Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
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BCCN/BFNT AG-Seminar

Wednesday, 15.05.2013 17 c.t.

Interplay of random and structured connectivity in the dynamics of neural networks

by Dr. Yashar Ahmadian
from Center for Theoretical Neuroscience, Columbia University, NY, USA

Contact person: Fred Wolf

Location

MPI DS seminar room (0.77/0.79)

Abstract

Neuronal networks exhibit significant randomness in their synaptic connectivity. But importantly, alongside randomness, the synaptic connectivity of most neuronal networks also features ordered structure on various levels. Investigating the interplay of these two features of connectivity and their respective role in the dynamics of neural networks and the computations they perform constitutes an important theoretical problem in neuroscience. As a step towards this goal, we have studied properties of large connectivity matrices of the form W = M + J, where M (average connectivity) is an arbitrary deterministic matrix which represents structure in the connectivity, and J is a zero-mean random matrix with possibly correlated and non-uniformly scaled elements. Specifically, using the Feynman diagram technique, we have derived a general formula for the eigenvalue distribution of matrices of the above type, generalizing the circular law for fully random matrices. Furthermore, with the aim of studying the effect of random connectivity on the hidden feedforward structure and transient amplification that are of interest in the context of nonnormal connectivity matrices, we have derived general formulae for the transient evolution of the magnitude and the frequency power spectrum of the linear response of firing rate networks to external inputs. I will present some example applications relevant for neuroscience, and in particular briefly discuss how our general formula for the eigenvalue distribution has been used in the study of a clustered neural network with random inter-cluster connectivity by our colleagues (M. Stern and L. Abbott), to map out the boundary between a chaotic and a glassy phase of the network.

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