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Entorhinal grid cells in mammals fire as a function of animal location, with spatially periodic response patterns. This nonlocal periodic representation of location, a local variable, is unlike other neural codes. There is no theoretical explanation for why such a code should exist. We examined how accurately the grid code with noisy neurons allows an ideal… (More)

A classical model for social-influence-driven opinion change is the threshold model. Here we study cascades of opinion change driven by threshold model dynamics in the case where multiple initiators trigger the cascade, and where all nodes possess the same adoption threshold ϕ. Specifically, using empirical and stylized models of social networks, we study… (More)

Temporal communities are the result of a consistent partitioning of nodes across multiple snapshots of an evolving network, and they provide insights into how dense clusters in a network emerge, combine, split and decay over time. To reliably detect temporal communities we need to not only find a good community partition in a given snapshot but also ensure… (More)

Monte Carlo simulations are performed to determine the critical percolation threshold for interpenetrating square objects in two dimensions and cubic objects in three dimensions. Simulations are performed for two cases: (i) objects whose edges are aligned parallel to one another and (ii) randomly oriented objects. For squares whose edges are aligned, the… (More)

We show how the prevailing majority opinion in a population can be rapidly reversed by a small fraction p of randomly distributed committed agents who consistently proselytize the opposing opinion and are immune to influence. Specifically, we show that when the committed fraction grows beyond a critical value p(c) ≈ 10%, there is a dramatic decrease in the… (More)

We consider the effect of network topology on the optimality of packet routing which is quantified by gammac, the rate of packet insertion beyond which congestion and queue growth occurs. We show that for any network, there exists an absolute upper bound, expressed in terms of vertex separators, for the scaling of gammac with network size N, irrespective of… (More)

Public opinion is often affected by the presence of committed groups of individuals dedicated to competing points of view. Using a model of pairwise social influence, we study how the presence of such groups within social networks affects the outcome and the speed of evolution of the overall opinion on the network. Earlier work indicated that a single… (More)

Using Monte Carlo simulations we calculate fc, the fraction of nodes that are randomly removed before global connectivity is lost, for networks with scale-free and bimodal degree distributions. Our results differ from the results predicted by an equation for fc proposed by Cohen We discuss the reasons for this disagreement and clarify the domain for which… (More)

We study the scaling behavior of the size of minimum dominating set (MDS) in scale-free networks, with respect to network size N and power-law exponent c, while keeping the average degree fixed. We study ensembles generated by three different network construction methods, and we use a greedy algorithm to approximate the MDS. With a structural cutoff imposed… (More)

Temporal communities result from a consistent partitioning of nodes across multiple snapshots of an evolving complex network that can help uncover how dense clusters in a network emerge, combine, split and decay with time. Current methods for finding communities in a single snapshot are not straightforwardly generalizable to finding temporal communities… (More)