相关论文: On Jensen's inequality for generalized Choquet int…
We prove the theorem converse to Jackson's theorem for a modulus of smoothness of the first order generalised by means of an asymmetric operator of generalised translation.
There has recently been renewed recognition of the need to understand the consistency properties that must be preserved when a generalized matrix inverse is required. The most widely known generalized inverse, the Moore-Penrose…
A model for a Choquet integral for arbitrary finite set systems is presented. The model includes in particular the classical model on the system of all subsets of a finite set. The general model associates canonical non-negative and…
Using the Laplace derivative a Perron type integral, the Laplace integral, is defined. Moreover, it is shown that this integral includes Perron integral and to show that the inclusion is proper, an example of a function is constructed,…
We generalize nonequilibrium integral equalities to situations involving absolutely irreversible processes for which the forward-path probability vanishes and the entropy production diverges, rendering conventional integral fluctuation…
Following and generalizing unpublished work of Ange, we prove a generalized version of R\'emond's generalized Vojta inequality. This generalization can be applied to arbitrary products of irreducible positive-dimensional projective…
By classical results of G.C. Evans and G. Choquet on "good kernels $G$ in potential theory", for every polar $K_\sigma$-set $P$, there exists a finite measure $\mu$ on $P$ such that $G\mu=\infty$ on $P$, and a set $P$ admits a finite…
We show that connections between a degree of incompatibility of pairs of observables and the strength of violations of Bell's inequality found in recent investigations can be extended to a general class of probabilistic physical models. It…
We establish a general transference principle for the irrationality measure of points with $\mathbb{Q}$-linearly independent coordinates in $\mathbb{R}^{n+1}$, for any given integer $n\geq 1$. On this basis, we recover an important…
Ambiguity and ambiguity aversion have been widely studied in decision theory and economics both at a theoretical and an experimental level. After Ellsberg's seminal studies challenging subjective expected utility theory (SEUT), several…
A general theory for computing information transfers in nonlinear stochastic systems driven by deterministic forcing and additive and/or multiplicative noises, is presented. It extends the Liang-Kleeman framework of causality inference to…
Many algorithms have been recently proposed for causal machine learning. Yet, there is little to no theory on their quality, especially considering finite samples. In this work, we propose a theory based on generalization bounds that…
Leggett formulated an inequality which seems to generalize the Bell theorem to non-local hidden variable theories. Leggett inequality is violated by quantum mechanics, as was confirmed by experiment. However, a careful analysis reveals that…
The Jarzynski equality is generalized to situations in which nonequilibrium systems are subject to a feedback control. The new terms that arise as a consequence of the feedback describe the mutual information content obtained by measurement…
In this paper, we study the generalized Douglas-Rachford algorithm and its cyclic variants which include many projection-type methods such as the classical Douglas-Rachford algorithm and the alternating projection algorithm. Specifically,…
Generalization bounds which assess the difference between the true risk and the empirical risk, have been studied extensively. However, to obtain bounds, current techniques use strict assumptions such as a uniformly bounded or a Lipschitz…
Two key identifying assumptions used to justify difference-in-differences are parallel trends and no anticipation, yet both may fail in practice. I propose a class of assumptions on anticipation and derive closed-form, sharp bounds on the…
The work concentrates on relations, which are general and model independent in chaotic system, between time averages of a few (typically {\it very few}) observables. Equilibrium thermodynamics provides a guide and here is attempted to argue…
We investigate a framework for robo-advisors to estimate non-expert clients' risk aversion using adaptive binary-choice questionnaires. We model risk aversion using cost functions and spectral risk measures in a static setting. We prove the…
Several Artificial Intelligence schemes for reasoning under uncertainty explore either explicitly or implicitly asymmetries among probabilities of various states of their uncertain domain models. Even though the correct working of these…