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Network structure can affect when and how widely new ideas, products, and behaviors are adopted. In widely-used models of biological contagion, interventions that randomly rewire edges (on average making them "longer") accelerate spread.…
Understanding spreading dynamics will benefit society as a whole in better preventing and controlling diseases, as well as facilitating the socially responsible information while depressing destructive rumors. In network-based spreading…
We analyze evolutionary dynamics in a confluent, branching cellular population, such as in a growing duct, vasculature, or in a branching microbial colony. We focus on the coarse-grained features of the evolution and build a statistical…
Robustness against unwanted perturbations is an important aspect of deploying neural network classifiers in the real world. Common natural perturbations include noise, saturation, occlusion, viewpoint changes, and blur deformations. All of…
The evolutionary origins of structural features in reconstructed gene-regulatory networks (GRNs) remain poorly understood, especially given the random aspects of gene expression. Here, we extend a classical model of GRN evolution to allow a…
Numerous concise models such as preferential attachment have been put forward to reveal the evolution mechanisms of real-world networks, which show that real-world networks are usually jointly driven by a hybrid mechanism of multiplex…
Various kinds of spread of influence occur in real world social and virtual networks. These phenomena are formulated by activation processes and irreversible dynamic monopolies in combinatorial graphs representing the topology of the…
In spite of its relevance to the origin of complex networks, the interplay between form and function and its role during network formation remains largely unexplored. While recent studies introduce dynamics by considering rewiring processes…
Evolutionary graph theory models the effects of natural selection and random drift on structured populations of competing mutant and non-mutant individuals. Recent studies have found that fixation times in such systems often have…
Population dynamics of a competitive two-species system under the influence of random events are analyzed and expressions for the steady-state population mean, fluctuations, and cross-correlation of the two species are presented. It is…
We highlight intriguing features of complex networks that are grown by \emph{redirection}. In this mechanism, a target node is chosen uniformly at random from the pre-existing network nodes and the new node attaches either to this initial…
Evolution is a dynamic process. The two classical forces of evolution are mutation and selection. Assuming small mutation rates, evolution can be predicted based solely on the fitness differences between phenotypes. Predicting an…
Evolutionary dynamics and patterns of molecular evolution are strongly influenced by selection on linked regions of the genome, but our quantitative understanding of these effects remains incomplete. Recent work has focused on predicting…
We consider the population dynamics of a set of species whose network of catalytic interactions is described by a directed graph. The relationship between the attractors of this dynamics and the underlying graph theoretic structures like…
Since network motifs are an important property of networks and some networks have the behaviors of rewiring or reducing or adding edges between old vertices before new vertices entering the networks, we construct our non-randomized model…
Networks describing the interaction of the elements that constitute a complex system grow and develop via a number of different mechanisms, such as the addition and deletion of nodes, the addition and deletion of edges, as well as the…
This work considers the robustness of uncertain consensus networks. The first set of results studies the stability properties of consensus networks with negative edge weights. We show that if either the negative weight edges form a cut in…
The networks of predator-prey interactions in ecological systems are remarkably complex, but nevertheless surprisingly stable in terms of long term persistence of the system as a whole. In order to understand the mechanism driving the…
Environment plays a fundamental role in the competition for resources, and hence in the evolution of populations. Here, we study a well-mixed, finite population consisting of two strains competing for the limited resources provided by an…
We study the temporal co-variation of network co-evolution via the cross-link structure of networks, for which we take advantage of the formalism of hypergraphs to map cross-link structures back to network nodes. We investigate two sets of…