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The small-world network model is a simple model of the structure of social networks, which simultaneously possesses characteristics of both regular lattices and random graphs. The model consists of a one-dimensional lattice with a low…
In this paper, we study a class of stochastic processes, called evolving network Markov chains, in evolving networks. Our approach is to transform the degree distribution problem of an evolving network to a corresponding problem of evolving…
In this paper a rigorous proof of the mean field limit for a pedestrian flow model in two dimensions is given by using a probabilistic method. The model under investigation is an interacting particle system coupled to the eikonal equation…
We introduce a mean-field term to an evolutionary spatial game model. Namely, we consider the game of Nowak and May, based on the Prisoner's dilemma, and augment the game rules by a self-consistent mean-field term. This way, an agent…
We show that there are two classes of finite size effects for dynamic models taking place on a scale-free topology. Some models in finite networks show a behavior that depends only on the system size N. Others present an additional distinct…
In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from…
Dynamical systems driven by strong external signals are ubiquituous in nature and engineering. Here we study "echo state networks", networks of a large number of randomly connected nodes, which represent a simple model of a neural network,…
We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the…
In transportation systems (e.g. highways, railways, airports), traffic flows with distinct origin-destination pairs usually share common facilities and interact extensively. Such interaction is typically stochastic due to natural…
In this paper we study coordinated multipath routing at the flow-level in networks with routes of length one. As a first step the static case is considered, in which the number of flows is fixed. A clustering pattern in the rate allocation…
In this article, we study an interacting particle system in the context of epidemiology where the individuals (particles) are characterized by their position and infection state. We begin with a description at the microscopic level where…
The study of the normalized sum of random variables and its asymptotic behaviour has been and continues to be a central chapter in probability and statistical mechanics. When those variables are independent the central limit theorem ensures…
Noise-assisted transport phenomena highlight the nontrivial interplay between environmental effects and quantum coherence in achieving maximal efficiency. Due to the complexity of biochemical systems and their environments, effective open…
Our investigation is specially motivated by the stochastic version of a common model of potential spread in a dendritic tree. We do not assume the noise in the junction points to be Markovian. In fact, we allow for long-range dependence in…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
Both natural ecosystems and biochemical reaction networks involve populations of heterogeneous agents whose cooperative and competitive interactions lead to a rich dynamics of species' abundances, albeit at vastly different scales. The…
We consider a finite number of $N$ statistically equal agents, each moving on a finite set of states according to a continuous-time Markov Decision Process (MDP). Transition intensities of the agents and generated rewards depend not only on…
We study the mean-field limit of a model of biological neuron networks based on the so-called stochastic integrate-and-fire (IF) dynamics. Our approach allows to derive a continuous limit for the macroscopic behavior of the system, the…
A model for the evolution of a large population interacting system is considered in which a marked Poisson processes influences their evolution, together with a Brownian motion. Mean field McKean-Vlasov limits of such system are formulated…
Neural computations emerge from myriads of neuronal interactions occurring in intricate spiking networks. Due to the inherent complexity of neural models, relating the spiking activity of a network to its structure requires simplifying…