Related papers: Slow dynamics of the contact process on complex ne…
Communication networks show the small-world property of short paths, but the spreading dynamics in them turns out slow. We follow the time evolution of information propagation through communication networks by using the SI model with…
We introduce a new class of latent process models for dynamic relational network data with the goal of detecting time-dependent structure. Network data are often observed over time, and static network models for such data may fail to…
We studied, both analytically and numerically, complex excitable networks, in which connections are time dependent and some of the nodes remain silent at each time step. More specifically, (a) there is a heterogenous distribution of…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…
We perform extensive Monte Carlo simulations of the 10-state Potts model on quenched two-dimensional $\Phi^3$ gravity graphs to study the effect of quenched connectivity disorder on the phase transition, which is strongly first order on…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
We analyze the non-equilibrium order-disorder transition of Axelrod's model of social interaction in several complex networks. In a small world network, we find a transition between an ordered homogeneous state and a disordered state. The…
We study the two-dimensional Ising model on a network with a novel type of quenched topological (connectivity) disorder. We construct random lattices of constant coordination number and perform large scale Monte Carlo simulations in order…
A road map to understand the relation between the onset of the superconducting state with the particular optimum heterogeneity in granular superconductors is to study a Random Tranverse Ising Model on complex networks with a scale-free…
In this paper, we review theoretical and experimental research on rare region effects at quantum phase transitions in disordered itinerant electron systems. After summarizing a few basic concepts about phase transitions in the presence of…
The ability to achieve coordinated behavior -- engineered or emergent -- on networked systems has attracted widespread interest over several fields. This interest has led to remarkable advances in developing a theoretical understanding of…
Hallmarks of criticality, such as power-laws and scale invariance, have been empirically found in cortical networks and it has been conjectured that operating at criticality entails functional advantages, such as optimal computational…
Recent studies of networks representing complex systems from the brain to social graphs have revealed their higher-order architecture, which can be described by aggregates of simplexes (triangles, tetrahedrons, and higher cliques). Current…
Disorder is an unavoidable ingredient of real systems. Spatial disorder generates Griffiths phases (GPs) which, in analogy to critical points, are characterized by a slow relaxation of the order parameter and divergences of quantities such…
Using a generalized random recurrent neural network model, and by extending our recently developed mean-field approach [J. Aljadeff, M. Stern, T. Sharpee, Phys. Rev. Lett. 114, 088101 (2015)], we study the relationship between the network…
Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example…
A characteristic feature of topological systems is the presence of robust gapless edge states. In this work the effect of time-dependent perturbations on the edge states is considered. Specifically we consider perturbations that can be…
Critical behavior of the contact process is studied in annealed scale-free networks by mapping it on the random walk problem. We obtain the analytic results for the critical scaling, using the event-driven dynamics approach. These results…
A sufficiently connected topology linking the constituent units of a complex system is usually seen as a prerequisite for the emergence of collective phenomena such as synchronization. We present a random network of heterogeneous phase…
Many networks in nature and applications have an approximate low-rank structure in the sense that their connectivity structure is dominated by a few dimensions. It is natural to expect that dynamics on such networks would also be…