Related papers: Mean field at distance one
In this work we study the dynamics of systems composed of numerous interacting elements interconnected through a random weighted directed graph, such as models of random neural networks. We develop an original theoretical approach based on…
Individuals are always limited by some inelastic resources, such as time and energy, which restrict them to dedicate to social interaction and limit their contact capacity. Contact capacity plays an important role in dynamics of social…
We introduce and study a nonlinear discrete dynamical system describing the evolution of a resource distribution among interacting agents. The model generalizes several classical mean-field and opinion-dynamics frameworks and is defined on…
One of the major issues in the theoretical modeling of epidemic spreading is the development of methods to control the transmission of an infectious agent. Human behavior plays a fundamental role in the spreading dynamics and can be used to…
Typically, contagion strength is modeled by a transmission rate $\lambda$, whereby all nodes in a network are treated uniformly in a mean-field approximation. However, local agents react differently to the same contagion based on their…
Since 1927, until recently, models describing the spread of disease have mostly been of the SIR-compartmental type, based on the assumption that populations are homogeneous and well-mixed. The focus of these models have typically been on…
Can evolving networks be inferred and modeled without directly observing their nodes and edges? In many applications, the edges of a dynamic network might not be observed, but one can observe the dynamics of stochastic cascading processes…
Background: Animal trade plays an important role for the spread of infectious diseases in livestock populations. As a case study, we consider pig trade in Germany, where trade actors (agricultural premises) form a complex network. The…
Social networks are an important infrastructure for information, viruses and innovations propagation. Since users behavior has influenced by other users activity, some groups of people would be made regard to similarity of users interests.…
We investigate the long-time properties of a dynamic, out-of-equilibrium network of individuals holding one of two opinions in a population consisting of two communities of different sizes. Here, while the agents' opinions are fixed, they…
Disease awareness in epidemiology can be modelled with adaptive contact networks, where the interplay of disease dynamics and network alteration often adds new phases to the standard models (Gross et al. 2006, Shaw et al. 2008) and, in…
The Susceptible-Infected-Susceptible model is a canonical model for emerging disease outbreaks. Such outbreaks are naturally modeled as taking place on networks. A theoretical challenge in network epidemiology is the dynamic correlations…
A fundamental premise of statistical physics is that the particles in a physical system are interchangeable, and hence the state of each specific component is representative of the system as a whole. This assumption breaks down for complex…
We study the dependence of the largest component in regular networks on the clustering coefficient, showing that its size changes smoothly without undergoing a phase transition. We explain this behaviour via an analytical approach based on…
Collective dynamics on small-world networks emerge in a broad range of systems with their spectra characterizing fundamental asymptotic features. Here we derive analytic mean field predictions for the spectra of small-world models that…
The epidemic spreading has been studied for years by applying the mean-field approach in both homogeneous case, where each node may get infected by an infected neighbor with the same rate, and heterogeneous case, where the infection rates…
Traditional mathematical models of epidemic disease had for decades conventionally considered static structure for contacts. Recently, an upsurge of theoretical inquiry has strived towards rendering the models more realistic by…
The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…
The spread of disease through a physical-contact network and the spread of information about the disease on a communication network are two intimately related dynamical processes. We investigate the asymmetrical interplay between the two…
The spreading of evolutionary novelties across populations is the central element of adaptation. Unless population are well-mixed (like bacteria in a shaken test tube), the spreading dynamics not only depends on fitness differences but also…