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A new integral equation for the first passage time density of the Ornstein-Uhlenbeck processAug 06 2019The Laplace transform of the first passage time density of the Ornstein--Uhlenbeck process for a constant threshold contains a ratio of two parabolic cylinder functions for which no analytical inversion formula is available. Recently derived inverse Laplace ... More

Revisiting Biorthogonal Polynomials. An $LU$ factorization discussionJul 09 2019The Gauss-Borel or $LU$ factorization of Gram matrices of bilinear forms is the pivotal element in the discussion of the theory of biorthogonal polynomials. The construction of biorthogonal families of polynomials and its second kind functions, of the ... More

Weak convergence of topological measuresJul 05 2019Topological measures and deficient topological measures are defined on open and closed subsets of a topological space, generalize regular Borel measures, and correspond to certain non-linear functionals. They lack subadditivity, and many standard techniques ... More

Isomorphism problems for tensors, groups, and cubic forms: completeness and reductionsJun 30 2019In this paper we consider the problems of testing isomorphism of tensors, $p$-groups, cubic forms, algebras, and more, which arise from a variety of areas, including machine learning, group theory, and cryptography. These problems can all be cast as orbit ... More

Integral representation using Green function for fractional Hardy equationJun 29 2019Our main aim is to study Green function for the fractional Hardy operator $P:=(-\Delta)^s -\frac{\theta}{|x|^{2s}}$ in $\mathbb{R}^N$, where $0<\theta<\Lambda_{N,s}$ and $\Lambda_{N,s}$ is the best constant in the fractional Hardy inequality. Using Green ... More

The p-norm of hypermatrices with symmetriesJun 25 2019The $p$-norm of $r$-matrices generalizes the $2$-norm of $2$-matrices. It is shown that if a nonnegative $r$-matrix is symmetric with respect to two indices $j$ and $k$, then the $p$-norm is attained for some set of vectors such that the $i$th and the ... More

Closed-form expressions for Farhi's constant and related integrals and its generalizationJun 10 2019In a recent work, Farhi developed a Fourier series expansion for the function $\,\ln{\Gamma(x)}\,$ on the interval $(0,1)$, which allowed him to derive a nice formula for the constant $\,\eta := 2 \int_0^1{\ln{\Gamma(x)} \, \sin{(2 \pi x)} \, dx}$. At ... More

Prokhorov-like conditions for weak compactness of sets of bounded Radon measures on different topological spacesJun 09 2019The paper presents some weak compactness criterion for a subset $M$ of the set $\mathfrak{RM}_b(T,\mathcal{G})$ of all positive bounded Radon measures on a Hausdorff topological space $(T,\mathcal{G})$ similar to the Prokhorov criterion for a complete ... More

A Heat Conduction Problem with Sources Depending on the Average of the Heat Flux on the BoundaryMay 29 2019Motivated by the modeling of temperature regulation in some mediums, we consider the non-classical heat conduction equation in the domain $D=\mathbb{R}^{n-1}\times\br^{+}$ for which the internal energy supply depends on an average in the time variable ... More

A basic framework for fixed point theorems: ball spaces and spherical completenessMay 22 2019We systematically develop a general framework in\linebreak which various notions of functions being contractive, as well as of spaces being complete, can be simultaneously encoded. Derived from the notions of ultrametric balls and spherical completeness, ... More

On liners viscoacoustic impedance boundary conditions for an array of Helmholtz resonators in 3DMay 21 2019The present work deals with the resolution of the Linearized Navier-Stokes problem in a domain made of an array that consists into a repetition of elongated resonators connected to an half-space. We provide and justify a limit equivalent model which takes ... More

Finite automata, probabilistic method, and occurrence enumeration of a pattern in words and permutationsMay 14 2019The main theme of this paper is the enumeration of the occurrence of a pattern in words and permutations. We mainly focus on asymptotic properties of the sequence $f_r^v(k,n),$ the number of $n$-array $k$-ary words that contain a given pattern $v$ exactly ... More

Algorithms and Complexity for some Multivariate ProblemsMay 03 2019We study multivariate problems like function approximation, numerical integration, global optimization and dispersion. We obtain new results on the information complexity $n(\varepsilon,d)$ of these problems. The information complexity is the amount of ... More

Almost product structures on statistical manifolds and para-Kähler-like statistical submersionsApr 20 2019The main purpose of the present work is to investigate statistical manifolds endowed with almost product structures. We prove that the statistical structure of a para-K\"{a}hler-like statistical manifold of constant curvature in the Kurose's sense is ... More

Almost product structures on statistical manifolds and para-Kähler-like statistical submersionsApr 20 2019Aug 15 2019The main purpose of the present work is to investigate statistical manifolds endowed with almost product structures. We prove that the statistical structure of a para-K\"{a}hler-like statistical manifold of constant curvature in the Kurose's sense is ... More

Phase transition in the exclusion process on the Sierpinski gasket with slowed boundary reservoirsApr 18 2019We derive the macroscopic laws that govern the evolution of the density of particles in the exclusion process evolving on the Sierpinski gasket in the presence of a slow boundary. Depending on the slowness of the boundary we obtain, at the hydrodynamics ... More

A Kaczmarz algorithm for sequences of projections, infinite products, and applications to frames in IFS $L^{2}$ spacesApr 09 2019We show that an idea, originating initially with a fundamental recursive iteration scheme (usually referred as "the" Kaczmarz algorithm), admits important applications in such infinite-dimensional, and non-commutative, settings as are central to spectral ... More

Learning the undecidable from networked systemsApr 08 2019Apr 22 2019This article presents a theoretical investigation of computation beyond the Turing barrier from emergent behavior in distributed (or parallel) systems. In particular, we present an algorithmic network that is a mathematical model of a networked population ... More

Learning the undecidable from networked systemsApr 08 2019This article presents a theoretical investigation of computation beyond the Turing barrier from emergent behavior in distributed (or parallel) systems. In particular, we present an algorithmic network that is a mathematical model of a networked population ... More

Galton-Watson gamesApr 08 2019We consider two-player combinatorial games in which the graph of positions is random and perhaps infinite, focusing on directed Galton-Watson trees. As the offspring distribution is varied, a game can undergo a phase transition, in which the probability ... More

A Polymatroid Approach to Generalized Weights of Rank Metric CodesApr 03 2019We consider the notion of a $(q,m)$-polymatroid, due to Shiromoto, and the more general notion of $(q,m)$-demi-polymatroid, and show how generalized weights can be defined for them. Further, we establish a duality for these weights analogous to Wei duality ... More

A Polymatroid Approach to Generalized Weights of Rank Metric CodesApr 03 2019May 27 2019We consider the notion of a $(q,m)$-polymatroid, due to Shiromoto, and the more general notion of $(q,m)$-demi-polymatroid, and show how generalized weights can be defined for them. Further, we establish a duality for these weights analogous to Wei duality ... More

Balanced frames: a useful tool in signal processing with good propertiesApr 01 2019So far there has not been paid attention in the literature to frames that are balanced, i.e. those frames which sum is zero. In this paper we study balanced frames, and in particular balanced unit norm tight frames in finite dimensional Hilbert spaces. ... More

Balanced frames: a useful tool in signal processing with good propertiesApr 01 2019Apr 12 2019So far there has not been paid attention in the literature to frames that are balanced, i.e. those frames which sum is zero. In this paper we consider balanced frames, and in particular balanced unit norm tight frames in finite dimensional Hilbert spaces. ... More

Asymptotic behaviour of the one-dimensional "rock-paper-scissors" cyclic cellular automatonMar 29 2019The one-dimensional three-state cyclic cellular automaton is a simple spatial model with three states in a cyclic "rock-paper-scissors" prey-predator relationship. Starting from a random configuration, similar states gather in increasingly large clusters; ... More

Combining Model and Parameter Uncertainty in Bayesian Neural NetworksMar 18 2019Mar 20 2019Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using Bayesian approach: ... More

Combining Model and Parameter Uncertainty in Bayesian Neural NetworksMar 18 2019Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using Bayesian approach: ... More

Combining Model and Parameter Uncertainty in Bayesian Neural NetworksMar 18 2019May 25 2019Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using Bayesian approach: ... More

Transfer operators, atomic decomposition and the BestiaryMar 16 2019Arbieto and S. recently used atomic decomposition to study transfer operators. We give a long list of old and new expanding dynamical systems for which those results can be applied, obtaining the quasi-compactness of transfer operator acting on Besov ... More

Transfer operators and atomic decompositionMar 16 2019Apr 16 2019We use the method of atomic decomposition and a new family of Banach spaces to study the action of transfer operators associated to piecewise-defined maps. It turns out that these transfer operators are quasi-compact even when the associated potential, ... More

Transfer operators and atomic decompositionMar 16 2019We use the method of atomic decomposition and a new family of Banach spaces to study the action of transfer operators associated to piecewise-defined maps. It turns out that these transfer operators are quasi-compact even when the associated potential, ... More

A logarithmic estimate for inverse source scattering problem with attenuation in a two-layered mediumMar 08 2019The paper aims a logarithmic stability estimate for the inverse source problem of the one-dimensional Helmholtz equation with attenuation factor in a two layer medium. We establish a stability by using multiple frequencies at the two end points of the ... More

Manifold interpolation and model reductionFeb 18 2019One approach to parametric and adaptive model reduction is via the interpolation of orthogonal bases, subspaces or positive definite system matrices. In all these cases, the sampled inputs stem from matrix sets that feature a geometric structure and thus ... More

Generalized semimodularity: order statisticsFeb 14 2019A notion of generalized $n$-semimodularity is introduced, which extends that of (sub/super)mod\-ularity in four ways at once. The main result of this paper, stating that every generalized $(n\colon\!2)$-semimodular function on the $n$th Cartesian power ... More

A Stochastic Approach to Eulerian NumbersFeb 08 2019We examine the aggregate behavior of one-dimensional random walks in a model known as (one-dimensional) Internal Diffusion Limited Aggregation. In this model, a sequence of $n$ particles perform random walks on the integers, beginning at the origin. Each ... More

Superposition, reduction of multivariable problems, and approximationFeb 07 2019We study reduction schemes for functions of "many" variables into system of functions in one variable. Our setting includes infinite-dimensions. Following Cybenko-Kolmogorov, the outline for our results is as follows: We present explicit reductions schemes ... More

Superposition, reduction of multivariable problems, and approximationFeb 07 2019Mar 06 2019We study reduction schemes for functions of "many" variables into system of functions in one variable. Our setting includes infinite-dimensions. Following Cybenko-Kolmogorov, the outline for our results is as follows: We present explicit reductions schemes ... More

Decomposition of Gaussian processes, and factorization of positive definite kernelsDec 28 2018We establish a duality for two factorization questions, one for general positive definite (p.d) kernels $K$, and the other for Gaussian processes, say $V$. The latter notion, for Gaussian processes is stated via Ito-integration. Our approach to factorization ... More

Hypercomplex Generalizations of Gaussian-type MeasuresDec 15 2018The article is devoted to a new type of measures which are hypercomplex generalizations of Gaussian-type measures. The considered such measures are related with solutions of high order hyperbolic PDEs and related Markov processes. Their characteristic ... More

A panorama of positivityDec 13 2018This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or mass distributions). ... More

A panorama of positivityDec 13 2018May 13 2019This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or mass distributions). ... More

Improved invariant polytope algorithm and applicationsDec 07 2018May 07 2019In several papers of 2013 - 2016, Guglielmi and Protasov made a breakthrough in the problem of the joint spectral radius computation, developing the invariant polytope algorithm which for most matrix families finds the exact value of the joint spectral ... More

Improved invariant polytope algorithm and applicationsDec 07 2018In several papers of 2013 - 2016, Guglielmi and Protasov made a breakthrough in the problem of the joint spectral radius computation, developing the invariant polytope algorithm which for most matrix families finds the exact value of the joint spectral ... More

On incompressible high order networksDec 04 2018Dec 13 2018This work presents a theoretical investigation of incompressible high order networks defined by a generalized graph representation. In particular, we study the incompressibility (i.e., algorithmic randomness) of snapshot-like dynamic networks in comparison ... More

The $p$-contest with $p\ne 1$Dec 03 2018We study asymptotic properties of a Markov system of $N \geq 3$ points in $[0,1]$ in which, at each step in discrete time, the point farthest from the current centre of mass, multiplied by a constant $p>0$, is removed and replaced by an independent $\zeta$-distributed ... More

Convergence in the $p$-contest modelDec 03 2018Mar 12 2019We study asymptotic properties of the following Markov system of $N \geq 3$ points in~$[0,1]$. At each time step, the point farthest from the current centre of mass, multiplied by a constant $p>0$, is removed and replaced by an independent $\zeta$-distributed ... More

Recovery guarantees for polynomial approximation from dependent data with outliersNov 25 2018Learning non-linear systems from noisy, limited, and/or dependent data is an important task across various scientific fields including statistics, engineering, computer science, mathematics, and many more. In general, this learning task is ill-posed; ... More

Two Models of Latent Consensus in Multi-Agent SystemsNov 23 2018In this paper, we propose several consensus protocols of the first and second order for networked multi-agent systems and provide explicit representations for their asymptotic states. These representations involve the eigenprojection of the Laplacian ... More

Slit-slide-sew bijections for bipartite and quasibipartite plane mapsNov 19 2018Dec 20 2018We unify and extend previous bijections on plane quadrangulations to bipartite and quasibipartite plane maps. Starting from a bipartite plane map with a distinguished edge and two distinguished corners (in the same face or in two different faces), we ... More

A central limit theorem for descents and major indices in fixed conjugacy classes of $S_n$Nov 12 2018The distribution of descents in fixed conjugacy classes of $S_n$ has been studied, and it is shown that its moments have interesting properties. Kim and Lee showed, by using Curtiss' theorem and moment generating functions, how to prove a central limit ... More

Sensitivity of $\ell_{1}$ minimization to parameter choiceOct 29 2018Apr 02 2019The use of generalized LASSO is a common technique for recovery of structured high-dimensional signals. Each generalized LASSO program has a governing parameter whose optimal value depends on properties of the data. At this optimal value, compressed sensing ... More

Sensitivity of $\ell_{1}$ minimization to parameter choiceOct 29 2018Apr 01 2019The use of generalized LASSO is a common technique for recovery of structured high-dimensional signals. Each generalized LASSO program has a governing parameter whose optimal value depends on properties of the data. At this optimal value, compressed sensing ... More

An algorithmically random family of MultiAspect Graphs and its topological propertiesOct 27 2018This article presents a theoretical investigation of incompressibility and randomness in generalized representations of graphs along with its implications on network topological properties. We extend previous studies on plain algorithmically random classical ... More

Algorithmically random generalized graphs and its topological propertiesOct 27 2018May 31 2019This article presents a theoretical investigation of incompressibility and randomness in generalized representations of graphs along with its implications on network topological properties. We extend previous studies on plain algorithmically random classical ... More

An algorithmically random family of MultiAspect Graphs and its topological propertiesOct 27 2018Mar 06 2019This article presents a theoretical investigation of incompressibility and randomness in generalized representations of graphs along with its implications on network topological properties. We extend previous studies on plain algorithmically random classical ... More

On random primitive sets, directable NDFAs and the generation of slowly synchronizing DFAsOct 24 2018We tackle the problem of the randomized generation of slowly synchronizing deterministic automata (DFAs) by generating random primitive sets of matrices. We show that when the randomized procedure is too simple the exponent of the generated sets is O(n ... More

On $n$-superharmonic functions and some geometric applicationsOct 24 2018In this paper we study asymptotic behavior of $n$-superharmonic functions at isolated singularity using the Wolff potential and $n$-capacity estimates in nonlinear potential theory. Our results are inspired by and extend those of Arsove-Huber and Taliaferro ... More

The $d$-dimensional softcore Coulomb potential and the generalized confluent Heun equationOct 15 2018An analysis of the generalized confluent Heun equation $(\alpha_2r^2+\alpha_1r)\,y''+(\beta_2r^2+\beta_1r+\beta_0)\,y'-(\varepsilon_1r+\varepsilon_0)\,y=0$ in $d$-dimensional space, where $\{\alpha_i, \beta_i, \varepsilon_i\}$ are real parameters, is ... More

Hindman's finite sums theorem and its application to topologizations of algebrasOct 03 2018The first part of the paper is a brief overview of Hindman's finite sums theorem, its prehistory and a few of its further generalizations, and a modern technique used in proving these and similar results, which is based on idempotent ultrafilters in ultrafilter ... More

Approximation and sampling of multivariate probability distributions in the tensor train decompositionOct 02 2018Jul 03 2019General multivariate distributions are notoriously expensive to sample from, particularly the high-dimensional posterior distributions in PDE-constrained inverse problems. This paper develops a sampler for arbitrary continuous multivariate distributions ... More

Approximation and sampling of multivariate probability distributions in the tensor train decompositionOct 02 2018Nov 21 2018General multivariate distributions are notoriously expensive to sample from, particularly the high-dimensional posterior distributions in PDE-constrained inverse problems. This paper develops a sampler for arbitrary continuous multivariate distributions ... More

An asymptotic expansion for the error term in the Brent-McMillan algorithm for Euler's constantSep 12 2018The Brent-McMillan algorithm is the fastest known procedure for the high-precision computation of Euler's constant $\gamma$ and is based on the modified Bessel functions $I_0(2x)$ and $K_0(2x)$. An error estimate for this algorithm relies on the optimally ... More

An asymptotic expansion for the error term in the Brent-McMillan algorithm for Euler's constantSep 12 2018Feb 16 2019The Brent-McMillan algorithm is the fastest known procedure for the high-precision computation of Euler's constant $\gamma$ and is based on the modified Bessel functions $I_0(2x)$ and $K_0(2x)$. An error estimate for this algorithm relies on the optimally ... More

SNS: A Solution-based Nonlinear Subspace method for time-dependent model order reductionSep 11 2018Feb 05 2019Several reduced order models have been successfully developed for nonlinear dynamical systems. To achieve a considerable speed-up, a hyper-reduction step is needed to reduce the computational complexity due to nonlinear terms. Many hyper-reduction techniques ... More

Stochastic order on metric spaces and the ordered Kantorovich monadAug 29 2018In earlier work, we had introduced the Kantorovich probability monad on complete metric spaces, extending a construction due to van Breugel. Here we extend the Kantorovich monad further to a certain class of ordered metric spaces, by endowing the spaces ... More

An explicit formula for a weight enumerator of linear-congruence codesAug 28 2018An explicit formula for a weight enumerator of linear-congruence codes is provided. This extends the work of Bibak and Milenkovic [IEEE ISIT (2018) 431-435] addressing the binary case to the non-binary case. Furthermore, the extension simplifies their ... More

Gradient Flows for Frame Potentials on the Wasserstein SpaceAug 28 2018In this paper we bring together some of the key ideas and methods of two very lively fields of mathematical research, frame theory and optimal transport, using the methods of the second to answer questions posed in the first. In particular, we construct ... More

Generalized exponential basis for efficient solving of homogeneous diffusion free boundary problems: Russian option pricingAug 24 2018This paper develops a method for solving free boundary problems for time-homogeneous diffusions. We combine the complete exponential system of solutions for the heat equation, transmutation operators and recently discovered Neumann series of Bessel functions ... More

Choosing 1 of N with and without lucky numbersAug 24 2018How many fair coin tosses to choose 1 of $n$ options with uniform probability? Although a probability problem, the solution is essentially number-theoretic, with special roles for Mersenne numbers, Fermat numbers, and the haupt exponent. We propose a ... More

The Bohr compactification of an abelian group as a quotient of its Stone-Čech compactificationAug 14 2018Aug 15 2018We will prove that, for any abelian group $G$, the canonical (surjective and continuous) mapping $\boldsymbol{\beta}G \to {\frak b}G$ from the Stone-\v{C}ech compactification $\boldsymbol{\beta}G$ of $G$ to its Bohr compactfication ${\frak b}G$ is a homomorphism ... More

Extended (p,q)-Mittag-Leffler function and its propertiesAug 04 2018In this study our aim to define the extended $(p,q)$-Mittag-Leffler(ML) function by using extension of beta functions and to obtain the integral representation of new function. We also take the Mellin transform of this new function in terms of Wright ... More

Reducing Simply Generated Trees by Iterative Leaf CuttingAug 01 2018We consider a procedure to reduce simply generated trees by iteratively removing all leaves. In the context of this reduction, we study the number of vertices that are deleted after applying this procedure a fixed number of times by using an additive ... More

Mixed mode oscillations and phase locking in coupled FitzHugh-Nagumo model neuronsJul 27 2018We study the dynamics of a low-dimensional system of coupled model neurons as a step towards understanding the vastly complex network of neurons in the brain. We analyze the bifurcation structure of a system of two model neurons with unidirectional coupling ... More

Laplacian growth & sandpiles on the Sierpinski gasket: limit shape universality and exact solutionsJul 23 2018Jun 19 2019We establish quantitative spherical shape theorems for rotor-router aggregation and abelian sandpile growth on the graphical Sierpinski gasket ($SG$) when particles are launched from the corner vertex. In particular, the abelian sandpile growth problem ... More

Laplacian growth & sandpiles on the Sierpinski gasket: limit shape universality and exact solutionsJul 23 2018Sep 06 2018We establish quantitative spherical shape theorems for rotor-router aggregation and abelian sandpile growth on the graphical Sierpinski gasket ($SG$) when particles are launched from the corner vertex. In particular, the abelian sandpile growth problem ... More

Laplacian growth & sandpiles on the Sierpinski gasket: limit shape universality and exact solutionsJul 23 2018Aug 05 2019We establish quantitative spherical shape theorems for rotor-router aggregation and abelian sandpile growth on the graphical Sierpinski gasket ($SG$) when particles are launched from the corner vertex. In particular, the abelian sandpile growth problem ... More

Multivariate Public Key Cryptography and Digital SignatureJul 20 2018Jul 23 2018In this paper, algorithms for multivariate public key cryptography and digital signature are described. Plain messages and encrypted messages are arrays, consisting of elements from a fixed finite ring or field. The encryption and decryption algorithms ... More

On reproducing kernels, and analysis of measuresJul 11 2018Jul 17 2018Starting with the correspondence between positive definite kernels on the one hand and reproducing kernel Hilbert spaces (RKHSs) on the other, we turn to a detailed analysis of associated measures and Gaussian processes. Point of departure: Every positive ... More

On reproducing kernels, and analysis of measuresJul 11 2018Feb 23 2019Starting with the correspondence between positive definite kernels on the one hand and reproducing kernel Hilbert spaces (RKHSs) on the other, we turn to a detailed analysis of associated measures and Gaussian processes. Point of departure: Every positive ... More

Lattice paths and branched continued fractions: An infinite sequence of generalizations of the Stieltjes--Rogers and Thron--Rogers polynomials, with coefficientwise Hankel-total positivityJul 09 2018We define an infinite sequence of generalizations, parametrized by an integer $m \ge 1$, of the Stieltjes--Rogers and Thron--Rogers polynomials; they arise as the power-series expansions of some branched continued fractions, and as the generating polynomials ... More

Thermodynamics of elastoplastic porous rocks at large strains towards earthquake modelingJul 02 2018Jul 05 2018A mathematical model for an elastoplastic porous continuum subject to large strains in combination with reversible damage (aging), evolving porosity, water and heat transfer is advanced. The inelastic response is modeled within the frame of plasticity ... More

On the parabolic Harnack inequality for non-local diffusion equationsJun 12 2018We settle the open question concerning the Harnack inequality for globally positive solutions to non-local in time diffusion equations by constructing a counter-example for dimensions $d\ge\beta$, where $\beta\in(0,2]$ is the order of the equation with ... More

Deep Bayesian regression modelsJun 06 2018Jun 07 2018Regression models are used for inference and prediction in a wide range of applications providing a powerful scientific tool for researchers and analysts from different fields. In many research fields the amount of available data as well as the number ... More

The lemniscate tree of a random polynomialJun 01 2018To each generic complex polynomial $p(z)$ there is associated a labeled binary tree (here referred to as a "lemniscate tree") that encodes the topological type of the graph of $|p(z)|$. The branching structure of the lemniscate tree is determined by the ... More

Counting partitions inside a rectangleMay 22 2018Feb 04 2019We consider the number of partitions of $n$ whose Young diagrams fit inside an $m \times \ell$ rectangle; equivalently, we study the coefficients of the $q$-binomial coefficient $\binom{m+\ell}{m}_q$. We obtain sharp asymptotics throughout the regime ... More

Selections and Higher Separation AxiomsMay 19 2018Oct 15 2018This survey presents some historical background and recent developments in the area of selections for set-valued mappings along with several open questions. It was written with the hope that the presented material may pique an interest in the selection ... More

Contour location via entropy reduction leveraging multiple information sourcesMay 19 2018Dec 19 2018We introduce an algorithm to locate contours of functions that are expensive to evaluate. The problem of locating contours arises in many applications, including classification, constrained optimization, and performance analysis of mechanical and dynamical ... More

The Kashaev Equation and Related RecurrencesMay 10 2018Feb 21 2019The hexahedron recurrence was introduced by R. Kenyon and R. Pemantle in the study of the double-dimer model in statistical mechanics. It describes a relationship among certain minors of a square matrix. This recurrence is closely related to the Kashaev ... More

The Hilbert transform and orthogonal martingales in Banach spacesMay 10 2018Let $X$ be a given Banach space and let $M$, $N$ be two orthogonal $X$-valued local martingales such that $N$ is weakly differentially subordinate to $M$. The paper contains the proof of the estimate $$ \mathbb E \Psi(N_t) \leq C_{\Phi,\Psi,X} \mathbb ... More

The Hilbert transform and orthogonal martingales in Banach spacesMay 10 2018Jul 02 2019Let $X$ be a given Banach space and let $M$, $N$ be two orthogonal $X$-valued local martingales such that $N$ is weakly differentially subordinate to $M$. The paper contains the proof of the estimate $$ \mathbb E \Psi(N_t) \leq C_{\Phi,\Psi,X} \mathbb ... More

Capacities, removable sets and $L^p$-uniqueness on Wiener spacesMay 10 2018We prove the equivalence of two different types of capacities in abstract Wiener spaces. This yields a criterion for the $L^p$-uniqueness of the Ornstein-Uhlenbeck operator and its integer powers defined on suitable algebras of functions vanishing in ... More

Reconstruction of a compactly supported sound profile in the presence of a random background mediumMay 05 2018May 25 2018In this paper, we present algorithms for reconstructing an unknown compact scatterer embedded in a random noisy background medium, given measurements of the scattered field and information about the background medium and the sound profile. We present ... More

Beyond Haar and Cameron-Martin: the Steinhaus supportApr 30 2018Mar 14 2019Motivated by a Steinhaus-like interior-point property involving the Cameron-Martin space of Gaussian measure theory, we study a group-theoretic analogue, the Steinhaus triple $(H,G,\mu)$, and construct a Steinhaus support, a Cameron-Martin-like subset, ... More

Beyond Haar and Cameron-Martin: the Steinhaus supportApr 30 2018Aug 14 2018Motivated by a Steinhaus-like interior-point property involving the Cameron-Martin space of Gaussian measure theory, we study a group-theoretic analogue, the Steinhaus triple $(H,G,\mu)$, and construct a Steinhaus support, a Cameron-Martin-like subset, ... More

A note on an integral of Dixit, Roy and ZaharescuApr 20 2018May 09 2018In a recent paper, Dixit {\it et al.\/} [Acta Arith. {\bf 177} (2017) 1--37] posed two open questions whether the integral \[{\hat J}_{k}(\alpha)=\int_0^\infty\frac{xe^{-\alpha x^2}}{e^{2\pi x}-1}\,{}_1F_1(-k,3/2;2\alpha x^2)\,dx\] for $\alpha>0$ could ... More

Bimonoidal Structure of Probability MonadsApr 10 2018Aug 22 2018We give a conceptual treatment of the notion of joints, marginals, and independence in the setting of categorical probability. This is achieved by endowing the usual probability monads (like the Giry monad) with a monoidal and an opmonoidal structure, ... More

Distribution of the Number of Corners in Tree--like TableauxApr 09 2018In this paper, we study tree--like tableaux and some of their probabilistic properties. Tree--like tableaux are in bijection with other combinatorial structures, including permutation tableaux, and have a connection to the partially asymmetric simple ... More

The variety of coset relation algebrasApr 07 2018Aug 12 2018A coset relation algebra is one embeddable into some full coset relation algebra, the latter is an algebra constructed from a system of groups, a coordinated system of isomorphisms between quotients of these groups, and a system of cosets that are used ... More

Memory equations as reduced Markov processesApr 06 2018A large class of linear memory differential equations in one dimension, where the evolution depends on the whole history, can be equivalently described as a projection of a Markov process living in a higher dimensional space. Starting with such a memory ... More

Energy estimates and model order reduction for stochastic bilinear systemsApr 05 2018In this paper, we investigate a large-scale stochastic system with bilinear drift and linear diffusion term. Such high dimensional systems appear for example when discretizing a stochastic partial differential equations in space. We study a particular ... More