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May 3, 2016 11:22 AM



\\ arXiv:1605.00218 Date: Sun, 1 May 2016 08:34:45 GMT (8kb)
Title: On the diamenter of Lascar strong types (after Ludomir Newelski) Authors: Domenico Zambella Categories: math.LO Comments: A contribution to Liber Amicorum Alberti dedicated to Albert Visser on the occasion of his 65th birthday MSCclass: 03C95 Journalref: Liber Amicorum Alberti, J.van Eijck, R.Iemhoff, J.J.Joosten (editors) College Publications (2016) \\ This is an exposition a theorem of mathematical logic which only assumes the notions of structure, elementary equivalence, and compactness (saturation). Newelski proved that typedefinable Lascar strong types have finite diameter. Our exposition is based on a proof that appears in Pelaez' thesis  up to a minor difference: the notion of weak cfree is replaced with the notion of nondrifting that is introduced here. \\ ( https://arxiv.org/abs/1605.00218 , 8kb)  \\ arXiv:1605.00263 Date: Sun, 1 May 2016 15:11:04 GMT (9kb)
Title: Unprovability of circuit upper bounds in Cook's theory PV Authors: Jan Krajicek and Igor C. Oliveira Categories: math.LO cs.CC MSCclass: 03F30, 68Q15 ACMclass: F.4.1 \\ We establish unconditionally that for every integer $k \geq 1$ there is a language $L \in \mbox{P}$ such that it is consistent with Cook's theory PV that $L \notin Size(n^k)$. Our argument is nonconstructive and does not provide an explicit description of this language. \\ ( https://arxiv.org/abs/1605.00263 , 9kb)  \\ arXiv:1605.00296 Date: Sun, 1 May 2016 19:29:55 GMT (34kb)
Title: Chang's Conjecture and semiproperness of nonreasonable posets Authors: Sean D. Cox Categories: math.LO \\ Let $\mathbb{Q}$ denote the poset which adds a Cohen real then shoots a club through the complement of $\big( [\omega_2]^\omega \big)^V$ with countable conditions. We prove that the version of Strong Chang's Conjecture from \cite{MR2965421} implies semiproperness of $\mathbb{Q}$, and that semiproperness of $\mathbb{Q}$in fact semiproperness of any poset which is sufficiently \emph{nonreasonable} in the sense of ForemanMagidor~\cite{MR1359154}implies the version of Strong Chang's Conjecture from \cite{MR2723878} and \cite{MR1261218}. In particular, semiproperness of $\mathbb{Q}$ has large cardinal strength, which answers a question of FriedmanKrueger~\cite{MR2276627}. One corollary of our work is that the version of Strong Chang's Conjecture from \cite{MR2965421} does not imply the existence of a precipitous ideal on $\omega_1$. \\ ( https://arxiv.org/abs/1605.00296 , 34kb)  \\ arXiv:1605.00473 Date: Mon, 2 May 2016 13:19:57 GMT (30kb)
Title: Automorphism groups of randomized structures Authors: Tom\'as Ibarluc\'ia Categories: math.LO math.DS Comments: 28 pages \\ We study automorphism groups of randomizations of separable structures, with focus on the $\aleph_0$categorical case. We give a description of the automorphism group of the Borel randomization in terms of the group of the original structure. In the $\aleph_0$categorical context, this provides a new source of Roelcke precompact Polish groups, and we describe the associated Roelcke compactifications. This allows us also to recover and generalize preservation results of stable and NIP formulas previously established in the literature, via a Banachtheoretic translation. Finally, we study the separable models of the theory of beautiful pairs of randomizations, and we show that this theory is in general not $\aleph_0$categorical. \\ ( https://arxiv.org/abs/1605.00473 , 30kb) 
\ arXiv:1605.00605 Date: Mon, 2 May 2016 18:27:53 GMT (28kb)
Title: Universal graphs at $\aleph_{\omega_1+1}$ Authors: Jacob Davis Categories: math.LO MSCclass: 03E35, 03E55, 03E75 \\ Starting from a supercompact cardinal we build a model in which $2^{\aleph_{\omega_1}}=2^{\aleph_{\omega_1+1}}=\aleph_{\omega_1+3}$ but there is a jointly universal family of size $\aleph_{\omega_1+2}$ of graphs on $\aleph_{\omega_1+1}$. The same technique will work for any uncountable cardinal in place of $\omega_1$. \\ ( https://arxiv.org/abs/1605.00605 , 28kb)  \\ arXiv:1605.00613 Date: Mon, 2 May 2016 18:44:20 GMT (18kb)
Title: The HOD Dichotomy Authors: Hugh Woodin, Jacob Davis, Daniel Rodriguez Categories: math.LO MSCclass: 03E45, 03E55, 03E57 \\ This paper provides an accessible introduction to some of the work of Woodin on suitable extender models. We define the HOD conjecture, prove it is equivalent to a formulation in terms of weak extender models for supercompactness, and give some of its consequences. \\ ( https://arxiv.org/abs/1605.00613 , 18kb)  \\ arXiv:1605.00641 Date: Mon, 2 May 2016 19:58:16 GMT (13kb)
Title: The isometry degree of a computable copy of $\ell^p$ Authors: Timothy H. McNicholl and D.M. Stull Categories: math.LO MSCclass: 03D78, 03D45 \\ When $p$ is a computable real so that $p \geq 1$, the isometry degree of a computable copy $\mathcal{B}$ of $\ell^p$ is defined to be the least powerful Turing degree that computes a linear isometry of $\ell^p$ onto $\mathcal{B}$. We show that this degree always exists and that when $p \neq 2$ these degrees are precisely the c.e. degrees. \\ ( https://arxiv.org/abs/1605.00641 , 13kb)  \\ arXiv:1605.00443 Date: Mon, 2 May 2016 11:47:31 GMT (51kb,D)
Title: On densities of lattice arrangements intersecting every idimensional affine subspace Authors: Bernardo Gonz\'alez Merino, Matthias Henze Categories: math.MG math.CO Comments: 19 pages \\ In 1978, Makai Jr. established a remarkable connection between the volumeproduct of a convex body, its maximal lattice packing density and the minimal density of a lattice arrangement of its polar body intersecting every affine hyperplane. Consequently, he formulated a conjecture that can be seen as a dual analog of Minkowski's fundamental theorem, and which is strongly linked to the wellknown Mahlerconjecture. Based on the covering minima of Kannan & Lov\'asz and a problem posed by Fejes T\'oth, we arrange Makai Jr.'s conjecture into a wider context and investigate densities of lattice arrangements of convex bodies intersecting every idimensional affine subspace. Then it becomes natural also to formulate and study a dual analog to Minkowski's second fundamental theorem. As our main results, we derive meaningful asymptotic lower bounds for the densities of such arrangements, and furthermore, we solve the problems exactly for the special, yet important, class of unconditional convex bodies. \\ ( https://arxiv.org/abs/1605.00443 , 51kb)  \\ arXiv:1605.00196 Date: Sun, 1 May 2016 01:58:47 GMT (20kb)
Title: Embedded Eigenvalues and NeumannWigner Potentials for Relativistic Schrodinger Operators Authors: Jozsef Lorinczi, Itaru Sasaki Categories: mathph math.MP MSCclass: 62M15 \\ We construct NeumannWigner type potentials for the massive relativistic Schrodinger operator in one and three dimensions for which an eigenvalue embedded in the absolutely continuous spectrum exists. First we consider the relativistic variants of the original example by von Neumann and Wigner, and as a second example we discuss the potential due to Moses and Tuan. We show that in the nonrelativistic limit these potentials converge to the classical NeumannWigner potentials. For the massless operator in one dimension we construct two families of potentials, different by the parities of the (generalized) eigenfunctions, for which an eigenvalue equal to zero or a 0resonance exists, dependent on the rate of decay of the corresponding eigenfunctions. \\ ( https://arxiv.org/abs/1605.00196 , 20kb)  \\ arXiv:1605.00237 Date: Thu, 28 Apr 2016 17:52:06 GMT (13kb)
Title: Stora's fine notion of divergent amplitudes Authors: Joseph C. V\'arilly and Jos\'e M. GraciaBond\'ia Categories: mathph hepth math.FA math.MP Comments: 10 pages, no figures. Contribution to Mathematical Foundations of Quantum Field Theory, special issue in memory of Raymond Stora, Nucl. Phys. B \\ Stora and coworkers refined the notion of divergent quantum amplitude, somewhat upsetting the standard powercounting recipe. This unexpectedly clears the way to new prototypes for free and interacting field theories of bosons of any mass and spin. \\ ( https://arxiv.org/abs/1605.00237 , 13kb)  \\ arXiv:1605.00325 Date: Mon, 2 May 2016 00:03:16 GMT (21kb)
Title: EinsteinHilbert action with cosmological term from ChernSimons gravity Authors: N.L. Gonz\'alez Albornoz, P. Salgado, G. Rubio, S. Salgado Categories: mathph math.MP Comments: 31 pages, no figures DOI: 10.1016/j.geomphys.2014.08.013 \\ We propose a modification to the Lie algebra $S$expansion method. The modification is carried out by imposing a condition on the $S$expansion procedure, when the semigroup is given by a cyclic group of even order. The $S$expanded algebras are called $S_{H}$expanded algebras where $S=Z_{2n}$. The invariant tensors for $S_{H}$expanded algebras are calculated and the dual formulation of $S_{H}$expansion procedure is proposed. We consider the $S_{H}$expansion of the fivedimensional $AdS$ algebra and its corresponding invariants tensors are found. Then a ChernSimons Lagrangian invariant under the fivedimensional $AdS$ algebra $S_{H}$expanded is constructed and its relationship to the general relativity is studied. \\ ( https://arxiv.org/abs/1605.00325 , 21kb)  \\ arXiv:1605.00447 Date: Mon, 2 May 2016 11:58:07 GMT (467kb)
Title: Trace identities for skewsymmetric matrices Authors: M. I. Krivoruchenko Categories: mathph math.MP Comments: 9 pages \\ We derive an expression for the product of the Pfaffians of skewsymmetric matrices A and B as a finite sum of the traces of powers of AB and an expression for the inverse matrix A$^{1}$, or equivalently B$^{1}$ as a finiteorder polynomial of AB with the coefficients depending on the traces of powers of AB. \\ ( https://arxiv.org/abs/1605.00447 , 467kb)  \\ arXiv:1605.00531 Date: Mon, 2 May 2016 15:36:44 GMT (1508kb,D)
Title: Random Antagonistic Matrices Authors: Giovanni M. Cicuta and Luca Guido Molinari Categories: mathph condmat.statmech math.MP qbio.PE Comments: 14 pages, 6 figures \\ The ensemble of antagonistic matrices is introduced and studied. In antagonistic matrices the entries $\mathcal A_{i,j}$ and $\mathcal A_{j,i}$ are real and have opposite signs, or are both zero, and the diagonal is zero. This generalization of antisymmetric matrices is suggested by the linearized dynamics of competitive species in ecology. \\ ( https://arxiv.org/abs/1605.00531 , 1508kb)  \\ arXiv:1605.00576 Date: Mon, 2 May 2016 17:34:47 GMT (33kb,D)
Title: Nonlinear heat conduction equations with memory: physical meaning and analytical results Authors: Pietro Artale Harris and Roberto Garra Categories: mathph math.MP \\ We study nonlinear heat conduction equations with memory effects within the framework of the fractional calculus approach to the generalized MaxwellCattaneo law. Our main aim is to derive the governing equations of heat propagation, considering both the empirical temperaturedependence of the thermal conductivity coefficient (which introduces nonlinearity) and memory effects, according to the general theory of Gurtin and Pipkin of finite velocity thermal propagation with memory. In this framework, we consider in detail two different approaches to the generalized MaxwellCattaneo law, based on the application of longtail MittagLeffler memory function and power law relaxation functions, leading to nonlinear timefractional telegraph and wavetype equations. We also discuss some explicit analytical results to the model equations based on the generalized separating variable method and discuss their meaning in relation to some wellknown results of the ordinary case. \\ ( https://arxiv.org/abs/1605.00576 , 33kb)  \\ arXiv:1605.00623 Date: Mon, 2 May 2016 19:07:32 GMT (3846kb,D)
Title: Real eigenvalues of nonsymmetric random matrices: Transitions and Universality Authors: Luis Carlos Garc\'ia del Molino, Khashayar Pakdaman and Jonathan Touboul Categories: mathph math.MP Comments: 10 pages, 12 figures \\ In the past 20 years, the study of real eigenvalues of nonsymmetric real random matrices has seen important progress. Notwithstanding, central questions still remain open, such as the characterization of their asymptotic statistics and the universality thereof. In this letter we show that for a wide class of matrices, the number $k_n$ of real eigenvalues of a matrix of size $n$ is asymptotically Gaussian with mean $\bar k_n=\mathcal{O}(\sqrt{n})$ and variance $\bar k_n(2\sqrt{2})$. Moreover, we show that the limit distribution of real eigenvalues undergoes a transition between bimodal for $k_n=o(\sqrt{n})$ to unimodal for $k_n=\mathcal{O}(n)$, with a uniform distribution at the transition. We predict theoretically these behaviours in the Ginibre ensemble using a loggas approach, and show numerically that they hold for a wide range of random matrices with independent entries beyond the universality class of the circular law. \\ ( https://arxiv.org/abs/1605.00623 , 3846kb)  \\ arXiv:1605.00132 Date: Sat, 30 Apr 2016 16:14:33 GMT (40kb)
Title: A systematic construction of finite element commuting exact sequences Authors: Bernardo Cockburn, Guosheng Fu Categories: math.NA Comments: 37pages \\ We present a systematic construction of finite element exact sequences with a commuting diagram for the de Rham complex in one, two and threespace dimensions. We apply the construction in twospace dimensions to rediscover two families of exact sequences for triangles and three for squares, and to uncover one new family of exact sequence for squares and two new families of exact sequences for general polygonal elements. We apply the construction in threespace dimensions to rediscover two families of exact sequences for tetrahedra, three for cubes, and one for prisms; and to uncover four new families of exact sequences for pyramids, three for prisms, and one for cubes. \\ ( https://arxiv.org/abs/1605.00132 , 40kb)  \\ arXiv:1605.00133 Date: Sat, 30 Apr 2016 16:20:30 GMT (6853kb,D)
Title: Accelerated HighResolution Photoacoustic Tomography via Compressed Sensing Authors: Simon Arridge, Paul Beard, Marta Betcke, Ben Cox, Nam Huynh, Felix Lucka, Olumide Ogunlade and Edward Zhang Categories: math.NA Comments: submitted to "Physics in Medicine and Biology" \\ Current 3D photoacoustic tomography (PAT) systems offer either high image quality or high frame rates but are not able to deliver high spatial and temporal resolution simultaneously, which limits their ability to image dynamic processes in living tissue. A particular example is the planar FabryPerot (FP) scanner, which yields highresolution images but takes several minutes to sequentially map the photoacoustic field on the sensor plane, pointbypoint. However, as the spatiotemporal complexity of many absorbing tissue structures is rather low, the data recorded in such a conventional, regularly sampled fashion is often highly redundant. We demonstrate that combining variational image reconstruction methods using spatial sparsity constraints with the development of novel PAT acquisition systems capable of subsampling the acoustic wave field can dramatically increase the acquisition speed while maintaining a good spatial resolution: First, we describe and model two general spatial subsampling schemes. Then, we discuss how to implement them using the FP scanner and demonstrate the potential of these novel compressed sensing PAT devices through simulated data from a realistic numerical phantom and through measured data from a dynamic experimental phantom as well as from invivo experiments. Our results show that images with good spatial resolution and contrast can be obtained from highly subsampled PAT data if variational image reconstruction methods that describe the tissues structures with suitable sparsityconstraints are used. In particular, we examine the use of total variation regularization enhanced by Bregman iterations. These novel reconstruction strategies offer new opportunities to dramatically increase the acquisition speed of PAT scanners that employ pointbypoint sequential scanning as well as reducing the channel count of parallelized schemes that use detector arrays. \\ ( https://arxiv.org/abs/1605.00133 , 6853kb)  \\ arXiv:1605.00156 Date: Sat, 30 Apr 2016 19:54:27 GMT (464kb,D)
Title: Robust Solvers for Maxwell's Equations with Dissipative Boundary Conditions Authors: James H. Adler and Xiaozhe Hu and Ludmil T. Zikatanov Categories: math.NA Comments: 18 pages, 2 figures \\ In this paper, we design robust and efficient linear solvers for the numerical approximation of solutions to Maxwell's equations with dissipative boundary conditions. We consider a structurepreserving finiteelement approximation with standard NedelecRaviartThomas elements in space and a CrankNicolson scheme in time to approximate the electric and magnetic fields. We focus on two types of block preconditioners. The first type is based on the wellposedness results of the discrete problem. The second uses an exact block factorization of the linear system, for which the structurepreserving discretization yields sparse Schur complements. We prove robustness and optimality of these block preconditioners, and provide supporting numerical tests. \\ ( https://arxiv.org/abs/1605.00156 , 464kb)  \\ arXiv:1605.00429 Date: Mon, 2 May 2016 10:50:40 GMT (341kb,D)
Title: Adaptive splitting methods for nonlinear Schr\"{o}dinger equations in the semiclassical regime Authors: Winfried Auzinger, Thomas Kassebacher, Othmar Koch, and Mechthild Thalhammer Categories: math.NA \\ The error behavior of exponential operator splitting methods for nonlinear Schr{\"o}dinger equations in the semiclassical regime is studied. For the Lie and Strang splitting methods, the exact form of the local error is determined and the dependence on the semiclassical parameter is identified. This is enabled within a defectbased framework which also suggests asymptotically correct a~posteriori local error estimators as the basis for adaptive time stepsize selection. Numerical examples substantiate and complement the theoretical investigations. \\ ( https://arxiv.org/abs/1605.00429 , 341kb)  \\ arXiv:1605.00437 Date: Mon, 2 May 2016 11:22:38 GMT (219kb,D)
Title: Convergence of a Strang splitting finite element discretization for the Schr\"odingerPoisson equation Authors: Winfried Auzinger, Thomas Kassebacher, Othmar Koch, Mechthild Thalhammer Categories: math.NA \\ Operator splitting methods combined with finite element spatial discretizations are studied for timedependent nonlinear Schr\"odinger equations. In particular, the Schr\"odingerPoisson equation under homogeneous Dirichlet boundary conditions on a finite domain is considered. A rigorous stability and error analysis is carried out for the secondorder Strang splitting method and conforming polynomial finite element discretizations. For sufficiently regular solutions the classical orders of convergence are retained, that is, secondorder convergence in time and polynomial convergence in space is proven. The established convergence result is confirmed and complemented by numerical illustrations. \\ ( https://arxiv.org/abs/1605.00437 , 219kb)  \\ arXiv:1605.00445 Date: Mon, 2 May 2016 11:54:12 GMT (21kb)
Title: Setup of Order Conditions for Splitting Methods Authors: Winfried Auzinger, Wolfgang Herfort, Harald Hofst\"atter and Othmar Koch Categories: math.NA \\ This article is based on earlier papers where an approach based on Taylor expansion and the structure of its leading term as an element of a free Lie algebra was described for the setup of a system of order conditions for operator splitting methods. Along with a brief review of these materials and some theoretical background, we discuss the implementation of the ideas from these papers in computer algebra, in particular using Maple 18. A parallel version of such a code is described. \\ ( https://arxiv.org/abs/1605.00445 , 21kb)  \\ arXiv:1605.00453 Date: Mon, 2 May 2016 12:14:08 GMT (28kb,D)
Title: Symbolic Manipulation of Flows of Nonlinear Evolution Equations, with Application in the Analysis of SplitStep Time Integrators Authors: Winfried Auzinger, Harald Hofstaetter, Othmar Koch Categories: math.NA \\ We describe a package realized in the Julia programming language which performs symbolic manipulations applied to nonlinear evolution equations, their flows, and commutators of such objects. This tool was employed to perform contrived computations arising in the analysis of the local error of operator splitting methods. It enabled the proof of the convergence of the basic method and of the asymptotical correctness of a defectbased error estimator. The performance of our package is illustrated on several examples. \\ ( https://arxiv.org/abs/1605.00453 , 28kb)  \\ arXiv:1605.00506 Date: Mon, 2 May 2016 14:37:44 GMT (75kb,D)
Title: On rational functions without Froissart doublets Authors: Bernhard Beckermann, George Labahn and Ana C. Matos Categories: math.NA Comments: 18 pages, 1 figure MSCclass: 41A21, 65F22 \\ In this paper we consider the problem of working with rational functions in a numeric environment. A particular problem when modeling with such functions is the existence of Froissart doublets, where a zero is close to a pole. We discuss three different parameters which allow one to monitor the absence of Froissart doublets for a given general rational function. These include the euclidean condition number of an underlying Sylvestertype matrix, a parameter for determing coprimeness of two numerical polynomials and bounds on the spherical derivative. We show that our parameters sharpen those found in a previous paper by two of the autours. \\ ( https://arxiv.org/abs/1605.00506 , 75kb)  \\ arXiv:1605.00551 Date: Mon, 2 May 2016 16:33:58 GMT (469kb,D)
Title: Compatible finite element spaces for geophysical fluid dynamics Authors: Andrea Natale and Colin J. Cotter Categories: math.NA physics.aoph \\ Compatible finite elements provide a framework for preserving important structures in equations of geophysical fluid dynamics, and are becoming important in their use for building atmosphere and ocean models. We survey the application of compatible finite element spaces to geophysical fluid dynamics, including the application to the nonlinear rotating shallow water equations, and the threedimensional compressible Euler equations. We summarise analytic results about dispersion relations and conservation properties, and present new results on approximation properties in three dimensions on the sphere, and on hydrostatic balance properties. \\ ( https://arxiv.org/abs/1605.00551 , 469kb)  \\ arXiv:1605.00568 Date: Mon, 2 May 2016 17:03:13 GMT (3861kb,D)
Title: A Lagrangian scheme for the incompressible Euler equation using optimal transport Authors: Thomas Gallou\"et, Quentin M\'erigot Categories: math.NA mathph math.AP math.MP Comments: 21p MSCclass: 35Q31, 65M12, 65M50, 65Z05 \\ We approximate the regular solutions of the incompressible Euler equation by the solution of ODEs on finitedimensional spaces. Our approach combines Arnold's interpretation of the solution of Euler's equation for incompressible and inviscid fluids as geodesics in the space of measurepreserving diffeomorphisms, and an extrinsic approximation of the equations of geodesics due to Brenier. Using recently developed semidiscrete optimal transport solvers, this approach yields numerical scheme able to handle problems of realistic size in 2D. Our purpose in this article is to establish the convergence of these scheme towards regular solutions of the incompressible Euler equation, and to provide numerical experiments on a few simple testcases in 2D. \\ ( https://arxiv.org/abs/1605.00568 , 3861kb)  \\ arXiv:1605.00588 Date: Mon, 2 May 2016 18:08:04 GMT (54kb,D)
Title: Discretising the HermanKluk Propagator Authors: Caroline Lasser and David Sattlegger Categories: math.NA MSCclass: 81Q20, 65D30, 65Z05, 65P10 \\ The HermanKluk propagator is a popular semiclassical approximation of the unitary evolution operator in quantum molecular dynamics. In this paper we formulate the HermanKluk propagator as a phase space integral and discretise it by Monte Carlo and quasiMonte Carlo quadrature. Then, we investigate the accuracy of a symplectic time discretisation by combining backward error analysis with Fourier integral operator calculus. Numerical experiments for two and sixdimensional model systems support our theoretical results. \\ ( https://arxiv.org/abs/1605.00588 , 54kb)  \\ arXiv:1605.00072 Date: Sat, 30 Apr 2016 07:49:33 GMT (9kb)
Title: Short interval results for a class of arithmetic functions Authors: Olivier Bordell\`es Categories: math.NT Comments: 13 pages MSCclass: 11A25, 11N37, 11L07 \\ Using estimates on Hooley's $\Delta$function and a short interval version of the celebrated Dirichlet hyperbola principle, we derive an asymptotic formula for a class of arithmetic functions over short segments. Numerous examples are also given. \\ ( https://arxiv.org/abs/1605.00072 , 9kb)  \\ arXiv:1605.00088 Date: Sat, 30 Apr 2016 10:13:38 GMT (11kb)
Title: Density of solutions to quadratic congruences Authors: Neha Prabhu Categories: math.NT MSCclass: 11D45, 11B25, 11N37 \\ A classical result in number theory is Dirichlet's theorem on the density of primes in an arithmetic progression. We prove a similar result for numbers with exactly k prime factors for k>1. Building upon a proof by E.M. Wright in 1954, we compute the natural density of such numbers where each prime satisfies a congruence condition. As an application, we obtain the density of squarefree n not greater than x with k prime factors such that a fixed quadratic equation has exactly 2^k solutions modulo n. \\ ( https://arxiv.org/abs/1605.00088 , 11kb)  \\ arXiv:1605.00131 Date: Sat, 30 Apr 2016 16:13:09 GMT (241kb,D)
Title: Some experiments on the growth of Mertens matrices Authors: JeanPaul Cardinal Categories: math.NT Comments: 7 pages, 3 figures \\ We give some experimental observations on the growth of the norm of certain matrices related to the Mertens function. The results obtained in these experiments convince us that linear algebra may help in the study of Mertens function and other arithmetic functions. \\ ( https://arxiv.org/abs/1605.00131 , 241kb)  \\ arXiv:1605.00351 Date: Mon, 2 May 2016 04:39:47 GMT (15kb)
Title: Irreducible polynomials with prescribed sums of coefficients Authors: Aleksandr Tuxanidy and Qiang Wang Categories: math.NT Comments: arXiv admin note: text overlap with arXiv:1604.04023 \\ Let $q$ be a power of a prime, let $\mathbb{F}_q$ be the finite field with $q$ elements and let $n \geq 2$. For a polynomial $h(x) \in \mathbb{F}_q[x]$ of degree $n \in \mathbb{N}$ and a subset $W \subseteq [0,n] := \{0, 1, \ldots, n\}$, we define the sumofdigits function $$S_W(h) = \sum_{w \in W}[x^{w}] h(x)$$ to be the sum of all the coefficients of $x^w$ in $h(x)$ with $w \in W$. In the case when $q = 2$, we prove, except for a few genuine exceptions, that for any $c \in \mathbb{F}_2$ and any $W \subseteq [0,n]$ there exists an irreducible polynomial $P(x)$ of degree $n$ over $\mathbb{F}_2$ such that $S_{W}(P) = c$. In particular, restricting ourselves to the case when $\# W = 1$, we obtain a new proof of the HansenMullen irreducibility conjecture (now a theorem) in the case when $q = 2$. In the case of $q> 2$, we prove that, for any $c \in \mathbb{F}_q$, any $n\geq 2$ and any $W \subseteq [0,n]$, there exists an irreducible polynomial $P(x)$ of degree $n$ such that $S_{W}(P) \neq c$. \\ ( https://arxiv.org/abs/1605.00351 , 15kb)  \\ arXiv:1605.00375 Date: Mon, 2 May 2016 07:36:39 GMT (25kb)
Title: Cuspidal divisor class groups of nonsplit Cartan modular curves Authors: Pierfrancesco Carlucci Categories: math.NT Comments: 35 pages \\ I find an explicit description of modular units in terms of Siegel functions for the modular curves $X^+_{ns}(p^k)$ associated to the normalizer of a nonsplit Cartan subgroup of level $p^k$ where $p\not=2,3$ is a prime. The Cuspidal Divisor Class Group $\mathfrak{C}^+_{ns}(p^k)$ on $X^+_{ns}(p^k)$ is explicitly described as a module over the group ring $R = \mathbb{Z}[(\mathbb{Z}/p^k\mathbb{Z})^*/\{\pm 1\}]$. In this paper I give a formula involving generalized Bernoulli numbers $B_{2,\chi}$ for $\mathfrak{C}^+_{ns}(p^k)$. \\ ( https://arxiv.org/abs/1605.00375 , 25kb)  \\ arXiv:1605.00378 Date: Mon, 2 May 2016 07:47:12 GMT (16kb)
Title: Metrical star discrepancy bounds for lacunary subsequences of digital Kroneckersequences and polynomial tractability Authors: Mario Neum\"uller and Friedrich Pillichshammer Categories: math.NT MSCclass: 11K38, 11K31, 11K45 \\ The star discrepancy $D_N^*(\mathcal{P})$ is a quantitative measure for the irregularity of distribution of a finite point set $\mathcal{P}$ in the multidimensional unit cube which is intimately related to the integration error of quasiMonte Carlo algorithms. It is known that for every integer $N \ge 2$ there are point sets $\mathcal{P}$ in $[0,1)^d$ with $\mathcal{P}=N$ and $D_N^*(\mathcal{P}) =O((\log N)^{d1}/N)$. However, for small $N$ compared to the dimension $d$ this asymptotically excellent bound is useless (e.g. for $N \le {\rm e}^{d1}$). In 2001 it has been shown by Heinrich, Novak, Wasilkowski and Wo\'{z}niakowski that for every integer $N \ge 2$ there exist point sets $\mathcal{P}$ in $[0,1)^d$ with $\mathcal{P}=N$ and $D_N^*(\mathcal{P}) \le C \sqrt{d/N}$. Although not optimal in an asymptotic sense in $N$, this upper bound has a much better (and even optimal) dependence on the dimension $d$. Unfortunately the result by Heinrich et al. and also later variants thereof by other authors are pure existence results and until now no explicit construction of point sets with the above properties are known. Quite recently L\"obbe studied lacunary subsequences of Kronecker's $(n \boldsymbol{\alpha})$sequence and showed a metrical discrepancy bound of the form $C \sqrt{d (\log d)/N}$ with implied absolute constant $C>0$ independent of $N$ and $d$. In this paper we show a corresponding result for digital Kronecker sequences, which are a nonarchimedean analog of classical Kronecker sequences. \\ ( https://arxiv.org/abs/1605.00378 , 16kb)  \\ arXiv:1605.00487 Date: Mon, 2 May 2016 13:55:02 GMT (36kb)
Title: Curtis homomorphisms and the integral Bernstein center for GL_n Authors: David Helm Categories: math.NT Comments: 35 pages MSCclass: 11F33, 11F70, 11F80 \\ We describe two conjectures, one strictly stronger than the other, that give descriptions of the integral Bernstein center for GL_n(F) (that is, the center of the category of smooth W(k)[GL_n(F)]modules, for F a padic field and k an algebraically closed field of characteristic l different from p) in terms of Galois theory. Moreover, we show that the weak version of the conjecture (for m at most n) implies the strong version of the conjecture. In a companion paper [HM] we show that the strong conjecture for n1 implies the weak conjecture for n; thus the two papers together give an inductive proof of both conjectures. The upshot is a description of the integral Bernstein center for GL_n in purely Galois theoretic terms; previous work of the author shows that such a description implies the conjectural "local Langlands correspondence in families" of Emerton and the author. \\ ( https://arxiv.org/abs/1605.00487 , 36kb)  \\ arXiv:1605.00501 Date: Mon, 2 May 2016 14:26:57 GMT (6kb)
Title: Fermat's Last Theorem: Algebra and Number Theory Authors: Felix Sidokhine Categories: math.NT \\ In our work we give the examples using Fermat's Last Theorem for solving some problems from algebra and number theory. \\ ( https://arxiv.org/abs/1605.00501 , 6kb)  \\ arXiv:1605.00511 Date: Mon, 2 May 2016 14:51:42 GMT (49kb)
Title: Geometric approach to the explicit local Langlands correspondence Authors: Yoichi Mieda Categories: math.NT math.AG math.RT Comments: 55 pages MSCclass: 11F70, 11F80, 11G25, 22E50 \\ We propose a geometric strategy of giving explicit description of the Langlands parameter of an irreducible supercuspidal representation of GL(n) over a nonarchimedean local field. The key is to compare the cohomology of an affinoid in the LubinTate space at infinite level and that of the reduction of its formal model. As examples, we treat the cases of depth 0 supercuspidal representations and simple supercuspidal representations. \\ ( https://arxiv.org/abs/1605.00511 , 49kb)  \\ arXiv:1605.00615 Date: Mon, 2 May 2016 18:56:41 GMT (22kb)
Title: LubinTate Deformation Spaces and $(\phi,\Gamma)$Modules Authors: Annie Carter Categories: math.NT \\ JeanMarc Fontaine has shown that there exists an equivalence of categories between the category of continuous $\mathbb{Z}_p$representations of a given Galois group and the category of \'{e}tale $(\phi,\Gamma)$modules over a certain ring. This work attempts to answer the question of whether there exists a theory of $(\phi,\Gamma)$modules for the LubinTate tower. We construct this tower via the rings $R_n$ which parametrize deformations of level $n$ of a given formal module. One can choose prime elements $\pi_n$ in each ring $R_n$ in a compatible way, and consider the tower of fields $(K'_n)_n$ obtained by localizing at $\pi_n$, completing, and passing to fraction fields. By taking the compositum $K_n = K_0 K'_n$ of each field with a certain unramified extension $K_0$ of the base field $K'_0$ one obtains a tower of fields $(K_n)_n$ which is strictly deeply ramified in the sense of Anthony Scholl. This is a first step towards showing that there exists a theory of $(\phi,\Gamma)$modules for this tower. \\ ( https://arxiv.org/abs/1605.00615 , 22kb)  \\ arXiv:1605.00038 Date: Fri, 29 Apr 2016 22:53:47 GMT (18kb)
Title: Anticommutation in the Presentations of ThetaDeformed Spheres Authors: Benjamin Passer Categories: math.OA math.AT Comments: 14 pages MSCclass: 46L85 \\ We consider an analogue of the thetadeformed even spheres, modifying the relations demanded of the selfadjoint generator x in the usual presentation. In this analogue, x is given anticommutation relations with all of the other generators, as opposed to being central. Using even Ktheory, we show that noncommutative BorsukUlam theorems hold for these algebras. \\ ( https://arxiv.org/abs/1605.00038 , 18kb)  \\ arXiv:1605.00226 Date: Sun, 1 May 2016 09:47:56 GMT (8kb)
Title: Two minimal unique ergodic diffeomorphisms on a manifolds and their smooth crossed product algebras Authors: Hongzhi Liu Categories: math.OA \\ In this article we construct two minimal unique ergodic diffeomorphisms $\alpha$ and $\beta$ on $S^3 \times S^{6} \times S^{8} $. We will show that $C(S^3 \times S^{6} \times S^{8}) \rtimes_\alpha \mathbb{Z} $ and $C(S^3 \times S^{6} \times S^{8})\rtimes_\beta \mathbb{Z} $ are equivalent to each other, while $C^\infty (S^3 \times S^{6} \times S^{8})\rtimes_\alpha \mathbb{Z} $ and $C^\infty(S^3 \times S^{6} \times S^{8} )\rtimes_\beta \mathbb{Z} $ are not. \\ ( https://arxiv.org/abs/1605.00226 , 8kb)  \\ arXiv:1605.00288 Date: Sun, 1 May 2016 18:26:31 GMT (22kb)
Title: $*$freeness in Finite Tensor Products Authors: Benoit Collins, Pierre Yves Gaudreau Lamarre Categories: math.OA math.GR \\ In this paper, we consider the following question and variants thereof: given $\mathbf D:=\big(a_{1;i}\otimes\cdots\otimes a_{K;i}:i\in I\big)$, a collection of elementary tensor noncommutative random variables in the tensor product of probability spaces $(\mathcal A_1\otimes\cdots\otimes\mathcal A_K,\phi_1\otimes\cdots\otimes\phi_K)$, when is $\mathbf D$ $*$free? (See Section 1.2 for a precise formulation of this problem.) Settling whether or not freeness occurs in tensor products is a recurring problem in operator algebras, and the following two examples provide a natural motivation for the above question: (A) If $(a_{1;i}:i\in I)$ is a $*$free family of Haar unitary variables and $a_{k,i}$ are arbitrary unitary variables for $k\geq2$, then the $*$freeness persists at the level of the tensor product $\mathbf D$. (B) A converse of (A) holds true if all variables $a_{k;i}$ are grouplike elements (see Corollary 1.7 of Proposition 1.6). It is therefore natural to seek to understand the extent to which such simple characterizations hold true in more general cases. While our results fall short of a complete characterization, we make notable steps toward identifying necessary and sufficient conditions for the freeness of $\mathbf D$. For example, we show that under evident assumptions, if more than one family $(a_{k,i}:i\in I)$ contains nonunitary variables, then the tensor family fails to be $*$free (see Theorem 1.8 (1)). \\ ( https://arxiv.org/abs/1605.00288 , 22kb)  \\ arXiv:1605.00315 Date: Sun, 1 May 2016 22:34:12 GMT (35kb)
Title: Universal Preparability of States and Asymptotic Completeness Authors: Rolf Gohm, Florian Haag, Burkhard K\"ummerer Categories: math.OA quantph Comments: 34 pages MSCclass: 46L50, 46L51, 46L55, 54H20 \\ We introduce a notion of universal preparability for a state of a system, more precisely: for a normal state on a von Neumann algebra. It describes a situation where from an arbitrary initial state it is possible to prepare a target state with arbitrary precision by a repeated interaction with a sequence of copies of another system. For $\mathcal{B}(\mathcal{H})$ we give criteria sufficient to ensure that all normal states are universally preparable which can be verified for a class of noncommutative birth and death processes realized, in particular, by the interaction of a micromaser with a stream of atoms. As a tool the theory of tight sequences of states and of stationary states is further developed and we show that in the presence of stationary faithful normal states universal preparability of all normal states is equivalent to asymptotic completeness, a notion studied earlier in connection with the scattering theory of noncommutative Markov processes. \\ ( https://arxiv.org/abs/1605.00315 , 35kb)  \\ arXiv:1605.00349 Date: Mon, 2 May 2016 04:22:27 GMT (11kb)
Title: Determinants associated to traces on operator bimodules Authors: K. Dykema, F. Sukochev and D. Zanin Categories: math.OA math.FA Comments: 11 pages MSCclass: 46L52 \\ Given a II$_1$factor $\mathcal{M}$ with tracial state $\tau$ and given an $\mathcal{M}$bimodule $\mathcal{E}(\mathcal{M},\tau)$ of operators affiliated to $\mathcal{M}$ and a trace $\varphi$ on $\mathcal{E}(\mathcal{M},\tau)$, (namely, a linear functional that is invariant under unitary conjugation), we prove that $\det_\varphi:\mathcal{E}_{\log}(\mathcal{M},\tau)\to[0,\infty)$ defined by $\det_\varphi(T)=\exp(\varphi(\log T))$ is a multiplicative map on the set $\mathcal{E}_{\log}(\mathcal{M},\tau)$ of all affiliated operators $T$ such that $\log_+(T)\in\mathcal{E}(\mathcal{M},\tau)$. \\ ( https://arxiv.org/abs/1605.00349 , 11kb)  \\ arXiv:1605.00042 Date: Fri, 29 Apr 2016 23:36:39 GMT (629kb)
Title: Improved Sparse LowRank Matrix Estimation Authors: Ankit Parekh and Ivan W. Selesnick Categories: math.OC Comments: 15 pages, 9 figures \\ This paper addresses the problem of estimating a sparse lowrank matrix from its noisy observation. We propose a convex objective function consisting of a datafidelity term and two parameterized nonconvex penalty functions. The nonconvex penalty functions induce sparsity of the singular values and the entries of the matrix to be estimated. We show how to set the parameters of the nonconvex penalty functions, in order to ensure that the objective function is strictly convex. The proposed objective function better estimates sparse lowrank matrices than the convex method which utilizes the sum of the nuclear norm and the $\ell_1$ norm. We derive an algorithm (as an instance of ADMM) to solve the proposed problem, and guarantee its convergence provided the scalar augmented Lagrangian parameter is set appropriately. \\ ( https://arxiv.org/abs/1605.00042 , 629kb)  \\ arXiv:1605.00071 Date: Sat, 30 Apr 2016 07:47:29 GMT (394kb,D)
Title: The Homotopy Method Revisited: Computing Solution Paths of $\ell_1$Regularized Problems Authors: Bj\"orn Bringmann, Daniel Cremers, Felix Krahmer, Michael M\"oller Categories: math.OC Comments: 19 pages, 4 figures MSCclass: 90C25 (Primary) 49N45, 62J07 (Secondary) \\ $ \ell_1 $regularized linear inverse problems are frequently used in signal processing, image analysis, and statistics. The correct choice of the regularization parameter $ t \in \mathbb{R}_{\geq 0} $ is a delicate issue. Instead of solving the variational problem for a fixed parameter, the idea of the homotopy method is to compute a complete solution path $ u(t) $ as a function of $ t $. In a celebrated paper by Osborne, Presnell, and Turlach, it has been shown that the computational cost of this approach is often comparable to the cost of solving the corresponding least squares problem. Their analysis relies on the oneatatime condition, which requires that different indices enter or leave the support of the solution at distinct regularization parameters. In this paper, we introduce a generalized homotopy algorithm based on a nonnegative least squares problem, which does not require such a condition, and prove its termination after finitely many steps. At every point of the path, we give a full characterization of all possible directions. To illustrate our results, we discuss examples in which the standard homotopy method either fails or becomes infeasible. To the best of our knowledge, our algorithm is the first to provably compute a full solution path for an arbitrary combination of an input matrix and a data vector. \\ ( https://arxiv.org/abs/1605.00071 , 394kb)  \\ arXiv:1605.00076 Date: Sat, 30 Apr 2016 08:17:35 GMT (3196kb)
Title: Asynchronous Optimization Over Heterogeneous Networks via Consensus ADMM Authors: Sandeep Kumar, Rahul Jain, Ketan Rajawat Categories: math.OC cs.IT cs.SI math.IT Comments: Submitted to Transactions on signal and information processing over Networks \\ This paper considers the distributed optimization of a sum of locally observable, nonconvex functions. The optimization is performed over a multiagent networked system, and each local function depends only on a subset of the variables. An asynchronous and distributed alternating directions method of multipliers (ADMM) method that allows the nodes to defer or skip the computation and transmission of updates is proposed in the paper. The proposed algorithm utilizes different approximations in the update step, resulting in proximal and majorized ADMM variants. Both variants are shown to converge to a local minimum, under certain regularity conditions. The proposed asynchronous algorithms are also applied to the problem of cooperative localization in wireless ad hoc networks, where it is shown to outperform the other stateoftheart localization algorithms. \\ ( https://arxiv.org/abs/1605.00076 , 3196kb)  \\ arXiv:1605.00117 Date: Sat, 30 Apr 2016 14:40:29 GMT (9kb)
Title: Existence of equilibrium of the generalized games in choice form and applications Authors: Monica Patriche Categories: math.OC Comments: 12 pages \\ In this paper, we introduce a generalized game in choice form, which differs slightly from the model defined by Ferrara and Stefanescu (2015) and we obtain the existence of the equilibrium for this model. As applications, we obtain new theorems concernong the existence of solutions for systems of vector equilibrium problems. \\ ( https://arxiv.org/abs/1605.00117 , 9kb)  \\ arXiv:1605.00125 Date: Sat, 30 Apr 2016 15:39:21 GMT (15kb)
Title: An accelerated algorithm for minimizing convex compositions Authors: Dmitriy Drusvyatskiy and Courtney Kempton Categories: math.OC Comments: 13 pages MSCclass: 97N60, 90C25, 90C06, 90C30 \\ We describe a new proximal algorithm for minimizing compositions of finitevalued convex functions with smooth mappings. When applied to convex optimization problems having an additive composite form, the algorithm reduces to FISTA. The method both realizes the best known complexity bound of $\mathcal{O}(1/\epsilon)$ in optimality conditions whenever the objective function has bounded domain, and achieves the accelerated rate $\mathcal{O}(1/\sqrt{\epsilon})$ in function values under standard convexity assumptions. A natural convexity parameter of the composition quantifies the transition between the two modes of convergence. \\ ( https://arxiv.org/abs/1605.00125 , 15kb)  \\ arXiv:1605.00158 Date: Sat, 30 Apr 2016 20:01:52 GMT (30kb)
Title: Necessary Optimality Conditions for Optimal Control Problems with Equilibrium Constraints Authors: Lei Guo and Jane Ye Categories: math.OC \\ This paper introduces and studies the optimal control problem with equilibrium constraints (OCPEC). The OCPEC is an optimal control problem with a mixed state and control equilibrium constraint formulated as a complementarity constraint and it can be seen as a dynamic mathematical program with equilibrium constraints. It provides a powerful modeling paradigm for many practical problems such as bilevel optimal control problems and dynamic principalagent problems. In this paper, we propose weak, Clarke, Mordukhovich and strong stationarities for the OCPEC. Moreover, we give some sufficient conditions to ensure that the local minimizers of the OCPEC are Fritz John type weakly stationary, Mordukhovich stationary and strongly stationary, respectively. Unlike Pontryagain's maximum principle for the classical optimal control problem with equality and inequality constraints, a counter example shows that for general OCPECs, there may exist two sets of multipliers for the complementarity constraints. A condition under which these two sets of multipliers coincide is given. \\ ( https://arxiv.org/abs/1605.00158 , 30kb)  \\ arXiv:1605.00197 Date: Sun, 1 May 2016 02:30:17 GMT (198kb,D)
Title: Software for cutgenerating functions in the GomoryJohnson model and beyond Authors: Chun Yu Hong, Matthias K\"oppe, Yuan Zhou Categories: math.OC Comments: 8 pages, 3 figures; to appear in Proc. International Congress on Mathematical Software 2016 MSCclass: 90C10 \\ We present software for investigations with cut generating functions in the GomoryJohnson model and extensions, implemented in the computer algebra system SageMath. \\ ( https://arxiv.org/abs/1605.00197 , 198kb)  \\ arXiv:1605.00201 Date: Sun, 1 May 2016 03:36:58 GMT (24kb,D)
Title: Further properties of the forwardbackward envelope with applications to differenceofconvex programming Authors: Tianxiang Liu and Ting Kei Pong Categories: math.OC stat.ML \\ In this paper, we further study the forwardbackward envelope first introduced in [27] and [29] for problems whose objective is the sum of a proper closed convex function and a smooth possibly nonconvex function with Lipschitz continuous gradient. We derive sufficient conditions on the original problem for the corresponding forwardbackward envelope to be a levelbounded and Kurdyka{\L}ojasiewicz function with an exponent of $\frac12$; these results are important for the efficient minimization of the forwardbackward envelope by classical optimization algorithms. In addition, we demonstrate how to minimize some differenceofconvex regularized least squares problems by minimizing a suitably constructed forwardbackward envelope. Our preliminary numerical results on randomly generated instances of largescale $\ell_{12}$ regularized least squares problems [36] illustrate that an implementation of this approach with a limitedmemory BFGS scheme outperforms some standard firstorder methods such as the nonmonotone proximal gradient method in [34]. \\ ( https://arxiv.org/abs/1605.00201 , 24kb)  \\ arXiv:1605.00267 Date: Sun, 1 May 2016 15:48:56 GMT (46kb)
Title: Distributed Algorithms for Aggregative Games on Graphs Authors: Jayash Koshal, Angelia Nedi\'c and Uday V. Shanbhag Categories: math.OC \\ We consider a class of Nash games, termed as aggregative games, being played over a networked system. In an aggregative game, a player's objective is a function of the aggregate of all the players' decisions. Every player maintains an estimate of this aggregate, and the players exchange this information with their local neighbors over a connected network. We study distributed synchronous and asynchronous algorithms for information exchange and equilibrium computation over such a network. Under standard conditions, we establish the almostsure convergence of the obtained sequences to the equilibrium point. We also consider extensions of our schemes to aggregative games where the players' objectives are coupled through a more general form of aggregate function. Finally, we present numerical results that demonstrate the performance of the proposed schemes. \\ ( https://arxiv.org/abs/1605.00267 , 46kb)  \\ arXiv:1605.00320 Date: Sun, 1 May 2016 23:15:59 GMT (13kb)
Title: A unified convergence bound for conjugate gradient and accelerated gradient Authors: Sahar Karimi, Stephen A. Vavasis Categories: math.OC MSCclass: 90C25 ACMclass: G.1.6 \\ Nesterov's accelerated gradient method for minimizing a smooth strongly convex function $f$ is known to reduce $f(\x_k)f(\x^*)$ by a factor of $\eps\in(0,1)$ after $k\ge O(\sqrt{L/\ell}\log(1/\eps))$ iterations, where $\ell,L$ are the two parameters of smooth strong convexity. Furthermore, it is known that this is the best possible complexity in the functiongradient oracle model of computation. The method of linear conjugate gradients (CG) also satisfies the same complexity bound in the special case of strongly convex quadratic functions, but in this special case it is faster than the accelerated gradient method. Despite similarities in the algorithms and their asymptotic convergence rates, the conventional analyses of the two methods are nearly disjoint. The purpose of this note is provide a single quantity that decreases on every step at the correct rate for both algorithms. Our unified bound is based on a potential similar to the potential in Nesterov's original analysis. As a side benefit of this analysis, we provide a direct proof that conjugate gradient converges in $O(\sqrt{L/\ell}\log(1/\eps))$ iterations. In contrast, the traditional indirect proof first establishes this result for the Chebyshev algorithm, and then relies on optimality of conjugate gradient to show that its iterates are at least as good as Chebyshev iterates. To the best of our knowledge, ours is the first direct proof of the convergence rate of linear conjugate gradient in the literature. \\ ( https://arxiv.org/abs/1605.00320 , 13kb)  \\ arXiv:1605.00479 Date: Mon, 2 May 2016 13:38:38 GMT (920kb,D)
Title: A Nonconvex Nonsmooth Regularization Method for Compressed Sensing and LowRank Matrix Completion Authors: ZhuoXu Cui, Qibin Fan Categories: math.OC Comments: 19 pages,4 figures \\ In this paper, nonconvex and nonsmooth models for compressed sensing (CS) and low rank matrix completion (MC) is studied. The problem is formulated as a nonconvex regularized leat square optimization problems, in which the l0norm and the rank function are replaced by l1norm and nuclear norm, and adding a nonconvex penalty function respectively. An alternating minimization scheme is developed, and the existence of a subsequence, which generate by the alternating algorithm that converges to a critical point, is proved. The NSP, RIP, and RIP condition for stable recovery guarantees also be analysed for the nonconvex regularized CS and MC problems respectively. Finally, the performance of the proposed method is demonstrated through experimental results. \\ ( https://arxiv.org/abs/1605.00479 , 920kb)  \\ arXiv:1605.00606 Date: Mon, 2 May 2016 18:29:34 GMT (411kb)
Title: A LimitedFeedback Approximation Scheme for Optimal Switching Problems with Execution Delays Authors: Magnus Perninge Categories: math.OC MSCclass: 60G40, 93E20, 49L20, 62P20 \\ We consider a type of optimal switching problems with nonuniform execution delays and ramping. Such problems frequently occur in the operation of economical and engineering systems. We first provide a solution to the problem by applying a probabilistic method. The main contribution is, however, a scheme for approximating the optimal control by limiting the information in the statefeedback. In a numerical example the approximation routine shows a considerable computational performance enhancement when compared to a conventional algorithm. \\ ( https://arxiv.org/abs/1605.00606 , 411kb)  \\ arXiv:1605.00627 Date: Mon, 2 May 2016 19:18:48 GMT (399kb)
Title: Random Access Design for Wireless Control Systems Authors: Konstantinos Gatsis, Alejandro Ribeiro, George J. Pappas Categories: math.OC \\ Interferences arising between wireless sensoractuator systems communicating over shared wireless channels adversely affect closed loop control performance. To mitigate this problem we design appropriate channel access policies for wireless control systems subject to channel fading. The design is posed as an optimization problem where the total transmit power of the sensors is minimized while desired control performance is guaranteed for each involved control loop. Control performance is abstracted as a desired expected decrease rate of a given Lyapunov function for each loop. We prove that the optimal channel access policies are decoupled and, intuitively, each sensor balances the gains from transmitting to its actuator with the negative interference effect on all other control loops. Moreover the optimal policies are of a threshold nature, that is, a sensor transmits only under favorable local fading conditions. Finally, we show that the optimal policies can be computed by a distributed iterative procedure which does not require coordination between the sensors. \\ ( https://arxiv.org/abs/1605.00627 , 399kb)  \\ arXiv:1605.00001 Date: Thu, 28 Apr 2016 21:05:40 GMT (17kb)
Title: Joint Statistics of Random Walk on $Z^1$ and Accumulation of Visits Authors: Jerome K. Percus and Ora E. Percus Categories: math.PR Comments: 8 pages, 1 figure MSCclass: Primary: 60G50, Secondary: 60J10 \\ We obtain the joint distribution $P_N (X, KZ)$ of the location $X$ of a onedimensional symmetric next neighbor random walk on the integer lattice, and the number of times the walk has visited a specified site $Z$. This distribution has a simple form in terms of the one variable distribution $p_{N'}(X')$, where $N'=NK$ and $X'$ is a function of $X, K$, and $Z$. The marginal distribution of $X$ and $K$ are obtained, as well as their diffusion scaling limits. \\ ( https://arxiv.org/abs/1605.00001 , 17kb)  \\ arXiv:1605.00024 Date: Fri, 29 Apr 2016 21:06:11 GMT (20kb)
Title: Intermittency for the Hyperbolic Anderson Model with rough noise in space Authors: Raluca M. Balan, Maria Jolis, Llu\'is QuerSardanyons Categories: math.PR \\ In this article, we consider the stochastic wave equation on the real line driven by a linear multiplicative Gaussian noise, which is white in time and whose spatial correlation corresponds to that of a fractional Brownian motion with Hurst index $H\in (\frac14,\frac12)$. Initial data are assumed to be constant. First, we prove that this equation has a unique solution (in the Skorohod sense) and obtain an exponential upper bound for the $p$th moment of the solution, for any $p\geq 2$. Condition $H>\frac14$ turns out to be necessary for the existence of solution. Secondly, we show that this solution coincides with the one obtained by the authors in a recent publication, in which the solution is interpreted in the It\^o sense. Finally, we prove that the solution of the equation in the Skorohod sense is weakly intermittent. \\ ( https://arxiv.org/abs/1605.00024 , 20kb)  \\ arXiv:1605.00039 Date: Fri, 29 Apr 2016 23:02:25 GMT (156kb,D)
Title: Nonzerosum stochastic differential games with impulse controls and applications to retail energy markets Authors: Ren\'e A\"id, Matteo Basei, Giorgia Callegaro, Luciano Campi, Tiziano Vargiolu Categories: math.PR qfin.EC Comments: 3 figures \\ We study the notion of Nash equilibrium in a general nonzerosum impulse game for two players. The main mathematical contribution of the paper is a verification theorem which provides, under some regularity conditions, the system of quasivariational inequalities identifying the value functions and the optimal strategies of the two players. As an application, we propose a model for the competition among retailers in electricity markets. We first consider a simplified oneplayer setting, where we obtain a quasiexplicit expression for the value function and the optimal control. Then, we turn to the twoplayer case and we provide a detailed heuristic analysis of the retail impulse game, conducted along the lines of the verification theorem obtained in the general setting. This allows to identify reasonable candidates for the intervention and continuation regions of both players and their strategies. \\ ( https://arxiv.org/abs/1605.00039 , 156kb)  \\ arXiv:1605.00118 Date: Sat, 30 Apr 2016 14:41:16 GMT (157kb,D)
Title: Eigenvectors of the critical 1dimensional random Schroedinger operator Authors: Ben Rifkind, Balint Virag Categories: math.PR \\ The purpose of this paper is to understand in more detail the shape of the eigenvectors of the random Schroedinger operator H = Delta+V. Here Delta is the discrete Laplacian and V is a random potential. It is well known that under certain assumptions on V the spectrum of this operator is pure point and its eigenvectors are exponentially localized; a phenomenon known as Anderson Localization. We restrict the operator to Z_n and consider the critical model H_n. We show that the shape of a uniformly chosen eigenvector of H_n converges in law to exp (t/4 + Z_t/sqrt(2)), where Z is twosided Brownian motion. \\ ( https://arxiv.org/abs/1605.00118 , 157kb)  \\ arXiv:1605.00162 Date: Sat, 30 Apr 2016 20:29:06 GMT (13kb)
Title: Fractional smoothness of images of logarithmically concave measures under polynomials Authors: Egor D. Kosov Categories: math.PR \\ We show that a measure on the real line that is the image of a logconcave measure under a polynomial of degree $d$ possesses a density from the Nikol'skiiBesov class of fractional order $1/d$. This result is used to prove an estimate of the total variation distance between such measures in terms of the FortetMourier distance. \\ ( https://arxiv.org/abs/1605.00162 , 13kb)  \\ arXiv:1605.00277 Date: Sun, 1 May 2016 16:47:54 GMT (6kb)
Title: Asymptotic bounds on renewal process stopping times Authors: Jesse Geneson Categories: math.PR Comments: 8 pages MSCclass: 60G50 \\ Let $M(t)$ denote the expected number of terms in the first partial sum of independent uniform $[0,1]$ random variables that exceeds $t$. Let $N(t)$ denote the expected number of terms in the first partial product of independent uniform $[1, e]$ random variables that exceeds $e^{t}$. It is known that $M(t) = 2t+\frac{2}{3}+o(1)$, $M(t) = \sum_{k = 0}^{\left \lceil{t}\right \rceil} \frac{(1)^{k} (tk)^{k}}{k!}e^{tk}$, and $N(1) = \frac{e1}{e}+e^{\frac{1}{e1}}$. We show that $\lim_{t \rightarrow \infty} \frac{N(t)}{t} = e1$ and $M(t) \geq N(t)$ for all $t \geq 0$. We also show that $N(t) = \frac{e1}{e}+e^{t1+\frac{t}{e1}}$ for $t \in [0,1]$ and we prove that $\frac{d}{dt}(N(t)e^{\frac{e}{e1}t}) = \frac{e}{e1}e^{\frac{e}{e1}t} N(t1)e^{\frac{e}{e1}t}$. In addition, we show that $N(t) = (e1)(t+\frac{e2}{2})+o(1)$, and we find asymptotic bounds on the stopping times of a more general family of renewal processes. \\ ( https://arxiv.org/abs/1605.00277 , 6kb)  \\ arXiv:1605.00285 Date: Sun, 1 May 2016 18:14:48 GMT (25kb)
Title: The BorellEhrhard Game Authors: Ramon van Handel Categories: math.PR math.FA math.MG Comments: 23 pages MSCclass: 60G15, 39B62, 52A40, 91A15 \\ A precise description of the convexity of Gaussian measures is provided by sharp BrunnMinkowski type inequalities due to Ehrhard and Borell. We show that these are manifestations of a gametheoretic mechanism: a minimax variational principle for Brownian motion. As an application, we obtain a Gaussian improvement of Barthe's reverse BrascampLieb inequality. \\ ( https://arxiv.org/abs/1605.00285 , 25kb)  \\ arXiv:1605.00361 Date: Mon, 2 May 2016 06:24:06 GMT (3510kb,D)
Title: Monte Carlo with Determinantal Point Processes Authors: R\'emi Bardenet, Adrien Hardy Categories: math.PR math.CA stat.CO stat.ME Comments: 48 pages, 2 figures \\ We show that repulsive random variables can yield Monte Carlo methods with faster convergence rates than the typical $N^{1/2}$, where $N$ is the number of integrand evaluations. More precisely, we propose stochastic numerical quadratures involving determinantal point processes associated with multivariate orthogonal polynomials, and we obtain root mean square errors that decrease as $N^{(1+1/d)/2}$, where $d$ is the dimension of the ambient space. First, we prove a central limit theorem (CLT) for the linear statistics of a class of determinantal point processes, when the reference measure is a product measure supported on a hypercube, which satisfies the Nevaiclass regularity condition, a result which may be of independent interest. Next, we introduce a Monte Carlo method based on these determinantal point processes, and prove a CLT with explicit limiting variance for the quadrature error, when the reference measure satisfies a stronger regularity condition. As a corollary, by taking a specific reference measure and using a construction similar to importance sampling, we obtain a general Monte Carlo method, which applies to any measure with continuously derivable density. Loosely speaking, our method can be interpreted as a stochastic counterpart to Gaussian quadrature, which, at the price of some convergence rate, is easily generalizable to any dimension and has a more explicit error term. \\ ( https://arxiv.org/abs/1605.00361 , 3510kb)  \\ arXiv:1605.00415 Date: Mon, 2 May 2016 10:03:07 GMT (117kb,D)
Title: Poisson approximation of the length spectrum of random surfaces Authors: Bram Petri, Christoph Thaele Categories: math.PR math.DG math.GT MSCclass: 57M50, 60C05, 60D05, 60F05 \\ Multivariate Poisson approximation of the length spectrum of random surfaces is studied by means of the ChenStein method. This approach delivers simple and explicit error bounds in Poisson limit theorems. They are used to prove that Poisson approximation applies to curves of length up to order $o(\log\log g)$ with $g$ being the genus of the surface. \\ ( https://arxiv.org/abs/1605.00415 , 117kb)  \\ arXiv:1605.00581 Date: Mon, 2 May 2016 17:43:28 GMT (613kb,D)
Title: Martingales in selfsimilar growthfragmentations and their connections with random planar maps Authors: Jean Bertoin, Timothy Budd, Nicolas Curien, Igor Kortchemski Categories: math.PR mathph math.MP Comments: 57 pages, 6 figures \\ The purpose of the present work is twofold. First, we develop the theory of general selfsimilar growthfragmentation processes by focusing on martingales which appear naturally in this setting. As an application, we establish manytoone formulas for growthfragmentations and define the notion of intrinsic area of a growthfragmentation. Second, we identify a distinguished family of growthfragmentations closely related to stable L\'evy processes, which are then shown to arise as the scaling limit of the perimeter process in Markovian explorations of certain random planar maps with large degrees (which are, roughly speaking, the dual maps of the stable maps of Le Gall & Miermont). This generalizes a geometric connection between large Boltzmann triangulations and a certain growthfragmentation process, which was established in arXiv:1507.02265 . \\ ( https://arxiv.org/abs/1605.00581 , 613kb)  \\ arXiv:1605.00227 Date: Sun, 1 May 2016 09:49:56 GMT (206kb)
Title: On FominKirillov Algebras for Complex Reflection Groups Authors: Robert Laugwitz Categories: math.QA math.RA Comments: 12 pages, 2 tables, TikZ figures MSCclass: 17B37, 16T05, 16T30 \\ This note is an application of classification results for finitedimensional Nichols algebras over groups. We apply these results to generalizations of FominKirillov algebras to complex reflection groups. First, we focus on the case of cyclic groups where the corresponding Nichols algebras are only finitedimensional up to order four, and we include results about the existence of Weyl groupoids and finitedimensional Nichols subalgebras for this class. Second, recent results by HeckenbergerVendramin [ArXiv eprints, 1412.0857 (December 2014)] on the classification of Nichols algebras of semisimple group type can be used to find that these algebras are infinitedimensional for many nonexceptional complex reflection groups in the ShephardTodd classification. \\ ( https://arxiv.org/abs/1605.00227 , 206kb)  \\ arXiv:1605.00254 Date: Sun, 1 May 2016 14:09:26 GMT (30kb)
Title: Homomorphisms and rigid isomorphisms of twisted group doubles Authors: Marc Keilberg Categories: math.QA math.GR math.RA Comments: 35 pages MSCclass: 16W20, 16T99, 20D99 \\ We prove several results concerning quasibialgebra morphisms $\mathcal{D}^\omega(G)\to\mathcal{D}^\eta(H)$ of twisted group doubles. We take a particular focus on the isomorphisms which are simultaneously isomorphisms $\mathcal{D}(G)\to\mathcal{D}(H)$. All such isomorphisms are shown to be morphisms of quasiHopf algebras, and a classification of all such isomorphisms is determined. Whenever $\omega\in Z^3(G/Z(G),U(1))$ this suffices to completely describe $\operatorname{Aut}(\mathcal{D}^\omega(G))$, the group of quasiHopf algebra isomorphisms of $\mathcal{D}^\omega(G)$, and so generalizes existing descriptions for the case where $\omega$ is trivial. \\ ( https://arxiv.org/abs/1605.00254 , 30kb)  \\ arXiv:1605.00268 Date: Sun, 1 May 2016 15:50:27 GMT (15kb)
Title: Cohomology and Deformation of Virasoro Extensions of qWitt HomLie superalgebra Authors: Abdenacer Makhlouf and Nejib Saadaoui Categories: math.QA mathph math.MP \\ The purpose of this paper is to study Virasoro extensions of the qdeformed Witt HomLie superalgebra. Moreover, we provide the cohomology and deformations of the Ramond Homsuperalgebra and special Ramond Homsuperalgebra. \\ ( https://arxiv.org/abs/1605.00268 , 15kb)  \\ arXiv:1605.00560 Date: Mon, 2 May 2016 16:45:48 GMT (22kb)
Title: Finite dimensional Hopf actions on algebraic quantizations Authors: Pavel Etingof and Chelsea Walton Categories: math.QA math.RA Comments: 27 pages \\ Let k be an algebraically closed field of characteristic zero. In joint work with J. Cuadra [arxiv.org/abs/1409.1644, arxiv.org/abs/1509.01165], we showed that a semisimple Hopf action on a Weyl algebra over a polynomial algebra k[z_1,...,z_s] factors through a group action, and this in fact holds for any finite dimensional Hopf action if s=0. We also generalized these results to finite dimensional Hopf actions on algebras of differential operators. In this work we establish similar results for Hopf actions on other algebraic quantizations of commutative domains. This includes universal enveloping algebras of finite dimensional Lie algebras, spherical symplectic reflection algebras, quantum Hamiltonian reductions of Weyl algebras (in particular, quantized quiver varieties), finite Walgebras and their central reductions, quantum polynomial algebras, twisted homogeneous coordinate rings of abelian varieties, and Sklyanin algebras. The generalization in the last three cases uses a result from algebraic number theory, due to A. Perucca. \\ ( https://arxiv.org/abs/1605.00560 , 22kb)  \\ arXiv:1605.00174 Date: Sat, 30 Apr 2016 22:12:38 GMT (23kb)
Title: Reduction Operators and Completion of Rewriting Systems Authors: Cyrille Chenavier Categories: math.RA \\ We propose a functional description of rewriting systems where reduction rules are represented by linear maps called reduction operators. We show that reduction operators admit a lattice structure. Using this structure we define the notion of confluence and we show that this notion is equivalent to the ChurchRosser property of reduction operators. In this paper we give an algebraic formulation of completion using the lattice structure. We relate reduction operators and Gr\"obner bases. Finally, we introduce generalised reduction operators relative to non total ordered sets. \\ ( https://arxiv.org/abs/1605.00174 , 23kb)  \\ arXiv:1605.00138 Date: Sat, 30 Apr 2016 17:08:50 GMT (55kb)
Title: Introduction to Walgebras and their representation theory Authors: Tomoyuki Arakawa Categories: math.RT mathph math.MP math.QA \\ These are lecture notes from author's minicourse during Session 1: "Vertex algebras, Walgebras, and application" of INdAM Intensive research period "Perspectives in Lie Theory", at the Centro di Ricerca Matematica Ennio De Giorgi, Pisa, Italy. December 9, 2014  February 28, 2015. \\ ( https://arxiv.org/abs/1605.00138 , 55kb)  \\ arXiv:1605.00192 Date: Sun, 1 May 2016 00:44:51 GMT (35kb)
Title: Tau Functions, Birkhoff Factorizations & Difference Equations Authors: Darlayne Addabbo and Maarten Bergvelt Categories: math.RT Comments: 51 pages \\ $Q$systems and $T$systems are integrable difference equations that recently have attracted much attention, and have wide applications in representation theory and statistical mechanics. We show that certain $\tau$functions, given as matrix elements of the action of the loop group of $\mathbf{GL}_{2}$ on two component Fermionic Fock space, give solutions of $Q$systems. An obvious generalization using the loop group of $\mathbf{GL}_{3}$ acting on three component Fermionic Fock space leads to a new system of 4 difference equations, with hopefully also interesting applications. \\ ( https://arxiv.org/abs/1605.00192 , 35kb)  \\ arXiv:1605.00228 Date: Sun, 1 May 2016 10:04:31 GMT (26kb)
Title: On the functor of Arakawa, Suzuki and Tsuchiya Authors: Sergey Khoroshkin, Maxim Nazarov Categories: math.RT math.QA Comments: 22 pages \\ Arakawa, Suzuki and Tsuchiya constructed a correspondence between certain modules of the trigonometric Cherednik algebra $\mathfrak{C}_N$ depending on a parameter $\kappa\in\mathbb{C}$, and certain modules of the affine Lie algebra $\widehat{\mathfrak{sl}}_m$ of level $\kappam$. We give a detailed proof of this correspondence by working with the affine Lie algebra $\widehat{\mathfrak{gl}}_m$ alongside of $\widehat{\mathfrak{sl}}_m$. We also relate this construction to a correspondence between certain modules of the degenerate affine Hecke algebra $\mathfrak{H}_N$ and all modules of $\mathfrak{sl}_m$ or $\mathfrak{gl}_m$. The latter correspondence was constructed earlier by Cherednik. \\ ( https://arxiv.org/abs/1605.00228 , 26kb)  \\ arXiv:1605.00229 Date: Sun, 1 May 2016 10:04:36 GMT (33kb)
Title: Cherednik algebras and Zhelobenko operators Authors: Sergey Khoroshkin, Maxim Nazarov Categories: math.RT math.QA Comments: 26 pages \\ We study canonical intertwining operators between modules of the trigonometric Cherednik algebra, induced from the standard modules of the degenerate affine Hecke algebra. We show that these operators correspond to the Zhelobenko operators for the affine Lie algebra $\widehat{\mathfrak{sl}}_m$. To establish the correspondence, we use the functor of Arakawa, Suzuki and Tsuchiya which maps certain $\widehat{\mathfrak{sl}}_m$modules to modules of the Cherednik algebra. \\ ( https://arxiv.org/abs/1605.00229 , 33kb)  \\ arXiv:1605.00242 Date: Sun, 1 May 2016 11:56:23 GMT (23kb)
Title: Hall algebras and quantum groups associated to Dynkin quivers Authors: Yun Gao, Limeng Xia Categories: math.RT math.QA \\ For Dynkin quivers, we find the Laurent polynomials $\widetilde{X}_{a, c}^{b}(v)$ and use $\widetilde{X}_{a, c}^{b}(v)$ to construct the Hall algebra $\hc_v(\cc(\cp))$ over $\mz[v, v^{1}]$, where $\widetilde{X}_{a, c}^{b}(\mf_q)$'s are structure constants used by Bridgeland. The Laurent polynomials $\widetilde{X}_{a, c}^{b}(v)$ are explicitly given in $A_1$ case. As an application, we obtain the full quantum groups $U_t(\sg)$ associated to the Dynkin quivers for arbitrary $t\not=0,\pm1$. \\ ( https://arxiv.org/abs/1605.00242 , 23kb)  \\ arXiv:1605.00262 Date: Sun, 1 May 2016 15:05:26 GMT (11kb)
Title: A note on the freeness of spherical Hecke modules of unramified $U(2,1)$ Authors: Peng Xu Categories: math.RT Comments: 11 pages, comments are welcome \\ Let $G$ be the unramified $U(2,1) (E/F)$ and $K$ be a maximal compact open subgroup of $G$. For an irreducible smooth representation $\sigma$ of $K$ over $\overline{\mathbf{F}}_p$, under a technical assumption we show the compactly induced representation $\text{ind}^G _K \sigma$ is free over the spherical Hecke algebra $\mathcal{H}(K, \sigma)$, and such an assumption is verified when $\sigma$ is either $\chi\circ \text{det}$ or $\chi\circ \text{det}\otimes St$. \\ ( https://arxiv.org/abs/1605.00262 , 11kb)  \\ arXiv:1605.00417 Date: Mon, 2 May 2016 10:18:31 GMT (26kb)
Title: Degree cones and monomial bases of Lie algebras and quantum groups Authors: Teodor Backhaus, Xin Fang and Ghislain Fourier Categories: math.RT math.QA Comments: 26 pages, no figure \\ We provide $\mathbb{N}$filtrations on the negative part $U_q(\mathfrak{n}^)$ of the quantum group associated to a finitedimensional simple Lie algebra $\mathfrak{g}$, such that the associated graded algebra is a skewpolynomial algebra on $\mathfrak{n}^$. The filtration is obtained by assigning degrees to Lusztig's quantum PBW root vectors. The possible degrees can be described as lattice points in certain polyhedral cones. In the classical limit, such a degree induces an $\mathbb{N}$filtration on any finite dimensional simple $\mathfrak{g}$module. We prove for type $\tt{A}_n$, $\tt{C}_n$, $\tt{B}_3$, $\tt{D}_4$ and $\tt{G}_2$ that a degree can be chosen such that the associated graded modules are defined by monomial ideals, and conjecture that this is true for any $\mathfrak{g}$. \\ ( https://arxiv.org/abs/1605.00417 , 26kb)  \\ arXiv:1605.00592 Date: Mon, 2 May 2016 18:11:17 GMT (40kb)
Title: Deformations of symplectic singularities and Orbit method for semisimple Lie algebras Authors: Ivan Losev Categories: math.RT math.AG math.QA Comments: 29 pages MSCclass: 16S80, 17B35 \\ We classify filtered quantizations of conical symplectic singularities and use this to show that all filtered quantizations of symplectic quotient singularities are spherical Symplectic reflection algebras of Etingof and Ginzburg. We further apply our classification and a classification of filtered Poisson deformations obtained by Namikawa to establish a version of the Orbit method for semisimple Lie algebras. Namely, we produce a natural map from the set of adjoint orbits in a semisimple Lie algebra to the set of primitive ideals in the universal enveloping algebra. We show that the map is injective for classical Lie algebras. \\ ( https://arxiv.org/abs/1605.00592 , 40kb)  \\ arXiv:1605.00577 Date: Mon, 2 May 2016 17:40:12 GMT (19kb)
Title: Notes on exploded manifolds and a tropical gluing formula for GromovWItten invariants Authors: Brett Parker Categories: math.SG math.AG math.DG Comments: 17 pages \\ Notes for a short lecture series, covering exploded manifolds, the moduli stack of curves in exploded manifolds, and a tropical gluing formula for GromovWitten invariants which gives a degeneration formula for GromovWitten invariants in normal crossing degenerations. I gave the original lecture series in April 2016 at the Simons Center for Geometry and Physics at Stonybrook. Video of the lectures is available on the SCGP website at http://scgp.stonybrook.edu/video_portal/video.php?id=2595 \\ ( https://arxiv.org/abs/1605.00577 , 19kb)  \\ arXiv:1605.00393 Date: Mon, 2 May 2016 08:49:11 GMT (25kb)
Title: Spectral analysis of two doubly infinite Jacobi matrices with exponential entries Authors: Mourad E. H. Ismail, Franti\v{s}ek \v{S}tampach Categories: math.SP Comments: 22 pages, preprint MSCclass: 47B36, 33D90 \\ We provide a complete spectral analysis of all selfadjoint operators acting on $\ell^{2}(\mathbb{Z})$ which are associated with two doubly infinite Jacobi matrices with entries given by $$ q^{n+1}\delta_{m,n1}+q^{n}\delta_{m,n+1} $$ and $$ \delta_{m,n1}+\alpha q^{n}\delta_{m,n}+\delta_{m,n+1}, $$ respectively, where $q\in(0,1)$ and $\alpha\in\mathbb{R}$. As an application, we derive orthogonality relations for the Ramanujan entire function and the third Jackson $q$Bessel function. \\ ( https://arxiv.org/abs/1605.00393 , 25kb)  \\ arXiv:1605.00157 Date: Sat, 30 Apr 2016 19:58:57 GMT (365kb,D)
Title: Empirical Likelihood Ratio Test with Distribution Function Constraints Authors: Yingxi Liu and Ahmed Tewfik Categories: math.ST stat.TH Journalref: IEEE Transactions on Signal Processing, vol. 61, no. 18, pp. 44634472, Sept.15, 2013 DOI: 10.1109/TSP.2013.2271484 \\ In this work, we study nonparametric hypothesis testing problem with distribution function constraints. The empirical likelihood ratio test has been widely used in testing problems with moment (in)equality constraints. However, some detection problems cannot be described using moment (in)equalities. We propose a distribution function constraint along with an empirical likelihood ratio test. This detector is applicable to a wide variety of robust parametric/nonparametric detection problems. Since the distribution function constraints provide a more exact description of the null hypothesis, the test outperforms the empirical likelihood ratio test with moment constraints as well as many popular goodnessoffit tests, such as the robust KolmogorovSmirnov test and the Cram\'ervon Mises test. Examples from communication systems with realworld noise samples are provided to show their performance. Specifically, the proposed test significantly outperforms the robust KolmogorovSmirnov test and the Cram\'ervon Mises test when the null hypothesis is nested in the alternative hypothesis. The same example is repeated when we assume no noise uncertainty. By doing so, we are able to claim that in our case, it is necessary to include uncertainty in noise distribution. Additionally, the asymptotic optimality of the proposed test is provided. \\ ( https://arxiv.org/abs/1605.00157 , 365kb)  \\ arXiv:1605.00189 Date: Sun, 1 May 2016 00:37:02 GMT (599kb,D)
Title: The Shapes of Things to Come: Probability Density Quantiles Authors: Robert G. Staudte Categories: math.ST stat.TH Comments: 23 pages, 10 figures, 4 tables \\ For every discrete or continuous locationscale family having a squareintegrable density, there is a unique continuous probability distribution on the unit interval that is determined by the densityquantile composition introduced by Parzen in 1979. These probability density quantiles (pdQs) only differ in shape, and any two of them can be compared with the Hellinger distance or KullbackLeibler divergences. In particular the Hellinger distance or rootdivergences of pdQs from the class of symmetric distributions on the unit interval are shown to be roughly proportional to the classical third moment skewness coefficient of the pdQ. Further, a more precise classification of shapes by tail behavior is defined in terms of limiting pdQ derivatives at 0 and 1. Convergent empirical estimates of these pdQ s are provided. Finally, divergence from, and convergence to, uniformity is investigated. \\ ( https://arxiv.org/abs/1605.00189 , 599kb)  \\ arXiv:1605.00265 Date: Sun, 1 May 2016 15:31:55 GMT (10kb)
Title: On the feasibility of semialgebraic sets in Poisson regression Authors: Thomas Kahle Categories: math.ST math.OC stat.TH Comments: Extended abstract for ICMS 2016 in Berlin. 6 pages MSCclass: 62K05, 14P10, 62J02 \\ Designing experiments for generalized linear models is difficult because optimal designs depend on unknown parameters. The local optimality approach is to study the regions in parameter space where a given design is optimal. In many situations these regions are semialgebraic. We investigate regions of optimality using computer tools such as yalmip, qepcad, and Mathematica. \\ ( https://arxiv.org/abs/1605.00265 , 10kb)  \\ arXiv:1605.00353 Date: Mon, 2 May 2016 04:47:43 GMT (54kb,D)
Title: RateOptimal Perturbation Bounds for Singular Subspaces with Applications to HighDimensional Statistics Authors: T. Tony Cai and Anru Zhang Categories: math.ST math.PR stat.ME stat.TH \\ Perturbation bounds for singular spaces, in particular Wedin's $\sin \Theta$ theorem, are a fundamental tool in many fields including highdimensional statistics, machine learning, and applied mathematics. In this paper, we establish separate perturbation bounds, measured in both spectral and Frobenius $\sin \Theta$ distances, for the left and right singular subspaces. Lower bounds, which show that the individual perturbation bounds are rateoptimal, are also given. The new perturbation bounds are applicable to a wide range of problems. In this paper, we consider in detail applications to lowrank matrix denoising and singular space estimation, highdimensional clustering, and canonical correlation analysis (CCA). In particular, separate matching upper and lower bounds are obtained for estimating the left and right singular spaces. To the best of our knowledge, this is the first result that gives different optimal rates for the left and right singular spaces under the same perturbation. In addition to these problems, applications to other highdimensional problems such as community detection in bipartite networks, multidimensional scaling, and crosscovariance matrix estimation are also discussed. \\ ( https://arxiv.org/abs/1605.00353 , 54kb)  \\ arXiv:1605.00533 Date: Mon, 2 May 2016 15:40:25 GMT (21kb)
Title: Real time changepoint detection in a nonlinear quantile model Authors: Gabriela Ciuperca Categories: math.ST stat.ME stat.TH \\ Most studies in real time changepoint detection either focus on the linear model or use the CUSUM method under classical assumptions on model errors. This paper considers the sequential changepoint detection in a nonlinear quantile model. A test statistic based on the CUSUM of the quantile process subgradient is proposed and studied. Under null hypothesis that the model does not change, the asymptotic distribution of the test statistic is determined. Under alternative hypothesis that at some unknown observation there is a change in model, the proposed test statistic converges in probability to $\infty$. These results allow to build the critical regions on openend and on closedend procedures. Simulation results, using Monte Carlo technique, investigate the performance of the test statistic, specially for heavytailed error distributions. We also compare it with the classical CUSUM test statistic. \\ ( https://arxiv.org/abs/1605.00533 , 21kb) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  \\ arXiv:1605.00562 (*crosslisting*) Date: Mon, 2 May 2016 16:49:36 GMT (4285kb,D)
Title: Persistent homology of timedependent functional networks constructed from coupled time series Authors: Bernadette J. Stolz, Heather A. Harrington and Mason A. Porter Categories: qbio.QM math.AT \\ We use topological data analysis to study "functional networks" that we construct from timeseries data from both experimental and synthetic sources. Specifically, we use persistent homology in combination with a weight rank clique filtration to gain insights into these functional networks, and we use persistence landscapes to interpret our results. Our first example consists of biological data in the form of functional magnetic resonance imaging (fMRI) data that was acquired from human subjects during a simple motorlearning task. Our second example uses timeseries output from networks of coupled Kuramoto oscillators. With these examples, we demonstrate that (1) using persistent homology to study functional networks provides fascinating insights into their properties and (2) the position of the features in a filtration can play a more vital role than persistence in the interpretation of topological features, even though the latter is used more commonly to distinguish between signal and noise. We find that in particular, persistent homology can detect differences in synchronisation patterns in our data sets over time giving insight on changes in community structure in the networks, and on increased synchronisation between brain regions forming loops in the functional network during motorlearning. For the motorlearning data we also observe that persistence landscapes reveal that the majority of changes in the loops of the network takes place on the second of three days of the learning process. \\ ( https://arxiv.org/abs/1605.00562 , 4285kb)  \\ arXiv:1605.00402 (*crosslisting*) Date: Mon, 2 May 2016 09:28:32 GMT (21kb)
Title: SymbolicNumeric Tools for Analytic Combinatorics in Several Variables Authors: Stephen Melczer and Bruno Salvy Categories: cs.SC math.CO Comments: As accepted to proceedings of ISSAC 2016 DOI: 10.1145/2930889.2930913 \\ Analytic combinatorics studies the asymptotic behaviour of sequences through the analytic properties of their generating functions. This article provides effective algorithms required for the study of analytic combinatorics in several variables, together with their complexity analyses. Given a multivariate rational function we show how to compute its smooth isolated critical points, with respect to a polynomial map encoding asymptotic behaviour, in complexity singly exponential in the degree of its denominator. We introduce a numerical Kronecker representation for solutions of polynomial systems with rational coefficients and show that it can be used to decide several properties (0 coordinate, equal coordinates, sign conditions for real solutions, and vanishing of a polynomial) in good bit complexity. Among the critical points, those that are minimala property governed by inequalities on the moduli of the coordinatestypically determine the dominant asymptotics of the diagonal coefficient sequence. When the Taylor expansion at the origin has all nonnegative coefficients (known as the `combinatorial case') and under regularity conditions, we utilize this Kronecker representation to determine probabilistically the minimal critical points in complexity singly exponential in the degree of the denominator, with good control over the exponent in the bit complexity estimate. Generically in the combinatorial case, this allows one to automatically and rigorously determine asymptotics for the diagonal coefficient sequence. Examples obtained with a preliminary implementation show the wide applicability of this approach. \\ ( https://arxiv.org/abs/1605.00402 , 21kb)  \\ arXiv:1605.00198 (*crosslisting*) Date: Sun, 1 May 2016 02:42:16 GMT (320kb,D)
Title: Delocalized Epidemics on Graphs: A Maximum Entropy Approach Authors: Faryad Darabi Sahneh, Aram Vajdi, Caterina Scoglio Categories: physics.socph cs.SI math.DS Comments: 6 pages, 5 figures, American Control Conference2016 \\ The susceptibleinfectedsusceptible (SIS) epidemic process on complex networks can show metastability, resembling an endemic equilibrium. In a general setting, the metastable state may involve a large portion of the network, or it can be localized on small subgraphs of the contact network. Localized infections are not interesting because a true outbreak concerns networkwide invasion of the contact graph rather than localized infection of certain sites within the contact network. Existing approaches to localization phenomenon suffer from a major drawback: they fully rely on the steadystate solution of meanfield approximate models in the neighborhood of their phase transition point, where their approximation accuracy is worst; as statistical physics tells us. We propose a dispersion entropy measure that quantifies the localization of infections in a generic contact graph. Formulating a maximum entropy problem, we find an upper bound for the dispersion entropy of the possible metastable state in the exact SIS process. As a result, we find sufficient conditions such that any initial infection over the network either dies out or reaches a localized metastable state. Unlike existing studies relying on the solution of meanfield approximate models, our investigation of epidemic localization is based on characteristics of exact SIS equations. Our proposed method offers a new paradigm in studying spreading processes over complex networks. \\ ( https://arxiv.org/abs/1605.00198 , 320kb)  \\ arXiv:1605.00031 (*crosslisting*) Date: Fri, 29 Apr 2016 21:40:16 GMT (157kb,D)
Title: Deep Convolutional Neural Networks on Cartoon Functions Authors: Philipp Grohs, Thomas Wiatowski, Helmut B\"olcskei Categories: cs.IT cs.AI cs.CV math.FA math.IT stat.ML Comments: IEEE International Symposium on Information Theory (ISIT), Barcelona, Spain, July 2016 \\ Wiatowski and B\"olcskei, 2015, proved that deformation stability and vertical translation invariance of deep convolutional neural networkbased feature extractors are guaranteed by the network structure per se rather than the specific convolution kernels and nonlinearities. While the translation invariance result applies to squareintegrable functions, the deformation stability bound holds for bandlimited functions only. Many signals of practical relevance (such as natural images) exhibit, however, sharp and curved discontinuities and are hence not bandlimited. The main contribution of this paper is a deformation stability result that takes these structural properties into account. Specifically, we establish deformation stability bounds for the class of cartoon functions introduced by Donoho, 2001. \\ ( https://arxiv.org/abs/1605.00031 , 157kb)  \\ arXiv:1605.00237 (*crosslisting*) Date: Thu, 28 Apr 2016 17:52:06 GMT (13kb)
Title: Stora's fine notion of divergent amplitudes Authors: Joseph C. V\'arilly and Jos\'e M. GraciaBond\'ia Categories: mathph hepth math.FA math.MP Comments: 10 pages, no figures. Contribution to Mathematical Foundations of Quantum Field Theory, special issue in memory of Raymond Stora, Nucl. Phys. B \\ Stora and coworkers refined the notion of divergent quantum amplitude, somewhat upsetting the standard powercounting recipe. This unexpectedly clears the way to new prototypes for free and interacting field theories of bosons of any mass and spin. \\ ( https://arxiv.org/abs/1605.00237 , 13kb)  \\ arXiv:1605.00127 (*crosslisting*) Date: Sat, 30 Apr 2016 15:41:18 GMT (100kb,D)
Title: Holographic Software for Quantum Networks Authors: Arthur Jaffe, Zhengwei Liu, and Alex Wozniakowski Categories: quantph hepth mathph math.MP \\ We introduce diagrammatic protocols and holographic software for quantum information. We give a dictionary to translate between diagrammatic protocols and the usual algebraic protocols. In particular we describe the intuitive diagrammatic protocol for teleportation. We introduce the string Fourier transform $\mathfrak{F}_{s}$ in quantum information, which gives a topological quantum computer. We explain why the string Fourier transform maps the zero particle state to the multiplequdit resource state, which maximizes the entanglement entropy. We give a protocol to construct this $n$qudit resource state $Max \rangle$, which uses minimal cost. We study Pauli $X,Y,Z$ matrices, and their relation with diagrammatic protocols. This work provides bridges between the new theory of planar para algebras and quantum information, especially in questions involving communication in quantum networks. \\ ( https://arxiv.org/abs/1605.00127 , 100kb)  \\ arXiv:1605.00222 (*crosslisting*) Date: Sun, 1 May 2016 08:54:48 GMT (77kb,D)
Title: Twoparticle atomic coalescences: Boundary conditions for the Fock coefficient components Authors: Evgeny Z. Liverts Categories: physics.atomph mathph math.MP physics.compph Comments: 26 pages, 2 figures \\ The exact values of the presently determined components 26of the angular Fock coefficients at the twoparticle coalescences were obtained and systematized. The Green Function approach was successfully applied to simplify the most complicated calculations. The boundary conditions for the Fock coefficient components in the hyperspherical angular coordinates, which follows from the Kato cusp conditions for the twoelectron wave function in the natural interparticle coordinates, were derived. The validity of the obtained boundary conditions was verified on examples of all the presently determined components. The additional boundary conditions are not arising from the Kato cusp conditions were obtained as well. The Wolfram Mathematica was used intensively. \\ ( https://arxiv.org/abs/1605.00222 , 77kb)  \\ arXiv:1605.00231 (*crosslisting*) Date: Sun, 1 May 2016 10:18:22 GMT (23kb)
Title: Conformal and projective symmetries in Newtonian cosmology Authors: Christian Duval (CPT), Gary Gibbons (DAMTP/CMS), Peter Horvathy Categories: grqc hepth mathph math.MP Comments: LaTeX, 25 pages \\ Definitions of nonrelativistic conformal transformations are considered both in the NewtonCartan and in the KaluzaKleintype Eisenhart/Bargmann geometrical frameworks. The symmetry groups that come into play are exemplified by the cosmological, and also the NewtonHooke solutions of Newton's gravitational field equations. It is shown, in particular, that the maximal symmetry group of the standard cosmological model is isomorphic to the 13dimensional conformalNewtonCartan group whose conformalBargmann extension is explicitly worked out. Attention is drawn to the appearance of independent space and time dilations, it contrast with the Schr{\"o}dinger group or the Conformal Galilei Algebra. \\ ( https://arxiv.org/abs/1605.00231 , 23kb)  \\ arXiv:1605.00321 (*crosslisting*) Date: Sun, 1 May 2016 23:34:38 GMT (64kb,D)
Title: Compressed Teleportation Authors: Arthur Jaffe, Zhengwei Liu, and Alex Wozniakowski Categories: quantph hepth mathph math.MP Comments: 3 pages \\ In a previous paper we introduced holographic software for quantum networks, inspired by work on planar para algebras. This software suggests the definition of a compressed transformation. Here we utilize the software to find a CT protocol to teleport compressed transformations. This protocol serves multiple parties with multiple persons. \\ ( https://arxiv.org/abs/1605.00321 , 64kb)  \\ arXiv:1605.00326 (*crosslisting*) Date: Mon, 2 May 2016 00:17:13 GMT (22kb)
Title: BransDicke Galileon and the Variational Principle Authors: Israel Quiros, Ricardo Garc\'iaSalcedo, Tame Gonzalez, F. Antonio HortaRangel, Joel Saavedra Categories: grqc mathph math.MP Comments: 20 pages, no figures. The content of this paper is specially recommended to those graduate and postgraduate students who are interested in the study of modifications of general relativity such as scalartensor and $f(R)$ theories \\ This paper is aimed at a (mostly) pedagogical exposition of the derivation of the motion equations of certain modifications of general relativity. Here we derive in all detail the motion equations in the BransDicke theory with the cubic selfinteraction. This is a modification of the Bransdicke theory by the addition of a term in the Lagrangian which is nonlinear in the derivatives of the scalar field: it contains secondorder derivatives. This is the basis of the socalled BransDicke Galileon. We pay special attention to the variational principle and to the algebraic details of the derivation. It is shown how higher order derivatives of the fields appearing in the intermediate computations cancel out leading to second order motion equations. The reader will find useful tips for the derivation of the field equations of modifications of general relativity such as the scalartensor theories and $f(R)$ theories, by means of the (stationary action) variational principle. The content of this paper is specially recommended to those graduate and postgraduate students who are interested in the study of the mentioned modifications of general relativity. \\ ( https://arxiv.org/abs/1605.00326 , 22kb)  \\ arXiv:1605.00441 (*crosslisting*) Date: Mon, 2 May 2016 11:42:13 GMT (819kb,D)
Title: Gaussian States Minimize the Output Entropy of the OneMode Quantum Attenuator Authors: Giacomo De Palma, Dario Trevisan and Vittorio Giovannetti Categories: quantph cs.IT mathph math.IT math.MP math.PR \\ We prove that Gaussian thermal input states minimize the output von Neumann entropy of the onemode Gaussian quantumlimited attenuator for fixed input entropy. The Gaussian quantumlimited attenuator models the attenuation of an electromagnetic signal in the quantum regime. The Shannon entropy of an attenuated realvalued classical signal is a simple function of the entropy of the original signal. A striking consequence of energy quantization is that the output von Neumann entropy of the quantumlimited attenuator is no more a function of the input entropy alone. The proof starts from the majorization result of De Palma et al., IEEE Trans. Inf. Theory 62, 2895 (2016), and is based on a new isoperimetric inequality. Our result implies that geometric input probability distributions minimize the output Shannon entropy of the thinning for fixed input entropy. Moreover, our result opens the way to the multimode generalization, that permits to determine both the triple tradeoff region of the Gaussian quantumlimited attenuator and the classical capacity region of the Gaussian degraded quantum broadcast channel. \\ ( https://arxiv.org/abs/1605.00441 , 819kb)  \\ arXiv:1605.00597 (*crosslisting*) Date: Mon, 2 May 2016 18:14:59 GMT (948kb,D)
Title: QuasiLongRange Order in Trapped 2D Bose Gases Authors: Igor Boettcher, Markus Holzmann Categories: condmat.quantgas condmat.statmech hepph mathph math.MP Comments: 6 pages + supplemental material \\ We study the fate of algebraic decay of correlations in a harmonically trapped twodimensional degenerate Bose gas. The analysis is inspired by recent experiments on ultracold atoms where powerlaw correlations have been observed despite the presence of the external potential. We generalize the spin wave description of phase fluctuations to the trapped case and obtain an analytical expression for the onebody density matrix within this approximation. We show that algebraic decay of the central correlation function persists to lengths of about 20% of the ThomasFermi radius. We establish that the trapaveraged correlation function decays algebraically with a strictly larger exponent weakly changing with trap size and find indications that the recently observed enhanced scaling exponents receive significant contributions from the normal component of the gas. We discuss radial and angular correlations and propose a local correlation approximation which captures the correlations very well. Our analysis goes beyond the usual local density approximation and the developed summation techniques constitute a powerful tool to investigate correlations in inhomogeneous systems. \\ ( https://arxiv.org/abs/1605.00597 , 948kb)  \\ arXiv:1605.00492 (*crosslisting*) Date: Mon, 2 May 2016 14:06:24 GMT (506kb,D)
Title: High level implementation of geometric multigrid solvers for finite element problems: applications in atmospheric modelling Authors: Lawrence Mitchell and Eike Hermann M\"uller Categories: cs.MS math.NA physics.fludyn Comments: 21 pages, 5 figures, 8 tables. Submitted to JCP MSCclass: 65F08, 65N55, 76M10, 86A10 ACMclass: D.2.2; G.1.3; G.1.8; G.4; J.2 \\ The implementation of efficient multigrid preconditioners for elliptic partial differential equations (PDEs) is a challenge due to the complexity of the resulting algorithms and corresponding computer code. For sophisticated finite element discretisations on unstructured grids an efficient implementation can be very time consuming and requires the programmer to have indepth knowledge of the mathematical theory, parallel computing and optimisation techniques on manycore CPUs. In this paper we show how the development of bespoke multigrid preconditioners can be simplified significantly by using a framework which allows the expression of the each component of the algorithm at the correct abstraction level. Our approach (1) allows the expression of the finite element problem in a language which is close to the mathematical formulation of the problem, (2) guarantees the automatic generation and efficient execution of parallel optimised lowlevel computer code and (3) is flexible enough to support different abstraction levels and give the programmer control over details of the preconditioner. We use the composable abstractions of the Firedrake/PyOP2 package to demonstrate the efficiency of this approach for the solution of strongly anisotropic PDEs in atmospheric modelling. The weak formulation of the PDE is expressed in Unified Form Language (UFL) and the lower PyOP2 abstraction layer allows the manual design of computational kernels for a bespoke geometric multigrid preconditioner. We compare the performance of this preconditioner to a singlelevel method and hypre's BoomerAMG algorithm. The Firedrake/PyOP2 code is inherently parallel and we present a detailled performance analysis for a single node (24 cores) on the ARCHER supercomputer. Our implementation utilises a significant fraction of the available memory bandwidth and shows very good weak scaling on up to 6,144 compute cores. \\ ( https://arxiv.org/abs/1605.00492 , 506kb)  \\ arXiv:1605.00609 (*crosslisting*) Date: Mon, 2 May 2016 18:32:19 GMT (283kb,D)
Title: Algorithms for Learning Sparse Additive Models with Interactions in High Dimensions Authors: Hemant Tyagi, Anastasios Kyrillidis, Bernd G\"artner, Andreas Krause Categories: cs.LG cs.IT math.IT math.NA stat.ML Comments: 45 pages, 6 figures, preliminary version of this paper to appear in proceedings of AISTATS 2016 (available here: arxiv.org/abs/1604.05307). arXiv admin note: text overlap with arXiv:1604.05307 \\ A function $f: \mathbb{R}^d \rightarrow \mathbb{R}$ is a Sparse Additive Model (SPAM), if it is of the form $f(\mathbf{x}) = \sum_{l \in \mathcal{S}}\phi_{l}(x_l)$ where $\mathcal{S} \subset [d]$, $\mathcal{S} \ll d$. Assuming $\phi$'s, $\mathcal{S}$ to be unknown, there exists extensive work for estimating $f$ from its samples. In this work, we consider a generalized version of SPAMs, that also allows for the presence of a sparse number of second order interaction terms. For some $\mathcal{S}_1 \subset [d], \mathcal{S}_2 \subset {[d] \choose 2}$, with $\mathcal{S}_1 \ll d, \mathcal{S}_2 \ll d^2$, the function $f$ is now assumed to be of the form: $\sum_{p \in \mathcal{S}_1}\phi_{p} (x_p) + \sum_{(l,l^{\prime}) \in \mathcal{S}_2}\phi_{(l,l^{\prime})} (x_l,x_{l^{\prime}})$. Assuming we have the freedom to query $f$ anywhere in its domain, we derive efficient algorithms that provably recover $\mathcal{S}_1,\mathcal{S}_2$ with finite sample bounds. Our analysis covers the noiseless setting where exact samples of $f$ are obtained, and also extends to the noisy setting where the queries are corrupted with noise. For the noisy setting in particular, we consider two noise models namely: i.i.d Gaussian noise and arbitrary but bounded noise. Our main methods for identification of $\mathcal{S}_2$ essentially rely on estimation of sparse Hessian matrices, for which we provide two novel compressed sensing based schemes. Once $\mathcal{S}_1, \mathcal{S}_2$ are known, we show how the individual components $\phi_p$, $\phi_{(l,l^{\prime})}$ can be estimated via additional queries of $f$, with uniform error bounds. Lastly, we provide simulation results on synthetic data that validate our theoretical findings. \\ ( https://arxiv.org/abs/1605.00609 , 283kb)  \\ arXiv:1605.00092 (*crosslisting*) Date: Sat, 30 Apr 2016 11:04:12 GMT (7kb)
Title: Discriminators and kRegular Sequences Authors: Sajed Haque and Jeffrey Shallit Categories: cs.DM cs.FL math.NT \\ The discriminator of an integer sequence s = (s(i))_{i >=1}, introduced by Arnold, Benkoski, and McCabe in 1985, is the map D_s(n) that sends n to the least integer m such that the numbers s(0), s(1),... , s(n1) are pairwise incongruent modulo m. In this note we consider the discriminators of a certain class of sequences, the kregular sequences. We compute the discriminators of two such sequences, the socalled "evil" and "odious" numbers, and show they are 2regular. We also give an example of a kregular sequence whose discriminator is not kregular. \\ ( https://arxiv.org/abs/1605.00092 , 7kb)  \\ arXiv:1605.00322 (*crosslisting*) Date: Sun, 1 May 2016 23:36:48 GMT (95kb)
Title: Adaptive Modulation in Networkcoded Twoway Relay Channel: A Supermodular Game Approach Authors: Ni Ding, Parastoo Sadeghi and Rodney A. Kennedy Categories: cs.IT cs.SY math.IT math.OC Comments: 10 figures \\ We study the adaptive modulation (AM) problem in a networkcoded twoway relay channel (NCTWRC), where each of the two users controls its own bit rate in the $m$ary quadrature amplitude modulation ($m$QAM) to minimize the transmission error rate and enhance the spectral efficiency. We show that there exists a strategic complementarity, one user tends to transmit while the other decides to do so in order to enhance the overall spectral efficiency, which is beyond the scope of the conventional singleagent AM scheduling method. We propose a twoplayer game model parameterized by the signaltonoise ratios (SNRs) of two usertouser channels and prove that it is a supermodular game where there always exist the extremal pure strategy Nash equilibria (PSNEs), the largest and smallest PSNEs. We show by simulation results that the extremal PSNEs incur a similar bit error rate (BER) as the conventional singleagent AM scheme, but significantly improve the spectral efficiency in the NCTWRC system. The study also reveals the Pareto order of the extremal PSNEs: The largest and smallest PSNEs are Pareto worst and best PSNEs, respectively. Finally, we derive the sufficient conditions for the extremal PSNEs to be symmetric and monotonic in channel SNRs. We also discuss how to utilize the symmetry and monotonicity to relieve the complexity in the PSNE learning process. \\ ( https://arxiv.org/abs/1605.00322 , 95kb)  \\ arXiv:1605.00086 (*crosslisting*) Date: Sat, 30 Apr 2016 09:35:18 GMT (436kb)
Title: Fractional Brownian motion timechanged by gamma and inverse gamma process Authors: A. Kumar, A. Wy{\l}oma\'nska, R. Po{\l}ocza\'nski, S. Sundar Categories: physics.dataan math.PR \\ Many real timeseries exhibit behavior adequate to long range dependent data. Additionally very often these timeseries have constant time periods and also have characteristics similar to Gaussian processes although they are not Gaussian. Therefore there is need to consider new classes of systems to model these kind of empirical behavior. Motivated by this fact in this paper we analyze two processes which exhibit long range dependence property and have additional interesting characteristics which may be observed in real phenomena. Both of them are constructed as the superposition of fractional Brownian motion (FBM) and other process. In the first case the internal process, which plays role of the time, is the gamma process while in the second case the internal process is its inverse. We present in detail their main properties paying main attention to the long range dependence property. Moreover, we show how to simulate these processes and estimate their parameters. We propose to use a novel method based on rescaled modified cumulative distribution function for estimation of parameters of the second considered process. This method is very useful in description of rounded data, like waiting times of subordinated processes delayed by inverse subordinators. By using the Monte Carlo method we show the effectiveness of proposed estimation procedures. \\ ( https://arxiv.org/abs/1605.00086 , 436kb)  \\ arXiv:1605.00155 (*crosslisting*) Date: Sat, 30 Apr 2016 19:49:20 GMT (313kb,D)
Title: Kernel Balancing: A flexible nonparametric weighting procedure for estimating causal effects Authors: Chad Hazlett Categories: stat.ME math.ST stat.AP stat.ML stat.TH Comments: Work originally included in PhD Thesis, May 2014, MIT \\ In the absence of unobserved confounders, matching and weighting methods are widely used to estimate causal quantities including the Average Treatment Effect on the Treated (ATT). Unfortunately, these methods do not necessarily achieve their goal of making the multivariate distribution of covariates for the control group identical to that of the treated, leaving some (potentially multivariate) functions of the covariates with different means between the two groups. When these "imbalanced" functions influence the nontreatment potential outcome, the conditioning on observed covariates fails, and ATT estimates may be biased. Kernel balancing, introduced here, targets a weaker requirement for unbiased ATT estimation, specifically, that the expected nontreatment potential outcome for the treatment and control groups are equal. The conditional expectation of the nontreatment potential outcome is assumed to fall in the space of functions associated with a choice of kernel, implying a set of basis functions in which this regression surface is linear. Weights are then chosen on the control units such that the treated and control group have equal means on these basis functions. As a result, the expectation of the nontreatment potential outcome must also be equal for the treated and control groups after weighting, allowing unbiased ATT estimation by subsequent difference in means or an outcome model using these weights. Moreover, the weights produced are (1) precisely those that equalize a particular kernelbased approximation of the multivariate distribution of covariates for the treated and control, and (2) equivalent to a form of stabilized inverse propensity score weighting, though it does not require assuming any model of the treatment assignment mechanism. An R package, KBAL, is provided to implement this approach. \\ ( https://arxiv.org/abs/1605.00155 , 313kb)  \\ arXiv:1605.00414 (*crosslisting*) Date: Mon, 2 May 2016 10:03:00 GMT (12kb)
Title: On sampling theorem with sparse decimated samples Authors: Nikolai Dokuchaev Categories: cs.IT math.IT math.ST stat.TH Comments: arXiv admin note: text overlap with arXiv:1603.04174 MSCclass: 42A38, 93E10, 562M15, 42B30 \\ The classical sampling NyquistShannonKotelnikov theorem states that a bandlimited continuous time function is uniquely defined by infinite twosided sampling series taken with a sufficient frequency. The paper shows that these bandlimited functions allows an arbitrarily close uniform approximation by functions that are uniquely defined by their extremely sparse subsamples representing arbitrarily small fractions of onesided equidistant sample series with fixed oversampling parameter. In particular, an arbitrarily small adjustment of a bandlimited underlying function makes redundant every (m1) members of any set of m samples for an arbitrarily large m. This allows to bypass, in a certain sense, the restriction on the sampling rate defined by the critical Nyquist rate. \\ ( https://arxiv.org/abs/1605.00414 , 12kb)  \\ arXiv:1605.00499 (*crosslisting*) Date: Mon, 2 May 2016 14:18:33 GMT (1133kb,D)
Title: MCMC Confidence Sets for Identified Sets Authors: Xiaohong Chen, Timothy Christensen and Elie Tamer Categories: stat.ME math.ST stat.TH \\ In complicated/nonlinear parametric models, it is hard to determine whether a parameter of interest is formally point identified. We provide computationally attractive procedures to construct confidence sets (CSs) for identified sets of parameters in econometric models defined through a likelihood or a vector of moments. The CSs for the identified set or for a function of the identified set (such as a subvector) are based on inverting an optimal sample criterion (such as likelihood or continuously updated GMM), where the cutoff values are computed directly from Markov Chain Monte Carlo (MCMC) simulations of a quasi posterior distribution of the criterion. We establish new Bernsteinvon Mises type theorems for the posterior distributions of the quasilikelihood ratio (QLR) and profile QLR statistics in partially identified models, allowing for singularities. These results imply that the MCMC criterionbased CSs have correct frequentist coverage for the identified set as the sample size increases, and that they coincide with Bayesian credible sets based on inverting a LR statistic for pointidentified likelihood models. We also show that our MCMC optimal criterionbased CSs are uniformly valid over a class of data generating processes that include both partially and point identified models. We demonstrate good finite sample coverage properties of our proposed methods in four nontrivial simulation experiments: missing data, entry game with correlated payoff shocks, Euler equation and finite mixture models. \\ ( https://arxiv.org/abs/1605.00499 , 1133kb) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  \\ arXiv:1302.1124 replaced with revised version Sat, 30 Apr 2016 10:54:55 GMT (15kb)
Title: On the upper semicontinuity of HSL numbers Authors: Serena Murru Categories: math.AC \\ ( https://arxiv.org/abs/1302.1124 , 15kb)  \\ arXiv:1503.08496 replaced with revised version Mon, 2 May 2016 03:24:37 GMT (16kb)
Title: The Realization Problem for Delta Sets of Numerical Semigroups Authors: Stefan Colton, Nathan Kaplan Categories: math.AC math.CO Comments: 13 pages MSCclass: 20M14, 20M13, 11B75 \\ ( https://arxiv.org/abs/1503.08496 , 16kb)  \\ arXiv:1511.06473 replaced with revised version Fri, 29 Apr 2016 20:44:04 GMT (20kb)
Title: Perinormality in pullbacks Authors: Neil Epstein and Jay Shapiro Categories: math.AC Comments: Major revision. Due to an error in the main theorem of section 3 in version 1, we have reworked the notion of fragility into three potentially separate notions. There are several related new localization results. Several other things in the paper have changed a bit, most notably Corollary 2.6 (also now corrected). 18 pages, comments welcome MSCclass: 13B21, 13F05, 13F45 \\ ( https://arxiv.org/abs/1511.06473 , 20kb)  \\ arXiv:1411.1766 replaced with revised version Sat, 30 Apr 2016 15:12:25 GMT (29kb)
Title: GaussManin connection in disguise: NoetherLefschetz and Hodge loci Authors: Hossein Movasati Categories: math.AG math.AT math.CV Comments: To appear in Asian Journal of Mathematics \\ ( https://arxiv.org/abs/1411.1766 , 29kb)  \\ arXiv:1507.04582 replaced with revised version Mon, 2 May 2016 08:33:47 GMT (18kb)
Title: On rational fixed points of finite group actions on the affine space Authors: Olivier Haution Categories: math.AG \\ ( https://arxiv.org/abs/1507.04582 , 18kb)  \\ arXiv:1508.02456 replaced with revised version Sat, 30 Apr 2016 10:36:35 GMT (38kb)
Title: Foliations with positive slopes and birational stability of orbifold cotangent bundles Authors: Frederic Campana, Mihai Paun Categories: math.AG Comments: No significant changes \\ ( https://arxiv.org/abs/1508.02456 , 38kb)  \\ arXiv:1510.08222 replaced with revised version Sat, 30 Apr 2016 04:07:15 GMT (19kb)
Title: The algebraic de Rham cohomology of representation varieties Authors: Eugene Z. Xia Categories: math.AG Comments: Minor stylistic revision from version 1, 21 pages MSCclass: 13D03, 14F40, 14L24, 14Q10, 14R20 \\ ( https://arxiv.org/abs/1510.08222 , 19kb)  \\ arXiv:1512.06717 replaced with revised version Mon, 2 May 2016 09:51:55 GMT (11kb)
Title: Worst Unstable Points of a Hilbert Scheme Authors: Cheolgyu Lee Categories: math.AG Comments: Revised the description of a result of [1] in page 3. Results not changed. Corrected a typo in page 7. Added assumption on P in Theorem 5.4, which was omitted in the previous version \\ ( https://arxiv.org/abs/1512.06717 , 11kb)  \\ arXiv:1603.01748 replaced with revised version Sat, 30 Apr 2016 10:33:59 GMT (37kb)
Title: Orbifold Slope RationalConnectedness Authors: Frederic Campana, Mihai Paun Categories: math.AG Comments: no changes \\ ( https://arxiv.org/abs/1603.01748 , 37kb)  \\ arXiv:1603.03411 replaced with revised version Sat, 30 Apr 2016 22:50:38 GMT (31kb)
Title: Modified mixed realizations, new additive invariants, and periods of dg categories Authors: Goncalo Tabuada Categories: math.AG math.AC math.AT math.KT math.RT Comments: 22 pages MSCclass: 14A22, 14C15, 14F10, 16D30, 18E30 \\ ( https://arxiv.org/abs/1603.03411 , 31kb)  \\ arXiv:1603.09569 replaced with revised version Mon, 2 May 2016 02:41:15 GMT (18kb)
Title: On Jacobi Inversion Formulae for Telescopic Curves Authors: Takanori Ayano Categories: math.AG Comments: 25 pages MSCclass: 14H42, 14H50, 14H55, 14H70, 14K20, 14K25 \\ ( https://arxiv.org/abs/1603.09569 , 18kb)  \\ arXiv:1604.08417 replaced with revised version Mon, 2 May 2016 13:39:02 GMT (14kb,D)
Title: Stable rationality of cyclic covers of projective spaces Authors: Takuzo Okada Categories: math.AG Comments: 12 pages, some typos and misleading explanations fixed \\ ( https://arxiv.org/abs/1604.08417 , 14kb)  \\ arXiv:1402.2193 replaced with revised version Fri, 29 Apr 2016 21:55:51 GMT (22kb)
Title: On the Schr\"odinger equations with isotropic and anisotropic fourthorder dispersion Authors: Carlos Banquet and Elder J. VillamizarRoa Categories: math.AP MSCclass: 35Q55, 35A01, 35A02, 35C06 \\ ( https://arxiv.org/abs/1402.2193 , 22kb)  \\ arXiv:1411.6141 replaced with revised version Sun, 1 May 2016 14:00:06 GMT (23kb)
Title: On the interpolation with the potential bound for global solutions of the defocusing cubic wave equation on T2 Authors: Tristan Roy Categories: math.AP Comments: 24 pages. To appear \\ ( https://arxiv.org/abs/1411.6141 , 23kb)  \\ arXiv:1503.08962 replaced with revised version Sun, 1 May 2016 14:02:58 GMT (14kb)
Title: BKM's criterion for the 3D nematic liquid crystal flows via two velocity components and molecular orientations Authors: Jihong Zhao Categories: math.AP Comments: 16pages \\ ( https://arxiv.org/abs/1503.08962 , 14kb)  \\ arXiv:1506.07660 replaced with revised version Mon, 2 May 2016 09:54:26 GMT (3131kb,D)
Title: Uncertainty quantification for hyperbolic conservation laws with flux coefficients given by spatiotemporal random fields Authors: Andrea Barth, Franz Georg Fuchs Categories: math.AP MSCclass: 35L40, 35L65, 65C05, 65C30, 65M08 \\ ( https://arxiv.org/abs/1506.07660 , 3131kb)  \\ arXiv:1507.05885 replaced with revised version Mon, 2 May 2016 15:12:41 GMT (18kb)
Title: Regularity criterion for the 3D Hallmagnetohydrodynamics Authors: Mimi Dai Categories: math.AP Comments: Typos fixed MSCclass: 76D03, 35Q35 Journalref: Journal of Differential Equations, 261 (2016), pp. 573591 \\ ( https://arxiv.org/abs/1507.05885 , 18kb)  \\ arXiv:1508.01362 replaced with revised version Mon, 2 May 2016 13:41:00 GMT (48kb,D)
Title: Convex integration for the MongeAmp\`ere equation in two dimensions Authors: Marta Lewicka and Mohammad Reza Pakzad Categories: math.AP mathph math.DG math.MP Comments: 30 pages, 1 figure MSCclass: 35D30 \\ ( https://arxiv.org/abs/1508.01362 , 48kb)  \\ arXiv:1509.04917 replaced with revised version Sun, 1 May 2016 10:43:58 GMT (261kb,D)
Title: Mathematical analysis of a coarsening model with local interactions Authors: Michael Helmers, Barbara Niethammer and Juan J. L. Velazquez Categories: math.AP Comments: Extended nonuniqueness section \\ ( https://arxiv.org/abs/1509.04917 , 261kb)  \\ arXiv:1511.08935 replaced with revised version Sat, 30 Apr 2016 10:51:04 GMT (46kb)
Title: Oblique boundary value problems for augmented Hessian equations I Authors: Feida Jiang and Neil S. Trudinger Categories: math.AP Comments: This version contains an extension of the tangential second derivative bounds, Lemma 2.3, in the nonlinear boundary condition case MSCclass: 35J66 (Primary) 35J25, 35J96 (Secondary) \\ ( https://arxiv.org/abs/1511.08935 , 46kb)  \\ arXiv:1603.06237 replaced with revised version Sat, 30 Apr 2016 16:21:42 GMT (1349kb,D)
Title: On the Hughes Model and Numerical Aspects Authors: Diogo A. Gomes, Roberto M. Velho Categories: math.AP math.OC Comments: 12 pages, 17 figures \\ ( https://arxiv.org/abs/1603.06237 , 1349kb)  \\ arXiv:1604.00826 replaced with revised version Mon, 2 May 2016 07:06:18 GMT (20kb)
Title: On the BrezisNirenberg type critical problem for nonlinear Choquard equation Authors: Fashun Gao, Minbo Yang Categories: math.AP Comments: 30 MSCclass: 35J25, 35J65 \\ ( https://arxiv.org/abs/1604.00826 , 20kb)  \\ arXiv:1604.03653 replaced with revised version Mon, 2 May 2016 06:32:51 GMT (21kb)
Title: Regularity of stationary solutions to the linearized Boltzmann equations Authors: IKun Chen Categories: math.AP Comments: 23 pages, add references, clarify writing \\ ( https://arxiv.org/abs/1604.03653 , 21kb)  \\ arXiv:1604.07945 replaced with revised version Mon, 2 May 2016 03:26:32 GMT (10kb)
Title: Instability of solitary waves for a generalized derivative nonlinear Schr\"odinger equation in a borderline case Authors: Noriyoshi Fukaya Categories: math.AP Comments: 16 pages \\ ( https://arxiv.org/abs/1604.07945 , 10kb)  \\ arXiv:1604.01478 replaced with revised version Fri, 29 Apr 2016 10:22:52 GMT (14kb)
Title: Higher order Whitehead products and $L_\infty$ structures on the homology of a DGL Authors: Francisco Belch\'i, Urtzi Buijs, Jos\'e M. MorenoFern\'andez and Aniceto Murillo Categories: math.AT Comments: New references and minor corrections \\ ( https://arxiv.org/abs/1604.01478 , 14kb)  \\ arXiv:1311.3681 replaced with revised version Sat, 30 Apr 2016 07:23:27 GMT (148kb,D)
Title: Induced Matchings and the Algebraic Stability of Persistence Barcodes Authors: Ulrich Bauer, Michael Lesnick Categories: math.AT cs.CG math.AC Comments: Expanded journal version, to appear in Journal of Computational Geometry. Includes a proof that no definition of induced matching can be fully functorial (Proposition 5.10), and an extension of our singlemorphism characterization of the interleaving relation to multidimensional persistence modules (Remark 6.7). Exposition is improved throughout. 11 Figures added MSCclass: 13P20, 55U99 Journalref: Journal of Computational Geometry 6:2 (2015), 162191 \\ ( https://arxiv.org/abs/1311.3681 , 148kb)  \\ arXiv:1502.06695 replaced with revised version Sat, 30 Apr 2016 01:47:13 GMT (30kb)
Title: HermitePade approximation, isomonodromic deformation and hypergeometric integral Authors: Toshiyuki Mano and Teruhisa Tsuda Categories: math.CA nlin.SI Comments: 35pages \\ ( https://arxiv.org/abs/1502.06695 , 30kb)  \\ arXiv:1505.01653 replaced with revised version Mon, 2 May 2016 16:52:37 GMT (22kb,D)
Title: Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions Authors: Bartosz Langowski Categories: math.CA MSCclass: 42C10 (Primary), 42C05, 42C20 (Secondary) Journalref: SIGMA 11 (2015), 073, 17 pages DOI: 10.3842/SIGMA.2015.073 \\ ( https://arxiv.org/abs/1505.01653 , 22kb)  \\ arXiv:1510.06990 replaced with revised version Mon, 2 May 2016 19:37:31 GMT (116kb)
Title: Multilinear singular integral forms of ChristJourn\'e type Authors: Andreas Seeger, Charles K. Smart, Brian Street Categories: math.CA math.AP Comments: To appear in Memoirs of the AMS MSCclass: 42B20 \\ ( https://arxiv.org/abs/1510.06990 , 116kb)  \\ arXiv:1512.06918 replaced with revised version Sat, 30 Apr 2016 16:50:40 GMT (27kb)
Title: A Discrete Quadratic Carleson Theorem on $ \ell ^2 $ with a Restricted Supremum Authors: Ben Krause and Michael Lacey Categories: math.CA Comments: 24 pages. Updated with referee suggestions. To appear in IMRN \\ ( https://arxiv.org/abs/1512.06918 , 27kb)  \\ arXiv:1604.06343 replaced with revised version Mon, 2 May 2016 10:23:59 GMT (28kb)
Title: The onephase problem for harmonic measure in twosided NTA domains Authors: Jonas Azzam, Mihalis Mourgoglou, and Xavier Tolsa Categories: math.CA math.AP Comments: In this version we have corrected minor typos, and also we have cited correctly some previous work by Kenig and Toro, of which we were not aware before MSCclass: 31B25, 31A15, 31B15, 35R35 \\ ( https://arxiv.org/abs/1604.06343 , 28kb)  \\ arXiv:1604.07909 replaced with revised version Sun, 1 May 2016 16:33:10 GMT (28kb)
Title: On the roots of a hyperbolic polynomial pencil Authors: Victor Katsnelson Categories: math.CA Comments: 9 pages MSCclass: 11C99, 26C10, 26C15, 15A22, 42A82 \\ ( https://arxiv.org/abs/1604.07909 , 28kb)  \\ arXiv:0804.0006 replaced with revised version Sat, 30 Apr 2016 21:12:50 GMT (14kb)
Title: Embedding in a perfect code Authors: Sergey Avgustinovich (Sobolev Institute of Mathematics, Novosibirsk, Russia), Denis Krotov (Sobolev Institute of Mathematics, Novosibirsk, Russia) Categories: math.CO cs.IT math.IT Comments: Eng: 5pp, Rus: 5pp. V3: revised, a survey added; the accepted version; Russian translation added MSCclass: 94B25, 05A16 Journalref: J. Comb. Des. 17(5) 2009, 419423 DOI: 10.1002/jcd.20207 \\ ( https://arxiv.org/abs/0804.0006 , 14kb)  \\ arXiv:1305.1451 replaced with revised version Mon, 2 May 2016 10:43:31 GMT (24kb)
Title: Explicit bounds for graph minors Authors: Jim Geelen, Tony Huynh, and R. Bruce Richter Categories: math.CO Comments: 24 pages, 0 figures MSCclass: 05C83 \\ ( https://arxiv.org/abs/1305.1451 , 24kb)  \\ arXiv:1406.5943 replaced with revised version Sat, 30 Apr 2016 20:10:24 GMT (69kb,D)
Title: The MoserTardos Framework with Partial Resampling Authors: David G. Harris and Aravind Srinivasan Categories: math.CO cs.DS \\ ( https://arxiv.org/abs/1406.5943 , 69kb)  \\ arXiv:1407.8498 replaced with revised version Sun, 1 May 2016 22:05:14 GMT (15kb)
Title: Intersections of the Hermitian Surface with irreducible Quadrics in even Characteristic Authors: Angela Aguglia and Luca Giuzzi Categories: math.CO cs.DM math.AG Comments: 20 pages; extensively revised and corrected version. This paper extends the results of arXiv:1307.8386 to the case q even MSCclass: 05B25, 51D20, 51E20 \\ ( https://arxiv.org/abs/1407.8498 , 15kb)  \\ arXiv:1410.7834 replaced with revised version Sun, 1 May 2016 10:35:16 GMT (16kb)
Title: FriedgutKalaiNaor theorem for slices of the Boolean cube Authors: Yuval Filmus Categories: math.CO Comments: 15 pages \\ ( https://arxiv.org/abs/1410.7834 , 16kb)  \\ arXiv:1503.02779 replaced with revised version Sat, 30 Apr 2016 01:02:55 GMT (48kb)
Title: On metric properties of maps between Hamming spaces and related graph homomorphisms Authors: Yury Polyanskiy Categories: math.CO cs.IT math.IT MSCclass: 05B40, 11H71, 52C35 \\ ( https://arxiv.org/abs/1503.02779 , 48kb)  \\ arXiv:1506.00467 replaced with revised version Mon, 2 May 2016 07:49:31 GMT (9kb)
Title: Ehrhart polynomials with negative coefficients Authors: Takayuki Hibi, Akihiro Higashitani, Akiyoshi Tsuchiya and Koutarou Yoshida Categories: math.CO Comments: 9 pages MSCclass: 52B20 (Primary), 52B11 (Secondary) \\ ( https://arxiv.org/abs/1506.00467 , 9kb)  \\ arXiv:1508.02596 replaced with revised version Mon, 2 May 2016 16:24:08 GMT (6kb)
Title: A revised Moore bound for mixed graphs Authors: Dominique Buset and Mourad El Amiri and Grahame Erskine and Hebert P\'erezRos\'es and Mirka Miller Categories: math.CO Comments: 5 pages, 2 figures; amended to remove unnecessary tables MSCclass: 05C35 Journalref: Discrete Mathematics, Volume 339, Issue 8, Pages 20662069 DOI: 10.1016/j.disc.2016.03.005 \\ ( https://arxiv.org/abs/1508.02596 , 6kb)  \\ arXiv:1508.05310 replaced with revised version Mon, 2 May 2016 14:10:58 GMT (95kb,D)
Title: Snow Leopard Permutations and Their Even and Odd Threads Authors: Eric S. Egge and Kailee Rubin Categories: math.CO Comments: 24 pages, 6 figures. Version 2 has minor corrections, changes in notation to conform with common conventions, and a new section on Future Directions MSCclass: 05A05, 05A15 \\ ( https://arxiv.org/abs/1508.05310 , 95kb)  \\ arXiv:1509.08623 replaced with revised version Mon, 2 May 2016 10:15:03 GMT (29kb)
Title: On a Conjecture of Cusick Concerning the Sum of Digits of n and n + t Authors: Michael Drmota, Manuel Kauers, Lukas Spiegelhofer Categories: math.CO cs.SC math.NT Comments: 27 pages MSCclass: 11A63, 05A20, 05A16, 11B50, 11B65 Journalref: SIAM J. Discrete Math., 30(2):621649, 2016 \\ ( https://arxiv.org/abs/1509.08623 , 29kb)  \\ arXiv:1510.04386 replaced with revised version Sat, 30 Apr 2016 19:43:39 GMT (45kb)
Title: Total positivity for the Lagrangian Grassmannian Authors: Rachel Karpman Categories: math.CO Comments: Revisions: Fixed typo. Corrected exposition in Remark 1, which relates results of this paper to results of Xuhua He and Thomas Lam. 40 pages, 14 figures \\ ( https://arxiv.org/abs/1510.04386 , 45kb)  \\ arXiv:1511.03069 replaced with revised version Mon, 2 May 2016 09:51:27 GMT (58kb)
Title: Solutions of Reeder's Puzzle Authors: Zachi Evenor Categories: math.CO MSCclass: 05E15 \\ ( https://arxiv.org/abs/1511.03069 , 58kb)  \\ arXiv:1511.03511 replaced with revised version Sun, 1 May 2016 09:34:57 GMT (8kb)
Title: On the signed graphs with two distinct eigenvalues Authors: F. Ramezani Categories: math.CO math.SP Comments: 11pages MSCclass: 05C50 \\ ( https://arxiv.org/abs/1511.03511 , 8kb)  \\ arXiv:1604.08521 replaced with revised version Mon, 2 May 2016 16:52:46 GMT (91kb,D)
Title: Quasiefficient domination in grids Authors: Sahar A. Aleid, Jos\'e C\'aceres and Mar\'ia Luz Puertas Categories: math.CO Comments: 17 pages, 16 figures \\ ( https://arxiv.org/abs/1604.08521 , 91kb)  \\ arXiv:1403.6596 replaced with revised version Sat, 30 Apr 2016 10:38:13 GMT (50kb)
Title: Value Distribution Theory for Parabolic Riemann Surfaces Authors: Mihai Paun, Nessim Sibony Categories: math.CV Comments: A few results added \\ ( https://arxiv.org/abs/1403.6596 , 50kb)  \\ arXiv:1412.8253 replaced with revised version Sat, 30 Apr 2016 02:37:34 GMT (76kb,D)
Title: Volume Approximations of Strictly Pseudoconvex Domains Authors: Purvi Gupta Categories: math.CV math.MG Comments: 29 pages, 3 figures; the introduction has been revised substantially; some typos have been fixed; concluding remarks have been dropped; to appear in J. Geom. Anal MSCclass: 32T15 \\ ( https://arxiv.org/abs/1412.8253 , 76kb)  \\ arXiv:1508.07486 replaced with revised version Mon, 2 May 2016 16:22:00 GMT (6kb)
Title: Entire functions of several variables of bounded index and PDE's Authors: Andriy Bandura and Oleh Skaskiv Categories: math.CV math.AP Comments: 128 pages, contents and introduction MSCclass: 32A15 (Primary), 32A17, 35B08 (Secondary) \\ ( https://arxiv.org/abs/1508.07486 , 6kb)  \\ arXiv:1604.07059 replaced with revised version Mon, 2 May 2016 12:56:13 GMT (0kb,I)
Title: HilbertSchmidt Hankel operators over semiReinhardt domains Authors: Tomasz Beberok and Nihat Gokhan Gogus Categories: math.CV Comments: This paper has been withdrawn by the authors due to mistake in the proof of Main theorem MSCclass: 47B35, 32A36 \\ ( https://arxiv.org/abs/1604.07059 , 0kb)  \\ arXiv:1604.08453 replaced with revised version Mon, 2 May 2016 16:54:13 GMT (20kb)
Title: Harmonic reflection in quasicircles and wellposedness of a RiemannHilbert problem on quasidisks Authors: Eric Schippers and Wolfgang Staubach Categories: math.CV Comments: 17 pages MSCclass: 35Q15, 30C62, 30E25, 31C25 (Primary), 31A20 (Secondary) \\ ( https://arxiv.org/abs/1604.08453 , 20kb)  \\ arXiv:1212.3595 replaced with revised version Mon, 2 May 2016 16:42:07 GMT (51kb)
Title: Pure spinors, intrinsic torsion and curvature in even dimensions Authors: Arman TaghaviChabert Categories: math.DG grqc mathph math.MP Comments: v2. Cleaned up version. Typos and errors fixed. Some reordering. v3. Restructured  some material moved to an additional appendix for clarity  further typos fixed and other minor improvements v4. Presentation improved. Some material removed to be included in a future article. v5. As published: Abstract and intro rewritten. Presentation simplified Journalref: Differential Geom. Appl. 46 (2016), 164203 DOI: 10.1016/j.difgeo.2016.02.006 \\ ( https://arxiv.org/abs/1212.3595 , 51kb)  \\ arXiv:1408.5549 replaced with revised version Mon, 2 May 2016 16:52:36 GMT (1446kb)
Title: On the Neuron Response Features of Convolutional Neural Networks for Remote Sensing Image Authors: Jie Chen, Min Deng, Haifeng Li Categories: math.DG \\ ( https://arxiv.org/abs/1408.5549 , 1446kb)  \\ arXiv:1402.1135 replaced with revised version Sun, 1 May 2016 17:09:16 GMT (53kb)
Title: FugledeKadison Determinants and Sofic Entropy Authors: Ben Hayes Categories: math.DS math.FA math.OA Comments: 56 pages. This is the final version to appear in Geometric and Functional Analysis \\ ( https://arxiv.org/abs/1402.1135 , 53kb)  \\ arXiv:1404.4951 replaced with revised version Sun, 1 May 2016 20:26:23 GMT (21kb)
Title: Mixing for invertible infinite measure systems Authors: Ian Melbourne Categories: math.DS Comments: Numbering of theorems etc updated to agree with numbering system of the published version MSCclass: 37A25 (Primary) 37A40, 37A50, 37D25 (Secondary) Journalref: Stochastics & Dynamics 15 (2015) 1550012 (25 pages) \\ ( https://arxiv.org/abs/1404.4951 , 21kb)  \\ arXiv:1505.02404 replaced with revised version Sat, 30 Apr 2016 18:45:44 GMT (214kb,D)
Title: Box dimension of a hyperbolic saddle loop Authors: Maja Resman Categories: math.DS Comments: 17 pages, 1 figure MSCclass: 37C10, 28A75, 37C27, 37C29 \\ ( https://arxiv.org/abs/1505.02404 , 214kb)  \\ arXiv:1509.01723 replaced with revised version Sat, 30 Apr 2016 20:35:49 GMT (44kb)
Title: von Neumann's problem and extensions of nonamenable equivalence relations Authors: Lewis Bowen, Daniel Hoff, and Adrian Ioana Categories: math.DS math.GR math.OA Comments: This version corrects a few minor errors and expands the introduction \\ ( https://arxiv.org/abs/1509.01723 , 44kb)  \\ arXiv:1509.03307 replaced with revised version Sat, 30 Apr 2016 05:28:46 GMT (38kb)
Title: On extensions of subshifts by finite groups Authors: Kengo Matsumoto Categories: math.DS math.OA Comments: 36 pages: Sections 7 and 8 were revised MSCclass: Primary 37B10, Secondary 28D20, 37B40, 46L80 \\ ( https://arxiv.org/abs/1509.03307 , 38kb)  \\ arXiv:1503.04856 replaced with revised version Mon, 2 May 2016 03:56:24 GMT (12kb)
Title: Fourier Series for Singular Measures Authors: John E. Herr and Eric S. Weber Categories: math.FA Comments: 12 pages \\ ( https://arxiv.org/abs/1503.04856 , 12kb)  \\ arXiv:1505.05108 replaced with revised version Sat, 30 Apr 2016 02:44:13 GMT (46kb)
Title: On the isomorphism problem for multiplier algebras of NevanlinnaPick spaces Authors: Michael Hartz Categories: math.FA math.OA Comments: 58 pages; small changes MSCclass: Primary 47L30, Secondary 46E22, 47A13 \\ ( https://arxiv.org/abs/1505.05108 , 46kb)  \\ arXiv:1602.06430 replaced with revised version Sun, 1 May 2016 19:22:19 GMT (4kb)
Title: More on the metric projection onto a closed convex set in a Hilbert space Authors: Biagio Ricceri Categories: math.FA \\ ( https://arxiv.org/abs/1602.06430 , 4kb)  \\ arXiv:1604.05298 replaced with revised version Sun, 1 May 2016 11:06:50 GMT (0kb,I)
Title: Remarks on bounded operators in $\ell$K\"othe spaces Authors: Ersin K{\i}zgut, Elif Uyan{\i}k, and Murat Yurdakul Categories: math.FA Comments: Withdrawn due to an error in Theorem 2.1 MSCclass: 46A03, 46A32, 46A45 \\ ( https://arxiv.org/abs/1604.05298 , 0kb)  \\ arXiv:1410.1358 replaced with revised version Sat, 30 Apr 2016 18:03:04 GMT (32kb,D)
Title: The pseudoAnosov and conjugacy problems are in $\textbf{NP} \cap \textbf{coNP}$ Authors: Mark C. Bell Categories: math.GT Comments: 26 pages, 6 figures, updated abstract, introduction and added section detailing the conjugacy problem \\ ( https://arxiv.org/abs/1410.1358 , 32kb)  \\ arXiv:1508.05555 replaced with revised version Mon, 2 May 2016 04:53:11 GMT (2624kb)
Title: New Parities and Coverings over Free Knots Authors: Vassily Olegovich Manturov Categories: math.GT Comments: 18 pages, 11 Figures \\ ( https://arxiv.org/abs/1508.05555 , 2624kb)  \\ arXiv:1512.00129 replaced with revised version Sun, 1 May 2016 19:36:27 GMT (50kb)
Title: Pretzel Knots and qSeries Authors: Mohamed Elhamdadi and Mustafa Hajij Categories: math.GT math.CO math.NT Comments: 22 Pages, 14 Figures \\ ( https://arxiv.org/abs/1512.00129 , 50kb)  \\ arXiv:1602.02416 replaced with revised version Sat, 30 Apr 2016 14:04:59 GMT (10kb)
Title: Godel's Second Incompleteness Theorem for Definable Theories Authors: Payam Seraji and Conden Chao Categories: math.LO \\ ( https://arxiv.org/abs/1602.02416 , 10kb)  \\ arXiv:1604.03841 replaced with revised version Sun, 1 May 2016 16:18:16 GMT (20kb)
Title: Type decomposition in NIP theories Authors: Pierre Simon Categories: math.LO Comments: 17 pages, small improvements of the presentation MSCclass: 03C45, 03C95 \\ ( https://arxiv.org/abs/1604.03841 , 20kb)  \\ arXiv:1504.02845 replaced with revised version Sun, 1 May 2016 10:50:49 GMT (232kb)
Title: The spherical dual transform is an isometry for spherical Wulff shapes Authors: Huhe Han and Takashi Nishimura Categories: math.MG Comments: 12 pages, 2 figures MSCclass: 47N10, 52A30, 82D25 \\ ( https://arxiv.org/abs/1504.02845 , 232kb)  \\ arXiv:1512.00267 replaced with revised version Sat, 30 Apr 2016 16:00:42 GMT (16kb)
Title: Elementary vectors and conformal sums in polyhedral geometry and their relevance for metabolic pathway analysis Authors: Stefan M\"uller, Georg Regensburger Categories: math.MG qbio.MN MSCclass: 52Bxx \\ ( https://arxiv.org/abs/1512.00267 , 16kb)  \\ arXiv:1603.05221 replaced with revised version Sun, 1 May 2016 18:56:08 GMT (33kb)
Title: Noncompact RCD(0,N) spaces with linear volume growth Authors: Xiantao Huang Categories: math.MG math.DG Comments: Significantly improved exposition. Typos corrected. All comments are welcome \\ ( https://arxiv.org/abs/1603.05221 , 33kb)  \\ arXiv:1505.05926 replaced with revised version Sat, 30 Apr 2016 20:08:32 GMT (27kb)
Title: Hypercomplex Fock States for Discrete Electromagnetic Schr\"odinger Operators: A Bayesian Probability Perspective Authors: Nelson Faustino Categories: mathph math.CA math.MP math.PR Comments: 28 pages; Section 2. on the previous version (v3) was reformulated; subsequent sections were readjusted; title has slightly changed MSCclass: 26A33, 30G35, 33C20, 62F15, 81Q60 \\ ( https://arxiv.org/abs/1505.05926 , 27kb)  \\ arXiv:1508.01752 replaced with revised version Mon, 2 May 2016 06:05:18 GMT (56kb,D)
Title: Variational Sequences, Representation Sequences and Applications in Physics Authors: Marcella Palese, Olga Rossi, Ekkehart Winterroth and Jana Musilov\'a Categories: mathph math.MP MSCclass: 55N30, 55R10, 58A12, 58A20, 58E30, 70S10 Journalref: SIGMA 12 (2016), 045, 45 pages DOI: 10.3842/SIGMA.2016.045 \\ ( https://arxiv.org/abs/1508.01752 , 56kb)  \\ arXiv:1508.07209 replaced with revised version Mon, 2 May 2016 09:22:31 GMT (16kb)
Title: A geometric approach to quantum control in a classicallike framework Authors: Davide Pastorello Categories: mathph math.MP Comments: 11 pages \\ ( https://arxiv.org/abs/1508.07209 , 16kb)  \\ arXiv:1512.01323 replaced with revised version Sun, 1 May 2016 17:06:53 GMT (290kb,D)
Title: The Cauchy Principal Value and the finite part integral as values of absolutely convergent integrals Authors: Eric A. Galapon Categories: mathph math.MP Journalref: Journal of Mathematical Physics 57, 033502 (2016) DOI: 10.1063/1.4943300 \\ ( https://arxiv.org/abs/1512.01323 , 290kb)  \\ arXiv:1602.03257 replaced with revised version Sun, 1 May 2016 05:05:49 GMT (58kb)
Title: Asymptotics of meanfield $O(N)$ models Authors: Kay Kirkpatrick and Tayyab Nawaz Categories: mathph math.MP \\ ( https://arxiv.org/abs/1602.03257 , 58kb)  \\ arXiv:1602.04610 replaced with revised version Mon, 2 May 2016 15:26:43 GMT (12kb,D)
Title: Spherically symmetric potential in noncommutative spacetime with a compactified extra dimensions Authors: S\^ecloka Lazare Guedezounme, Antonin Danvid\'e Kanfon, Dine Ousmane Samary Categories: mathph math.MP \\ ( https://arxiv.org/abs/1602.04610 , 12kb)  \\ arXiv:1604.03023 replaced with revised version Sat, 30 Apr 2016 07:57:34 GMT (34kb)
Title: Multivariate Trace Inequalities Authors: David Sutter, Mario Berta, Marco Tomamichel Categories: mathph cs.IT math.IT math.MP quantph Comments: v2: 21 pages, 2 figures, minor changes; v1: 20 pages, 2 figures \\ ( https://arxiv.org/abs/1604.03023 , 34kb)  \\ arXiv:1501.01350 replaced with revised version Sat, 30 Apr 2016 13:44:37 GMT (519kb)
Title: Highorder fractionalcompact finite difference method for Riesz spatial telegraph equation Authors: Hengfei Ding, Changpin Li Categories: math.NA Comments: 30 pages, 3 figures \\ ( https://arxiv.org/abs/1501.01350 , 519kb)  \\ arXiv:1505.03335 replaced with revised version Sat, 30 Apr 2016 13:27:21 GMT (406kb)
Title: Highorder numerical algorithms for Riesz derivatives via constructing new generating functions Authors: Hengfei Ding, Changpin Li Categories: math.NA Comments: 32 pages, 2figures \\ ( https://arxiv.org/abs/1505.03335 , 406kb)  \\ arXiv:1512.03284 replaced with revised version Mon, 2 May 2016 13:17:14 GMT (40kb)
Title: An adaptive linear homotopy method to approximate eigenpairs of homogeneous polynomial systems Authors: Paul Breiding Categories: math.NA \\ ( https://arxiv.org/abs/1512.03284 , 40kb)  \\ arXiv:1512.07342 replaced with revised version Sun, 1 May 2016 18:16:00 GMT (1877kb)
Title: Cheap arbitrary high order methods for single integrand SDEs Authors: Kristian Debrabant and Anne Kv{\ae}rn{\o} Categories: math.NA MSCclass: 65C30, 60H35, 65C20 DOI: 10.1007/s1054301606198 \\ ( https://arxiv.org/abs/1512.07342 , 1877kb)  \\ arXiv:1602.03260 replaced with revised version Sun, 1 May 2016 20:33:35 GMT (271kb,D)
Title: A Nonconforming Finite Element Method for the Biot's Consolidation Model in Poroelasticity Authors: Xiaozhe Hu and Carmen Rodrigo and Francisco J. Gaspar and Ludmil T. Zikatanov Categories: math.NA MSCclass: 65N30 \\ ( https://arxiv.org/abs/1602.03260 , 271kb)  \\ arXiv:1504.04917 replaced with revised version Mon, 2 May 2016 07:59:13 GMT (22kb)
Title: On the complete faithfulness of the $p$free quotient modules of dual Selmer groups Authors: Meng Fai Lim Categories: math.NT Comments: 24 pages. Several changes and corrections. arXiv admin note: text overlap with arXiv:1408.2599 MSCclass: 11F80, 11G05, 11R23, 11R34, 16S34 \\ ( https://arxiv.org/abs/1504.04917 , 22kb)  \\ arXiv:1505.02279 replaced with revised version Mon, 2 May 2016 08:28:11 GMT (202kb,D)
Title: A generalization of reduced Arakelov divisors of a number field Authors: Nguyen Thanh Ha Tran Categories: math.NT DOI: 10.1016/j.jnt.2016.03.006 \\ ( https://arxiv.org/abs/1505.02279 , 202kb)  \\ arXiv:1603.03983 replaced with revised version Sat, 30 Apr 2016 11:22:28 GMT (11kb)
Title: On roots of unity in orbits of rational functions Authors: Alina Ostafe Categories: math.NT Comments: The case of of rational functions h=f/g with deg f  deg g<0 has been removed due to a gap in the argument. The main result holds for the case deg f  deg g > 1 only \\ ( https://arxiv.org/abs/1603.03983 , 11kb)  \\ arXiv:1604.01914 replaced with revised version Mon, 2 May 2016 11:55:31 GMT (60kb)
Title: Traces des op\'erateurs de Hecke sur les espaces de formes automorphes de $\mathrm{SO}_7$, $\mathrm{SO}_8$ ou $\mathrm{SO}_9$ en niveau $1$ et poids arbitraire Authors: Thomas M\'egarban\'e Categories: math.NT Comments: 58 pages, in French, 11 tables MSCclass: 11F46, 11F55, 11F60, 11H55, 11H56 \\ ( https://arxiv.org/abs/1604.01914 , 60kb)  \\ arXiv:1604.02019 replaced with revised version Mon, 2 May 2016 18:59:59 GMT (45kb)
Title: Lower bounds for Maass forms on semisimple groups Authors: Farrell Brumley, Simon Marshall Categories: math.NT math.AP MSCclass: 35P20, 11F60 \\ ( https://arxiv.org/abs/1604.02019 , 45kb)  \\ arXiv:1604.07977 replaced with revised version Sat, 30 Apr 2016 13:18:17 GMT (75kb)
Title: Some divisibility properties of qFibonacci numbers Authors: Johann Cigler Categories: math.NT Comments: Since I became aware of the fact that some of my experimentally found results have already been proved in a paper by H. Pan I changed the title and revised the paper thoroughly MSCclass: 05A30, 11A07, 11B39 \\ ( https://arxiv.org/abs/1604.07977 , 75kb)  \\ arXiv:1604.08670 replaced with revised version Mon, 2 May 2016 19:37:32 GMT (5kb)
Title: A Characteristic Function for the Primes Authors: Jesse Aaron Zinn Categories: math.NT MSCclass: 11A41 \\ ( https://arxiv.org/abs/1604.08670 , 5kb)  \\ arXiv:1604.08940 replaced with revised version Mon, 2 May 2016 07:38:06 GMT (10kb)
Title: Comparison estimates for linear forms in additive number theory Authors: Melvyn B. Nathanson Categories: math.NT Comments: 16 pages. A section on open problems has been added to the paper MSCclass: 05A17, 11B13, 11B30, 11B75, 11P99 \\ ( https://arxiv.org/abs/1604.08940 , 10kb)  \\ arXiv:1402.5830 replaced with revised version Mon, 2 May 2016 14:55:37 GMT (228kb)
Title: A hybrid swarmbased algorithm for singleobjective optimization problems involving highcost analyses Authors: Enrico Ampellio and Luca Vassio Categories: math.OC cs.AI cs.DC cs.NE Comments: 19 pages, 4 figures, Springer Swarm Intelligence Journalref: Swarm Intelligence 2016 DOI: 10.1007/s1172101601216 \\ ( https://arxiv.org/abs/1402.5830 , 228kb)  \\ arXiv:1503.08239 replaced with revised version Mon, 2 May 2016 11:03:22 GMT (1091kb)
Title: Constraint backoffs for safe, sufficient excitation: a general theory with application to experimental optimization Authors: Gene A. Bunin Categories: math.OC Comments: 21 pages, 4 figures, resubmitted to Computers & Chemical Engineering as a regular paper (following second round of reviews) \\ ( https://arxiv.org/abs/1503.08239 , 1091kb)  \\ arXiv:1504.04680 replaced with revised version Sat, 30 Apr 2016 23:40:15 GMT (3617kb,D)
Title: Zoned HVAC Control via PDEConstrained Optimization Authors: Runxin He and Humberto Gonzalez Categories: math.OC \\ ( https://arxiv.org/abs/1504.04680 , 3617kb)  \\ arXiv:1506.07924 replaced with revised version Mon, 2 May 2016 18:20:31 GMT (688kb)
Title: Decentralized QLearning for Stochastic Teams and Games Authors: G\"urdal Arslan and Serdar Y\"uksel Categories: math.OC cs.GT cs.LG Comments: To appear in IEEE Trans. Automatic Control \\ ( https://arxiv.org/abs/1506.07924 , 688kb)  \\ arXiv:1511.02398 replaced with revised version Sun, 1 May 2016 17:57:54 GMT (579kb)
Title: On the relationship between imitative logit dynamics in the population game theory and mirror descent method in the online optimization using the example of the Shortest Path Problem Authors: Alexander Gasnikov, Anastasia Lagunovskaya, Larisa Morozova Categories: math.OC Comments: 9 pages, in Russian Journalref: TRUDY MIPT. 2015. V. 7. no. 4. P. 104113 \\ ( https://arxiv.org/abs/1511.02398 , 579kb)  \\ arXiv:1512.00620 replaced with revised version Sun, 1 May 2016 09:06:21 GMT (16kb)
Title: Optimality of the generalized c\mu rule in the moderate deviation regime Authors: Rami Atar and Subhamay Saha Categories: math.OC Comments: 15 pages MSCclass: 60F10, 60K25, 93E20, 49N70 \\ ( https://arxiv.org/abs/1512.00620 , 16kb)  \\ arXiv:1604.04841 replaced with revised version Fri, 29 Apr 2016 23:57:26 GMT (16kb)
Title: On the Solution Existence of Nonconvex Quadratic Programming Problems in Hilbert Spaces Authors: Vu Van Dong, Nguyen Nang Tam Categories: math.OC MSCclass: 90C20, 90C26, 90C30 \\ ( https://arxiv.org/abs/1604.04841 , 16kb)  \\ arXiv:1604.05275 replaced with revised version Sun, 1 May 2016 17:54:26 GMT (660kb)
Title: Universal fast gradient method for stochastic composit optimization problems Authors: Alexander Gasnikov and Yurii Nesterov Categories: math.OC Comments: 21 pages, in Russian \\ ( https://arxiv.org/abs/1604.05275 , 660kb)  \\ arXiv:1604.08096 replaced with revised version Mon, 2 May 2016 16:35:45 GMT (2537kb,D)
Title: Forwardbackward quasiNewton methods for nonsmooth optimization problems Authors: Lorenzo Stella, Andreas Themelis, Panagiotis Patrinos Categories: math.OC \\ ( https://arxiv.org/abs/1604.08096 , 2537kb)  \\ arXiv:1604.08194 replaced with revised version Sun, 1 May 2016 17:52:29 GMT (343kb)
Title: Primaldual mirror descent for the stochastic programming problems with functional constraints Authors: Alexander Gasnikov, Evgenia Gasnikova, Sergey Matsievsky Categories: math.OC Comments: 7 pages, in Russian, Information Technology and Systems. 2016 \\ ( https://arxiv.org/abs/1604.08194 , 343kb)  \\ arXiv:1011.4043 replaced with revised version Sun, 1 May 2016 18:42:45 GMT (23kb)
Title: A note about the uniform distribution on the intersection of a simplex and a sphere Authors: Sourav Chatterjee Categories: math.PR Comments: 21 pages. To appear in J. Topol. Anal MSCclass: 35Q55, 82B26, 82B10, 60F10 \\ ( https://arxiv.org/abs/1011.4043 , 23kb)  \\ arXiv:1507.05522 replaced with revised version Mon, 2 May 2016 09:09:05 GMT (0kb,I)
Title: The tail of the crossing probability in nearcritical percolation  an appendix to Ahlberg & Steif [arXiv:1405.7144] Authors: G\'abor Pete Categories: math.PR mathph math.CO math.MP Comments: A significantly revised version of this appendix now appears as part of arXiv:1405.7144. In particular, the discussion of the highdimensional case is changed completely, making a new conjecture \\ ( https://arxiv.org/abs/1507.05522 , 0kb)  \\ arXiv:1508.04645 replaced with revised version Sun, 1 May 2016 23:32:30 GMT (314kb,D)
Title: The multiplicative coalescent, inhomogeneous continuum random trees, and new universality classes for critical random graphs Authors: Shankar Bhamidi, Remco van der Hofstad, Sanchayan Sen Categories: math.PR math.CO Comments: 67 pages, 5 figures, added proof of lower bound on Minkowski dimension MSCclass: 60C05, 05C80 \\ ( https://arxiv.org/abs/1508.04645 , 314kb)  \\ arXiv:1508.07768 replaced with revised version Sat, 30 Apr 2016 08:28:00 GMT (25kb)
Title: Random conical tessellations Authors: Daniel Hug, Rolf Schneider Categories: math.PR math.MG Comments: Introduction is expanded, references are updated, strategy of proof is explained in several places, major results are emphasized MSCclass: 60D05, 52A22, secondary 52A55, 52C35, 52B05 \\ ( https://arxiv.org/abs/1508.07768 , 25kb)  \\ arXiv:1511.04840 replaced with revised version Sun, 1 May 2016 07:16:00 GMT (39kb)
Title: A family of selfavoiding random walks interpolating the looperased random walk and a selfavoiding walk on the Sierpinski gasket Authors: Kumiko Hattori, Noriaki Ogo, Takafumi Otsuka Categories: math.PR Comments: 23 pages, 5 figures MSCclass: 60F99, 60G17, 28A80, 37F25, 37F35 \\ ( https://arxiv.org/abs/1511.04840 , 39kb)  \\ arXiv:1511.04923 replaced with revised version Sat, 30 Apr 2016 06:24:07 GMT (24kb)
Title: A stroll along the gamma Authors: Benjamin Arras and Yvik Swan Categories: math.PR Comments: Complete reorganization of the previous version. Sections 5 and 6 are new with new results MSCclass: 60E15, 26D10, 60B10 \\ ( https://arxiv.org/abs/1511.04923 , 24kb)  \\ arXiv:1602.05207 replaced with revised version Sat, 30 Apr 2016 19:59:25 GMT (25kb)
Title: Fractional smoothness of distributions of polynomials and a fractional analog of the HardyLandauLittlewood inequality Authors: Vladimir I. Bogachev, Egor D. Kosov, Georgii I. Zelenov Categories: math.PR \\ ( https://arxiv.org/abs/1602.05207 , 25kb)  \\ arXiv:1507.02792 replaced with revised version Mon, 2 May 2016 09:34:56 GMT (28kb)
Title: Nonassociative geometry in quasiHopf representation categories II: Connections and curvature Authors: Gwendolyn E. Barnes, Alexander Schenkel, Richard J. Szabo Categories: math.QA hepth mathph math.CT math.MP Comments: 29 pages. v2: Final version published in Journal of Geometry and Physics Reportno: EMPG1510 MSCclass: 16T05, 17B37, 46L87, 53D55 Journalref: Journal of Geometry and Physics, Volume 106, August 2016, Pages 234255 DOI: 10.1016/j.geomphys.2016.04.005 \\ ( https://arxiv.org/abs/1507.02792 , 28kb)  \\ arXiv:1602.02662 replaced with revised version Sun, 1 May 2016 22:25:05 GMT (893kb,D)
Title: Planar Para Algebras, Reflection Positivity Authors: Arthur Jaffe and Zhengwei Liu Categories: math.QA condmat.meshall hepth mathph math.MP Comments: 41 pages \\ ( https://arxiv.org/abs/1602.02662 , 893kb)  \\ arXiv:1602.08587 replaced with revised version Sat, 30 Apr 2016 13:51:23 GMT (30kb)
Title: Explicit Forms of Cluster Variables on Double Bruhat Cells G^{u,e} of type B Authors: Yuki Kanakubo Categories: math.QA Comments: 37 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1504.07813 \\ ( https://arxiv.org/abs/1602.08587 , 30kb)  \\ arXiv:1604.01247 replaced with revised version Sun, 1 May 2016 15:16:42 GMT (23kb)
Title: Exceptional quantum geometry and particle physics Authors: Michel DuboisViolette Categories: math.QA grqc hepth mathph math.MP math.RA Comments: 37 pages ; some minor typo corrections. To appear in Nucl. Pays. B (2016), http://dx.doi.org/10.1016/j.nuclphysb.2016.04.018 Reportno: LPTORSAY 1630 \\ ( https://arxiv.org/abs/1604.01247 , 23kb)  \\ arXiv:1601.00748 replaced with revised version Sun, 1 May 2016 04:30:49 GMT (21kb)
Title: On the flatness and the projectivity over Hopf subalgebras of Hopf algebras over discrete valuation rings Authors: Nguyen Dai Duong, Phung Ho Hai and Nguyen Huy Hung Categories: math.RA Comments: An updated and corrected version. Section 4 are completely rewritten \\ ( https://arxiv.org/abs/1601.00748 , 21kb)  \\ arXiv:1307.5297 replaced with revised version Sun, 1 May 2016 09:49:50 GMT (57kb)
Title: $Q$polynomial distanceregular graphs and a double affine Hecke algebra of rank one Authors: JaeHo Lee Categories: math.RT math.CO Comments: 79 pages, 1 fugure. arXiv admin note: text overlap with arXiv:1205.2144, arXiv:math/0608694, arXiv:1108.0458 by other authors MSCclass: 05E30, 33D80 Journalref: Linear Algebra Appl. 439 (2013), no. 10, 31843240 \\ ( https://arxiv.org/abs/1307.5297 , 57kb)  \\ arXiv:1505.01409 replaced with revised version Sat, 30 Apr 2016 20:02:45 GMT (17kb,D)
Title: Dual space and hyperdimension of compact hypergroups Authors: Mahmood Alaghmandan, Massoud Amini Categories: math.RT Comments: Some revisions to Sections 3 following improvements suggested by the referee \\ ( https://arxiv.org/abs/1505.01409 , 17kb)  \\ arXiv:1507.01349 replaced with revised version Sun, 1 May 2016 10:17:20 GMT (17kb)
Title: Leibniz algebras associated with representations of the Diamond Lie algebra Authors: S. Uguz, I.A. Karimjanov, B.A. Omirov Categories: math.RT math.RA Comments: 18 pages MSCclass: 17A32, 17B30, 17B10 \\ ( https://arxiv.org/abs/1507.01349 , 17kb)  \\ arXiv:1512.00039 replaced with revised version Fri, 29 Apr 2016 08:53:12 GMT (26kb)
Title: Uniqueness of extremal Lagrangian tori in the fourdimensional disc Authors: Georgios Dimitroglou Rizell Categories: math.SG Comments: 18 pages, 3 figures MSCclass: 53D12, 53D42 \\ ( https://arxiv.org/abs/1512.00039 , 26kb)  \\ arXiv:1206.3707 replaced with revised version Sat, 30 Apr 2016 19:58:09 GMT (65kb)
Title: Symplectic geometry of quantum noise Authors: Leonid Polterovich Categories: math.SG mathph math.MP quantph Comments: Revised version, 57 pages, 3 figures. Incorporates arXiv:1203.2348 MSCclass: 53Dxx, 81Sxx Journalref: Communications in Mathematical Physics 327 (2014), 481519 \\ ( https://arxiv.org/abs/1206.3707 , 65kb)  \\ arXiv:1412.4495 replaced with revised version Mon, 2 May 2016 04:40:07 GMT (11kb)
Title: Superheavy Lagrangian immersion in 2torus Authors: Morimichi Kawasaki Categories: math.SG Comments: 11 pages, added a new result (Theorem 6.1) MSCclass: 37J10, 53D12, 53D40, 57R17 \\ ( https://arxiv.org/abs/1412.4495 , 11kb)  \\ arXiv:1511.04350 replaced with revised version Sun, 1 May 2016 15:17:23 GMT (103kb,D)
Title: Smoothness of Kuranishi atlases on GromovWitten moduli spaces Authors: Robert Castellano Categories: math.SG Comments: 42 pages, 5 figures; v3 correct errors in the gluing theorem MSCclass: 53D45, 53D05, 57R17 \\ ( https://arxiv.org/abs/1511.04350 , 103kb)  \\ arXiv:1209.1031 replaced with revised version Sun, 1 May 2016 18:54:46 GMT (506kb)
Title: Testing the Fractional Integration Parameter Revisited: a Fractional DickeyFuller Test Authors: Ahmed Bensalma and Mohamed Bentarzi Categories: math.ST stat.TH MSCclass: 62F03, 62F05, 62F12, 62M10 \\ ( https://arxiv.org/abs/1209.1031 , 506kb)  \\ arXiv:1308.1269 replaced with revised version Sat, 30 Apr 2016 07:34:37 GMT (40kb)
Title: On bbit minwise hashing for largescale regression and classification with sparse data Authors: Rajen D. Shah and Nicolai Meinshausen Categories: math.ST stat.ML stat.TH Comments: 36 pages \\ ( https://arxiv.org/abs/1308.1269 , 40kb)  \\ arXiv:1411.6719 replaced with revised version Sun, 1 May 2016 18:30:16 GMT (34kb)
Title: Asymptotically Optimal Discrete Time Nonlinear Filters From Stochastically Convergent State Process Approximations Authors: Dionysios S. Kalogerias, Athina P. Petropulu Categories: math.ST cs.SY math.OC stat.AP stat.ME stat.TH Comments: EXTENDED version of an original paper published in the IEEE Transactions on Signal Processing; 37 pages \\ ( https://arxiv.org/abs/1411.6719 , 34kb)  \\ arXiv:1503.06388 replaced with revised version Sat, 30 Apr 2016 22:32:52 GMT (79kb,D)
Title: Adaptive Concentration of Regression Trees, with Application to Random Forests Authors: Stefan Wager and Guenther Walther Categories: math.ST stat.ML stat.TH \\ ( https://arxiv.org/abs/1503.06388 , 79kb)  \\ arXiv:1510.01290 replaced with revised version Mon, 2 May 2016 09:39:29 GMT (64kb)
Title: Total positivity in Markov structures Authors: Shaun Fallat, Steffen Lauritzen, Kayvan Sadeghi, Caroline Uhler, Nanny Wermuth, Piotr Zwiernik Categories: math.ST stat.TH MSCclass: 60E15, 62H99, 15B48 \\ ( https://arxiv.org/abs/1510.01290 , 64kb)  \\ arXiv:1602.03436 replaced with revised version Mon, 2 May 2016 08:13:04 GMT (188kb,D)
Title: HighDimensional Estimation of Structured Signals from NonLinear Observations with General Convex Loss Functions Authors: Martin Genzel Categories: math.ST stat.TH \\ ( https://arxiv.org/abs/1602.03436 , 188kb)  \\ arXiv:1603.00285 replaced with revised version Sat, 30 Apr 2016 12:06:39 GMT (100kb)
Title: Kernelbased Tests for Joint Independence Authors: Niklas Pfister, Peter B\"uhlmann, Bernhard Sch\"olkopf, and Jonas Peters Categories: math.ST stat.ML stat.TH Comments: 59 pages \\ ( https://arxiv.org/abs/1603.00285 , 100kb)  \\ arXiv:1603.09071 replaced with revised version Mon, 2 May 2016 16:51:33 GMT (191kb,D)
Title: Robust LowRank Matrix Estimation Authors: Andreas Elsener, Sara van de Geer Categories: math.ST stat.TH Comments: 34 pages, 2 figures; Lemmas B.1 and B.2 revised MSCclass: 62J05, 62F30 \\ ( https://arxiv.org/abs/1603.09071 , 191kb)  \\ arXiv:1604.02576 replaced with revised version Mon, 2 May 2016 01:20:33 GMT (35kb)
Title: Hypothesis Testing via Affine Detectors Authors: Anatoli Juditsky and Arkadi Nemirovski Categories: math.ST stat.TH MSCclass: 62F10, 62G10, 90C25, 90C47 \\ ( https://arxiv.org/abs/1604.02576 , 35kb)  \\ arXiv:1604.06906 replaced with revised version Sat, 30 Apr 2016 12:05:05 GMT (611kb)
Title: NonCentral Multivariate ChiSquare and Gamma Distributions Authors: Thomas Royen Categories: math.ST stat.TH Comments: 15 pages \\ ( https://arxiv.org/abs/1604.06906 , 611kb)  \\ arXiv:1604.02732 replaced with revised version Sat, 30 Apr 2016 14:02:10 GMT (22kb)
Title: Framed motives of relative motivic spheres Authors: Grigory Garkusha, Alexander Neshitov, Ivan Panin Categories: math.KT math.AG math.AT Comments: In order to make the paper selfcontained, Theorem 1.2 has been added to the new version \\ ( https://arxiv.org/abs/1604.02732 , 22kb)  \\ arXiv:1312.1231 (*crosslisting*) replaced with revised version Sat, 30 Apr 2016 10:00:26 GMT (49kb,D)
Title: The Morse theory of \v{C}ech and Delaunay complexes Authors: Ulrich Bauer, Herbert Edelsbrunner Categories: cs.CG math.AT math.GT math.MG Comments: 21 pages, 2 figures, improved exposition MSCclass: 52C99, 51F99, 55U10, 57Q10 \\ ( https://arxiv.org/abs/1312.1231 , 49kb)  \\ arXiv:1505.05926 replaced with revised version Sat, 30 Apr 2016 20:08:32 GMT (27kb)
Title: Hypercomplex Fock States for Discrete Electromagnetic Schr\"odinger Operators: A Bayesian Probability Perspective Authors: Nelson Faustino Categories: mathph math.CA math.MP math.PR Comments: 28 pages; Section 2. on the previous version (v3) was reformulated; subsequent sections were readjusted; title has slightly changed MSCclass: 26A33, 30G35, 33C20, 62F15, 81Q60 \\ ( https://arxiv.org/abs/1505.05926 , 27kb)  \\ arXiv:1510.05167 (*crosslisting*) replaced with revised version Sat, 30 Apr 2016 14:26:08 GMT (704kb)
Title: Viral epidemiology of the adult Apis Mellifera infested by the Varroa destructor mite Authors: Sara Bernardi, Ezio Venturino Categories: qbio.PE math.DS MSCclass: 92D25, 92D30 \\ ( https://arxiv.org/abs/1510.05167 , 704kb)  \\ arXiv:1507.08850 (*crosslisting*) replaced with revised version Sat, 30 Apr 2016 22:33:19 GMT (6kb)
Title: Generalization of paritytime and partial paritytime symmetry Authors: Francisco M. Fern\'andez Categories: quantph mathph math.MP \\ ( https://arxiv.org/abs/1507.08850 , 6kb)  \\ arXiv:1509.04914 (*crosslisting*) replaced with revised version Mon, 2 May 2016 15:57:25 GMT (50kb,D)
Title: Geodesics in nonexpanding impulsive gravitational waves with $\Lambda$, Part I Authors: Clemens S\"amann, Roland Steinbauer, Alexander Lecke, Ji\v{r}\'i Podolsk\'y Categories: grqc mathph math.MP Comments: 32 pages, 3 figures, minor revisions, included "Part I" in the title, final version MSCclass: 83C15, 83C35, 46F10, 34A36 Journalref: Class. Quantum Grav. 33 115002 (2016) DOI: 10.1088/02649381/33/11/115002 \\ ( https://arxiv.org/abs/1509.04914 , 50kb)  \\ arXiv:1602.05407 (*crosslisting*) replaced with revised version Mon, 2 May 2016 13:35:41 GMT (150kb,D)
Title: Random bosonic states for robust quantum metrology Authors: Micha{\l} Oszmaniec, Remigiusz Augusiak, Christian Gogolin, Jan Ko{\l}ody\'nski, A. Ac\'in, Maciej Lewenstein Categories: quantph mathph math.MP Comments: 8 pages + 20 pages of appendix, 4 figures, v2:changed title, minor corrections, new references added, comments and suggestions are welcome \\ ( https://arxiv.org/abs/1602.05407 , 150kb)  \\ arXiv:1602.06786 (*crosslisting*) replaced with revised version Sun, 1 May 2016 03:17:11 GMT (24kb)
Title: Generalized quarkantiquark potentials from a $q$deformed AdS$_5 \times $S$^5$ background Authors: Takashi Kameyama, Kentaroh Yoshida Categories: hepth mathph math.MP nlin.SI Comments: 34 pages, no figure, LaTeX; v3: references added and minor changes Reportno: KUNS2610 \\ ( https://arxiv.org/abs/1602.06786 , 24kb)  \\ arXiv:1603.07508 (*crosslisting*) replaced with revised version Mon, 2 May 2016 09:09:22 GMT (31kb,D)
Title: Entanglement and coherence in quantum state merging Authors: A. Streltsov, E. Chitambar, S. Rana, M. N. Bera, A. Winter, M. Lewenstein Categories: quantph mathph math.MP physics.optics Comments: 9 pages, 1 figure. Lemma 5 in Appendix D of the previous version was not correct. This did not affect the results of the main text \\ ( https://arxiv.org/abs/1603.07508 , 31kb)  \\ arXiv:1601.07810 (*crosslisting*) replaced with revised version Mon, 2 May 2016 08:27:17 GMT (2453kb,D)
Title: The Unfitted Discontinuous Galerkin Method for Solving the EEG Forward Problem Authors: Andreas N\"u{\ss}ing, Carsten H. Wolters, Heinrich Brinck, Christian Engwer Categories: cs.CE math.NA qbio.NC Comments: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible MSCclass: 35J25, 35J75, 35Q92, 65N30, 68U20, 92C50 ACMclass: G.1.8; G.1.10; I.6.0; J.3 \\ ( https://arxiv.org/abs/1601.07810 , 2453kb)  \\ arXiv:1505.03259 (*crosslisting*) replaced with revised version Sat, 30 Apr 2016 01:20:56 GMT (109kb,D)
Title: Coordination Over MultiAgent Networks With Unmeasurable States and FiniteLevel Quantization Authors: Yang Meng, Tao Li, JiFeng Zhang Categories: cs.SY math.OC Comments: 10 pages, 2 figures \\ ( https://arxiv.org/abs/1505.03259 , 109kb)  \\ arXiv:1602.04662 (*crosslisting*) replaced with revised version Sat, 30 Apr 2016 13:24:40 GMT (490kb,D)
Title: Optimal Control of an Energy Storage Facility Under a Changing Economic Environment and Partial Information Authors: Anton A. Shardin, Michaela Sz\"olgyenyi Categories: qfin.MF math.OC Comments: Forthcoming in International Journal of Theoretical and Applied Finance MSCclass: 93E20, 93E11, 60H10 \\ ( https://arxiv.org/abs/1602.04662 , 490kb)  \\ arXiv:1604.07478 (*crosslisting*) replaced with revised version Fri, 29 Apr 2016 20:02:38 GMT (225kb,D)
Title: Collection and Dissemination of Data on TimeVarying Digraphs Authors: Kevin Topley Categories: cs.SY math.OC Comments: 12 pages, 8 figures MSCclass: 68M10, 68M14, 90B18 ACMclass: E.1; G.2.2; H.2.4; H.3.4 \\ ( https://arxiv.org/abs/1604.07478 , 225kb)  \\ arXiv:1604.07884 replaced with revised version Mon, 2 May 2016 19:21:11 GMT (109kb)
Title: Spatial BirthDeath Wireless Networks Authors: Abishek Sankararaman, Francois Baccelli Categories: cs.IT math.IT math.PR Comments: Submitted to IEEE Transactions on Information Theory. Corrected some typos from an earlier version \\ ( https://arxiv.org/abs/1604.07884 , 109kb)  \\ arXiv:1604.08437 (*crosslisting*) replaced with revised version Mon, 2 May 2016 06:39:12 GMT (103kb,D)
Title: Optimal pattern matching algorithms Authors: Gilles Didier Categories: cs.CC math.PR \\ ( https://arxiv.org/abs/1604.08437 , 103kb)  \\ arXiv:1604.08059 (*crosslisting*) replaced with revised version Sun, 1 May 2016 13:53:59 GMT (37kb)
Title: New Bounds for Hypergeometric Creative Telescoping Authors: Hui Huang Categories: cs.SC math.RA Comments: 8 pages, ISSAC 2016 submission ACMclass: I.1.2 DOI: 10.1145/2930889.2930893 \\ ( https://arxiv.org/abs/1604.08059 , 37kb)  \\ arXiv:1602.05126 (*crosslisting*) replaced with revised version Mon, 2 May 2016 16:52:31 GMT (16kb)
Title: PoissonLie Tduality as a boundary phenomenon of ChernSimons theory Authors: Pavol \v{S}evera Categories: hepth math.SG Comments: 17 pages \\ ( https://arxiv.org/abs/1602.05126 , 16kb) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% For general information on the new math archive (partitioned by keyword subject classification), see http://arxiv.org/new/math.html For subscribe options to combined math archives, email To: math@arxiv.org, Subject: subscribe _______________________________________ Snark Más información en http://mailman.uba.ar/mailman/listinfo/snark



