<> "The repository administrator has not yet configured an RDF license."^^ . <> . . . "Networks of recurrent events, a theory of records, and an application to finding causal signatures in seismicity"^^ . "We propose a method to search for signs of causal structure in spatiotemporal data making minimal a priori\r\nassumptions about the underlying dynamics. To this end, we generalize the elementary concept of recurrence\r\nfor a point process in time to recurrent events in space and time. An event is defined to be a recurrence of any\r\nprevious event if it is closer to it in space than all the intervening events. As such, each sequence of recurrences\r\nfor a given event is a record breaking process. This definition provides a strictly data driven technique to search for structure. Defining events to be nodes, and linking each event to its recurrences, generates a network of recurrent events. Significant deviations in statistical properties of that network compared to networks arising\r\nfrom (acausal) random processes allows one to infer attributes of the causal dynamics that generate observable\r\ncorrelations in the patterns. We derive analytically a number of properties for the network of recurrent events\r\ncomposed by a random process in space and time. We extend the theory of records to treat not only the variable\r\nwhere records happen, but also time as continuous. In this way, we construct a fully symmetric theory of\r\nrecords leading to a number of results. Those analytic results are compared in detail to the properties of a\r\nnetwork synthesized from time series of epicenter locations for earthquakes in Southern California. Significant\r\ndisparities from the ensemble of acausal networks that can be plausibly attributed to the causal structure of\r\nseismicity are as follows. (1) Invariance of network statistics with the time span of the events considered. (2)\r\nThe appearance of a fundamental length scale for recurrences, independent of the time span of the catalog,\r\nwhich is consistent with observations of the “rupture length.” (3) Hierarchy in the distances and times of\r\nsubsequent recurrences. As expected, almost all of the statistical properties of a network constructed from a\r\nsurrogate in which the original magnitudes and locations of earthquake epicenters are randomly “shuffled” are\r\ncompletely consistent with predictions from the acausal null model."^^ . "2008-06-06" . . "77" . "6" . . "The American Physical Society"^^ . . . "Physical Review E"^^ . . . "15393755" . . . . . . . . . . . . . "Peter"^^ . "Grassberger"^^ . "Peter Grassberger"^^ . . "Jörn"^^ . "Davidsen"^^ . "Jörn Davidsen"^^ . . "Maya"^^ . "Paczuski"^^ . "Maya Paczuski"^^ . . "Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, Alberta, Canada T2N 1N4"^^ . . . "Institute for Biocomplexity and Informatics, University of Calgary, Calgary, Alberta, Canada"^^ . . . . . . "HTML Summary of #196 \n\nNetworks of recurrent events, a theory of records, and an application to finding causal signatures in seismicity\n\n" . "text/html" . . . "Clustering and migration" . .