Berlin 2012 – scientific programme

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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 14: Networks, From Topology to Dynamics III (joint w. DY)

SOE 14.6: Talk

Wednesday, March 28, 2012, 16:15–16:30, MA 004

Complete Reconstruction of Correlation Networks — •Jan Nagler, Magdalena Kersting, Annette Witt, and Theo Geisel — MPI DS, Göttingen

Consider a network of N vertices, each associated with a wide-sense stationary stochastic process. To what extent is it possible to reconstruct the interrelationships of the whole network knowing only a limited number of correlation functions? Under what circumstances is the system over- or underdetermined? Compared with the usual time series analysis we present a different approach to these questions by means of the Wiener-Khintchine Theorem and unfold the basic structure underlying correlation networks. Except for networks with certain loop structures, we show that either N crosscorrelation functions, or N−1 crosscorrelation functions together with a single autocorrelation function determine the full network dynamics. We analytically derive explicit expressions for the missing correlation functions and study exemplarily the ubiquitous case of exponentially decaying correlation functions.