TY  - JOUR
ID  - epos196
UR  - http://dx.doi.org/10.1103/PhysRevE.77.066104
IS  - 6
A1  - Davidsen, Jörn
A1  - Grassberger, Peter
A1  - Paczuski, Maya
Y1  - 2008/06/06/
N2  - We propose a method to search for signs of causal structure in spatiotemporal data making minimal a priori
assumptions about the underlying dynamics. To this end, we generalize the elementary concept of recurrence
for a point process in time to recurrent events in space and time. An event is de?ned to be a recurrence of any
previous event if it is closer to it in space than all the intervening events. As such, each sequence of recurrences
for a given event is a record breaking process. This de?nition provides a strictly data driven technique to search for structure. De?ning events to be nodes, and linking each event to its recurrences, generates a network of recurrent events. Signi?cant deviations in statistical properties of that network compared to networks arising
from (acausal) random processes allows one to infer attributes of the causal dynamics that generate observable
correlations in the patterns. We derive analytically a number of properties for the network of recurrent events
composed by a random process in space and time. We extend the theory of records to treat not only the variable
where records happen, but also time as continuous. In this way, we construct a fully symmetric theory of
records leading to a number of results. Those analytic results are compared in detail to the properties of a
network synthesized from time series of epicenter locations for earthquakes in Southern California. Signi?cant
disparities from the ensemble of acausal networks that can be plausibly attributed to the causal structure of
seismicity are as follows. (1) Invariance of network statistics with the time span of the events considered. (2)
The appearance of a fundamental length scale for recurrences, independent of the time span of the catalog,
which is consistent with observations of the ?rupture length.? (3) Hierarchy in the distances and times of
subsequent recurrences. As expected, almost all of the statistical properties of a network constructed from a
surrogate in which the original magnitudes and locations of earthquake epicenters are randomly ?shuf?ed? are
completely consistent with predictions from the acausal null model.
PB  - The American Physical Society
JF  - Physical Review E
VL  - 77
SN  - 1539-3755
TI  - Networks of recurrent events, a theory of records, and an application to finding causal signatures in seismicity
AV  - none
ER  -