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Regensburg 2019 – wissenschaftliches Programm

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BP: Fachverband Biologische Physik

BP 12: Poster II

BP 12.55: Poster

Dienstag, 2. April 2019, 14:00–16:00, Poster B2

Taming Stochastic, Nonlinear Rate Neurons With Field Theory — •Jonas Stapmanns1,2, Tobias Kühn1, David Dahmen1, Carsten Honerkamp2, and Moritz Helias1,31Institute of Neuroscience and Medicine (INM-6), Forschungszentrum Juelich, Germany — 2Institute for Theoretical Solid State Physics, RWTH Aachen, Germany — 3Department of Physics, Faculty 1, RWTH Aachen, Germany

Many phenomena observed in biological neural networks can only be explained by assuming nonlinear interactions. Due to effects like synaptic failure and channel noise, neuronal dynamics is also inherently stochastic. The investigation of the interaction of both of these properties is challenging because due to the nonlinearity, correlations of higher order influence those of lower order.

To cope with this problem, the dynamics of a self-interacting stochastic rate neuron is reformulated in the language of field theory by means of the Martin, Siggia, Rose, de Dominicis and Janssen formalism. The loop-wise fluctuation expansion of the corresponding effective action then incorporates corrections to the mean dynamics and time-dependent statistics due to fluctuations in the presence of nonlinear neuronal gain. From this, we derive a deterministic non-Markovian equation of motion of the mean value which illustrates that the interaction of nonlinearity and stochasticity introduces memory into the system.

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