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    Order patterns networks (orpan) - A method to estimate time-evolving functional connectivity from multivariate time series
    (Lausanne : Frontiers Research Foundation, 2012) Schinkel, S.; Zamora-López, G.; Dimigen, O.; Sommer, W.; Kurths, J.
    Complex networks provide an excellent framework for studying the function of the human brain activity. Yet estimating functional networks from measured signals is not trivial, especially if the data is non-stationary and noisy as it is often the case with physiological recordings. In this article we propose a method that uses the local rank structure of the data to define functional links in terms of identical rank structures. The method yields temporal sequences of networks which permits to trace the evolution of the functional connectivity during the time course of the observation. We demonstrate the potentials of this approach with model data as well as with experimental data from an electrophysiological study on language processing.
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    Communication activity in a social network: Relation between long-term correlations and inter-event clustering
    (London : Nature Publishing Group, 2012) Rybski, D.; Buldyrev, S.V.; Havlin, S.; Liljeros, F.; Makse, H.A.
    Human communication in social networks is dominated by emergent statistical laws such as non-trivial correlations and temporal clustering. Recently, we found long-term correlations in the user's activity in social communities. Here, we extend this work to study the collective behavior of the whole community with the goal of understanding the origin of clustering and long-term persistence. At the individual level, we find that the correlations in activity are a byproduct of the clustering expressed in the power-law distribution of inter-event times of single users, i.e. short periods of many events are separated by long periods of no events. On the contrary, the activity of the whole community presents long-term correlations that are a true emergent property of the system, i.e. they are not related to the distribution of inter-event times. This result suggests the existence of collective behavior, possibly arising from nontrivial communication patterns through the embedding social network.