Related papers: Resolvent metrics and heat kernel estimates
We solve the metrisability problem for generic three-dimensional projective structures.
We introduce higher-order Stein kernels relative to the standard Gaussian measure, which generalize the usual Stein kernels by involving higher-order derivatives of test functions. We relate the associated discrepancies to various metrics…
The problem of resolving the fine details of a signal from its coarse scale measurements or, as it is commonly referred to in the literature, the super-resolution problem arises naturally in engineering and physics in a variety of settings.…
Classical and nonclassical symmetries of the nonlinear heat equation $$u_t=u_{xx}+f(u),\eqno(1)$$ are considered. The method of differential Gr\"obner bases is used both to find the conditions on $f(u)$ under which symmetries other than the…
In this article, we consider the problem of estimating the heat kernel on measure-metric spaces equipped with a resistance form. Such spaces admit a corresponding resistance metric that reflects the conductivity properties of the set. In…
This document provides a brief overview of different metrics and terminology that is used to measure the performance of binary classification systems.
We generalize Killing equations to a test particle system which is subjected to external force. We relax the conservation condition by virtue of reparametrization invariance of a particle orbit. As a result, we obtain generalized Killing…
Indefinite Kaehler solutions of the Einstein equations are studied, and it is almost completely determined which compact complex surfaces admit such metrics.
The goal in thinning is to summarize a dataset using a small set of representative points. Remarkably, sub-Gaussian thinning algorithms like Kernel Halving and Compress can match the quality of uniform subsampling while substantially…
This paper proposes new algorithms for the metric learning problem. We start by noticing that several classical metric learning formulations from the literature can be viewed as modified covariance matrix estimation problems. Leveraging…
This paper presents a novel feature of the kernel-based system identification method. We prove that the regularized kernel-based approach for the estimation of a finite impulse response is equivalent to a robust least-squares problem with a…
A survey of problems, conjectures, and theorems about quasi-isometric classification and rigidity for finitely generated solvable groups.
We define measures on central extension of current groups in any dimension by using infinite dimensional Brownian motion.
In his celebrated article, Aronson established Gaussian bounds for the fundamental solution to the Cauchy problem governed by a second order divergence form operator with uniformly elliptic coefficients. We extend Aronson's proof of upper…
The present paper proposes generalized Gaussian kernel adaptive filtering, where the kernel parameters are adaptive and data-driven. The Gaussian kernel is parametrized by a center vector and a symmetric positive definite (SPD) precision…
This paper is an exposition of several questions linking heat kernel measures on infinite dimensional Lie groups, limits associated with critical Sobolev exponents, and Feynmann-Kac measures for sigma models.
We study the gradient regularity of solutions to measure data elliptic systems with Uhlenbeck-type structure and Orlicz growth. For any bounded Borel measure, pointwise estimates for the gradient of solutions are provided in terms of the…
A robust mean value is often a good alternative to the standard mean value when dealing with data containing many outliers. An efficient method for samples of one-dimensional features and the truncated quadratic error norm is presented and…
Resilient systems are able to recover quickly and easily from disturbed system states that might result from hazardous events or malicious attacks. In this paper a novel resilience metric for linear time invariant systems is proposed: the…
This paper is devoted to the analysis of resonant MEMS sensors based on discrete relay feedback techniques. One drawback of such techniques is that some synchronization usually occurs between the discrete part and the continuous part of the…