SpringerLink - Journal Article

Correlations in spiking neuronal networks with distance dependent connections

Birgit Kriener^{1, 2, 4, 5}, Moritz Helias^{1, 2}, Ad Aertsen^{1, 2} and Stefan Rotter^{1, 3}

(1)	Bernstein Center for Computational Neuroscience, Albert-Ludwig University, Freiburg, Germany

(2)	Neurobiology and Biophysics, Faculty of Biology, Albert-Ludwig University, Freiburg, Germany

(3)	Computational Neuroscience, Faculty of Biology, Albert-Ludwig University, Freiburg, Germany

(4)	Present address: Network Dynamics Group, Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany

(5)	Bernstein Center for Computational Neuroscience, Göttingen, Germany

Received: 10 July 2008 Revised: 11 December 2008 Accepted: 31 December 2008 Published online: 1 July 2009

Action Editor: Alain Destexhe

Abstract Can the topology of a recurrent spiking network be inferred from observed activity dynamics? Which statistical parameters of network connectivity can be extracted from firing rates, correlations and related measurable quantities? To approach these questions, we analyze distance dependent correlations of the activity in small-world networks of neurons with current-based synapses derived from a simple ring topology. We find that in particular the distribution of correlation coefficients of subthreshold activity can tell apart random networks from networks with distance dependent connectivity. Such distributions can be estimated by sampling from random pairs. We also demonstrate the crucial role of the weight distribution, most notably the compliance with Dales principle, for the activity dynamics in recurrent networks of different types.

Keywords Spiking neural networks - Small-world networks - Pairwise correlations - Distribution of correlation coefficients

Birgit Kriener
Email: kriener@nld.ds.mpg.de

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