-We present a model that explores the influence of persuasion in a population of agents with positive and negative opinion orientations. The opinion of each agent is represented by an integer number k that expresses its level of agreement on a given issue, from totally against k = −M to totally in favor k = M . Same-orientation agents persuade each other with probability p, becoming more extreme, while opposite-orientation agents become more moderate as they reach a compromise with probability q. The population initially evolves to (a) a polarized state for r = p/q > 1, where opinions' distribution is peaked at the extreme values k = ±M , or (b) a centralized state for r < 1, with most opinions around k = ±1. When r ≫ 1, polarization lasts for a time that diverges as r M ln N , where N is the population's size. Finally, an extremist consensus (k = M or −M ) is reached in a time that scales as r −1 for r ≪ 1.
Recent network research has focused on the cascading failures in a system of interdependent networks and the necessary preconditions for system collapse. An important question that has not been addressed is how to repair a failing system before it suffers total breakdown. Here we introduce a recovery strategy for nodes and develop an analytic and numerical framework for studying the concurrent failure and recovery of a system of interdependent networks based on an efficient and practically reasonable strategy. Our strategy consists of repairing a fraction of failed nodes, with probability of recovery γ, that are neighbors of the largest connected component of each constituent network. We find that, for a given initial failure of a fraction 1 − p of nodes, there is a critical probability of recovery above which the cascade is halted and the system fully restores to its initial state and below which the system abruptly collapses. As a consequence we find in the plane γ − p of the phase diagram three distinct phases. A phase in which the system never collapses without being restored, another phase in which the recovery strategy avoids the breakdown, and a phase in which even the repairing process cannot prevent system collapse.
In this paper we derive analytically the evolution equation of the interface for a model of surface growth with relaxation to the minimum (SRM) in complex networks. We were inspired by Even though for Euclidean lattices the evolution equation is linear, we find that in complex heterogeneous networks non-linear terms appear due to the heterogeneity and the lack of symmetry of the network; they produce a logarithmic divergency of the saturation roughness with the system size as found by Pastore y Piontti et al. for λ < 3.
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