Related papers: On Endogenous Random Consensus and Averaging Dynam…
We consider a family of one-dimensional diffusions, in dynamical Wiener mediums, which are random perturbations of the Ornstein-Uhlenbeck diffusion process. We prove quenched and annealed convergences in distribution and under weighted…
We study the joint evolution of worldviews by proposing a model of opinion dynamics, which is inspired in notions from evolutionary ecology. Agents update their opinion on a specific issue based on their propensity to change -- asserted by…
The original Hegselmann-Krause (HK) model is composed of a finite number of agents characterized by their opinion, a number in $[0,1]$. An agent updates its opinion via taking the average opinion of its neighbors whose opinion differs by at…
We investigate the emergence of periodic behavior in opinion dynamics and its underlying geometry. For this, we use a bounded-confidence model with contrarian agents in a convolution social network. This means that agents adapt their…
We study dynamical systems forced by a combination of random and deterministic noise and provide criteria, in terms of Lyapunov exponents, for the existence of random attractors with continuous structure in the fibres. For this purpose, we…
The Hegselmann-Krause (HK) model allows one to characterize the continuous change of agents' opinions with the bounded confidence threshold $\varepsilon$. To consider the heterogeneity of agents in characteristics, we study the HK model on…
We study the long-term average evolution of the random ensemble along integrable Hamiltonian systems with time $T$-periodic transitions. More precisely, for any observable $G$, it is demonstrated that the ensemble under $G$ in long time…
We model dynamically changing candidate positions in the face of a dynamic electorate. To formulate our equations, we use a space-time-continuous Hegselmann-Krause equation, which we solve using a particle method. We use the combined…
The dynamical evolution of many economic, sociological, biological and physical systems tends to be dominated by a relatively small number of unexpected, large changes (`extreme events'). We study the large, internal changes produced in a…
Topic models and all their variants analyse text by learning meaningful representations through word co-occurrences. As pointed out by Williamson et al. (2010), such models implicitly assume that the probability of a topic to be active and…
A curious phenomenon observed in some dynamical generative models is the following: despite learning errors in the score function or the drift vector field, the generated samples appear to shift \emph{along} the support of the data…
We study opinion dynamics in a social network with stubborn agents who influence their neighbors but who themselves always stick to their initial opinion. We consider first the well-known DeGroot model. While it is known in the literature…
The modeling of opinion dynamics has seen much study in varying academic disciplines. Understanding the complex ways information can be disseminated is a complicated problem for mathematicians as well as social scientists. We present a…
The networked opinion diffusion in online social networks (OSN) is often governed by the two genres of opinions - endogenous opinions that are driven by the influence of social contacts among users, and exogenous opinions which are formed…
Many classical models of collective behavior assume that emergent dynamics result from external and observable interactions among individuals. However, how collective dynamics in human populations depend on the internal psychological…
A hybrid model for opinion dynamics in complex multi-agent networks is introduced, wherein some continuous-valued agents average neighbors' opinions to update their own, while other discrete-valued agents use stochastic copying and voting…
Opinion polarization is a ubiquitous phenomenon in opinion dynamics. In contrast to the traditional consensus oriented group decision making (GDM) framework, this paper proposes a framework with the co-evolution of both opinions and…
We study concentration inequalities in gossip opinion dynamics over random graphs. In the model, a network is generated from a random graph model with independent edges, and agents interact pairwise randomly over the network. During the…
With the analysis of noise-induced synchronization of opinion dynamics with bounded confidence (BC), a natural and fundamental question is what opinion structures can be synchronized by noise. In the traditional Hegselmann-Krause (HK)…
We combine momentum from machine learning with evolutionary dynamics, where momentum can be viewed as a simple mechanism of intergenerational memory. Using information divergences as Lyapunov functions, we show that momentum accelerates the…