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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Book ChapterDOI
Waves in Synaptically Coupled Spiking Networks
TL;DR: In this chapter, neural network models of wave propagation in the cortex and other parts of the nervous system are considered, involving simplified neuron models that hopefully capture important aspects of wave phenomena, while allowing a more concise mathematical treatment.
Book ChapterDOI
Waves in Excitable Neural Fields
TL;DR: It is shown how many of the PDE methods and results from the analysis of waves in reaction–diffusion equations considered in Chap.
Book ChapterDOI
Wave Propagation Along Spiny Dendrites
TL;DR: In this article, two different models of traveling waves along spiny dendrites are presented: a spike-diffuse-spike model of propagating voltage spikes mediated by active dendritic spines and a reaction-diffusion model of Ca2+−calmodulin-dependent protein kinase II (CaMKII) translocation waves.
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: In this article, the authors extend the master equation formulation by introducing 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 and spiking activity, and reduces to the neural master equation in a particular limit.
Journal ArticleDOI
Stochastic Network Models in Neuroscience: A Festschrift for Jack Cowan. Introduction to the Special Issue.
TL;DR: This accompanying Festschrift celebrates Cowan’s contributions by assembling current research in stochastic phenomena in neural networks by combining historical perspectives with new results including applications to epilepsy, path-integral methods, Stochastic synchronization, higher-order correlation analysis, and pattern formation in visual cortex.
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.
Michael A. Buice,Jack D. Cowan +1 more
Excitatory and Inhibitory Interactions in Localized Populations of Model Neurons
Hugh R. Wilson,Jack D. Cowan +1 more