Moritz Helias, Forschungszentrum Jülich | Field Theory for Collective Neuronal Statistics

Bernstein Seminar

When	Apr 10, 2019 from 10:15 AM to 11:15 AM
Where	Lecture Hall, Bernstein Center Freiburg
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Abstract

Collective phenomena putatively form the basis of information processing in neuronal networks. Activity in such networks is complicated by two interplaying phenomena: fluctuations and non-linearities. Different orders of the statistics are hence coupled.

Similar problems arise in various fields of physics. The common language towards a solution, which crystallized out of
parallel developments over five decades, is (statistical) field theory; it is also applicable to neuronal systems [1].
We here present two methods that employ concepts from field theory to arrive at systematic approximations of such statistics: The perturbation expansion of self-consistency equations around a non-Gaussian solvable problem [2] and the functional renormalizationgroup [3].
We demonstrate the use of these approaches for the inverse problem,determining parameters from given statistics, and we derive effectivedeterministic equations that implicitly capture statistical corrections.

Literature

[1] Helias M, Dahmen D (2019); Statistical field theory for neural networks; arXiv:1901.10416 [cond-mat.dis-nn]
[2] Kuehn T, Helias M (2018); Expansion of the effective action around non-Gaussian theories, J Phys A: Math Theor 51, 375004
[3] Stapmanns J, Kühn T, Dahmen D, Luu T, Honerkamp C, Helias M; Self-consistent formulations for stochastic nonlinear neuronal dynamics