Related papers: Epi-Convergence of Expectation Functions under Var…

We introduce a class of functional analogs of the symmetric difference metric on the space of coercive convex functions on $\mathbb{R}^n$ with full-dimensional domain. We show that convergence with respect to these metrics is equivalent to…

We study conformal iterated function systems (IFS) $\mathcal S = \{\phi_i\}_{i \in I}$ with arbitrary overlaps, and measures $\mu$ on limit sets $\Lambda$, which are projections of equilibrium measures $\hat \mu$ with respect to a certain…

This paper deals with functions that defined in metric spaces and valued in complete paranormed vector spaces or valued in Banach spaces, and obtains some necessary and sufficient conditions for weak convergence of finite measures.

We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…

This paper is devoted to the study of the expected-integral multifunctions given in the form \begin{equation*} \operatorname{E}_\Phi(x):=\int_T\Phi_t(x)d\mu, \end{equation*} where $\Phi\colon T\times\mathbb{R}^n \rightrightarrows…

We extend Hochman's work on exponentially separated self-similar measures on $\mathbb{R}$ to the real analytic setting. More precisely, let $\Phi=\left\{ \varphi_{i}\right\} _{i\in\Lambda}$ be an iterated function system on $I:=[0,1]$…

In this paper we consider adaptive sampling's local-feature size, used in surface reconstruction and geometric inference, with respect to an arbitrary landmark set rather than the medial axis and relate it to a path-based adaptive metric on…

We derive necessary and sufficient conditions for epi-convergence in distribution of normal integrands. As a basic tool for the proof a new characterisation for distributional convergence of random closed sets is used. Our approach via the…

We study the consistency of stochastic dynamic programs under converging probability distributions and other approximations. Utilizing results on the epi-convergence of expectation functions with varying measures and integrands, and the…

If $u : \Omega\subset \mathbb{R}^d \to {\rm X}$ is a harmonic map valued in a metric space ${\rm X}$ and ${\sf E} : {\rm X} \to \mathbb{R}$ is a convex function, in the sense that it generates an ${\rm EVI}_0$-gradient flow, we prove that…

Using the results of \cite{P1}, we get some estimates of warping functions for isometric immersions by changing the target manifolds by some types of Riemannian manifolds: constant space forms and Hermitian symmetric spaces. And we deal…

We investigate the problem of approximate Bayesian inference for a general class of observation models by means of the expectation propagation (EP) framework for large systems under some statistical assumptions. Our approach tries to…

The estimation of information measures of continuous distributions based on samples is a fundamental problem in statistics and machine learning. In this paper, we analyze estimates of differential entropy in $K$-dimensional Euclidean space,…

We introduce a natural definition of $L^p$-convergence of maps, $p \ge 1$, in the case where the domain is a convergent sequence of measured metric space with respect to the measured Gromov-Hausdorff topology and the target is a…

This article deals with the lower compactness property of a sequence of integrands and the use of this key notion in various domains: convergence theory, optimal control, non-smooth analysis. First about the interchange of the weak…

We obtain a compact Sobolev embedding for $H$-invariant functions in compact metric-measure spaces, where $H$ is a subgroup of the measure preserving bijections. In Riemannian manifolds, $H$ is a subgroup of the volume preserving…

We prove that admissible functions for Fubini-Study metrics on the complex projective space $P_{m}C$, of complex dimension $m$, invariant by a convenient automorphisms group, are lower bounded by a function going to minus infinity on the…

We present a new framework for analysing the Expectation Maximization (EM) algorithm. Drawing on recent advances in the theory of gradient flows over Euclidean-Wasserstein spaces, we extend techniques from alternating minimization in…

The aim of this paper is to study ultralimits of pointed metric measure spaces (possibly unbounded and having infinite mass). We prove that ultralimits exist under mild assumptions and are consistent with the pointed measured…

In this paper, we use a unified framework introduced in [3] to study two classes of nonconforming immersed finite element (IFE) spaces with integral value degrees of freedom. The shape functions on interface elements are piecewise…