Related papers: The gradient flow of the polarization measure. Wit…
In opinion dynamics, as in general usage, polarisation is subjective. To understand polarisation, we need to develop more precise methods to measure the agreement in society. This paper presents four mathematical measures of polarisation…
In this paper we study a gradient flow approach to the problem of quantization of measures in one dimension. By embedding our problem in $L^2$, we find a continuous version of it that corresponds to the limit as the number of particles…
A measure of the degree of polarization for the three-dimensional polarization matrix (coherence matrix) of an electromagnetic field is proposed, based on Rayleigh scattering. The degree of polarization, due to dipole scattering of the…
Quantifying the amount of polarization is crucial for understanding and studying political polarization in political and social systems. Several methods are used commonly to measure polarization in social networks by purely inspecting their…
Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of…
As performance gains through scaling data and/or model size experience diminishing returns, it is becoming increasingly popular to turn to ensembling, where the predictions of multiple models are combined to improve accuracy. In this paper,…
This article overviews how gradient flows, and discretizations thereof, are useful to design and analyze optimization and sampling algorithms. The interplay between optimization, sampling, and gradient flows is an active research area; our…
The absolute values of the three degrees of mutual coherence between the analytic signals representing the components of the electric field of a given three-dimensional (3D) polarization state are relative quantities that depend on the…
We demonstrate that the multipoles associated with the density matrix are truly observable quantities that can be unambiguously determined from intensity moments. Given their correct transformation properties, these multipoles are the…
This paper provides a novel summary measure of ideological polarization in the American public based on the joint distribution of survey responses. Intuitively, polarization is maximized when views are concentrated at opposing extremes with…
Linear polarization measurements provide access to two quantities, the degree (DOP) and the angle of polarization (AOP). The aim of this work is to give a complete and concise overview of how to analyze polarimetric measurements. We review…
We consider the notions of agreement, diversity, and polarization in ordinal elections (that is, in elections where voters rank the candidates). While (computational) social choice offers good measures of agreement between the voters, such…
The study of complex political phenomena such as parties' polarization calls for mathematical models of political systems. In this paper, we aim at modeling the time evolution of a political system whereby various parties selfishly interact…
Polarization is a major concern for a well-functioning society. Often, mass polarization of a society is driven by polarizing political representation, even when the latter is easily preventable. The existing computational social choice…
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
An index is a function that given an election outputs a value between 0 and 1, indicating the extent to which this election has a particular feature. We seek indices that capture agreement, diversity, and polarization among voters in…
We examine the infinite-dimensional optimization problem of finding a decomposition of a probability measure into K probability sub-measures to minimize specific loss functions inspired by applications in clustering and user grouping. We…
This paper introduces a definition of ideological polarization of an electorate around a particular central point. By being flexible about the location or width of the center, this measure enables the researcher to analyze polarization…
Politics around the world exhibits increasing polarization, demonstrated in part by rigid voting configurations in institutions like legislatures or courts. A crux of polarization is separation along a unidimensional ideological axis, but…
Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. In this paper, we have considered a Borel probability measure…