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We embark in a program of studying the problem of better approximating surfaces by triangulations(triangular meshes) by considering the approximating triangulations as finite metric spaces and the target smooth surface as their…
This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principle - measuring the average amount of symmetry broken by an object. It attributes low (although different)…
Several new geometric quantile-based measures for multivariate dispersion, skewness, kurtosis, and spherical asymmetry are defined. These measures differ from existing measures, which use volumes and are easy to calculate. Some theoretical…
In this work, we propose to study the global geometrical properties of generative models. We introduce a new Riemannian metric to assess the similarity between any two data points. Importantly, our metric is agnostic to the parametrization…
The widespread use of AI and ML models in sensitive areas raises significant concerns about fairness. While the research community has introduced various methods for bias mitigation in binary classification tasks, the issue remains…
Geodesic metric spaces support a variety of averaging constructions for given finite sets. Computing such averages has generated extensive interest in diverse disciplines. Here we consider the inverse problem of recognizing computationally…
We compare and contrast fourteen measures that have been proposed for the purpose of quantifying partisan gerrymandering. We consider measures that, rather than examining the shapes of districts, utilize only the partisan vote distribution…
The main goal of this article is to find the exact difference between a convex function and its secant, as a limit of positive quantities. This idea will be expressed as a convex inequality that leads to refinements and reversals of well…
We give an upper bound for the weighted geometric mean using the weighted arithmetic mean and the weighted harmonic mean. We also give a lower bound for the weighted geometric mean. These inequalities are proven for two invertible positive…
Using Blackwell's definition of comparing two experiments, a comparison is made with \textit{generalized AG - divergence} measure having one and two scalar parameters. Connection of \textit{generalized AG - divergence} measure with…
This paper, in considering aspects of the geometric mean sequence, offers new results connecting generalized Tribonacci and third-order Horadam numbers which are established and then proved independently.
The problem of classification of cubic homogeneous Finslerian 3D metrics with respect to their isometries is considered. It is shown, that there are 6 different general affine types of such metrics. Algebras of isometries are presented in…
We are going to classify sets by a given mean in two ways. Firstly we study small and big sets regarding a given mean. Secondly we study sets that have the same weight according to a mean. We also generalize the notion of roundness and get…
A generic rectangulation is a partition of a rectangle into finitely many interior-disjoint rectangles, such that no four rectangles meet in a point. In this work we present a versatile algorithmic framework for exhaustively generating a…
In this note we present a refinement of the AM-GM inequality, and then we estimate in a special case the typical size of the improvement.
This paper is dedicated to the analysis and detailed study of a procedure to generate both the weighted arithmetic and harmonic means of $n$ positive real numbers. Together with this interpretation, we prove some relevant properties that…
The standardized mean difference (SMD) is a widely used measure of effect size, particularly common in psychology, clinical trials, and meta-analysis involving continuous outcomes. Traditionally, under the equal variance assumption, the SMD…
Some mathematical inequalities among various weighted means are studied. Inequalities on weighted logarithmic mean are given. Besides, the gap in Jensen's inequality is studied as a convex function approach. Consequently, some non-trivial…
This paper is devoted to the statistical and numerical properties of the geometric median, and its applications to the problem of robust mean estimation via the median of means principle. Our main theoretical results include (a) an upper…
Given a function $f\in C(\mathbb{R}^d)$ of linear growth, we give a new way of representing accumulation points of \begin{equation} \int_\Omega f(v_i(z))d\mu(z), \end{equation} where $\mu\in \mathcal{M}^+(\Omega)$, and $(v_i)_{i\in…