Dresden 2014 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 17: Modeling and Data Analysis

DY 17.8: Vortrag

Mittwoch, 2. April 2014, 11:30–11:45, ZEU 146

Reconstruction of correlates and construction of surrogates in networked systems — •Annette Witt¹ and Jan Nagler² — ¹Max-Planck Institute for Dynamics and Self-Organization and BCCN, Göttingen, Germany — ²ETH Zürich, Switzerland

Networks with N nodes are considered, each node is associated either to a time series (on the data level) or to its generating stochastic process (on the model level). A link between nodes is represented by a cross correlation functions (ccf), self-loops stand for autocorrelation functions (acf). For the data level we establish conditions for the reconstruction of the complete network from a subnetwork and show that subnetworks which are minimal for reconstruction must connect all N nodes and belong to one of the two network types, namely (i) single-self-loop-trees, where the subnetwork is a tree (i.e. loop-free) with N-1 ccfs and a single acf, and (ii) single-odd-loop-networks, where the given subnetwork consists of N ccfs of which an odd number forms a single loop. For the first time, a parameter-free exact method for the construction of networks on the realization level from networked stochastic processes is given which is employed for generating multi-variate series time with a prescribed cross-spectral matrix. Consequently, the framework is applicable to short- and long-range correlated time series.