553 nm emission peak due to absence of energy levels of sr ( ii ) sites which results in a single broad emission at ~ 460nm. it was shown that the emission peak blue shifted with increase in mg concentration which may be attributed to change in crystal field environment around sr ( i ) sites. therefore the ( mg0. 78sr0. 20eu0. 02 ) 2sio4 : eu2 + nanophosphor can be used for blue emission and the sr2sio4 : eu0. 042 + for green - yellow emission at 395 nm excitations. the cie coordinates for mixed powders of ( mg0. 78sr0. 20eu0. 02 ) 2sio4 and sr2sio4 : eu0. 042 + ( in 1 : 1 ratio ) falls in the white region demonstrating the possible use of the mixture in white light generation using near uv excitation source.
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arxiv:1512.00157
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generative ai appears poised to transform white collar professions, with more than 90 % of fortune 500 companies using openai ' s flagship gpt models, which have been characterized as " general purpose technologies " capable of effecting epochal changes in the economy. but how will such technologies impact organizations whose job is to verify and report factual information, and to ensure the health of the information ecosystem? to investigate this question, we conducted 30 interviews with n = 38 participants working at 29 fact - checking organizations across six continents, asking about how they use generative ai and the opportunities and challenges they see in the technology. we found that uses of generative ai envisioned by fact - checkers differ based on organizational infrastructure, with applications for quality assurance in editing, for trend analysis in investigation, and for information literacy in advocacy. we used the toe framework to describe participant concerns ranging from the technological ( lack of transparency ), to the organizational ( resource constraints ), to the environmental ( uncertain and evolving policy ). building on the insights of our participants, we describe value tensions between fact - checking and generative ai, and propose a novel verification dimension to the design space of generative models for information verification work. finally, we outline an agenda for fairness, accountability, and transparency research to support the responsible use of generative ai in fact - checking. throughout, we highlight the importance of human infrastructure and labor in producing verified information in collaboration with ai. we expect that this work will inform not only the scientific literature on fact - checking, but also contribute to understanding of organizational adaptation to a powerful but unreliable new technology.
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arxiv:2405.15985
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algebraic basics on temperley - lieb algebras are proved in an elementary and straightforward way with the help of tensor categories behind them.
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arxiv:math/0405267
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physical places help shape how we perceive the experiences we have there. for the first time, we study the relationship between social media text and the type of the place from where it was posted, whether a park, restaurant, or someplace else. to facilitate this, we introduce a novel data set of $ \ sim $ 200, 000 english tweets published from 2, 761 different points - of - interest in the u. s., enriched with place type information. we train classifiers to predict the type of the location a tweet was sent from that reach a macro f1 of 43. 67 across eight classes and uncover the linguistic markers associated with each type of place. the ability to predict semantic place information from a tweet has applications in recommendation systems, personalization services and cultural geography.
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arxiv:2009.14734
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we present here the first results from two recently completed, fully sampled redshift surveys comprising 3703 iras faint source survey ( fss ) galaxies. an unbiased counts - in - cells analysis finds a clustering strength in broad agreement with other recent redshift surveys and at odds with the standard cold dark matter model. we combine our data with those from the qdot and 1. 2 jy surveys, producing a single estimate of the iras galaxy clustering strength. we compare the data with the power spectrum derived from a mixed dark matter universe. direct comparison of the clustering strength seen in the iras samples with that seen in the apm - stromlo survey suggests b _ o / b _ i = 1. 20 + / - 0. 05 assuming a linear, scale independent biasing. we also perform a cell by cell comparison of our fss - z sample with galaxies from the first cfa slice, testing the viability of a linear - biasing scheme linking the two. we are able to rule out models in which the fss - z galaxies identically trace the cfa galaxies on scales 5 - 20h ^ { - 1 } mpc. on scales of 5 and 10h ^ { - 1 } mpc no linear - biasing model can be found relating the two samples. we argue that this result is expected since the cfa sample includes more elliptical galaxies which have different clustering properties from spirals. on scales of 20h ^ { - 1 } mpc no linear - biasing model with b _ o / b _ i < 1. 70 is acceptable. when comparing the fss - z galaxies to the cfa spirals, however, the two populations trace the same structures within our uncertainties.
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arxiv:astro-ph/9604038
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the radio - metric doppler tracking data from the pioneer 10 / 11 spacecraft, from between 20 - 70 au, yields an unambiguous and independently confirmed anomalous blue shift drift of a _ t = ( 2. 92 \ pm 0. 44 ) \ times 10 ^ { - 18 } s / s ^ 2. it can be interpreted as being due to a constant acceleration of a _ p = ( 8. 74 \ pm 1. 33 ) \ times 10 ^ { - 8 } cm / s ^ 2 directed towards the sun. no systematic effect has been able to explain the anomaly, even though such an origin is an obvious candidate. we discuss what has been learned ( and what might still be learned ) from the data about the anomaly, its origin, and the mission design characteristics that would be needed to test it. future mission options are proposed.
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arxiv:gr-qc/0411077
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we present a model - predictive control ( mpc ) framework for legged robots that avoids the singularities associated with common three - parameter attitude representations like euler angles during large - angle rotations. our method parameterizes the robot ' s attitude with singularity - free unit quaternions and makes modifications to the iterative linear - quadratic regulator ( ilqr ) algorithm to deal with the resulting geometry. the derivation of our algorithm requires only elementary calculus and linear algebra, deliberately avoiding the abstraction and notation of lie groups. we demonstrate the performance and computational efficiency of quaternion mpc in several experiments on quadruped and humanoid robots.
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arxiv:2409.09940
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in this note we analyse the propagation of a small density perturbation in a one - dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the caputo fractional derivative in the constitutive equations. by doing so, we embrace a vast phenomenology, including subdiffusive, superdiffusive and also memoryless processes like classical diffusions. from a mathematical point of view, we study systems of coupled fractional equations, leading to fractional diffusion equations or to equations with sequential fractional derivatives. in this framework we also propose a method to solve partial differential equations with sequential fractional derivatives by analysing the corresponding coupled system of equations.
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arxiv:1304.1055
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one parameter quantization ambiguity is existed in loop quantum gravity which is called the immirzi parameter. in this paper, we fix this free paremater by considering the quasinormal mode spectrum of black holes in four and higher spacetime dimensions. as a consequence, our result consistents with bekenstein - hawking entropy of a black hole. moreover, we also give a possible quantum gravity explanation of the universal $ \ ln ( 3 ) $ behavior of the quasinormal mode spectrum.
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arxiv:1506.05739
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population - wise matching of the cortical fold is necessary to identify biomarkers of neurological or psychiatric disorders. the difficulty comes from the massive interindividual variations in the morphology and spatial organization of the folds. this task is challenging at both methodological and conceptual levels. in the widely used registration - based techniques, these variations are considered as noise and the matching of folds is only implicit. alternative approaches are based on the extraction and explicit identification of the cortical folds. in particular, representing cortical folding patterns as graphs of sulcal basins - termed sulcal graphs - enables to formalize the task as a graph - matching problem. in this paper, we propose to address the problem of sulcal graph matching directly at the population level using multi - graph matching techniques. first, we motivate the relevance of multi - graph matching framework in this context. we then introduce a procedure to generate populations of artificial sulcal graphs, which allows us benchmarking several state of the art multi - graph matching methods. our results on both artificial and real data demonstrate the effectiveness of multi - graph matching techniques to obtain a population - wise consistent labeling of cortical folds at the sulcal basins level.
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arxiv:2301.13532
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reconfigurable intelligent surface ( ris ) can significantly enhance the service coverage of tera - hertz massive multiple - input multiple - output ( mimo ) communication systems. however, obtaining accurate high - dimensional channel state information ( csi ) with limited pilot and feedback signaling overhead is challenging, severely degrading the performance of conventional spatial division multiple access. to improve the robustness against csi imperfection, this paper proposes a deep learning ( dl ) - based rate - splitting multiple access ( rsma ) scheme for ris - aided tera - hertz multi - user mimo systems. specifically, we first propose a hybrid data - model driven dl - based rsma precoding scheme, including the passive precoding at the ris as well as the analog active precoding and the rsma digital active precoding at the base station ( bs ). to realize the passive precoding at the ris, we propose a transformer - based data - driven ris reflecting network ( rrn ). as for the analog active precoding at the bs, we propose a match - filter based analog precoding scheme considering that the bs and ris adopt the los - mimo antenna array architecture. as for the rsma digital active precoding at the bs, we propose a low - complexity approximate weighted minimum mean square error ( awmmse ) digital precoding scheme. furthermore, for better precoding performance as well as lower computational complexity, a model - driven deep unfolding active precoding network ( dfapn ) is also designed by combining the proposed awmmse scheme with dl. then, to acquire accurate csi at the bs for the investigated rsma precoding scheme to achieve higher spectral efficiency, we propose a csi acquisition network ( can ) with low pilot and feedback signaling overhead, where the downlink pilot transmission, csi feedback at the user equipments ( ues ), and csi reconstruction at the bs are modeled as an end - to - end neural network based on transformer.
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arxiv:2209.08456
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