相关论文: Modeling of Political Systems using Wasserstein Gr…
Uncertainty persists over how and why some countries become democratic and others do not, or why some countries remain democratic and others 'backslide' toward autocracy. Furthermore, while scholars generally agree on the nature of…
We present a novel approach to approximate Gaussian and mixture-of-Gaussians filtering. Our method relies on a variational approximation via a gradient-flow representation. The gradient flow is derived from a Kullback--Leibler discrepancy…
Numerous biological and physical processes can be modeled as systems of interacting entities evolving continuously over time, e.g. the dynamics of communicating cells or physical particles. Learning the dynamics of such systems is essential…
This paper revisits the limitations of the Median Voter Theorem and introduces a novel framework to analyze the optimal economic ideological positions of political parties. By incorporating Nash equilibrium, we examine the mechanisms and…
We propose a new version of the spatial model of voting. Platforms of five parties are evolving in a two-dimensional landscape of political issues so as to get maximal numbers of voters. For a Gaussian landscape the evolution leads to a…
Discussions of political disagreement emphasize two patterns: polarization, where beliefs diverge toward opposite extremes on each issue dimension; and issue alignment, where individuals' views across issues become more internally…
Many machine learning problems can be seen as approximating a \textit{target} distribution using a \textit{particle} distribution by minimizing their statistical discrepancy. Wasserstein Gradient Flow can move particles along a path that…
Ideological leanings of an individual can often be gauged by the sentiment one expresses about different issues. We propose a simple framework that represents a political ideology as a distribution of sentiment polarities towards a set of…
It is widely believed that society is becoming increasingly polarized around important issues, a dynamic that does not align with common mathematical models of opinion formation in social networks. In particular, measures of polarization…
The electoral college of voting system for the US presidential election is analogous to a coarse graining procedure commonly used to study phase transitions in physical systems. In a recent paper, opinion dynamics models manifesting a phase…
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…
We present an opinion model founded upon the principles of the bounded confidence interaction among agents. Our objective is to explain the polarization effects inherent to vector-valued opinions. The evolutionary process adheres to the…
In modern democracies, the outcome of elections and referendums is often remarkably tight. The repetition of these divisive events are the hallmark of a split society; to the physicist, however, it is an astonishing feat for such large…
We study the effect of time-fluctuating social influences on the formation of polarization and consensus in a three-party community consisting of two types of voters ("leftists" and "rightists") holding extreme opinions, and moderate agents…
Deterministic dynamics is a mathematical model used to describe the temporal evolution of a system, generally expressed as dx/dt = F(x), where x represents the system's state, and F(x) determines its dynamics. It is employed to understand…
The blooming diffusion probabilistic models (DPMs) have garnered significant interest due to their impressive performance and the elegant inspiration they draw from physics. While earlier DPMs relied upon the Markovian assumption, recent…
Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…
While we typically focus on data visualization as a tool for facilitating cognitive tasks (e.g., learning facts, making decisions), we know relatively little about their second-order impacts on our opinions, attitudes, and values. For…
A multi-level model of opinion formation is presented which takes into account that attitudes on different issues are usually not independent. In the model, agents exchange beliefs regarding a series of facts. A cognitive structure of…
This is an expository paper on the theory of gradient flows, and in particular of those PDEs which can be interpreted as gradient flows for the Wasserstein metric on the space of probability measures (a distance induced by optimal…