Related papers: Harmonic analysis and distribution-free inference …
A new family of distributions on the circle is introduced which are a generalization of the Cardioid distributions. The elementary properties such as mean, variance and the characteristic function are computed. The distribution is either…
Fourier methods are fundamental tools to analyze random fields. Statistical structures of homogeneous Gaussian random fields are completely characterized by the power spectrum. In non-Gaussian random fields, polyspectra, higher-order…
In this pedagogically structured article, we describe a generalized harmonic formulation of the Einstein equations in spherical symmetry which is regular at the origin. The generalized harmonic approach has attracted significant attention…
We study the general problem of testing whether an unknown distribution belongs to a specified family of distributions. More specifically, given a distribution family $\mathcal{P}$ and sample access to an unknown discrete distribution…
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…
We present a general framework for studying harmonic analysis of functions in the settings of various emerging problems in the theory of diffusion geometry. The starting point of the now classical diffusion geometry approach is the…
We study a 2-parametric family of probability measures on an infinite-dimensional simplex (the Thoma simplex). These measures originate in harmonic analysis on the infinite symmetric group (S.Kerov, G.Olshanski and A.Vershik, Comptes Rendus…
3D image processing constitutes nowadays a challenging topic in many scientific fields such as medicine, computational physics and informatics. Therefore, development of suitable tools that guaranty a best treatment is a necessity.…
Symbolic Data Analysis works with variables for which each unit or class of units takes a finite set of values/categories, an interval or a distribution (an histogram, for instance). When to each observation corresponds an empirical…
We compare the parton distributions deduced in the framework of a quantum statistical approach for both the longitudinal and transverse degrees of freedom with the unpolarized distributions measured at Hera and with the polarized ones…
This is a survey of the "Fourier symmetry" of measures and distributions on the circle in relation with the size of their support. Mostly it is based on our paper arxiv:1004.3631 and a talk given by the second author in the 2012 Abel…
We present a theoretical and exact analysis of the bispectrum of projected galaxy catalogues. The result can be generalized to evaluate the projection in spherical harmonics of any 3D bispectrum and therefore has applications to cosmic…
This note gives a summary of ideas concerning Applied Fourier Analysis, mostly formulated for those who have to give such courses to engineers or mathematicians interested in real life applications. It tries to answer recurrent questions…
Covariance representations are developed for the uniform distributions on the Euclidean spheres in terms of spherical gradients and Hessians. They are applied to derive a number of Sobolev type inequalities and to recover and refine the…
The starting point of the current paper is a sequence of uncorrelated random variables. The distribution functions of these variables are assumed to be given but no assumptions on the types or the structure of these distributions are made.…
This paper considers distributed statistical inference for general symmetric statistics %that encompasses the U-statistics and the M-estimators in the context of massive data where the data can be stored at multiple platforms in different…
Understanding how particles are arranged on the sphere is not only central to numerous physical, biological, and materials systems but also finds applications in mathematics and in analysis of geophysical and meteorological measurements. In…
In 2020, two novel distributions for the analysis of directional data were introduced: the spherical Cauchy distribution and the Poisson kernel-based distribution. This paper provides a detailed exploration of both distributions within…
$\alpha$-stable distributions are utilised as models for heavy-tailed noise in many areas of statistics, finance and signal processing engineering. However, in general, neither univariate nor multivariate $\alpha$-stable models admit closed…
Diffusion models (DMs) have emerged as powerful tools for modeling complex data distributions and generating realistic new samples. Over the years, advanced architectures and sampling methods have been developed to make these models…