Concentration Inequalities on the Multislice and for Sampling Without Replacement

We present concentration inequalities on the multislice which are based on (modified) log-Sobolev inequalities. This includes bounds for convex functions and multilinear polynomials. As an application, we show concentration results for the triangle count in the G(n, M) Erdős–Rényi model resembling known bounds in the G(n, p) case. Moreover, we give a proof of Talagrand’s convex distance inequality for the multislice. Interpreting the multislice in a sampling without replacement context, we furthermore present concentration results for n out of N sampling without replacement. Based on a bounded difference inequality involving the finite-sampling correction factor $$1 - (n / N)$$ 1 - ( n / N ) , we present an easy proof of Serfling’s inequality with a slightly worse factor in the exponent, as well as a sub-Gaussian right tail for the Kolmogorov distance between the empirical measure and the true distribution of the sample.

DESIGUALDADE, DIFERENÇA, ARTICULAÇÃO

<p>Neste artigo, estudam-se as tensões e superposições entre desigualdade e diferença a partir de duas questões complementares: Quando diferenças se tornam politicamente relevantes? Como desigualdades e diferenças se correlacionam? O argumento é desenvolvido, primeiramente, mediante a discussão crítica de três abordagens influentes nos debates acadêmicos e políticos contemporâneos, a saber: o paradigma do reconhecimento-redistribuição, como é desenvolvido por N. Fraser e A. Honneth, a abordagem das desigualdades categoriais de C. Tilly e a abordagem das desigualdades horizontais-verticais de F. Stewart. A despeito de suas divergências, essas três abordagens apresentam uma limitação conceitual comum, que é tratar diferenças dinâmicas como categorias binárias e fixas: brancos-negros, homens-mulheres, mestiços-indígenas, etc. Para superar esse déficit, com base no conceito de articulação, desenvolve-se uma matriz analítica segundo a qual diferenças representam posicionalidades ou lugares de enunciação no âmbito de relações sociais hierárquicas. O nexo entre diferenças e desigualdades é ilustrado por meio da articulação recente dos quilombolas no Brasil.</p><p><strong>INEQUALITY, DIFFERENCE, ARTICULATION </strong></p><p>This article studies the tensions and overlaps between inequality and difference starting from two complementary questions: When do differences become politically relevant? How do inequalities and differences correlate? The argument is first developed through a critical discussion of three influential approaches in contemporary academic and political debates: the recognition-redistribution paradigm, as developed by N. Fraser and A. Honneth, the categorical inequalities approach of C. Tilly and the horizontal-vertical inequalities approach of F. Stewart. In spite of their divergences, these three approaches present a common conceptual limitation, which is to treat dynamic differences as binary and fixed categories: black-whites, menwomen, mestizos-indigenous, etc. To overcome this deficit, I develop in the present article, starting from the concept of articulation, an analytical matrix according to which differences represent positionalities or sites of enunciation within hierarchical social relations. The nexus between differences and inequalities is illustrated by the recent articulation of the quilombolas in Brazil.</p><p>Key words: Difference. Inequality. Articulation. Positionality. Quilombolas.</p><p><strong>INÉGALITÉ, DIFFÉRENCE, ARTICULATION </strong></p><p>Cet article étudie les tensions et les chevauchements entre inégalités et différences à partir de deux questions complémentaires: Quand les différences deviennent-elles politiquement pertinentes? Quel est la corrélation entre les inégalités et les différences? L’argument est d’abord développé à travers une discussion critique de trois approches influentes dans les débats académiques et politiques contemporains: le paradigme reconnaissanceredistribution, tel que développé par N. Fraser et A. Honneth, l’approche d’inégalité catégorielle de C. Tilly et l’approche des inégalités horizontaleverticale de F. Stewart. Malgré leurs divergences, ces trois approches présentent une limitation conceptuelle commune, qui consiste à traiter les différences dynamiques comme catégories binaires et fixes: blanc-noir, hommes-femmes, métis-indigènes, etc. Pour surmonter ce déficit, le présent article développe, à partir du concept d’articulation, une matrice analytique selon laquelle les différences représentent des positionalités ou des sites d’énonciation dans des relations sociales hiérarchisées. Le lien entre les différences et les inégalités est illustré par la récente articulation des quilombolas au Brésil.</p><p>Mots-clés: Différence. Inégalité. Articulation. Positionnalité. Quilombolas.</p>

Listening past difference: Towards a compassionate ethics of communication

This article attempts to contribute to the discussion about reading the Bible in a contemporary social and political context by highlighting one of the most pertinent influences on our understanding of that context, namely the global media. While the article therefore does not claim any authority in terms of Biblical hermeneutics, it hopes to make a modest contribution to our understanding of how we experience our place in a globalised world, how we make meaning out of the images and messages circulating around us every day, and how we respond ethically to the pervasive nature of global media, especially in the South African context. The central question to be answered pertains to the ethics of mediation, representation and communication in a world marked by difference, inequality and struggle. Of particular importance is the question of how we communicate with each other across the many differences that lie between us.

A Class of Difference Inequality with Three Iterative Summation

The main objective of this paper is to establish a class of difference inequality with three iterative summation. By amplification method, technique of change of variable, difference and summation, upper bound estimations of unknown functions in the difference inequality are given. Finally, we give the estimation of the solution of a class of difference equation by our derived results.

A Class of Nonlinear Singular Difference Inequality in Engineering

In this paper, we discuss a class of new nonlinear weakly singular difference inequality. Using change of variable, discrete Jensen inequality, amplification method, the mean-value theorem for integrals and Gamma function, explicit bounds for the unknown functions in the inequality is given clearly. The derived results can be applied in the study of fractional difference equations in Engineering.

A Class of Singular Volterra-Fredholm Type Difference Inequality in Engineering

In this paper, we discuss a class of new weakly singular Volterra-Fredholm difference inequality, which is solved using change of variable, discrete Jensen inequality, Beta function, the mean-value theorem for integrals and amplification method, and explicit bounds for the unknown functions is given clearly. The derived results can be applied in the study of fractional difference equations in engineering.