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In this manuscript, we introduce and study a variant of the agent-based opinion dynamics proposed in a recent work [8], within the framework of an interacting multi-agent system, where agents are assumed to interact with each other and…
We introduce a family of stochastic models motivated by the study of nonequilibrium steady states of fluid equations. These models decompose the deterministic dynamics of interest into fundamental building blocks, i.e., minimal vector…
Recently, significant attention has been dedicated to the models of opinion dynamics in which opinions are described by real numbers, and agents update their opinions synchronously by averaging their neighbors' opinions. The neighbors of…
The Deffuant-Weisbuch (DW) model is a bounded-confidence opinion dynamics model that has attracted much recent interest. Despite its simplicity and appeal, the DW model has proved technically hard to analyze and its most basic convergence…
This paper examines the interplay of opinion exchange dynamics and communication network formation. An opinion formation procedure is introduced which is based on an abstract representation of opinions as $k$--dimensional bit--strings.…
We introduce a utility-driven bounded-confidence model of opinion dynamics in which opinions associated with higher utility exert stronger social influence. In the regime where all agents belong to a single opinion cluster, we derive a…
The evolution of finitely many particles obeying Langevin dynamics is described by Dean-Kawasaki equations, a class of stochastic equations featuring a non-Lipschitz multiplicative noise in divergence form. We derive a regularised…
We introduce multi-population opinion dynamics models linked to the bounded confidence model, aiming to explore how interactions between individuals contribute to the emergence of consensus, polarization, or fragmentation. Existing models…
A continuous-opinion model accounting for the social compromise propensity is theoretically and numerically analysed. An agent's opinion is represented by a real number that can be changed through social interactions with her neighbours.…
Understanding and predicting the dynamical properties of systems involving dry friction is a major concern in physics and engineering. It abounds in many mechanical processes, from the sound produced by a violin to the screeching of chalk…
A two state model for opinion forming, which has proven heuristic power, is reviewed with a novel emphasis on the existence or absence of a threshold for the dynamics. Monitored by repeated small groups discussions floater agents update…
We investigate high-dimensional sparse regression when both the noise and the design matrix exhibit heavy-tailed behavior. Standard algorithms typically fail in this regime, as heavy-tailed covariates distort the empirical risk geometry. We…
Often in the setting of human-based interactions, the existence of a temporal hierarchy of information plays an important role in diffusion and opinion dynamics within communities. For example at the individual agent level, more recently…
Polarization is a well-documented phenomenon across a wide range of social issues. However, prevailing theories often compartmentalize the examination of herding behavior and opinion convergence within different contexts. In this study, we…
We have examined a class of cohesive-zone models of dynamic mode-I fracture, looking both at steady-state crack propagation and its stability against out-of-plane perturbations. Our work is an extension of that of Ching, Langer, and…
We derive here a linear elastic stochastic description for slow crack growth in heterogeneous materials. This approach succeeds in reproducing quantitatively the intermittent crackling dynamics observed recently during the slow propagation…
Robust stability and stochastic stability have separately seen intense study in control theory for many decades. In this work we establish relations between these properties for discrete-time systems and employ them for robust control…
Neuron models have attracted a lot of attention recently, both in mathematics and neuroscience. We are interested in studying long-time and large-population emerging properties in a simplified toy model. From a mathematical perspective,…
This paper provides the relevant literature with a complete toolkit for conducting robust estimation and inference about the parameters of interest involved in a high-dimensional panel data framework. Specifically, (1) we allow for…
We use a statistical model to discuss nonequilibrium fragmentation phenomena taking place in the stochastic dynamics of the log sector in log gravity. From the canonical Gibbs model, a combinatorial analysis reveals an important aspect of…