Related papers: Kinetic Equations for Processes on Co-evolving Net…
We consider stochastic reaction-diffusion equations on a finite network represented by a finite graph. On each edge in the graph a multiplicative cylindrical Gaussian noise driven reaction-diffusion equation is given supplemented by a…
Many decision-making algorithms draw inspiration from the inner workings of individual biological systems. However, it remains unclear whether collective behavior among biological species can also lead to solutions for computational tasks.…
Most statistical models for networks focus on pairwise interactions between nodes. However, many real-world networks involve higher-order interactions among multiple nodes, such as co-authors collaborating on a paper. Hypergraphs provide a…
We provide a well-posedness theory for a class of nonlocal continuity equations on co-evolving graphs. We describe the connection among vertices through an edge weight function and we let it evolve in time, coupling its dynamics with the…
Big networks express various large-scale networks in many practical areas such as computer networks, internet of things, cloud computation, manufacturing systems, transportation networks, and healthcare systems. This paper analyzes such big…
We consider systems of agents interacting through topological interactions. These have been shown to play an important part in animal andhuman behavior. Precisely, the system consists of a finite number of particles characterized by their…
We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their…
We consider two-opinion voter models on dense dynamic random graphs. Our goal is to understand and describe the occurrence of consensus versus polarisation over long periods of time. The former means that all vertices have the same opinion,…
This paper proposes the first distributed algorithm that solves the weight-balancing problem using only finite rate and simplex communications among nodes, compliant with the directed nature of the graph edges. It is proved that the…
We introduce a class of Kac-like kinetic equations on the real line, with general random collisional rules, which include as particular cases models for wealth redistribution in an agent-based market or models for granular gases with a…
We formulate a general, high-dimensional kinetic theory describing the internal state (such as gene expression or protein levels) of cells in a stochastically evolving population. The resolution of our kinetic theory also allows one to…
This paper investigates the long time dynamics of interacting particle systems subject to singular interactions. We consider a microscopic system of $N$ interacting point particles, where the time evolution of the joint distribution…
The purpose of this paper is to study the properties of kinetic models for traffic flow described by a Boltzmann-type approach and based on a continuous space of microscopic velocities. In our models, the particular structure of the…
In this paper, we propose co-evolution models for both dynamics of opinions (people's view on a particular topic) and dynamics of social appraisals (the approval or disapproval towards each other). Opinion dynamics and dynamics of signed…
We explore the coupled dynamics of the internal states of a set of interacting elements and the network of interactions among them. Interactions are modeled by a spatial game and the network of interaction links evolves adapting to the…
Modeling stochastic dynamics from discrete observations is a key interdisciplinary challenge. Existing methods often fail to estimate the continuous evolution of probability densities from trajectories or face the curse of dimensionality.…
In this paper, we study network linear equations subject to digital communications with a finite data rate, where each node is associated with one equation from a system of linear equations. Each node holds a dynamic state and interacts…
We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity,…
By combining methods of kinetic and density functional theory, we present a description of molecular fluids which accounts for their microscopic structure and thermodynamic properties as well as for the hydrodynamic behavior. We focus on…
We study reaction-diffusion particle systems with several interaction mechanisms. As the number of particles tends to infinity, the system admits a mean-field limit describing the bulk behaviour. We focus on determining the propagation…