Berlin 2008 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 21: Nonlinear dynamics, synchronization and chaos III

DY 21.4: Vortrag

Mittwoch, 27. Februar 2008, 17:30–17:45, MA 001

Measuring interaction complexity — Thomas Kahle, •Eckehard Olbrich, Nihat Ay, and Jürgen Jost — Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

We introduce a new vector valued complexity measure, which we will call interaction complexity, whose components quantify the complexity in terms of k-th order statistical dependencies that cannot be explained by interactions between k−1 units. Formally the measure I:=(I₁,…,I_N) is defined in terms of Kullback-Leibler distances to exponential families of k-interactions for k=1,...,N. By applying this measure on probability distributions generated by dynamical systems such as coupled map lattices and cellular automata, we demonstrate that these measure allows a refined analysis of complex dynamical regimes. We discuss possible applications for biological data, such as genomic sequences or multielectrode recordings in neural systems.