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Bernstein Seminar | Moritz Helias | Forschungszentrum Jülich

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Wednesday, April 10, 2019

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

MORITZ HELIAS ►

Institute of Neuroscience and Medicine | Forschungszentrum Jülich

Hosted by Stefan Rotter


Field Theory for Collective Neuronal Statistics
 

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.

[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
 

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