Related papers: The Gini Index of an Integer Partition
Inequality measures such as the Gini coefficient are used to inform and motivate policymaking, and are increasingly applied to digital platforms. We analyze how measures fare in pseudonymous settings that are common in the digital age. One…
As AI systems, particularly generative models, increasingly influence decision-making, ensuring that they are able to fairly represent diverse human preferences becomes crucial. This paper introduces a novel framework for evaluating…
Let $\pi$ be a set partition of $[n]=\{1,2,...,n\}$. The standard representation of $\pi$ is the graph on the vertex set $[n]$ whose edges are the pairs $(i,j)$ of integers with $i<j$ in the same block which does not contain any integer…
Given an integer partition $\la=(\la_1, ..., \la_\ell)$ and an integer k, denote by $\la^{(k)}$ the sequence of length $\ell$ obtained by reordering the values $|\la_i-k|$ in non-increasing order. If $\la$ dominates $\mu$ and has the same…
We associate a half-integer number, called {\em the quantum index}, to algebraic curves in the real plane satisfying to certain conditions. The area encompassed by the logarithmic image of such curves is equal to $\pi^2$ times the quantum…
Classification is a machine learning method used in many practical applications: text mining, handwritten character recognition, face recognition, pattern classification, scene labeling, computer vision, natural langage processing. A…
We investigate the effect of tax evasion on the income distribution and the inequality index of a society through a kinetic model described by a set of nonlinear ordinary differential equations. The model allows to compute the global…
The scaled standard Wigner matrix (symmetric with mean zero, variance one i.i.d. entries), and its limiting eigenvalue distribution, namely the semi-circular distribution, has attracted much attention. The $2k$th moment of the limit equals…
Ferrers diagrams are used to visually represent integer partitions. We describe a way to use Ferrers diagrams to uniquely represent integers in terms of their prime factors. This leads to a lower bound on the number of primes less than a…
In this article, we discuss a dynamical stochastic model that represents the time evolution of income distribution of a population, where the dynamics develop from an interplay of multiple economic exchanges in the presence of…
This study examines the relationship between globalization and income inequality, utilizing panel data spanning from 1992 to 2020. Globalization is measured by the World Bank global-link indicators such as FDI, Remittance, Trade Openness,…
Wealth distribution is a complex and critical aspect of any society. Information exchange is considered to have played a role in shaping wealth distribution patterns, but the specific dynamic mechanism is still unclear. In this research, we…
The impact of rising consumption on wealth inequality remains an open question. Here we revisit and extend the Social Architecture of Capitalism agent-based model proposed by Ian Wright, which reproduces stylized facts of wealth and income…
This paper introduces a novel methodology for constructing multiclass ROC curves using the multidimensional Gini index. The proposed methodology leverages the established relationship between the Gini coefficient and the ROC Curve and…
We present a model in which we investigate the structure and evolution of a random network that connects agents capable of exchanging wealth. Economic interactions between neighbors can occur only if the difference between their wealth is…
The level of aggregation in parasite populations is frequently incorporated into ecological studies. It is measured in various ways including variance-to-mean ratio, mean crowding, the $k$ parameter of the negative binomial distribution and…
Income segregation measures the extent to which households choose to live near other households with similar incomes. Sociologists theorize that income segregation can exacerbate the impacts of income inequality, and have developed indices…
To gain insights into the problem of regional inequality, we proposed new regional asset exchange models based on existing kinetic income-exchange models in economic physics. We did this by setting the spatial exchange range and adding bias…
We model the societal task of redistricting political districts as a partitioning problem: Given a set of $n$ points in the plane, each belonging to one of two parties, and a parameter $k$, our goal is to compute a partition $\Pi$ of the…
Analyzing a large data set of publications drawn from the most competitive journals in the natural and social sciences we show that research careers exhibit the broad distributions of individual achievement characteristic of systems in…