Related papers: Parameter estimation in interacting particle syste…
Processes on networks consist of two interdependent parts: the network topology, consisting of the links between nodes, and the dynamics, specified by some governing equations. This work considers the prediction of the future dynamics on an…
We consider a random graph model evolving in discrete time-steps that is based on 3-interactions among vertices. Triangles, edges and vertices have different weights; objects with larger weight are more likely to participate in future…
A common goal in network modeling is to uncover the latent community structure present among nodes. For many real-world networks, the true connections consist of events arriving as streams, which are then aggregated to form edges, ignoring…
We study finite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which…
In recent decades, it has been emphasized that the evolving structure of networks may be shaped by interaction principles that yield sparse graphs with a vertex degree distribution exhibiting an algebraic tail, and other structural traits…
Motivated by a general principle governing regulation mechanisms in biological cells, we investigate a general interaction scheme between different populations of particles and specific particles, referred to as agents. Assuming that each…
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,…
Duplication-divergence models are a popular model for the evolution of gene and protein interaction networks. However, existing duplication-divergence models often neglect realistic features such as loss of interactions. Thus, in this paper…
Consider an interacting particle system indexed by the vertices of a (possibly random) locally finite graph whose vertices and edges are equipped with marks representing parameters of the model such as the environment and initial…
In this work, we investigate the dynamics of interacting particle systems subjected to repulsive forces, such as lattices of magnetized particles. To this end, we first develop a general model capable of capturing the complete dynamical…
Networks play a central role in modern data analysis, enabling us to reason about systems by studying the relationships between their parts. Most often in network analysis, the edges are given. However, in many systems it is difficult or…
Many algorithms have been proposed for predicting missing edges in networks, but they do not usually take account of which edges are missing. We focus on networks which have missing edges of the form that is likely to occur in real…
In this paper we develop a theory to describe innovation processes in a network of interacting units. We introduce a stochastic picture that allows for the clarification of the role of fluctuations for the survival of innovations in such a…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
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 study a class models of correlated random networks in which vertices are characterized by \textit{hidden variables} controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological…
Many natural and artificial networks evolve in time. Nodes and connections appear and disappear at various timescales, and their dynamics has profound consequences for any processes in which they are involved. The first empirical analysis…
We investigate how a residual network can learn to predict the dynamics of interacting shapes purely as an image-to-image regression task. With a simple 2d physics simulator, we generate short sequences composed of rectangles put in motion…
In this work we study a kinetic model of active particles with delayed dynamics, and its limit when the number of particles goes to infinity. This limit turns out to be related to delayed differential equations with random initial…
An analytical approach to network dynamics is used to show that when agents copy their state randomly the network arrives to a stationary status in which the distribution of states is independent of the agents degree. The effects of network…