Titlebook: Statistical Field Theory for Neural Networks; Moritz Helias,David Dahmen Book 2020 Springer Nature Switzerland AG 2020 Statistical physics

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Book 2020These powerful analytical techniques, which are well established in other fields of physics, are the basis of current developments and offer solutions to pressing open problems in theoretical neuroscience and also machine learning. They enable a systematic and quantitative understanding of the dynam

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0075-8450 elevant for network dynamics, including diagrammatic techniq.This book presents a self-contained introduction to techniques from field theory applied to stochastic and collective dynamics in neuronal networks. These powerful analytical techniques, which are well established in other fields of physic

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Functional Formulation of Stochastic Differential Equations,Moreover, this formulation will be essential for the treatment of disordered systems in Chap. ., following the spirit of the work by De Dominicis and Peliti (Phys Rev B 18:353, 1978) to obtain a generating functional that describes an average system belonging to an ensemble of systems with random parameters.

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Loopwise Expansion of the Effective Action,mmatic series will proceed according to the power of each term in units of the magnitude of fluctuations. This formulation is in particular suitable to study non-vanishing mean values of the stochastic variables and is therefore a central tool in quantum field theory and statistical field theory, in particular in the study of phase transitions.

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Introduction,re many features with interacting many particle systems in physics. Even if the single neuron dynamics is rather simple, interesting behavior of networks arises from the interaction of these many components. As a result, the activity the electrically active tissue of the brain exhibits is correlated on a multitude of spatial and temporal scales.

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