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We perform a new analysis on the dissipative Olami-Feder-Christensen model on a small world topology considering avalanche size differences. We show that when criticality appears the Probability Density Functions (PDFs) for the avalanche size differences at different times have fat tails with a q-Gaussian shape. This behaviour does not depend on the time interval adopted and is found also when considering energy differences between real earthquakes. Such a result can be analytically understood if the sizes (released energies) of the avalanches (earthquakes) have no correlations. Our findings support the hypothesis that a self-organized criticality mechanism with long-range interactions is at the origin of seismic events and indicate that it is not possible to predict the magnitude of the next earthquake knowing those of the previous ones.PACS numbers: 05.65.+b, 91.30.Px, 05.45.Tp In the last years there has been an intense debate on earthquake predictability [1] and a great effort in studying earthquake triggering and interaction [2][3][4][5]. Along these lines the possible application of the Self-Organized Criticality (SOC) paradigm [6][7][8][9][10][11][12][13][14] has been discussed. Earthquakes trigger dynamic and static stress changes. The first acts at short time and spatial scales, involving the brittle upper crust, while the second involves relaxation processes in the asthenosphere and acts at long time and spatial scales [15][16][17][18][19][20][21]. In this letter, by means of a new analysis, we show that it is possible to reproduce statistical features of earthquakes catalogs [22,23] within a SOC scenario taking into account longrange interactions. We consider the dissipative OlamiFeder-Christensen model [12] on a small world topology [24,25] and we show that the Probability Density Functions (PDFs) for the avalanche size differences at different times have fat tails with a q-Gaussian shape [26][27][28][29] when finite-size scaling is present. This behaviour does not depend on the time interval adopted and is found also when considering energy differences between real earthquakes. It is possible to explain this result analytically assuming the absence of correlations among the sizes (released energies) of the avalanches (earthquakes). This finding does not allow to predict the magnitude of the next earthquake knowing those of the previous ones.The Olami-Feder-Christensen (OFC) model [12] is one of the most interesting models displaying Self-Organized Criticality. Despite of its simplicity, it exhibits a rich phenomenology resembling real seismicity, like the presence of aftershocks and foreshocks [14]. In its original version the OFC model consists of a two-dimensional square lattice of N = L 2 sites, each one connected to its 4 nearest neighbours and carrying a seismogenic force represented by a real variable F i , which initially takes a random value in the interval (0, F th ). In order to mimic a uniform tectonic loading all the forces are increased simultaneously and uniformly, until one of them...

Based on cluster desynchronization properties of phase oscillators, we introduce an efficient method for the detection and identification of modules in complex networks. The performance of the algorithm is tested on computer generated and real-world networks whose modular structure is already known or has been studied by means of other methods. The algorithm attains a high level of precision, especially when the modular units are very mixed and hardly detectable by the other methods, with a computational effort O(KN) on a generic graph with N nodes and K links.

We study the continuum opinion dynamics of the compromise model of Krause and Hegselmann for a community of mutually interacting agents by solving numerically a rate equation. The opinions are here represented by two-dimensional vectors with real-valued components. We study the situation starting from a uniform probability distribution for the opinion configuration and for different shapes of the confidence range. In all cases, we find that the thresholds for consensus and cluster merging either coincide with their one-dimensional counterparts, or are very close to them. The symmetry of the final opinion configuration, when more clusters survive, is determined by the shape of the opinion space. If the latter is a square, which is the case we consider, the clusters in general occupy the sites of a square lattice, although we sometimes observe interesting deviations from this general pattern, especially near the center of the opinion space.

We present a molecular dynamics test of the Central Limit Theorem (CLT) in a paradigmatic long-range-interacting many-body classical Hamiltonian system, the HMF model. We calculate sums of velocities at equidistant times along deterministic trajectories for different sizes and energy densities. We show that, when the system is in a chaotic regime (specifically, at thermal equilibrium), ergodicity is essentially verified, and the Pdfs of the sums appear to be Gaussians, consistently with the standard CLT. When the system is, instead, only weakly chaotic (specifically, along longstanding metastable Quasi-Stationary States), nonergodicity (i.e., discrepant ensemble and time averages) is observed, and robust q-Gaussian attractors emerge, consistently with recently proved generalizations of the CLT.