Related papers: Heterogeneous pair-approximation for the contact p…
We review recent quantitative results on the approximation of mean field diffusion equations by large systems of interacting particles, obtained by optimal coupling methods. These results concern a larger range of models, more precise…
Contagion processes relying on the exposure to multiple sources are prevalent in social systems, and are effectively represented by hypergraphs. In this Letter, we derive a mean-field model that goes beyond node- and pair-based…
We develop an advanced mean field method for approximating averages in probabilistic data models that is based on the TAP approach of disorder physics. In contrast to conventional TAP, where the knowledge of the distribution of couplings…
A mathematical model for behavioral changes by pair interactions (i.e. due to direct contact) of individuals is developed. Three kinds of pair interactions can be distinguished: Imitative processes, avoidance processes, and compromising…
We typically interact in groups, not just in pairs. For this reason, it has recently been proposed that the spread of information, opinion or disease should be modelled over a hypergraph rather than a standard graph. The use of hyperedges…
We instigate the properties of the threshold contact process (TCP), a process showing an absorbing-state phase transition with infinitely many absorbing states, on random complex networks. The finite size scaling exponents characterizing…
We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in…
The contact process is a particular case of birth-and-death processes on infinite particle configurations. We consider the contact models on locally compact separable metric spaces. We prove the existence of a one-parameter set of invariant…
A comparative study between two distinct perturbative series expansions for the pair-creation contact process is presented. In contrast to the ordinary contact process, whose supercritical series expansions provide accurate estimates for…
The growing complexity of heterogeneous cellular networks (HetNets) has necessitated the need to consider variety of user and base station (BS) configurations for realistic performance evaluation and system design. This is directly…
We investigate systems of interacting stochastic differential equations with two kinds of heterogeneity: one originating from different weights of the linkages, and one concerning their asymptotic relevance when the system becomes large. To…
Given an arbitrary finite dimensional Hamiltonian H_0, we consider the model H=H_0+\Delta H, where \Delta H is a generic fully connected interaction. By using the strong law of large numbers we easily prove that, for all such models, a…
Dynamical reaction-diffusion processes and meta-population models are standard modeling approaches for a wide variety of phenomena in which local quantities - such as density, potential and particles - diffuse and interact according to the…
Functions correspond to one of the key concepts in mathematics and science, allowing the representation and modeling of several types of signals and systems. The present work develops an approach for characterizing the coverage and…
The statement of the mean field approximation theorem in the mean field theory of Markov processes particularly targets the behaviour of population processes with an unbounded number of agents. However, in most real-world engineering…
Heider balance theory provides a fundamental framework for understanding the formation of friendly and hostile relations in social networks. Existing stochastic formulations typically assume a uniform social temperature, implying that all…
We study the dynamics of the contact-process, one of the simplest nonequilibrium stochastic processes, taking place on a scale-free network. We consider the network topology as annealed, i.e. all links are rewired at each microscopic time…
We study Markov population processes on large graphs, with the local state transition rates of a single vertex being linear function of its neighborhood. A simple way to approximate such processes is by a system of ODEs called the…
Dynamic processes on networks are fundamental to understanding modern-day phenomena such as information diffusion and opinion polarization on the internet or epidemics spreading through society. However, such processes are notoriously…
In this paper we are concerned with the contact process on the squared lattice. The contact process intuitively describes the spread of the infectious disease on a graph, where an infectious vertex becomes healthy at a constant rate while a…