相关论文: Characterization algorithms for shift radix system…
The subject of this paper is a connection between d-orthogonal polynomials and the Toda lattice hierarchy. In more details we consider some polynomial systems similar to Hermite polynomials, but satisfying $d+2$-term recurrence relation, $d…
Given a positive integer $d$, the d-CUT is the problem of deciding if an undirected graph $G=(V,E)$ has a cut $(A,B)$ such that every vertex in $A$ (resp. $B$) has at most $d$ neighbors in $B$ (resp. $A$). For $d=1$, the problem is referred…
In this paper, we propose a strategy to determine the Dirichlet-to-Neumann (DtN) operator for infinite, lossy and locally perturbed hexagonal periodic media. We obtain a factorization of this operator involving two non local operators. The…
For an integer d>=1, let tau(d) be the smallest integer with the following property: If v1,v2,...,vt is a sequence of t>=2 vectors in [-1,1]^d with v1+v2+...+vt in [-1,1]^d, then there is a subset S of {1,2,...,t} of indices,…
For discrete spectrum of 1D second-order differential/difference operators (with or without potential (killing), with the maximal/minimal domain), a pair of unified dual criteria are presented in terms of two explicit measures and the…
Analytic representation of both position as well as momentum waveforms of the two-dimensional (2D) circular quantum dots with the Dirichlet and Neumann boundary conditions (BCs) allowed an efficient computation in either space of Shannon…
An infinite structure has the finite length property (over a given field) if, for each of its finite powers, chains of equivariant subspaces in the corresponding free vector space are bounded in length. Prior work showed that the countable…
In this thesis, we introduce the subject of D-spaces and some of its most important open problems which are related to well known covering properties. We then introduce a new approach for studying D-spaces and covering properties in…
We give an algebraic characterization of when a $d$-dimensional periodic framework has no non-trivial, symmetry preserving, motion for any choice of periodicity lattice. Our condition is decidable, and we provide a simple algorithm that…
This paper provides an algorithmic pipeline for studying the intrinsic structure of a finite discrete dynamical system (DDS) modelling an evolving phenomenon. Here, by intrinsic structure we mean, regarding the dynamics of the DDS under…
We analyze symmetries corresponding to separated topological sectors of 3d ${\cal} N=4$ gauge theories with Higgs vacua, compactified on a circle. The symmetries are encoded in Schwinger-Dyson identities satisfied by correlation functions…
An arithmetical discrete plane is said to have critical connecting thickness if its thickness is equal to the infimum of the set of values that preserve its $2$-connectedness. This infimum thickness can be computed thanks to the fully…
Let $X$ be a $2$-dimensional subshift of finite type generated by a finite set of forbidden blocks (of finite size). We give an algorithm for generating the elements of the shift space using sequence of finite matrices (of increasing size).…
The Lasserre's reconstruction algorithm is extended to the D-polytopes with the construction of their shape space. Thus, the areas of d-skeletons $(1\leq d\leq D)$ can be expressed as functions of the areas and normal bi-vectors of the…
We study regularized deep neural networks (DNNs) and introduce a convex analytic framework to characterize the structure of the hidden layers. We show that a set of optimal hidden layer weights for a norm regularized DNN training problem…
The problem of optimizing over random structures emerges in many areas of science and engineering, ranging from statistical physics to machine learning and artificial intelligence. For many such structures finding optimal solutions by means…
We study the parameterized complexity of the following fundamental geometric problems with respect to the dimension $d$: i) Given $n$ points in $\Rd$, compute their minimum enclosing cylinder. ii) Given two $n$-point sets in $\Rd$, decide…
Number Decision Diagrams (NDD) provide a natural finite symbolic representation for regular set of integer vectors encoded as strings of digit vectors (least or most significant digit first). The convex hull of the set of vectors…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…
We study the natural extended-variable formulation for the disjunction of $n+1$ polytopes in $\mathbb{R}^d$. We demonstrate that the convex hull $D$ in the natural extended-variable space $\mathbb{R}^{d+n}$ is given by full optimal big-M…