Related papers: On the Search for Tight Frames of Low Coherence

In this note, we propose a framework for proving computational lower bounds in norm approximation by leveraging a reverse detection--estimation gap. The starting point is a testing problem together with an estimator whose error is…

We consider the compressive sensing of a sparse or compressible signal ${\bf x} \in {\mathbb R}^M$. We explicitly construct a class of measurement matrices, referred to as the low density frames, and develop decoding algorithms that produce…

We investigate a quasi-one-dimensional (Q1D) system of hard spheres confined within a cylindrical pore so narrow that only nearest-neighbor interactions occur. By mapping this Q1D system onto a one-dimensional polydisperse mixture of…

The objective of this paper is to improve the customary definition of redundancy by providing quantitative measures in its place, which we coin upper and lower redundancies, that match better with an intuitive understanding of redundancy…

$D$-optimal designs originate in statistics literature as an approach for optimal experimental designs. In numerical analysis points and weights resulting from maximal determinants turned out to be useful for quadrature and interpolation.…

Object proposals are an ensemble of bounding boxes with high potential to contain objects. In order to determine a small set of proposals with a high recall, a common scheme is extracting multiple features followed by a ranking algorithm…

In this paper we propose a family of tractable kernels that is dense in the family of bounded positive semi-definite functions (i.e. can approximate any bounded kernel with arbitrary precision). We start by discussing the case of stationary…

We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generate background meshes (e.g., a simple Cartesian mesh) that cut…

We present algorithms for computing weakly singular and near-singular integrals arising when solving the 3D Helmholtz equation with curved boundary elements. These are based on the computation of the preimage of the singularity in the…

The purpose of this article is to construct highly localized summability kernels on the unit sphere in ${\mathbb R}^d$ that are restrictions to the sphere of linear combinations of a small number of shifts of the fundamental solution of the…

This article deals with the convergence of finite volume scheme (FVS) for solving coagulation and multiple fragmentation equations having locally bounded coagulation kernel but singularity near the origin due to fragmentation rates. Thanks…

This thesis is devoted to the Differential Geometry of curves and surfaces along with applications in Quantum Mechanics. In the 1st part we introduce the well known Frenet frame. Later, we show that the curvature function is a lower bound…

We consider a space-time of a spherically symmetric black hole with one simple horizon. As a standard coordinate frame fails in its vicinity, this requires continuation across the horizon and constructing frames which are regular there. Up…

Although deep neural networks have been a dominant method for many 2D vision tasks, it is still challenging to apply them to 3D tasks, such as medical image segmentation, due to the limited amount of annotated 3D data and limited…

Strictly proper kernel scores are well-known tool in probabilistic forecasting, while characteristic kernels have been extensively investigated in the machine learning literature. We first show that both notions coincide, so that insights…

Thin beams made of magnetorheological elastomers embedded with hard magnetic particles (hard-MREs) are capable of large deflections under an applied magnetic field. We propose a comprehensive framework, comprising a beam model and 3D finite…

In this note, we develop some of the basic theory of s-finite (measures and) kernels, a little-studied class that Staton has recently argued convincingly to be precisely the semantic counterpart of (first-order) probabilistic programs. We…

Collisional breakage in the particulate process has a lot of recent curiosity. We study the pure collisional breakage equation which is nonlinear in nature accompanied by locally bounded breakage kernel and collision kernel. The continuous…

Almost exponentially localized polynomial kernels are constructed on the unit ball $B^d$ in $\RR^d$ with weights %functions $W_\mu(x)= (1-|x|^2)^{\mu-1/2}$, $\mu \ge 0$, by smoothing out the coefficients of the corresponding orthogonal…

Kernel based methods provide a way to reconstruct potentially high-dimensional functions from meshfree samples, i.e., sampling points and corresponding target values. A crucial ingredient for this to be successful is the distribution of the…