Regensburg 2016 – wissenschaftliches Programm
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BP: Fachverband Biologische Physik
BP 53: Posters - Statistical Physics of Biological Systems
BP 53.10: Poster
Mittwoch, 9. März 2016, 17:00–19:00, Poster C
Correlated fluctuations in strongly-coupled binary networks beyond equilibrium — •David Dahmen1, Hannah Bos1, and Moritz Helias1,2 — 1Inst. of Neurosci. and Medicine (INM-6) and Inst for Advanced Simulation (IAS-6) and JARA BRAIN Institute I, Jülich Research Centre — 2Dept. of Physics, Faculty 1, RWTH Aachen University
Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems. Their phase diagram is obtained by averaging over the quenched random couplings, but many applications require the activity statistics for a single realization of the possibly asymmetric couplings in finite-sized networks: the reconstruction of couplings from the observed dynamics, learning in the central nervous system by correlation-sensitive synaptic plasticity, and representation of probability distributions for sampling-based inference. We present a systematic cumulant expansion for kinetic binary (Ising) threshold units with strong, random and asymmetric couplings that goes beyond mean-field theory and is applicable outside thermodynamic equilibrium; a system of approximate non-linear equations predicts average activities and pairwise covariances in quantitative agreement with full simulations down to hundreds of units [Dahmen et al. 2015, arXiv]. The linearized theory yields an expansion of the correlation- and response functions in collective eigenmodes, leads to an efficient algorithm solving the inverse problem, and shows that correlations are invariant under scaling of the interaction strengths. Partly supported by Helmholtz association: VH-NG-1028 and SMHB; EU Grant 604102 (HBP).