Related papers: Cheeger's isoperimetric problem for Gaussian mixtu…

We study the isoperimetric problem in Euclidean space endowed with a density. We first consider piecewise constant densities and examine particular cases related to the characteristic functions of half-planes, strips and balls. We also…

In this paper, we are concerned with the compressible Euler-Maxwell equations with a nonconstant background density (e.g. of ions) in three dimensional space. There exist stationary solutions when the background density is a small…

We have previously reported a Bayesian algorithm for determining the coordinates of points in three-dimensional space from uncertain constraints. This method is useful in the determination of biological molecular structure. It is limited,…

The $\mu$-conductance measure proposed by Lov\'asz and Simonovits is a size-specific conductance score that identifies the set with smallest conductance while disregarding those sets with volume smaller than a $\mu$ fraction of the whole…

In this article, we present some specific aspects of symmetric Gamma process mixtures for use in regression models. We propose a new Gibbs sampler for simulating the posterior and we establish adaptive posterior rates of convergence related…

Consider a Gaussian stationary sequence with unit variance $X=\{X_k;k\in {\mathbb{N}}\cup\{0\}\}$. Assume that the central limit theorem holds for a weighted sum of the form $V_n=n^{-1/2}\sum^{n-1}_{k=0}f(X_k)$, where $f$ designates a…

We calculate the average differential entropy of a $q$-component Gaussian mixture in $\mathbb R^n$. For simplicity, all components have covariance matrix $\sigma^2 {\mathbf 1}$, while the means $\{\mathbf{W}_i\}_{i=1}^{q}$ are i.i.d.…

This paper addresses the problem of separating spectral sources which are linearly mixed with unknown proportions. The main difficulty of the problem is to ensure the full additivity (sum-to-one) of the mixing coefficients and…

We examine critically the Gambier equation and show that it is the generic linearisable equation containing, as reductions, all the second-order equations which are integrable through linearisation. We then introduce the general discrete…

Gaussian mixtures are a common density representation in nonlinear, non-Gaussian Bayesian state estimation. Selecting an appropriate number of Gaussian components, however, is difficult as one has to trade of computational complexity…

For a general class of gas models ---which includes discrete and continuous Gibbsian models as well as contour or polymer ensembles--- we determine a \emph{diluteness condition} that implies: (1) Uniqueness of the infinite-volume…

We consider the problem of identifying the parameters of an unknown mixture of two arbitrary $d$-dimensional gaussians from a sequence of independent random samples. Our main results are upper and lower bounds giving a computationally…

This paper deals with Bayesian inference of a mixture of Gaussian distributions. A novel formulation of the mixture model is introduced, which includes the prior constraint that each Gaussian component is always assigned a minimal number of…

In this paper, we study the problem of learning one-dimensional Gaussian mixture models (GMMs) with a specific focus on estimating both the model order and the mixing distribution from independent and identically distributed (i.i.d.)…

Let $\pi(x;\gamma_1,\gamma_2)$ denote the number of primes $p$ with $p\leqslant x$ and $p=\lfloor n^{1/\gamma_1}_1\rfloor=\lfloor n^{1/\gamma_2}_2\rfloor$, where $\lfloor t\rfloor$ denotes the integer part of $t\in\mathbb{R}$ and…

Bayesian nonparametric mixture models are common for modeling complex data. While these models are well-suited for density estimation, recent results proved posterior inconsistency of the number of clusters when the true number of…

We study the Mosco-convergence of Cheeger energies on Gromov-Hausdorff converging spaces satisfying different types of curvature dimension conditions. The case of functions of bounded variation is also considered. Applications to the…

The complex Gaussian Multiplicative Chaos (or complex GMC) is informally defined as a random measure $e^{\gamma X} \mathrm{d} x$ where $X$ is a log correlated Gaussian field on $\mathbb R^d$ and $\gamma=\alpha+i\beta$ is a complex…

The first main result presented in the paper shows that the perimeters of inner parallel sets of planar shapes having a given constant width are minimal for the Reuleaux triangles. This implies that the areas of inner parallel sets and,…

Approximating the solution of the nonlinear filtering problem with Gaussian mixtures has been a very popular method since the 1970s. However, the vast majority of such approximations are introduced in an ad-hoc manner without theoretical…