相关论文: On Fourier-based inequality indices
In the paper we study the infimum convolution inequalites. Such an inequality was first introduced by B. Maurey to give the optimal concentration of measure behaviour for the product exponential measure. We show how IC-inequalities are tied…
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.
Fair machine learning is receiving an increasing attention in machine learning fields. Researchers in fair learning have developed correlation or association-based measures such as demographic disparity, mistreatment disparity, calibration,…
The absolute value of matrices is used in order to give inequalities for the trace of products. An application gives a very short proof of the tracial matrix Hoelder inequality
Several numerical indices that control the normalization of ideals are introduced and some relationships among them are derived.
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…
This paper studies the effects on Zernike coefficients of aperture scaling, translation and rotation, when a given aberrated wavefront is described on the Zernike polynomial basis. It proposes a new analytical method for computing the…
Analyzing the internal loss characteristics and multimodedness of (integrated) optical devices can prove difficult. One technique to recover this information is to Fourier transform the transmission spectrum of optical components. This…
A good deal of science and technology concepts and methods rely on comparing and relating entities in quantitative terms. Among the several possible approaches, similarity indices allow some interesting features, especially the ability to…
The Fenchel-Young inequality is fundamental in Convex Analysis and Optimization. It states that the difference between certain function values of two vectors and their inner product is nonnegative. Recently, Carlier introduced a very nice…
The development of global sensitivity analysis of numerical model outputs has recently raised new issues on 1-dimensional Poincar\'e inequalities. Typically two kind of sensitivity indices are linked by a Poincar\'e type inequality, which…
We introduce a continuous analog of the Fourier ratio for compactly supported Borel measures. For a measure \(\mu\) on \(\mathbb{R}^d\) and \(f\in L^2(\mu)\), the Fourier ratio compares \(L^1\) and \(L^2\) norms of a regularized Fourier…
This paper develops semiparametric methods for estimation and inference of widely used inequality measures when survey data are subject to nonignorable nonresponse, a challenging setting in which response probabilities depend on the…
In this paper, we will study the continuity of the Fourier transform of measures with respect to the vague topology. We show that the Fourier transform is vaguely discontinuous on R, but becomes continuous when restricting to a class of…
The use of quantitative indicators of scientific productivity seems now quite widespread for assessing researchers and research institutions. There is a general perception, however, that these indicators are not necessarily representative…
We characterize the equality between ultradifferentiable function classes defined in terms of abstractly given weight matrices and in terms of the corresponding matrix of associated weight functions by using new growth indices. These…
It is well known that general variational inequalities provide us with a unified, natural, novel and simple framework to study a wide class of unrelated problems, which arise in pure and applied sciences. In this paper, we present a number…
The underlying idea behind the construction of indices of economic inequality is based on measuring deviations of various portions of low incomes from certain references or benchmarks, that could be point measures like population mean or…
We give a~new proof of the known criteria for the inequality \begin{equation*} \left(\int_{0}^{\infty}\left(\int_{0}^{t}f\right)^{q}w(t)\,dt\right)^{\frac{1}{q}} \leq C \left(\int_{0}^{\infty}f^{p}v\right)^{\frac{1}{p}}. \end{equation*} The…
When using machine learning to aid decision-making, it is critical to ensure that an algorithmic decision is fair and does not discriminate against specific individuals/groups, particularly those from underprivileged populations. Existing…