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We consider kinetic systems and prove their stability working in weighted spaces in which the systems are symmetric. We prove stability for various explicit and implicit semi-discrete and fully discrete schemes. The applications include…
Building upon earlier work in which axioms were formulated for multivariate measures of concordance, we examine properties of such measures. In particular, we examine the relations between the measure of concordance of an $n$-copula and the…
We establish bounds for the measure of deviation sets associated to continuous observables with respect to not necessarily invariant weak Gibbs measures. Under some mild assumptions, we obtain upper and lower bounds for the measure of…
Several performance measures are used to evaluate binary and multiclass classification tasks. But individual observations may often have distinct weights, and none of these measures are sensitive to such varying weights. We propose a new…
We describe a general framework for weighted parametric multiple test procedures based on the closure principle. We utilize general weighting strategies that can reflect complex study objectives and include many procedures in the literature…
We investigate stability conditions related to the existence of solutions of the Hull-Strominger system with prescribed balanced class. We build on recent work by the authors, where the Hull-Strominger system is recasted using non-Hermitian…
Let $K\subset\mathbb{C}$ be non-polar, compact and polynomially convex. We study the limits of equilibrium measures on preimages of compact sets, under $K$-regular sequences of polynomials, that center on $K$ and under the sequences of…
We study skew product lifts and overlap numbers for equilibrium measures \mu_\psi of H\"older continuous potentials \psi on such lifts. We find computable formulas and estimates for the overlap numbers in several concrete significant cases…
This is the first in a series of two papers studying mu-cscK metrics and muK-stability, from a new perspective evoked from observations in arXiv:2004.06393 and in this first article. The first paper is about a characterization of mu-cscK…
A notion of indicator for a plurisubharmonic function u of logarithmic growth in C^n is introduced and studied. It is applied to evaluation of the total Monge-Amp\`ere measure (dd^cu)^n({C}^n). Upper bounds for the measure are obtained in…
The basic disentanglement theorem established by the present authors states that estimates on a weighted geometric mean over (convex) families of functions can be disentangled into quantitatively linked estimates on each family separately.…
Necessary and sufficient conditions for weak and vague convergence of measures are important for a diverse host of applications. This paper aims to give a comprehensive description of the relationship between the two modes of convergence…
We establish up to the boundary regularity estimates in weighted $L^{p}$ spaces with Muckenhoupt weights $A_{p}$ for weak solutions to the Hodge systems \begin{align*} d^{\ast}\left(Ad\omega\right) +…
We prove that the existence of extremal metrics implies asymptotically relative Chow stability. An application of this is the uniqueness, up to automorphisms, of extremal metrics in any polarization.
Methods for measuring convexity defects of compacts in R^n abound. However, none of the those measures seems to take into account continuity. Continuity in convexity measure is essential for optimization, stability analysis, global…
In this paper we investigate the question of how much combined measurements can increase the accuracy of additive quantities. Therefore, we consider a set of measurements from a selection of all possible combinations of the $n$ labeled…
We study the masses charged by $(dd^cu)^n$ at isolated singularity points of plurisubharmonic functions $u$. It is done by means of the local indicators of plurisubharmonic functions. As a consequence, bounds for the masses are obtained in…
The power of multiple testing procedures can be increased by using weighted p-values (Genovese, Roeder and Wasserman 2005). We derive the optimal weights and we show that the power is remarkably robust to misspecification of these weights.…
Results of an updated global electoweak fit to the Standard Model (SM) are presented, where special attention is paid to some key observables, such as the weak mixing angle, the $W$ boson mass, and the anomalous magnetic moment of the muon.…
We study experimentally systems of orthogonal polynomials with respect to self-similar measures. When the support of the measure is a Cantor set, we observe some interesting properties of the polynomials, both on the Cantor set and in the…