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Literature DB >> 25243014

Beyond mean field theory: statistical field theory for neural networks.

Abstract

Mean field theories have been a stalwart for studying the dynamics of networks of coupled neurons. They are convenient because they are relatively simple and possible to analyze. However, classical mean field theory neglects the effects of fluctuations and correlations due to single neuron effects. Here, we consider various possible approaches for going beyond mean field theory and incorporating correlation effects. Statistical field theory methods, in particular the Doi-Peliti-Janssen formalism, are particularly useful in this regard.

Entities: Chemical Disease Species

Keywords: Boltzmann equation; dynamics (theory); finite-size scaling; neuronal networks (theory)

Year: 2013 PMID： 25243014 PMCID： PMC4169078 DOI： 10.1088/1742-5468/2013/03/P03003

Source DB: PubMed Journal: J Stat Mech ISSN： 1742-5468 Impact factor: 2.231

37 in total

1. Population dynamics of spiking neurons: fast transients, asynchronous states, and locking.

Authors: W Gerstner
Journal: Neural Comput Date: 2000-01 Impact factor: 2.026

2. The number of synaptic inputs and the synchrony of large, sparse neuronal networks.

Authors: D Golomb; D Hansel
Journal: Neural Comput Date: 2000-05 Impact factor: 2.026

3. An effective kinetic representation of fluctuation-driven neuronal networks with application to simple and complex cells in visual cortex.

Authors: David Cai; Louis Tao; Michael Shelley; David W McLaughlin
Journal: Proc Natl Acad Sci U S A Date: 2004-05-06 Impact factor: 11.205

4. Self-organized critical forest-fire model.

Authors:
Journal: Phys Rev Lett Date: 1992-09-14 Impact factor: 9.161

5. Stochastic dynamics of a finite-size spiking neural network.

Authors: Hédi Soula; Carson C Chow
Journal: Neural Comput Date: 2007-12 Impact factor: 2.026

6. Correlations, fluctuations, and stability of a finite-size network of coupled oscillators.

Authors: Michael A Buice; Carson C Chow
Journal: Phys Rev E Stat Nonlin Soft Matter Phys Date: 2007-09-13

7. A master equation formalism for macroscopic modeling of asynchronous irregular activity states.

Authors: Sami El Boustani; Alain Destexhe
Journal: Neural Comput Date: 2009-01 Impact factor: 2.026

8. Dynamics of pattern formation in lateral-inhibition type neural fields.

Authors: S Amari
Journal: Biol Cybern Date: 1977-08-03 Impact factor: 2.086

9. Excitatory and inhibitory interactions in localized populations of model neurons.

Authors: H R Wilson; J D Cowan
Journal: Biophys J Date: 1972-01 Impact factor: 4.033

10. Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons.

Authors: Javier Baladron; Diego Fasoli; Olivier Faugeras; Jonathan Touboul
Journal: J Math Neurosci Date: 2012-05-31 Impact factor: 1.300

14 in total

1. Before and beyond the Wilson-Cowan equations.

Authors: Carson C Chow; Yahya Karimipanah
Journal: J Neurophysiol Date: 2020-03-18 Impact factor: 2.714

2. Prefronto-cortical dopamine D1 receptor sensitivity can critically influence working memory maintenance during delayed response tasks.

Authors: Melissa Reneaux; Rahul Gupta
Journal: PLoS One Date: 2018-05-29 Impact factor: 3.240

Beyond mean field theory: statistical field theory for neural networks.

1. Population dynamics of spiking neurons: fast transients, asynchronous states, and locking.

2. The number of synaptic inputs and the synchrony of large, sparse neuronal networks.

3. An effective kinetic representation of fluctuation-driven neuronal networks with application to simple and complex cells in visual cortex.

4. Self-organized critical forest-fire model.

5. Stochastic dynamics of a finite-size spiking neural network.

6. Correlations, fluctuations, and stability of a finite-size network of coupled oscillators.

7. A master equation formalism for macroscopic modeling of asynchronous irregular activity states.

8. Dynamics of pattern formation in lateral-inhibition type neural fields.

9. Excitatory and inhibitory interactions in localized populations of model neurons.

10. Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons.

1. Before and beyond the Wilson-Cowan equations.

2. Prefronto-cortical dopamine D1 receptor sensitivity can critically influence working memory maintenance during delayed response tasks.

3. Finite-size effects for spiking neural networks with spatially dependent coupling.

4. Linking structure and activity in nonlinear spiking networks.

5. Inference of stochastic time series with missing data.

6. The Mean Field Approach for Populations of Spiking Neurons.

Review 7. From the statistics of connectivity to the statistics of spike times in neuronal networks.

8. Synchronization, Stochasticity, and Phase Waves in Neuronal Networks With Spatially-Structured Connectivity.

9. Path integral methods for stochastic differential equations.

10. Path-integral methods for analyzing the effects of fluctuations in stochastic hybrid neural networks.