Related papers: Interacting Particle Systems in Complex Networks

The random walk with hyperbolic probabilities that we are introducing is an example of stochastic diffusion in a one-dimensional heterogeneous media. Although driven by site-dependent one-step transition probabilities, the process retains…

We have numerically studied the trapping problem in a two-dimensional lattice where particles are continuously generated. We have introduced interaction between particles and directionality of their movement. This model presents a critical…

In a cellular medium, the plasmic membrane is a place of interactions between the cell and its direct external environment. A classic model describes it as a fluid mosaic. The fluid phase of the membrane allows a lateral degree of freedom…

Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…

We study stochastic particle systems with stationary product measures that exhibit a condensation transition due to particle interactions or spatial inhomogeneities. We review previous work on the stationary behaviour and put it in the…

Most models of complex systems have been homogeneous, i.e., all elements have the same properties (spatial, temporal, structural, functional). However, most natural systems are heterogeneous: few elements are more relevant, larger,…

The interest in non-Markovian dynamics within the complex systems community has recently blossomed, due to a new wealth of time-resolved data pointing out the bursty dynamics of many natural and human interactions, manifested in an…

We investigate the behaviour of a system of particles with the different character of interaction. The approach makes it possible to describe systems of interacting particles by statistical methods taking into account a spatial…

Correlations and other collective phenomena in a schematic model of heterogeneous binary agents (individual spin-glass samples) are considered on the complete graph and also on 2d and 3d regular lattices. The system's stochastic dynamics is…

The diffusion of molecules in complex intracellular environments can be strongly influenced by spatial heterogeneity and stochasticity. A key challenge when modelling such processes using stochastic random walk frameworks is that negative…

We study the transport properties of a system of active particles moving at constant speed in an heterogeneous two-dimensional space. The spatial heterogeneity is modeled by a random distribution of obstacles, which the active particles…

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…

We study a model for a random walk of two classes of particles (A and B). Where both species are present in the same site, the motion of A's takes precedence over that of B's. The model was originally proposed and analyzed in Maragakis et…

Networks and graphs provide a simple but effective model to a vast set of systems which building blocks interact throughout pairwise interactions. Unfortunately, such models fail to describe all those systems which building blocks interact…

Dynamic systems characterized by diversified evolutions are not only more flexible, but also more resilient to attacks, failures and changing conditions. This article addresses the quantification of the diversity of non-linear transient…

Random walks are basic diffusion processes on networks and have applications in, for example, searching, navigation, ranking, and community detection. Recent recognition of the importance of temporal aspects on networks spurred studies of…

Random walkers characterized by random positions and random velocities lead to normal diffusion. A random walk was originally proposed by Einstein to model Brownian motion and to demonstrate the existence of atoms and molecules. Such a…

A particle subject to successive, random displacements is said to execute a random walk (in position or some other coordinate). The mathematical properties of random walks have been very thoroughly investigated, and the model is used in…

The article considers systems of interacting particles on networks with adaptively coupled dynamics. Such processes appear frequently in natural processes and applications. Relying on the notion of graph convergence, we prove that for large…

Inferring the laws of interaction between particles and agents in complex dynamical systems from observational data is a fundamental challenge in a wide variety of disciplines. We propose a non-parametric statistical learning approach to…