Bernstein Seminar  Moritz Helias  Forschungszentrum Jülich
Wednesday, April 10, 2019
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When 
Apr 10, 2019 from 10:15 AM to 11:15 AM 
Where  Lecture Hall, Bernstein Center Freiburg 
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MORITZ HELIAS ►
Institute of Neuroscience and Medicine  Forschungszentrum Jülich
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 nonlinearities. 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 selfconsistency equations around a nonGaussian 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 [condmat.disnn]
[2] Kuehn T, Helias M (2018)
Expansion of the effective action around nonGaussian theories
J Phys A: Math Theor 51, 375004
[3] Stapmanns J, Kühn T, Dahmen D, Luu T, Honerkamp C, Helias M
Selfconsistent formulations for stochastic nonlinear neuronal dynamics