Related papers: On the identifiability of Dirichlet mixture models

Dust particles recovered from the soles of shoes may be indicative of the sites recently visited by an individual, and, in particular, of the presence of an individual at a particular site of interest, e.g., the scene of a crime. By…

We present a numerical approximation method for linear diffusion-reaction problems with possibly discontinuous Dirichlet boundary conditions. The solution of such problems can be represented as a linear combination of explicitly known…

Recently, the theory of diffusion maps was extended to a large class of local kernels with exponential decay which were shown to represent various Riemannian geometries on a data set sampled from a manifold embedded in Euclidean space.…

We study pairs of Dirichlet forms related by an intertwining order isomorphisms between the associated $L^2$-spaces. We consider the measurable, the topological and the geometric setting respectively. In the measurable setting, we deal with…

We compute explicitly traces of the Dirichlet form related to the Bessel process with respect to discrete measures as well as measures of mixed type. Then some global properties of the obtained Dirichlet forms, such as conservativeness,…

Let $H$ be a generalized Liu algebra over an algebraically closed field $k$ of characteristic zero. We prove that all simple Yetter-Drinfeld modules over $H$ are finite-dimensional and present an explicit classification of these modules.…

The Convex Envelope of a given function was recently characterized as the solution of a fully nonlinear Partial Differential Equation (PDE). In this article we study a modified problem: the Dirichlet problem for the underlying PDE. The main…

In this paper we shall prove the weak convergence of the associated diffusion processes of regular subspaces with monotone characteristic sets for a fixed Dirichlet form. More precisely, given a fixed 1-dimensional diffusion process and a…

We analyze the asymptotic behavior of the eigenvalues of nonlinear elliptic problems under Dirichlet boundary conditions and mixed (Dirichlet, Neumann) boundary conditions on domains becoming unbounded. We make intensive use of Picone…

We develop a family of finite element spaces of differential forms defined on cubical meshes in any number of dimensions. The family contains elements of all polynomial degrees and all form degrees. In two dimensions, these include the…

We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…

A mixing time density of $A + B \to 0$ on a finite one dimensional domain is defined for general initial and boundary conditions in which $A$ and $B$ diffuse at the same rate. The density is a measure of the number of $A$ and $B$ particles…

We present the multidimensional membership mixture (M3) models where every dimension of the membership represents an independent mixture model and each data point is generated from the selected mixture components jointly. This is helpful…

This work presents a Finite Element Model Updating inverse methodology for reconstructing heterogeneous material distributions based on an efficient isogeometric shell formulation. It uses nonlinear hyperelastic material models suitable for…

The Schl\"omilch integral, a generalization of the Dirichlet integral on the simplex, and related probability distributions are reviewed. A distribution that unifies several generalizations of the Dirichlet distribution is presented, with…

Coupled Wright-Fisher diffusions have been recently introduced to model the temporal evolution of finitely-many allele frequencies at several loci. These are vectors of multidimensional diffusions whose dynamics are weakly coupled among…

Multipliers of reproducing kernel Hilbert spaces can be characterized in terms of positivity of $n \times n$ matrices analogous to the classical Pick matrix. We study for which reproducing kernel Hilbert spaces it suffices to consider…

This article is motivated by challenges in conducting Bayesian inferences on unknown discrete distributions, with a particular focus on count data. To avoid the computational disadvantages of traditional mixture models, we develop a novel…

When estimating finite mixture models, it is common to make assumptions on the mixture components, such as parametric assumptions. In this work, we make no distributional assumptions on the mixture components and instead assume that…

We consider the set of monic irreducible polynomials $P$ over a finite field $\mathbb{F}_q$ such that the multiplicative order modulo $P$ of some a in $\mathbb{F}_q(T)$ is divisible by a fixed positive integer $d$. Call $R_q(a,d)$ this set.…