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On the geometry of polytopes generated by heavy-tailed random vectorsJul 16 2019We study the geometry of centrally-symmetric random polytopes, generated by $N$ independent copies of a random vector $X$ taking values in $\mathbb{R}^n$. We show that under minimal assumptions on $X$, for $N \gtrsim n$ and with high probability, the ... More

Image-Driven Biophysical Tumor Growth Model CalibrationJul 16 2019We present a novel formulation for the calibration of a biophysical tumor growth model from a single-time snapshot, MRI scan of a glioblastoma patient. Tumor growth models are typically nonlinear parabolic partial differential equations (PDEs). Thus, ... More

Asymptotic stabilization of a system of coupled $n$th--order differential equations with potentially unbounded high-frequency oscillating perturbationsJul 15 2019This paper deals with an analysis and design of robust, state-feedback control law uniform-asymptotically stabilizing at origin the system consisting of coupled $n$th--order ordinary differential equations in the presence of a non-vanishing at $x=0$ or ... More

Discretized Fast-Slow Systems with Canard Points in Two DimensionsJul 15 2019We study the behaviour of slow manifolds for two different discretization schemes of fast-slow systems with canard fold points. The analysis uses the blow-up method to deal with the loss of normal hyperbolicity at the canard point. While the Euler method ... More

Where did the tumor start? An inverse solver with sparse localization for tumor growth modelsJul 15 2019We present a numerical scheme for solving an inverse problem for parameter estimation in tumor growth models for glioblastomas, a form of aggressive primary brain tumor. The growth model is a reaction-diffusion partial differential equation (PDE) for ... More

A Versatile Queuing System For Sharing Economy Platform OperationsJul 12 2019The paper deals with a sharing economy system with various management factors by using a bulk input G/M/1 type queuing model. The effective management of operating costs is vital for controlling the sharing economy platform and this research builds the ... More

Characterizations of nested GVZ-groups by central seriesJul 10 2019Many properties of groups can be defined by the existence of a particular normal series. The classic examples being solvability, supersolvability and nilpotence. Among the nilpotent groups are the so-called nested GVZ-groups --- groups where the centers ... More

Ollivier Ricci Curvature of Directed HypergraphsJul 10 2019We develop a definition of Ricci curvature on directed hypergraphs and explore the consequences of that definition. The definition generalizes Ollivier's definition for graphs. It involves a carefully designed optimal transport problem between sets of ... More

Riesz bases of exponentials for convex polytopes with symmetric facesJul 10 2019We prove that for any convex polytope $\Omega \subset \mathbb{R}^d$ which is centrally symmetric and whose faces of all dimensions are also centrally symmetric, there exists a Riesz basis of exponential functions in the space $L^2(\Omega)$.

On a $q-$analog of a singularly perturbed problem of irregular type with two complex time variablesJul 09 2019Analytic solutions and their formal asymptotic expansions for a family of the singularly perturbed $q-$difference-differential equations in the complex domain are constructed. They stand for a $q-$analog of the singularly perturbed partial differential ... More

On The Structure of Dyck LanguagesJul 04 2019We prove that the closure of the one-sided Dyck language in a free monoid is a two-sided Dyck language.

Lattice paths and branched continued fractions. II. Multivariate Lah polynomials and Lah symmetric functionsJul 04 2019We introduce the generic Lah polynomials $L_{n,k}(\phi)$, which enumerate unordered forests of increasing ordered trees with a weight $\phi_i$ for each vertex with $i$ children. We show that, if the weight sequence $\phi$ is Toeplitz-totally positive, ... More

Enriched Regular TheoriesJul 04 2019Regular and exact categories were first introduced by Michael Barr in 1971; since then, the theory has developed and found many applications in algebra, geometry, and logic. In particular, a small regular category determines a certain theory, in the sense ... More

Injective envelopes of transition systems and Ferrers languagesJul 04 2019We consider reflexive and involutive transition systems over an ordered alphabet $A$ equipped with an involution. We give a description of the injective envelope of any two-element set in terms of Galois lattice, from which we derive a test of its finiteness. ... More

Holonomy groups of compact flat solvmanifoldsJul 03 2019This article is concerned with the study of the holonomy group of flat solvmanifolds. It is known that the holonomy group of a flat solvmanifold is abelian; we give an elementary proof of this fact and moreover we prove that any finite abelian group is ... More

Anti-invariant Riemannian submersions from locally conformal Kaehler manifoldsJul 03 2019B. Sahin [9] introduced the notion of anti-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. In the present paper we extend the notion of anti-invariant and Lagrangian Riemannian submersions (a special anti-invariant ... More

Simplicial complexity of surface groups and systolic areaJul 02 2019The simplicial complexity is an invariant for finitely presentable groups that was recently introduced by Babenko, Balacheff and Bulteau to study systolic area. The simplicial complexity $\kappa(G)$ was proved to be a good approximation of the systolic ... More

A Note on Graphs of Dichromatic Number 2Jun 30 2019Neumann-Lara and \v{S}krekovski conjectured that every planar digraph is $2$-colourable. We show that this conjecture is equivalent to the more general statement that all oriented $K_5$-minor-free graphs are $2$-colourable.

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

Complexity of acyclic colorings of graphs and digraphs with degree and girth constraintsJun 28 2019We consider acyclic r-colorings in graphs and digraphs: they color the vertices in r colors, each of which induces an acyclic graph or digraph. (This includes the dichromatic number of a digraph, and the arboricity of a graph.) For any girth and sufficiently ... More

Evaluation of Abramowitz functions in the right half of the complex planeJun 28 2019A numerical scheme is developed for the evaluation of Abramowitz functions $J_n$ in the right half of the complex plane. For $n=-1,\, \ldots,\, 2$, the scheme utilizes series expansions for $|z|<1$ and asymptotic expansions for $|z|>R$ with $R$ determined ... More

The minimal observable clade size of exchangeable coalescentsJun 27 2019For $\Lambda$-$n$-coalescents with mutation, we analyse the size $O_n$ of the partition block of $i\in\{1,\ldots,n\}$ at the time where the first mutation appears on the tree that affects $i$ and is shared with any other $j\in\{1,\ldots,n\}$. We provide ... More

The Choi-Jamiolkowski isomorphism and covariant quantum channelsJun 27 2019A generalization of the Choi-Jamiolkowski isomorphism for completely positive maps between operator algebras is introduced. Particular emphasis is placed on the case of normal unital completely positive maps defined between von Neumann algebras. This ... More

Approximating the pth Root by Composite Rational FunctionsJun 26 2019A landmark result from rational approximation theory states that $x^{1/p}$ on $[0,1]$ can be approximated by a type-$(n,n)$ rational function with root-exponential accuracy. Motivated by the recursive optimality property of Zolotarev functions (for the ... More

A sharp upper bound for the size of Lusztig seriesJun 26 2019Jul 14 2019The paper is concerned with the character theory of finite groups of Lie type. The set of irreducible characters of a group $G$ of Lie type is partitioned into the Lusztig series. We determine the maximum of the sizes of such series for classical groups ... More

Using Markov chains to determine expected propagation time for probabilistic zero forcingJun 25 2019Zero forcing is a coloring game played on a graph where each vertex is initially colored blue or white and the goal is to color all the vertices blue by repeated use of a (deterministic) color change rule starting with as few blue vertices as possible. ... More

The complex Monge-Ampère equation with a gradient termJun 24 2019We consider the complex Monge-Amp\`ere equation with an additional linear gradient term inside the determinant. We prove existence and uniqueness of solutions to this equation on compact Hermitian manifolds.

Existence and almost uniqueness for $p$-harmonic Green functions on bounded domains in metric spacesJun 24 2019We study ($p$-harmonic) singular functions, defined by means of upper gradients, in bounded domains in metric measure spaces. It is shown that singular functions exist if and only if the complement of the domain has positive capacity, and that they satisfy ... More

Adding reversible reactions involving new species preserves oscillation in chemical reaction networksJun 21 2019We show that if a chemical reaction network (CRN) admits nondegenerate (resp., linearly stable) oscillation, and we add new reversible reactions involving new species to this CRN, then the new CRN so created also admits nondegenerate (resp., linearly ... More

Minimal resolutions of monomial idealsJun 20 2019An explicit combinatorial minimal free resolution of an arbitrary monomial ideal $I$ in a polynomial ring in $n$ variables over a field of characteristic $0$ is defined canonically, without any choices, using higher-dimensional generalizations of combined ... More

Multisymplectic actions of compact Lie groups on spheresJun 20 2019We give a geometric description of the obstruction to the existence of homotopy comoment maps in multisymplectic geometry. We apply this description to determine the existence of comoments for multisymplectic compact group actions on spheres and provide ... More

Optimal Reinsurance and Investment Strategies under Mean-Variance Criteria: Partial and Full InformationJun 20 2019Jul 04 2019This paper is concerned with an optimal reinsurance and investment problem for an insurance firm under the criterion of mean-variance. The driving Brownian motion and the rate in return of the risky asset price dynamic equation cannot be directly observed. ... More

Optimal Reinsurance and Investment Strategies under Mean-Variance Criteria: Partial and Full InformationJun 20 2019This paper is concerned with an optimal reinsurance and investment problem for an insurance firm under the criterion of mean-variance. The driving Brownian motion and the rate in return of the risky asset price dynamic equation cannot be directly observed. ... More

Group-theoretic generalisations of vertex and edge connectivitiesJun 19 2019Jun 25 2019Let $p$ be an odd prime. Let $P$ be a finite $p$-group of class $2$ and exponent $p$, whose commutator quotient $P/[P,P]$ is of order $p^n$. We define two parameters for $P$ related to central decompositions. The first parameter, $\kappa(P)$, is the smallest ... More

Refined Enumeration of Symmetry Classes of Alternating Sign MatricesJun 18 2019We prove refined enumeration results on several symmetry classes as well as related classes of alternating sign matrices with respect to classical boundary statistics, using the six-vertex model of statistical physics. More precisely, we study vertically ... More

A tunable multiresolution smoother for scattered data with application to particle filteringJun 16 2019A smoothing algorithm is presented that can reduce the small-scale content of data observed at scattered locations in a spatially extended domain. The smoother works by forming a Gaussian interpolant of the input data, and then convolving the interpolant ... More

On the halves of a Riordan array and their antecedentsJun 14 2019Jun 29 2019Every Riordan array has what we call a horizontal half and a vertical half. These halves of a Riordan array have been studied separately before. Here, we place them in a common context, showing that one may be obtained from the other. We also ask and ... More

On the halves of a Riordan array and their antecedentsJun 14 2019Every Riordan array has what we call a horizontal half and a vertical half. These halves of a Riordan array have been studied separately before. Here, we place them in a common context, showing that one may be obtained from the other. We also ask and ... More

Constant coefficient Laurent biorthogonal polynomials, Riordan arrays and moment sequencesJun 14 2019We study properties of constant coefficient Laurent biorthogonal polynomials using Riordan arrays. We give details of related orthogonal polynomials, and we explore relationships between the moments of these orthogonal polynomials, the moments of the ... More

Second-order cone representations of SONC conesJun 14 2019The second-order cone is a class of simple convex cones and the optimization problem over second-order cones can be solved more efficiently than semidefinite programming. Given that second-order cones have a strong expressive ability, it is interesting ... More

A Semi-strong Perfect Digraph TheoremJun 13 2019Reed showed that, if two graphs are $P_4$-isomorphic, then either both are perfect or none of them is. In this note we will derive an analogous result for perfect digraphs.

The $h^*$-polynomials of locally anti-blocking lattice polytopes and their $γ$-positivityJun 11 2019A lattice polytope $\mathcal{P} \subset \mathbb{R}^d$ is called a locally anti-blocking polytope if for any closed orthant $\mathbb{R}^d_{\varepsilon}$ in $\mathbb{R}^d$, $\mathcal{P} \cap \mathbb{R}^d_{\varepsilon}$ is unimodularly equivalent to an anti-blocking ... More

Schur ring and Codes for $S$-subgroups over $\Z_{2}^{n}$Jun 10 2019In this paper the relationship between $S$-subgroups in $\Z_{2}^{n}$ and binary codes is shown. If the codes used are both $P(T)$-codes and $G$-codes, then the $S$-subgroup is free. The codes constructed are cyclic, decimated or symmetric and the $S$-subgroups ... More

Randomization and reweighted $\ell_1$-minimization for A-optimal design of linear inverse problemsJun 10 2019We consider optimal design of PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We focus on the A-optimal design criterion, defined as the average posterior variance and quantified by the trace of the posterior covariance ... More

Weil representations via abstract data and Heisenberg groups: a comparisonJun 08 2019Let $B$ be a ring, not necessarily commutative, having an involution $*$ and let ${\mathrm U}_{2m}(B)$ be the unitary group of rank $2m$ associated to a hermitian or skew hermitian form relative to $*$. When $B$ is finite, we construct a Weil representation ... More

Antipodes, preantipodes and Frobenius functorsJun 08 2019We prove that a quasi-bialgebra admits a preantipode if and only if the associated free quasi-Hopf bimodule functor is Frobenius, if and only if the relative (opmonoidal) monad is a Hopf monad. The same results hold in particular for a bialgebra, tightening ... More

Invariant Schreier decorations of unimodular random networksJun 07 2019We prove that every $2d$-regular unimodular random network carries an invariant random Schreier decoration. Equivalently, it is the Schreier coset graph of an invariant random subgroup of the free group $F_d$. As a corollary we get that every $2d$-regular ... More

Three real Artin-Tate motivesJun 07 2019We analyze the spectrum of the tensor-triangulated category of Artin-Tate motives over the base field R of real numbers, with integral coefficients. Away from 2, we obtain the same spectrum as for complex Tate motives, previously studied by the second-named ... More

Explicit logarithmic formulas of special values of hypergeometric functions 3F2Jun 07 2019In a joint paper [4] by Otsubo, Terasoma and the first author, we proved that the special value 3F2(a,b,q;a+b,q;1) of the generalized hypergeometric function is a linear combination of log of algebraic numbers if the triplet (a,b,q) of rational numbers ... More

On the $r$-shifted central triangles of a Riordan arrayJun 04 2019Let $A$ be a proper Riordan array with general element $a_{n,k}$. We study the one parameter family of matrices whose general elements are given by $a_{2n+r, n+k+r}$. We show that each such matrix can be factored into a product of a Riordan array and ... More

Unconditional reflexive polytopesJun 03 2019A convex body is unconditional if it is symmetric with respect to reflections in all coordinate hyperplanes. In this paper, we investigate unconditional lattice polytopes with respect to geometric, combinatorial, and algebraic properties. In particular, ... More

A $2$-compact group as a spetsJun 03 2019Jun 12 2019In 1998 Malle introduced spetses which are mysterious objects with non-real Weyl groups. In algebraic topology, a $p$-compact group $\mathbf{X}$ is a space which is a homotopy-theoretic $p$-local analogue of a compact Lie group. A connected $p$-compact ... More

A $2$-compact group as a spetsJun 03 2019Jun 20 2019In 1998 Malle introduced spetses which are mysterious objects with non-real Weyl groups. In algebraic topology, a $p$-compact group $\mathbf{X}$ is a space which is a homotopy-theoretic $p$-local analogue of a compact Lie group. A connected $p$-compact ... More

A $2$-compact group as a spetsJun 03 2019In 1999 Brou\'{e}, Malle and Michel introduced the concept of a ``spets'' which is a mysterious object with a non-real Weyl group. In algebraic topology, a $p$-compact group $X$ is a space which is a homotopy-theoretic $p$-local analogue of a compact ... More

Cohomology ring of the flag variety vs Chow cohomology ring of the Gelfand-Zetlin toric varietyJun 01 2019We compare the cohomology ring of the flag variety $FL_n$ and the Chow cohomology ring of the Gelfand-Zetlin toric variety $X_{GZ}$. We show that $H^*(FL_n, \mathbb{Q})$ is the Gorenstein quotient of the subalgebra $L$ of $A^*(X_{GZ}, \mathbb{Q})$ generated ... 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

Singular Curves of Low Degree and Multifiltrations from Osculating SpacesMay 28 2019In order to study projections of smooth curves, we introduce multifiltrations obtained by combining flags of osculating spaces. We first use these multifiltrations to show that under the assumption $2\rho_g-2<d<2n$, the arithmetic genus of any non-degenerate ... More

A Note on a Unitary Analog to Redheffer's MatrixMay 27 2019May 28 2019We study a unitary analog to Redheffer's matrix. It is first proved that the determinant of this matrix is the unitary analogue to that of Redheffer's matrix. We also show that the coefficients of the characteristic polynomial may be expressed as sums ... More

A Note on a Unitary Analog to Redheffer's MatrixMay 27 2019We study a unitary analog to Redheffer's matrix. It is first proved that the determinant of this matrix is the unitary analogue to that of Redheffer's matrix. We also show that the coefficients of the characteristic polynomial may be expressed as sums ... More

Consecutive Detecting Arrays for Interaction FaultsMay 27 2019The concept of detecting arrays was developed to locate and detect interaction faults arising between the factors in a component-based system during software testing. In this paper, we propose a family of consecutive detecting arrays (CDAs) in which the ... More

RSN: Randomized Subspace NewtonMay 26 2019We develop a randomized Newton method capable of solving learning problems with huge dimensional feature spaces, which is a common setting in applications such as medical imaging, genomics and seismology. Our method leverages randomized sketching in a ... More

Basic sets for quasi-isolated blocks of finite groups of exceptional Lie typeMay 26 2019Let $G$ be a simple, simply connected algebraic group of exceptional type defined over $\mathbb{F}_q$ with Frobenius endomorphism $F: G \to G$. We prove that generalized $e$-Harish-Chandra theory holds for $\mathcal{E}(G^F,s)$ where $s \in G^{*F}$ is ... More

On the structure of power set ringMay 25 2019Jun 02 2019In this paper, Stone's Representation Theorem is generalized from Boolean rings to arbitrary commutative rings, and the generalized form is proved by an easy and natural approach. We have also made new progresses in the understanding the structure of ... More

On the structure of power set ringMay 25 2019May 28 2019In this paper, Stone's Representation Theorem is generalized from Boolean rings to arbitrary commutative rings, and the generalized form is proved by an easy and natural approach. We have also made new progresses in the understanding the structure of ... More

Abelian subgroups, nilpotent subgroups, and the largest character degree of a finite groupMay 25 2019Let $H$ be an abelian subgroup of a finite group $G$ and $\pi$ the set of prime divisors of $|H|$. We prove that $|H O_{\pi}(G)/ O_{\pi}(G)|$ is bounded above by the largest character degree of $G$. A similar result is obtained when $H$ is nilpotent.

Convergence towards the end space for random walks on Schreier graphsMay 24 2019We consider a transitive action of a finitely generated group $G$ and the Schreier graph $\Gamma$ it defines. For a probability measure $\mu$ on $G$ with a finite first moment we show that if the induced random walk is transient, it converges towards ... More

Classification of uniformly distributed measures of dimension $1$ in general codimensionMay 23 2019Starting with the work of Preiss on the geometry of measures, the classification of uniform measures in $\mathbb R^d$ has remained open, except for $d=1$ and for compactly supported measures in $d=2$, and for codimension $1$. In this paper we study $1$-dimensional ... More

Zero divisors of support size $3$ in group algebras and trinomials divided by irreducible polynomials over $GF(2)$May 23 2019A famous conjecture about group algebras of torsion-free groups states that there is no zero divisor in such group algebras. A recent approach to settle the conjecture is to show the non-existence of zero divisors with respect to the length of possible ... More

Blind identification of stochastic block models from dynamical observationsMay 22 2019We consider a blind identification problem in which we aim to recover a statistical model of a network without knowledge of the network's edges, but based solely on nodal observations of a certain process. More concretely, we focus on observations that ... 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

Complete Acyclic ColoringsMay 21 2019We study two parameters that arise from the dichromatic number and the vertex-arboricity in the same way that the achromatic number comes from the chromatic number. The adichromatic number of a digraph is the largest number of colors its vertices can ... 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

A Riesz basis criterion for Schrödinger operators with boundary conditions dependent on the eigenvalue parameterMay 20 2019We establish a criterion for a set of eigenfunctions of the one-dimensional Schr\"{o}dinger operator with distributional potentials and boundary conditions containing the eigenvalue parameter to be a Riesz basis for $\mathscr{L}_2(0,\pi)$.

Computing symmetric determinantal representationsMay 16 2019We introduce the DeterminantalRepresentations package for Macaulay2, which computes definite symmetric determinantal representations of real polynomials. We focus on quadrics and plane curves of low degree (i.e. cubics and quartics). Our algorithms are ... More

Gelfand-Naimark-Stone duality for normal spaces and insertion theoremsMay 16 2019Gelfand-Naimark-Stone duality provides an algebraic counterpart of compact Hausdorff spaces in the form of uniformly complete bounded archimedean $\ell$-algebras. In [4] we extended this duality to completely regular spaces. In this article we use this ... More

A projection algorithm on the set of polynomials with two boundsMay 14 2019The motivation of this work stems from the numerical approximation of bounded functions by polynomials satisfying the same bounds. The present contribution makes use of the recent algebraic characterization found in [B. Despr\'es, Numer. Algorithms, 76(3), ... More

A projection algorithm on the set of polynomials with two boundsMay 14 2019May 17 2019The motivation of this work stems from the numerical approximation of bounded functions by polynomials satisfying the same bounds. The present contribution makes use of the recent algebraic characterization found in [B. Despr\'es, Numer. Algorithms, 76(3), ... More

A Linear-algebraic Proof of Hilbert's Ternary Quartic TheoremMay 12 2019Hilbert's ternary quartic theorem states that every nonnegative degree 4 homogeneous polynomial in three variables can be written as a sum of three squares of homogeneous quadratic polynomials. We give a linear-algebraic approach to Hilbert's theorem ... More

Linearly continuous functions and $F_σ$-measurabilityMay 11 2019The linear continuity of a function defined on a vector space means that its restriction on every affine line is continuous. For functions defined on $\mathbb R^m$ this notion is near to the separate continuity for which it is required only the continuity ... More

Linearly continuous functions and $F_σ$-measurabilityMay 11 2019May 20 2019The linear continuity of a function defined on a vector space means that its restriction on every affine line is continuous. For functions defined on $\mathbb R^m$ this notion is near to the separate continuity for which it is required only the continuity ... More

Integrality and arithmeticity of solvable linear groupsMay 10 2019We develop a practical algorithm to decide whether a finitely generated subgroup of a solvable algebraic group $G$ is arithmetic. This incorporates a procedure to compute a generating set of an arithmetic subgroup of $G$. We also provide a simple new ... More

Properties of the Riemann-Lebesgue integrability in the non-additive caseMay 10 2019We study Riemann-Lebesgue integrability of a vector function relative to an arbitrary non-negative set function. We obtain some classical integral properties. Results regarding the continuity properties of the integral and relationships among Riemann-Lebesgue, ... More

Seshadri-type constants and Newton-Okounkov bodies for non-positive at infinity valuations of Hirzebruch surfacesMay 09 2019We consider flags $E_\bullet=\{X\supset E\supset \{q\}\}$, where $E$ is an exceptional divisor defining a non-positive at infinity divisorial valuation $\nu_E$ of a Hirzebruch surface $\mathbb{F}_\delta$ and $X$ the surface given by $\nu_E,$ and determine ... More

Learning to EvolveMay 08 2019Evolution and learning are two of the fundamental mechanisms by which life adapts in order to survive and to transcend limitations. These biological phenomena inspired successful computational methods such as evolutionary algorithms and deep learning. ... More

Extremal eigenvalues of critical Erdős-Rényi graphsMay 08 2019May 28 2019We complete the analysis of the extremal eigenvalues of the the adjacency matrix $A$ of the Erd\H{o}s-R\'enyi graph $G(N,d/N)$ in the critical regime $d \asymp \log N$ of the transition uncovered in [arXiv:1704.02953,arXiv:1704.02945], where the regimes ... More

Extremal eigenvalues of critical Erdős-Rényi graphsMay 08 2019We complete the analysis of the extremal eigenvalues of the the adjacency matrix $A$ of the Erd\H{o}s-R\'enyi graph $G(N,d/N)$ in the critical regime $d \asymp \log N$ of the transition uncovered in [arXiv:1704.02953,arXiv:1704.02945], where the regimes ... More

Cuntz semigroups of ultraproduct C*-algebrasMay 08 2019We prove that the category of abstract Cuntz semigroups is bicomplete. As a consequence, the category admits products and ultraproducts. We further show that the scaled Cuntz semigroup of the (ultra)product of a family of C*-algebras agrees with the (ultra)product ... More

Convolution systems on discrete abelian groups as a unifying strategy in sampling theoryMay 08 2019A regular sampling theory in a multiply generated unitary invariant subspace of a separable Hilbert space $\mathcal{H}$ is proposed. This subspace is associated to a unitary representation of a countable discrete abelian group $G$ on $\mathcal{H}$. The ... More

The strong approximation theorem and computing with linear groupsMay 07 2019We obtain a computational realization of the strong approximation theorem. That is, we develop algorithms to compute all congruence quotients modulo rational primes of a finitely generated Zariski dense group $H \leq \mathrm{SL}(n, \mathbb{Z})$ for $n ... More

A Riesz-Thorin type interpolation theorem in Euclidean Jordan algebrasMay 07 2019In a Euclidean Jordan algebra $V$ of rank $n$ which carries the trace inner product, to each element $a$ we associate the eigenvalue vector $\lambda(a)$ in $R^n$ whose components are the eigenvalues of $a$ written in the decreasing order. For any $p\in ... More

Incorporating Weisfeiler-Leman into algorithms for group isomorphismMay 06 2019In this paper we combine many of the standard and more recent algebraic techniques for testing isomorphism of finite groups (GpI) with combinatorial techniques that have typically been applied to Graph Isomorphism. In particular, we show how to combine ... More

Regular irreducible represntations of classical reductive groups over finite quotient ringsMay 04 2019A parametrization of irreducible representations associated with a regular adjoint orbit of a reductive group over finite quotient rings of a non-dyadic non-archimedean local filed is presented. The parametrization is given by means of (a subset of) the ... 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

Discrete time stochastic and deterministic Petri box calculusMay 01 2019We propose an extension with deterministically timed multiactions of discrete time stochastic and immediate Petri box calculus (dtsiPBC), previously presented by I.V. Tarasyuk, H. Maci\`a and V. Valero. In dtsdPBC, non-negative integers specify multiactions ... More

Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary samplingApr 30 2019Infinite-dimensional compressed sensing deals with the recovery of analog signals (functions) from linear measurements, often in the form of integral transforms such as the Fourier transform. This framework is well-suited to many real-world inverse problems, ... More

Widths of resonances above an energy-level crossingApr 29 2019We study the existence and location of the resonances of a $2\times 2$ semiclassical system of coupled Schr\"odinger operators, in the case where the two electronic levels cross at some point, and one of them is bonding, while the other one is anti-bonding. ... More

Ranking top-k trees in tree-based phylogenetic networksApr 29 2019'Tree-based' phylogenetic networks proposed by Francis and Steel have attracted much attention of theoretical biologists in the last few years. At the heart of the definitions of tree-based phylogenetic networks is the notion of 'support trees', about ... More

Combinatorics and structure of Hecke-Kiselman algebrasApr 27 2019Hecke-Kiselman monoids $\textrm{HK}_{\Theta}$ and their algebras $K[\textrm{HK}_{\Theta}]$, over a field $K$, associated to finite oriented graphs $\Theta$ are studied. In the case $\Theta $ is a cycle of length $n\geqslant 3$, a hierarchy of certain ... More

Vanishing-off subgroups and supercharacter theory productsApr 26 2019In this paper, we study the vanishing-off subgroups of supercharacters, and use these to determine several new characterizations of supercharacter theory products. In particular, we give a character theoretic characterization that allows us to conclude ... More

Deformation quantization and Kähler geometry with moment mapApr 26 2019In the first part of this paper we outline the constructions and properties of Fedosov star product and Berezin-Toeplitz star product. In the second part we outline the basic ideas and recent developments on Yau-Tian-Donaldson conjecture on the existence ... More