Related papers: Point compression for the trace zero subgroup over…
Given an integer $q$ and a polynomial $f\in \mathbb Z_{q}[X]$ of degree $d$ with coefficients in the residue ring $\mathbb Z_q=\mathbb Z/q\mathbb Z,$ we obtain new results concerning the number of solutions to congruences of the form…
A hybrid computational approach that integrates the finite element method (FEM) with least squares support vector regression (LSSVR) is introduced to solve partial differential equations. The method combines FEM's ability to provide the…
This is the third of three papers about the Compression Theorem: if M^m is embedded in Q^q X R with a normal vector field and if q-m > 0, then the given vector field can be straightened (ie, made parallel to the given R direction) by an…
Tucker decomposition is proposed to reduce the memory requirement of the far-fields in the fast multipole method (FMM)-accelerated surface integral equation simulators. It is particularly used to compress the far-fields of FMM groups, which…
We study the problem of compression for the purpose of similarity identification, where similarity is measured by the mean square Euclidean distance between vectors. While the asymptotical fundamental limits of the problem - the minimal…
We consider so-called branched transport and variants thereof in two space dimensions. In these models one seeks an optimal transportation network for a given mass transportation task. In two space dimensions, they are closely connected to…
In this paper we present three related results on the subject of fields of parametrization. Let C be a rational curve over a field of characteristic zero. Let K be a field finitely generated over Q, such that it is a field of definition of…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
For minimization problems without 2nd derivative information, methods that estimate Hessian matrices can be very effective. However, conventional techniques generate dense matrices that are prohibitive for large problems. Limited-memory…
We propose a novel diagrammatic method for computing transport coefficients in relativistic quantum field theory. The self-consistent equation for summing the diagrams with pinch singularities has a form of a linearized kinetic equation as…
Suppose that Q is a family of seminorms on a locally convex space E which determines the topology of E. We study the existence of Q-nonexpansive retractions for families of Q-nonexpansive mappings and prove that a separated and sequentially…
We formulate a problem called \emph{Generalized Root Extraction} in finite Abelian groups that have more than one generator. We then study this problem for the specific case of the torsion subgroups of elliptic curves. We give a necessary…
The ever-increasing 3D application makes the point cloud compression unprecedentedly important and needed. In this paper, we propose a patch-based compression process using deep learning, focusing on the lossy point cloud geometry…
This paper studies stochastic minimization of a finite-sum loss $ F (\mathbf{x}) = \frac{1}{N} \sum_{\xi=1}^N f(\mathbf{x};\xi) $. In many real-world scenarios, the Hessian matrix of such objectives exhibits a low-rank structure on a batch…
We consider the solution of large stiff systems of ordinary differential equations with explicit exponential Runge--Kutta integrators. These problems arise from semi-discretized semi-linear parabolic partial differential equations on…
We study worst-case signal compression under an $\ell^2$ energy constraint, with coordinate-dependent quantization precisions. The compression problem is reduced to counting lattice points in a diagonal ellipsoid. Under balanced precision…
The JPEG algorithm is a defacto standard for image compression. We investigate whether adaptive mesh refinement can be used to optimize the compression ratio and propose a new adaptive image compression algorithm. We prove that it produces…
In this work, we investigate the numerical reconstruction of inclusions in a semilinear elliptic equation arising in the mathematical modeling of cardiac ischemia. We propose an adaptive finite element method for the resulting constrained…
We introduce new discrete best approximation problems, formulated and solved in the framework of tropical algebra, which deals with semirings and semifields with idempotent addition. Given a set of samples, each consisting of the input and…
The recently developed theory of higher--rank numerical ranges originated in problems of error correction in quantum information theory but its mathematical implications now include a quite satisfactory understanding of \emph{scalar}…