Majorization order

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August undefined, 2024

In discrete mathematics, dominance order (synonyms: dominance ordering, majorization order, natural ordering) is a partial order on the set of partitions of a positive integer n that plays an important role in algebraic combinatorics and representation theory, especially in the context of symmetric functions and representation theory of the symmetric group. In mathematics, majorization is a preorder on vectors of real numbers. Let $${\displaystyle {x}_{(i)}^{},\ i=1,\,\ldots ,\,n}$$ denote the $${\displaystyle i}$$-th largest element of the vector $${\displaystyle \mathbf {x} \in \mathbb {R} ^{n}}$$. Given Meer weergeven (Strong) majorization: $${\displaystyle (1,2,3)\prec (0,3,3)\prec (0,0,6)}$$. For vectors with $${\displaystyle n}$$ components (Weak) … Meer weergeven • Majorization in MathWorld • Majorization in PlanetMath Meer weergeven • Muirhead's inequality • Karamata's Inequality • Schur-convex function Meer weergeven 1. ^ Marshall, Albert W. (2011). Inequalities : theory of majorization and its applications. Ingram Olkin, Barry C. Arnold (2nd ed.). New York: … Meer weergeven • OCTAVE/MATLAB code to check majorization Meer weergeven

Extremal distributions under approximate majorization

Web10 jul. 2024 · In this sense, the submajorization order can be separated into majorization and pointwise inequality in the two ways. The signs of the w and the z can matter: in … Web12 apr. 2024 · At present, majorization-minimization-like learning framework algorithm is commonly used for 1-D high-order TV denoising model in many works [19, 41, 46]. However, it is too dependent on users’ subjective experience, which has … gabby thornton coffee table

Majorization and Dynamics of Continuous Distributions - MDPI

Web1 feb. 1994 · We review some recent developments on majorization inequalities in probability and statistics. In section 2 we describe some related generalizations, … Web5 A. This theorem proves that g is an order-preserving mapping from (𝐑+)𝑁 with the majorization order to the positive real-numbers with their natural order. Web24 mrt. 2024 · Majorization. Let and be nonincreasing sequences of real numbers. Then majorizes if, for each , 2, ..., , with equality if . Note that some caution is needed when … gabby tonal

Econometrica, Vol. 89, No. 4 (July, 2024), 1557–1593

h -Type indices, partial sums and the majorization order

WebBook Title: Majorization and the Lorenz Order with Applications in Applied Mathematics and Economics. Authors: Barry C. Arnold, José María Sarabia. Series Title: Statistics … Web31 okt. 2024 · To measure the magnitude among random variables, we can apply a partial order connection defined on a distribution class, which contains the symmetry. In this paper, based on majorization order and symmetry or asymmetry functions, we carry out stochastic comparisons of lifetimes of [...] Read more. gabby sumrall hudlWebdefine a stochastic majorization ordering. The advantage of choosing 5 is that the stochastic majorization ordering induced by (5 is closely related to stochastic convexity [28], [29]. In Lemma 2.4, we show that (4 is a richer class of functions than (3 and 64. This inclusion relationship is then used in the proof of Theorem 2.7 to gabby street baseball reference

"Webtheme: Majorization, here, there and everywhere. Nevertheless it is my hope that the examples se-lected will be found to be interesting, to be suﬃ-ciently diverse in order to illustrate the potential ubiquity of dispersion ordering (a.k.a. majorization) concepts and, perhaps, to inspire researchers to seek " - Majorization order

Majorization order

Majorization and the Lorenz Order: A Brief Introduction

WebIn this paper we develop a majorization formulation of the uncertainty principle. Majorization provides a partial order on probability vectors which characterizes the …

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Weberal majorization framework for assessing designs, which includes a stringent criterion of majorization via pairwise coincidences and ﬂex-ible surrogates via convex functions. Classical orthogonality, aber-ration and uniformity criteria are uniﬁed by choosing combinatorial and exponential kernels. A construction method is also sketched out. 1. Web1 jul. 2024 · respects the majorization order (or its converse) will have an optimum on an element that is the least variable (most variable) in a given set. Thus, under conditions …

Web16 jan. 2024 · The majorization order is a partial order, i.e., not every two vectors are comparable under majorization. When studying majorization among two vectors of different dimensions, we append 0... Web15 jan. 2024 · This paper deals with the important notion of majorization. We study majorization for matrices, and focus on (0, 1)-matrices.We prove several results concerning such matrix majorization orders on the set of (0,1)-matrices, including characterizations for certain orders, and separate sufficient and necessary conditions for the so-called matrix …

Web1 Introduction.- 2 Majorization in IR.- Exercises.- 3 The Lorenz order in the space of distribution functions.- Exercises.- 4 Transformations and their effects.- Exercises.- 5 Multivariate and stochastic majorization.- 1 Multivariate majorization.- 2 Stochastic majorization.- Exercises.- 6 Some related orderings.- 1 Star ordering.- 2 Stochastic … Web11 apr. 2024 · Abstract. The value at risk (VaR) and the conditional value at risk (CVaR) are two popular risk measures to hedge against the uncertainty of data. In this paper, we provide a computational toolbox for solving high-dimensional sparse linear regression problems under either VaR or CVaR measures, the former being nonconvex and the latter convex.

WebThe notion of majorization ordering was introduced by Hardy, Littlewood and Polya ([11]) and is closely connected with the economic theory of disparity indices ([2]). But this concept can rst be found in Schur ([19]) who inves-tigated functions which preserve the majorization order, the so-called Schur-convex functions.

Web1 feb. 2024 · Concretely, we show that h ( PX) can be described in terms of the Lorenz curve of the array X and obtain a relation between the sum of the components of PX and the Gini index of X. Moreover, we obtain sharp lower and upper bounds for h -type indices of PX. partial sums of an array, h -index, g -index, R -index, Gini index, Lorenz curve. gabby tamilia twitterWebA theory of majorization and Schur convexity with respect to partial orders over subsets of Euclidean spaces is developed, which is used in Hwang, Rothblum and Shepp 1993 to … gabby tailoredWeb14 jun. 2024 · The concept of majorization has shown a particular interest in the last decades, mainly due to its wide range of applicability in information and quantum theory, among others [1,2,3,4,5,6,7,8,9].The majorization is an operation between a pair of finite-dimensional vectors that gives a partial order in a finite dimensional vectorial space. gabby thomas olympic runner news and twitterWeb17 nov. 2015 · The objective of this study is to develop a majorization-based tool to compare financial networks with a focus on the implications of liability concentration. Specifically, we quantify liability concentration by applying the majorization order to the liability matrix that captures the interconnectedness of banks in a financial network. gabby tattooWebmajorization order (or its converse) will have an optimum on an element that is the least variable (most variable) in a given set. Thus, under conditions that are often present in applications and that can be easily checked, the optimum is either achieved at the a-priori xed function f or at a step function gwith at most two steps. gabby tailored fabricsWebIn discrete mathematics, dominance order(synonyms: dominance ordering, majorization order, natural ordering) is a partial orderon the set of partitionsof a positive integer nthat plays an important role in algebraic combinatoricsand representation theory, especially in the context of symmetric functionsand representation theory of the symmetric … gabby stumble guysWeb27 mrt. 2024 · In fact, the connection between interpolation and majorization led us to discover that the crossing conditions of distribution functions of [ 44] imply majorization … gabby thomas sprinter