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We introduce a numerical method to solve epidemic models on the underlying topology of complex networks. The approach exploits the mean-field-like rate equations describing the system and allows us to work with very large system sizes, where Monte Carlo simulations are useless due to memory needs. We then study the susceptible-infected-removed(More)
We derive the mean-field equations characterizing the dynamics of a rumor process that takes place on top of complex heterogeneous networks. These equations are solved numerically by means of a stochastic approach. First, we present analytical and Monte Carlo calculations for homogeneous networks and compare the results with those obtained by the numerical(More)
– In this work, we study the synchronization of coupled phase oscillators on the underlying topology of scale-free networks. In particular, we assume that each network's component is an oscillator and that each interacts with the others following the Kuramoto model. We then study the onset of global phase synchronization and fully characterize the system's(More)
– The instability introduced in a large scale-free network by the triggering of node-breaking avalanches is analyzed using the fiber-bundle model as conceptual framework. We found, by measuring the size of the giant component, the avalanche size distribution and other quantities, the existence of an abrupt transition. This test of strength for complex(More)
Using error diagrams, we quantify the forecasting of characteristic-earthquake occurrence in a recently introduced minimalist model. Initially we connect the earthquake alarm at a fixed time after the ocurrence of a characteristic event. The evaluation of this strategy leads to a one-dimensional numerical exploration of the loss function. This first(More)
We report on a stochastic analysis of Earth's vertical velocity time series by using methods originally developed for complex hierarchical systems and, in particular, for turbulent flows. Analysis of the fluctuations of the detrended increments of the series reveals a pronounced transition in their probability density function from Gaussian to non-Gaussian.(More)
Using the global fiber bundle model as a tractable scheme of progressive fracture in heterogeneous materials, we define the branching ratio in avalanches as a suitable order parameter to clarify the order of the phase transition occurring at the collapse of the system. The model is analyzed using a probabilistic approach suited to smooth fluctuations. The(More)
A network with local dynamics of logistic type is considered. We implement a mean-field multiplicative coupling among first-neighbor nodes. When the coupling parameter is small the dynamics is dissipated and there is no activity: the network is turned off. For a critical value of the coupling a non-null stable synchronized state, which represents a turned(More)
The time to failure, T, of dynamical models of fracture for a hierarchical load-transfer geometry is studied. Using a probabilistic strategy and juxtaposing hierarchical structures of height n, we devise an exact method to compute T, for structures of height n+1. Bounding T, for large n, we are able to deduce that the time to failure tends to a nonzero(More)