Related papers: Spherical Means and Pinned Distance Sets
In this paper we study the geometry of metric spheres in the curve complex of a surface, with the goal of determining the "average" distance between points on a given sphere. Averaging is not technically possible because metric spheres in…
In directional statistics, the von Mises-Fisher (vMF) distribution is one of the most basic and popular probability distributions for data on the unit hypersphere. Recently, the spherical normal (SN) distribution was proposed as an…
One of the major problems for maximum likelihood estimation in the well-established directional models is that the normalising constants can be difficult to evaluate. A new general method of "score matching estimation" is presented here on…
A formalism is presented for analytically obtaining the probability density function, (P_{n}(s)), for the random distance (s) between two random points in an (n)-dimensional spherical object of radius (R). Our formalism allows (P_{n}(s)) to…
Motivated by the statistical and computational challenges of computing Wasserstein distances in high-dimensional contexts, machine learning researchers have defined modified Wasserstein distances based on computing distances between…
The primary goal of this paper is to introduce bilinear analogues of uncentered spherical averages, Nikodym averages associated with spheres and the associated bilinear maximal functions. We obtain $L^p$-estimates for uncentered bilinear…
We provide explicit formulaes for the first Kantorovich-Wasserstein distance between stationary measures for iterated function scheme on the unit interval. In particular, we consider two stationary measures with different configurations of…
We consider the minimal distance between orbits of measure preserving dynamical systems. In the spirit of dynamical shrinking target problems we identify distance rates for which almost sure asymptotic closeness properties can be ensured.…
We present new tight bounds for averaging differential inclusions, which we apply to multi-frequency inclusions consisting of a sum of time periodic set-valued mappings. For this family of inclusions we establish an a tight estimate of…
Meta-analysis aims to combine effect measures from several studies. For continuous outcomes, the most popular effect measures use simple or standardized differences in sample means. However, a number of applications focus on the absolute…
We propose a computer-efficient and accurate method of estimation of spatially correlated errors in astrometric positions, parallaxes and proper motions obtained by space and ground-based astrometry missions. In our method, the simulated…
We apply a new notion of angle between projections to deduce criteria for uniform convergence results of the alternating projections method under several different settings: averaged projections, cyclic products, quasi-periodic products and…
This article investigates the convergence properties of s-numbers of certain truncations of bounded linear operators between Banach spaces. We prove a generalized version of a known convergence result for the approximation numbers of…
This paper is a survey of recent contributions on estimation in stochastic differential equations with mixed-effects. These models involve N stochastic differential equations with common drift and diffusion functions but random parameters…
The aim of this paper is to provide an overview of recent development related to Bregman distances outside its native areas of optimization and statistics. We discuss approaches in inverse problems and image processing based on Bregman…
In this work, we consider the problem of estimating the parameters of polynomially damped sinusoidal signals, commonly encountered in, for instance, spectroscopy. Generally, finding the parameter values of such signals constitutes a…
Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…
Wasserstein distances are increasingly used in a wide variety of applications in machine learning. Sliced Wasserstein distances form an important subclass which may be estimated efficiently through one-dimensional sorting operations. In…
Numerical approximation of the long time behavior of a stochastic differential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical…
Spherometer is an instrument widely used for measuring the radius of curvature of a spherical surface. Cylindrometer is a modified spherometer, which can measure the radii of both spherical and cylindrical surfaces. Both of these…