Renormalization of Collective Modes in Large-Scale Neural DynamicsReport as inadecuate

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Journal of Statistical Physics

, Volume 167, Issue 3–4, pp 543–558

First Online: 04 March 2017Received: 20 October 2016Accepted: 21 February 2017DOI: 10.1007-s10955-017-1753-7

Cite this article as: Moirogiannis, D., Piro, O. & Magnasco, M.O. J Stat Phys 2017 167: 543. doi:10.1007-s10955-017-1753-7


The bulk of studies of coupled oscillators use, as is appropriate in Physics, a global coupling constant controlling all individual interactions. However, because as the coupling is increased, the number of relevant degrees of freedom also increases, this setting conflates the strength of the coupling with the effective dimensionality of the resulting dynamics. We propose a coupling more appropriate to neural circuitry, where synaptic strengths are under biological, activity-dependent control and where the coupling strength and the dimensionality can be controlled separately. Here we study a set of \N ightarrow \infty \ strongly- and nonsymmetrically-coupled, dissipative, powered, rotational dynamical systems, and derive the equations of motion of the reduced system for dimensions 2 and 4. Our setting highlights the statistical structure of the eigenvectors of the connectivity matrix as the fundamental determinant of collective behavior, inheriting from this structure symmetries and singularities absent from the original microscopic dynamics.

KeywordsRenormalization Neural networks Coarse-graining Neural dynamics Cortical models Dedicated to the memory of Leo Kadanoff.

Author: Dimitrios Moirogiannis - Oreste Piro - Marcelo O. Magnasco


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