Related papers: Emergence of Network Structure in Models of Collec…
Firing rate fluctuations in neural populations are observed experimentally over multiple time scales, in single neurons, across trials when elicited by stimuli, and across populations. In this work, we examine how firing rate fluctuations…
We introduce a growing network model---the copying model---in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability $p$. When…
Evolution occurs in populations of reproducing individuals. The structure of a biological population affects which traits evolve. Understanding evolutionary game dynamics in structured populations is difficult. Precise results have been…
With the premise that social interactions are described by power-law distributions, we study a SIR stochastic dynamic on a static scale-free random network generated via configuration model. We verify our model with respect to deterministic…
It is suggested that the degree distribution for networks of the cell-metabolism for simple organisms reflects an ubiquitous randomness. This implies that natural selection has exerted no or very little pressure on the network degree…
Search for possible relationships between phylogeny and ontogeny is one of the most important issues in the field of evolutionary developmental biology. By representing developmental dynamics of spatially located cells with gene expression…
In this article, we propose a growing network model based on an optimal policy involving both topological and geographical measures. In this model, at each time step, a new node, having randomly assigned coordinates in a $1 \times 1$…
Unlike the well-studied models of growing networks, where the dominant dynamics consist of insertions of new nodes and connections, and rewiring of existing links, we study {\em ad hoc} networks, where one also has to contend with rapid and…
A key issue in complex systems regards the relationship between topology and dynamics. In this work, we use a recently introduced network property known as steering coefficient as a means to approach this issue with respect to different…
Many real-world complex networks arise as a result of a competition between growth and rewiring processes. Usually the initial part of the evolution is dominated by growth while the later one rather by rewiring. The initial growth allows…
We study the evolution of the probability density of an asexual, one locus population under natural selection and random evolution. This evolution is governed by a Fokker-Planck equation with degenerate coefficients on the boundaries,…
Understanding the evolution of cooperation in structured populations represented by networks is a problem of long research interest, and a most fundamental and widespread property of social networks related to cooperation phenomena is that…
In this work, the primary goal is to establish rigorous connection between the Fokker-Planck equation of neural networks with its microscopic model: the diffusion-jump stochastic process that captures the mean field behavior of collections…
Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…
Real-world networks grow over time; statistical models based on node exchangeability are not appropriate. Instead of constraining the structure of the \textit{distribution} of edges, we propose that the relevant symmetries refer to the…
We determine stability and attractor properties of random Boolean genetic network models with canalyzing rules for a variety of architectures. For all power law, exponential, and flat in-degree distributions, we find that the networks are…
It is well-known that population structure is a catalyst for the evolution of cooperation since individuals can reciprocate with their neighbors through local interactions defined by network structures. Previous research typically relies on…
We study the importance of local structural properties in networks which have been evolved for a power-law scaling in their Laplacian spectrum. To this end, the degree distribution, two-point degree correlations, and degree-dependent…
Several networks occurring in real life have modular structures that are arranged in an hierarchical fashion. In this paper, we have proposed a model for such networks, using a stochastic generation method. Using this model we show that,…
In studying network growth, the conventional approach is to devise a growth mechanism, quantify the evolution of a statistic or distribution (such as the degree distribution), and then solve the equations in the steady state (the…