Related papers: Factorisation in Restriction theory and near extre…
We present a general class of compressed sensing matrices which are then demonstrated to have associated sublinear-time sparse approximation algorithms. We then develop methods for constructing specialized matrices from this class which are…
Hamiltonian models based on a localized basis set are widely used in condensed matter physics, as, for example, for the calculation of electronic structures or transport properties. The presence of a weak and homogeneous magnetic field can…
Let $S \subset \Bbb R^n$ be a smooth compact hypersurface with a strictly positive second fundamental form, $E$ be the Fourier extension operator on $S$, and $X$ be a Lebesgue measurable subset of $\Bbb R^n$. If $X$ contains a ball of each…
Matrix Factorization plays an important role in machine learning such as Non-negative Matrix Factorization, Principal Component Analysis, Dictionary Learning, etc. However, most of the studies aim to minimize the loss by measuring the…
We study the localization of sets with constant nonlocal mean curvature and prescribed small volume in a bounded open set with smooth boundary, proving that they are {\em sufficiently close} to critical points of a suitable non-local…
We consider algorithms for the factorization of linear partial differential operators. We introduce several new theoretical notions in order to simplify such considerations. We define an obstacle and a ring of obstacles to factorizations.…
Conditional on Fourier restriction estimates for elliptic hypersurfaces, we prove optimal restriction estimates for polynomial hypersurfaces of revolution for which the defining polynomial has non-negative coefficients. In particular, we…
This paper is concerned with the inverse elastic scattering problem to determine the shape and location of an elastic cavity. By establishing a one-to-one correspondence between the Herglotz wave function and its kernel, we introduce the…
The present work re-enacts the classical theory of t-structures reducing the classical definition given in *Faisceaux Pervers* to a rather primitive categorical gadget: suitable reflective factorization systems. This translation is only…
We discuss the structure of infrared singularities in on-shell QCD amplitudes with massive partons and present a general factorization formula in the limit of small parton masses. The factorization formula gives rise to an all-order…
Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In this approach, rather than discretizing the partial…
Using factorization theorems for sparse polynomials, we compute the trace field of Dehn fillings of the Whitehead link, and (assuming Lehmer's Conjecture) the minimal polynomial of the small dilatation pseudo-Anosov maps and the trace field…
Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…
Compact categories have lately seen renewed interest via applications to quantum physics. Being essentially finite-dimensional, they cannot accomodate (co)limit-based constructions. For example, they cannot capture protocols such as quantum…
The calculations of the double parton scattering cross sections are discussed. It is shown that the commonly used factorised formula is valid only in the limit of low cross sections. The applicability of this approximation is studied with a…
In this paper we give an additive representation of the factorial, which can be proven by a simple quick analytical argument. We also present some generalizations, which are linked, on the one hand to an arithmetical theorem proven by Euler…
We introduce the notion of quantum duplicates of an (associative, unital) algebra, motivated by the problem of constructing toy-models for quantizations of certain configuration spaces in quantum mechanics. The proposed (algebraic) model…
We prove a theorem on algebraic osculation and we apply our result to the Computer Algebra problem of polynomial factorization. We consider X a smooth completion of the complex plane and D an effective divisor supported on the boundary of…
We prove a rigidity theorem in Poisson geometry around compact Poisson submanifolds, using the Nash-Moser fast convergence method. In the case of one-point submanifolds (fixed points), this immediately implies a stronger version of Conn's…
We study a family of (potentially non-convex) constrained optimization problems with convex composite structure. Through a novel analysis of non-smooth geometry, we show that proximal-type algorithms applied to exact penalty formulations of…