Related papers: Measuring multidimensional inequality: a new propo…
The starting point of this paper is the introduction of a new measure of inclusion of fuzzy set A in fuzzy set B. Previously used inclusion measures take values in the interval [0,1]; the inclusion measure proposed here takes values in a…
To solve the problems in measuring coefficient of skewness related to extreme value, irregular distance from the middle point and distance between two consecutive numbers, "Rank skewness" a new measure of the coefficient of skewness has…
It is shown how it is possible to reconstruct the initial state of a one-dimensional system by measuring sequentially two conjugate variables. The procedure relies on the quasi-characteristic function, the Fourier-transform of the Wigner…
A novel algorithm is proposed for quantitative comparisons between compact surfaces embedded in the three-dimensional Euclidian space. The key idea is to identify those objects with the associated surface measures and compute a weak…
There is growing interest in designing recommender systems that aim at being fair towards item producers or their least satisfied users. Inspired by the domain of inequality measurement in economics, this paper explores the use of…
Let $\mu$ be a probability measure on $\mathbb{R}$. We give conditions on the Fourier transform of its density for functionals of the form $H(a)=\int_{\mathbb{R}^n}h(\langle a,x\rangle)\mu^n(dx)$ to be Schur monotone. As applications, we…
Invariance to geometric transformations is a highly desirable property of automatic classifiers in many image recognition tasks. Nevertheless, it is unclear to which extent state-of-the-art classifiers are invariant to basic transformations…
In coherent diffraction imaging (CDI) experiments, the intensity of the scattered wave impinging on an object is measured on an array of detectors. This signal can be interpreted as the square of the modulus of the Fourier transform of the…
We introduce a class of integral theorems based on cyclic functions and Riemann sums approximating integrals. The Fourier integral theorem, derived as a combination of a transform and inverse transform, arises as a special case. The…
Our purpose is to offer a logical analysis of the system of units and to explore possible paths towards a consistent and unified system with an original perspective. The path taken here builds on the fact that, thanks to optical or…
Full-Waveform Inversion (FWI) has now become a widely accepted tool to obtain high-resolution velocity models from seismic data. Typically, the velocity model in its discrete form is represented on a rectangular grid, and we solve for the…
The pursuit of having an appropriate level of income inequality should be viewed as one of the biggest challenges facing academic scholars as well as policy makers. Unfortunately, research on this issue is currently lacking. This study is…
In a recent paper (Efron (2004)), Efron pointed out that an important issue in large-scale multiple hypothesis testing is that the null distribution may be unknown and need to be estimated. Consider a Gaussian mixture model, where the null…
In this paper we introduce a measure of genuine quantum incompatibility in the estimation task of multiple parameters, that has a geometric character and is backed by a clear operational interpretation. This measure is then applied to some…
Being motivated by general interest as well as by certain concrete problems of Fourier Analysis, we construct analogs of the Lp spaces for measures. It turns out that most of standard properties of the usual Lp spaces for functions are…
We study the problem of recovering an unknown compactly-supported multivariate function from samples of its Fourier transform that are acquired nonuniformly, i.e. not necessarily on a uniform Cartesian grid. Reconstruction problems of this…
Pairwise comparisons are an important tool of modern (multiple criteria) decision making. Since human judgments are often inconsistent, many studies focused on the ways how to express and measure this inconsistency, and several…
The statistical measure of spatial inhomogeneity for n points placed in chi cells each of size kxk is generalized to incorporate finite size objects like black pixels for binary patterns of size LxL. As a function of length scale k, the…
Disparities in the societal harms and impacts of Generative AI (GenAI) systems highlight the critical need for effective unfairness measurement approaches. While numerous benchmarks exist, designing valid measurements requires proper…
This article deals with the analysis of high dimensional data that come from multiple sources (experiments) and thus have different possibly correlated responses, but share the same set of predictors. The measurements of the predictors may…