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Asymmetric statistical errors arise for experimental results obtained by Maximum Likelihood estimation, in cases where the number of results is finite and the log likelihood function is not a symmetric parabola. This note discusses how…

Large Language Models (LLMs) have demonstrated remarkable success across various domains. However, despite their promising performance in numerous real-world applications, most of these algorithms lack fairness considerations. Consequently,…

We study scaling function geometry. We show the existence of the scaling function of a geometrically finite one-dimensional mapping. This scaling function is discontinuous. We prove that the scaling function and the asymmetries at the…

The incompatibility of quantum measurements, i.e. the fact that certain observable quantities cannot be measured jointly is widely regarded as a distinctive quantum feature with important implications for the foundations and the…

It is shown that operations of equivalence cannot serve for building algebras which would induce orthomodular lattices as the operations of implication can. Several properties of equivalence operations have been investigated. Distributivity…

We study the problem of fair classification within the versatile framework of Dwork et al. [ITCS '12], which assumes the existence of a metric that measures similarity between pairs of individuals. Unlike earlier work, we do not assume that…

We continue the investigation of symmetries and anomalies of $T[M]$ theories obtained by compactifying 6d SCFTs on an internal manifold $M$. We extend the notion of "polarizations on a manifold $M$" to cases where $M$ may have boundaries or…

There are several relations which may fall short of genuine identity, but which behave like identity in important respects. Such grades of discrimination have recently been the subject of much philosophical and technical discussion. This…

The assumption of normality in data has been considered in the field of statistical analysis for a long time. However, in many practical situations, this assumption is clearly unrealistic. It has recently been suggested that the use of…

We give several unequivalent notions of convergency of meromorphic functions and more generally meromorphic mappings (strong, weak, $\Gamma $-convergency and some others). Relations between them are investigated. A version of Rouche theorem…

Plethysm is a fundamental operation in symmetric function theory, derived directly from its connection with representation theory. However, it does not admit a simple combinatorial interpretation, and finding coefficients of Schur function…

This paper presents a brief survey of the most important and the most remarkable inequalities involving the basic arithmetic functions.

We prove an elementary yet useful inequality bounding the maximal value of certain linear programs. This leads directly to a bound on the martingale difference for arbitrarily dependent random variables, providing a generalization of some…

In this paper, we study the strong convergence of an algorithm to solve the variational inequality problem which extends(Thong et al, Numerical Algorithms. 78, 1045-1060 (2018)). We have reduced and refined some of their algorithm's…

Although state-of-the-art LLMs can solve math problems, we find that they make errors on numerical comparisons with mixed notation: "Which is larger, $5.7 \times 10^2$ or $580$?" This raises a fundamental question: Do LLMs even know how big…

We prove that the $f$-divergences between univariate Cauchy distributions are all symmetric, and can be expressed as strictly increasing scalar functions of the symmetric chi-squared divergence. We report the corresponding scalar functions…

Various inequalities (Boole inequality, Chung-Erd\"os inequality, Frechet inequality) for Kolmogorov (classical) probabilities are considered. Quantum counterparts of these inequalities are introduced, which have an extra `quantum…

We show that any joint probability mass function (PMF) can be expressed as a product of parity check factors and factors of degree one with the help of some auxiliary variables, if the alphabet size is appropriate for defining a parity…

Shared resources synchronization is a well studied problem, in both shared memory environment or distributed memory environment. Many synchronization mechanisms are proposed, with their own way to reach certain consistency level. This…

Feature matching is one of the most fundamental and active research areas in computer vision. A comprehensive evaluation of feature matchers is necessary, since it would advance both the development of this field and also high-level…