Related papers: Cluster approximations for infection dynamics on r…
We study the diffusion of epidemics on networks that are partitioned into local communities. The gross structure of hierarchical networks of this kind can be described by a quotient graph. The rationale of this approach is that individuals…
Stochastic processes on complex networks, where each node is in one of several compartments, and neighboring nodes interact with each other, can be used to describe a variety of real-world spreading phenomena. However, computational…
Much recent research activity has been devoted to empirical study and theoretical models of complex networks (random graphs) with three qualitative features: power-law degree distribution, local clustering of edges, and small diameter. We…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
Binary-state dynamics (such as the susceptible-infected-susceptible (SIS) model of disease spread, or Glauber spin dynamics) on random networks are accurately approximated using master equations. Standard mean-field and pairwise theories…
In this paper, we present a framework for the analysis of self-organized distributed coalition formation process for spectrum sharing in interference channel for large-scale ad hoc networks. In this approach, we use the concept of coalition…
Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many…
Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical…
A key feature of the classical Fluctuation Dissipation theorem is its ability to approximate the average response of a dynamical system to a sufficiently small external perturbation from an appropriate time correlation function of the…
Apart from the role the clustering coefficient plays in the definition of the small-world phenomena, it also has great relevance for practical problems involving networked dynamical systems. To study the impact of the clustering coefficient…
In this paper we consider a model for the spread of a stochastic SIR (Susceptible $\to$ Infectious $\to$ Recovered) epidemic on a network of individuals described by a random intersection graph. Individuals belong to a random number of…
Fluctuations of the amplitude of the order parameter govern the properties of superconducting systems close to the critical transition temperature. In the BCS regime we examine the contribution of these pairing fluctuations to the…
We carry out an analytic investigation of stochastic oscillations in a susceptible-infected-recovered model of disease spread on a network of $n$ cities. In the model a fraction $f_{jk}$ of individuals from city $k$ commute to city $j$,…
Cooperation in cellular networks has been recently suggested as a promising scheme to improve system performance. In this work, clusters are formed based on the Mutually Nearest Neighbour relation, which defines which stations cooperate in…
A wide class of binary-state dynamics on networks---including, for example, the voter model, the Bass diffusion model, and threshold models---can be described in terms of transition rates (spin-flip probabilities) that depend on the number…
Recent works have shown that the contact process running on the top of highly heterogeneous random networks is described by the heterogeneous mean-field theory. However, some important aspects as the transition point and strong corrections…
The clustering property of complex networks indicates the abundance of small dense subgraphs in otherwise sparse networks. For a community-affiliation network defined by a superposition of Bernoulli random graphs, which has a nonvanishing…
Biological and social systems consist of myriad interacting units. The interactions can be represented in the form of a graph or network. Measurements of these graphs can reveal the underlying structure of these interactions, which provides…
In this paper, we consider networks consisting of a finite number of non-overlapping communities. To extract these communities, the interaction between pairs of nodes may be sampled from a large available data set, which allows a given node…
Biochemical processes typically involve many chemical species, some in abundance and some in low molecule numbers. Here we first identify the rate constant limits under which the concentrations of a given set of species will tend to…