Related papers: Functional Inequalities: New Perspectives and New …

The aim of this article is to establish new two-functions minimax inequalities extending classical results such as Simons' minimax theorem. Our results will be proved in a non-compact setting. We also prove, under general conditions, that…

There are many books on the classical subject of special relativity. However, after having spent a number of years, both in relativistic engineering and research with relativity, I have come to the conclusion that there exist a place for a…

In this work, a generalization of the well known Bernoulli inequality is obtained by using the theory of discrete fractional calculus. As far as we know our approach is novel.

In this paper, we establish (presumably new type) integral inequalities for convex functions via the Hermite--Hadamard's inequalities. As applications, we apply these new inequalities to construct inequalities involving special means of…

The aim of this short paper is to give a practical introduction to functional interpretation of proofs for computer scientists interested in synthesis.

The purpose of this survey is to give a comprehensive introduction to some classes of classical and recent analytic inequalities in Inner Product Spaces.

Algorithmic fairness is a new interdisciplinary field of study focused on how to measure whether a process, or algorithm, may unintentionally produce unfair outcomes, as well as whether or how the potential unfairness of such processes can…

We study functional inequality of the form $$|T(f,h)-T(f,g)T(g,h)| \leq F(f,g)F(g,h) -F(f,h)$$ where $T$ is a complex-valued functional and $F$ is a real-valued map. Motivation for our studies comes from some generalizations of Gr\"uss…

This is a survey paper concerning some theorems on stochastic convex ordering and their applications to functional inequalities for convex functions. We present the recent results on those subjects

It appears paradoxical that science is producing outstanding new results and theories at a rapid rate at the same time that researchers are identifying serious problems in the practice of science that cause many reports to be irreproducible…

In this paper we first introduce the Heron and Heinz means of two convex functionals. Afterwards, some inequalities involving these functional means are investigated. The operator versions of our theoretical functional results are…

Deep learning models for semantics are generally evaluated using naturalistic corpora. Adversarial methods, in which models are evaluated on new examples with known semantic properties, have begun to reveal that good performance at these…

This book deals with functions allowing to express the dissimilarity (discrepancy) between two data fields or ''divergence functions'' with the aim of applications to linear inverse problems. Most of the divergences found in the litterature…

The definition and implementation of fairness in automated decisions has been extensively studied by the research community. Yet, there hides fallacious reasoning, misleading assertions, and questionable practices at the foundations of the…

The rapid developments of various machine learning models and their deployments in several applications has led to discussions around the importance of looking beyond the accuracies of these models. Fairness of such models is one such…

We propose a new definition of actual cause, using structural equations to model counterfactuals. We show that the definition yields a plausible and elegant account of causation that handles well examples which have caused problems for…

We consider the problem of evaluating certain types of functional aggregation queries on relational data subject to additive inequalities. Such aggregation queries, with a smallish number of additive inequalities, arise naturally/commonly…

We propose measurement modeling from the quantitative social sciences as a framework for understanding fairness in computational systems. Computational systems often involve unobservable theoretical constructs, such as socioeconomic status,…

Interpolation inequalities play an essential role in Analysis with fundamental consequences in Mathematical Physics, Nonlinear Partial Differential Equations (PDEs), Markov Processes, etc., and have a wide range of applications in various…

In recent years fairness in machine learning (ML) has emerged as a highly active area of research and development. Most define fairness in simple terms, where fairness means reducing gaps in performance or outcomes between demographic…