Book ChapterDOI
Stochastic neurodynamics and the system size expansion
Toru Ohira,Jack D. Cowan +1 more
- pp 290-294
TLDR
In this paper, the authors present a method for the study of stochastic neurodynamics in the master equation framework and obtain a statistical description of the dynamics of fluctuations and correlations of neural activity in large neural networks.Abstract:
We present here a method for the study of stochastic neurodynamics in the master equation framework. Our aim is to obtain a statistical description of the dynamics of fluctuations and correlations of neural activity in large neural networks. We focus on a macroscopic description of the network via a master equation for the number of active neurons in the network. We present a systematic expansion of this equation using the “system size expansion”. We obtain coupled dynamical equations for the average activity and of fluctuations around this average. These equations exhibit non-monotonic approaches to equilibrium, as seen in Monte Carlo simulations.read more
Citations
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Journal ArticleDOI
Metastability in a Stochastic Neural Network Modeled as a Velocity Jump Markov Process
Paul C. Bressloff,Jay M. Newby +1 more
TL;DR: This paper introduces a stochastic model of neural population dynamics in the form of a velocity jump Markov process, which has the advantage of keeping track of synaptic processing as well as spiking activity, and reduces to the neural master equation in a particular limit.
Journal ArticleDOI
Correlated Fluctuations in Strongly Coupled Binary Networks Beyond Equilibrium
TL;DR: The systematic cumulant expansion for kinetic binary (Ising) threshold units with strong, random and asymmetric couplings presented here goes beyond mean-field theory and is applicable outside thermodynamic equilibrium; a system of approximate non-linear equations predicts average activities and pairwise covariances in quantitative agreement with full simulations down to hundreds of units.
Journal ArticleDOI
Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise
TL;DR: The theory of noise-induced phase synchronization is extended to the case of a neural master equation describing the stochastic dynamics of an ensemble of uncoupled neuronal population oscillators with intrinsic and extrinsic noise, and it is shown how the combination of intrinsic independent noise and intrinsic common noise can lead to clustering of the population oscillations due to the multiplicative nature of both noise sources under the Langevin approximation.
Journal ArticleDOI
Path-Integral Methods for Analyzing the Effects of Fluctuations in Stochastic Hybrid Neural Networks
TL;DR: A variational principle for maximum-likelihood paths of escape from a metastable state (large deviations in the small noise limit ϵ→0$\epsilon\rightarrow0$) is derived and the resulting Langevin equation can be used to analyze the effects of fluctuations within the basin of attraction of a metastables state, ignoring theeffects of large deviations.
Journal ArticleDOI
Laws of large numbers and langevin approximations for stochastic neural field equations.
Martin G. Riedler,Evelyn Buckwar +1 more
TL;DR: It is shown that the Wilson–Cowan equation can be obtained as the limit in uniform convergence on compacts in probability for a sequence of microscopic models when the number of neuron populations distributed in space and thenumber of neurons per population tend to infinity.
References
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Book
Monte Carlo methods in statistical physics
Mark Newman,Gerard T. Barkema +1 more
TL;DR: This book provides an introduction to Monte Carlo simulations in classical statistical physics and is aimed both at students beginning work in the field and at more experienced researchers who wish to learn more about Monte Carlo methods.
Journal ArticleDOI
Statistical neurodynamics of associative memory
Shun-ichi Amari,Kenjiro Maginu +1 more
TL;DR: A new statistical neurodynamical method is proposed for analyzing the non-equilibrium dynamical behaviors of an autocorrelation associative memory model and explains the strange behaviors due to strange shapes of the basins of attractors.
Journal ArticleDOI
Theory of correlations in stochastic neural networks.
TL;DR: The theory of neuronal correlation functions in large networks comprising of several highly connected subpopulations, and obeying stochastic dynamic rules is developed and extended to networks with random connectivity, such as randomly dilute networks.
Related Papers (5)
Field-theoretic approach to fluctuation effects in neural networks.
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