IMT Institutional Repository: No conditions. Results ordered -Date Deposited. 2024-03-28T12:47:39ZEPrintshttp://eprints.imtlucca.it/images/logowhite.pnghttp://eprints.imtlucca.it/2015-11-16T09:04:49Z2015-11-16T09:04:49Zhttp://eprints.imtlucca.it/id/eprint/2899This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28992015-11-16T09:04:49ZCorrelated bursts and the role of memory rangeInhomogeneous temporal processes in natural and social phenomena have been described by bursts that are rapidly occurring events within short time periods alternating with long periods of low activity. In addition to the analysis of heavy-tailed inter-event time distributions, higher-order correlations between inter-event times, called correlated bursts, have been studied only recently. As the possible mechanisms underlying such correlated bursts are far from being fully understood, we devise a simple model for correlated bursts by using a self-exciting point process with variable memory range. Here the probability that a new event occurs is determined by a memory function that is the sum of decaying memories of the past events. In order to incorporate the noise and/or limited memory capacity of systems, we apply two memory loss mechanisms, namely either fixed number or variable number of memories. By using theoretical analysis and numerical simulations we find that excessive amount of memory effect may lead to a Poissonian process, which implies that for memory effect there exists an intermediate range that will generate correlated bursts of magnitude comparable to empirical findings. Hence our results provide deeper understanding of how long-range memory affects correlated bursts.Hang-Hyun JoJuan I. Perottijuanignacio.perotti@imtlucca.itKimmo KaskiJános Kertész2014-12-04T11:05:47Z2014-12-04T11:45:24Zhttp://eprints.imtlucca.it/id/eprint/2403This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24032014-12-04T11:05:47ZAnalytically solvable model of spreading dynamics with non-Poissonian processesNon-Poissonian bursty processes are ubiquitous in natural and social phenomena, yet little is known about their effects on the large-scale spreading dynamics. In order to characterize these effects, we devise an analytically solvable model of susceptible-infected spreading dynamics in infinite systems for arbitrary inter-event time distributions and for the whole time range. Our model is stationary from the beginning, and the role of the lower bound of inter-event times is explicitly considered. The exact solution shows that for early and intermediate times, the burstiness accelerates the spreading as compared to a Poisson-like process with the same mean and same lower bound of inter-event times. Such behavior is opposite for late-time dynamics in finite systems, where the power-law distribution of inter-event times results in a slower and algebraic convergence to a fully infected state in contrast to the exponential decay of the Poisson-like process. We also provide an intuitive argument for the exponent characterizing algebraic convergence.Hang-Hyun JoJuan I. Perottijuanignacio.perotti@imtlucca.itKimmo KaskiJános Kertész