Related papers: Diffusion Processes on Small-World Networks with D…

A common theme among the proposed models for network epidemics is the assumption that the propagating object, i.e., a virus or a piece of information, is transferred across the nodes without going through any modification or evolution.…

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 consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process,…

The small-world property is known to have a profound effect on the navigation efficiency of complex networks [J. M. Kleinberg, Nature 406, 845 (2000)]. Accordingly, the proper addition of shortcuts to a regular substrate can lead to the…

In this paper the multi-dimensional random walk models governed by distributed fractional order differential equations and multi-term fractional order differential equations are constructed. The scaling limits of these random walks to a…

Human mobility and activity patterns mediate contagion on many levels, including the spatial spread of infectious diseases, diffusion of rumors, and emergence of consensus. These patterns however are often dominated by specific locations…

We introduce a self-organized model of graph evolution associated with preferential network random walkers. The idea is developed by using two different types of walkers, the interactions of which lead to a dynamic graph. The walkers of the…

We study the small-world network model, which mimics the transition between regular-lattice and random-lattice behavior in social networks of increasing size. We contend that the model displays a normal continuous phase transition with a…

In this paper a lattice model for the diffusional transport of particles in the interphase cell nucleus is proposed. The dynamic behaviour of single chains on the lattice is investigated and Rouse scaling is verified. Dynamical dense…

Diffusion processes in networks are increasingly used to model the spread of information and social influence. In several applications in computational sustainability such as the spread of wildlife, infectious diseases and traffic mobility…

Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently…

Random walks as well as diffusions in random media are considered. Methods are developed that allow one to establish large deviation results for both the `quenched' and the `averaged' case.

Diffusive dynamics abound in nature and have been especially studied in physical, biological, and financial systems. These dynamics are characterised by a linear growth of the mean squared displacement (MSD) with time. Often, the conditions…

Massively parallel recordings of spiking activity in cortical networks show that covariances vary widely across pairs of neurons. Their low average is well understood, but an explanation for the wide distribution in relation to the static…

Small-world networks are networks in which the graphical diameter of the network is as small as the diameter of random graphs but whose nodes are highly clustered when compared with the ones in a random graph. Examples of small-world…

We propose a simple model of the evolution of a social network which involves local search and volatility (random decay of links). The model captures the crucial role the network plays for information diffusion. This is responsible for a…

Epidemic spreading processes in the real world can interact with each other in a cooperative, competitive, or asymmetric way, requiring a description based on coevolution dynamics. Rich phenomena such as discontinuous outbreak transitions…

Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…

Random scale-free overlay topologies provide a number of properties like for example high resilience against failures of random nodes, small (average) diameter as well as good expansion and congestion characteristics that make them…

We study the dynamics of diffusion processes acting on directed multiplex networks, i.e., coupled multilayer networks where at least one layer consists of a directed graph. We reveal that directed multiplex networks may exhibit a faster…