Related papers: A particle method for continuous Hegselmann-Krause…
In this paper, we construct a type of interacting particle systems to approximate a class of stochastic different equations whose coefficients depend on the conditional probability distributions of the processes given partial observations.…
This paper is concerned with the probability of consensus in a multivariate, spatially explicit version of the Hegselmann-Krause model for the dynamics of opinions. Individuals are located on the vertices of a finite connected graph…
We study the dynamics of opinion formation in the situation where changing opinion involves a cost for the agents. To do so we couple the dynamics of a heterogeneous bounded confidence Hegselmann-Krause model with that of the resources that…
We propose a zero-order optimization method for sequential min-max problems based on two populations of interacting particles. The systems are coupled so that one population aims to solve the inner maximization problem, while the other aims…
We study multidimensional continuous opinion dynamics, where opinions are nonnegative vectors which components sum up to one. Examples of such opinions are budgets or other allocation vectors which display a distribution of a fixed amount…
A model for Opinion Particles, based on Bayesian-inspired models of Opinion Dynamics such as the CODA model is presented. By extending the discrete time characteristic of those models to continuous time, a theory for the movement of opinion…
We propose a novel projection-based particle method for solving the McKean-Vlasov stochastic differential equations. Our approach is based on a projection-type estimation of the marginal density of the solution in each time step. The…
We perform a detailed study of the Hegselmann-Krause bounded confidence opinion dynamics model with heterogeneous confidence $\varepsilon_i$ drawn from uniform distributions in different intervals $[\varepsilon_l, \varepsilon_u]$. The phase…
We propose and investigate different kinetic models for opinion formation, when the opinion formation process depends on an additional independent variable, e.g. a leadership or a spatial variable. More specifically, we consider:(i) opinion…
We consider a continuous version of the Hegselmann-Krause model of opinion dynamics. Interaction between agents either leads to a state of consensus, where agents converge to a single opinion as time evolves, or to a fragmented state with…
The original Hegselmann-Krause (HK) model comprises a set of $n$ agents characterized by their opinion, a number in $[0,1]$. Agent $i$ updates its opinion $x_i$ via taking the average opinion of its neighbors whose opinion differs by at…
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is…
This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed…
We suggest kinetic models of dissipation for an ensemble of interacting oriented particles, for example, moving magnetized particles. This is achieved by introducing a double bracket dissipation in kinetic equations using an oriented…
We consider the Hegselmann-Krause model for opinion dynamics and study the evolution of the system under various settings. We first analyze the termination time of the synchronous Hegselmann-Krause dynamics in arbitrary finite dimensions…
An integro-differential equation, modeling dynamic fractional order viscoelasticity, with a Mittag-Leffler type convolution kernel is considered. A discontinuous Galerkin method, based on piecewise constant polynomials is formulated for…
Eliminating disagreement in a group is usually beneficial to the social stability. In this paper, using the well-known Hegselmann-Krause (HK) model, we design a quite simple strategy that could resolve the opinion difference of the system…
Krause's model of opinion dynamics has recently been the object of several studies, partly because it is one of the simplest multi-agent systems involving position-dependent changing topologies. In this model, agents have an opinion…
We present a model of coupling between a point wise particle and a compressible inviscid fluid following the Euler equations. The interaction between the fluid and the particle is achieved through a drag force. It writes as the product of a…
We study the particle method to approximate the gradient flow on the $L^p$-Wasserstein space. This method relies on the discretization of the energy introduced by [3] via nonoverlapping balls centered at the particles and preserves the…