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Literature DB >> 20658138

A discrete time neural network model with spiking neurons: II: dynamics with noise.

Abstract

We provide rigorous and exact results characterizing the statistics of spike trains in a network of leaky Integrate-and-Fire neurons, where time is discrete and where neurons are submitted to noise, without restriction on the synaptic weights. We show the existence and uniqueness of an invariant measure of Gibbs type and discuss its properties. We also discuss Markovian approximations and relate them to the approaches currently used in computational neuroscience to analyse experimental spike trains statistics.

Mesh：

Year: 2010 PMID： 20658138 DOI： 10.1007/s00285-010-0358-4

Source DB: PubMed Journal: J Math Biol ISSN： 0303-6812 Impact factor: 2.259

28 in total

1. Precise spike synchronization in monkey motor cortex involved in preparation for movement.

Authors: F Grammont; A Riehle
Journal: Exp Brain Res Date: 1999-09 Impact factor: 1.972

2. Rate coding versus temporal order coding: what the retinal ganglion cells tell the visual cortex.

Authors: R Van Rullen; S J Thorpe
Journal: Neural Comput Date: 2001-06 Impact factor: 2.026

3. Generalized integrate-and-fire models of neuronal activity approximate spike trains of a detailed model to a high degree of accuracy.

Authors: Renaud Jolivet; Timothy J Lewis; Wulfram Gerstner
Journal: J Neurophysiol Date: 2004-08 Impact factor: 2.714

A discrete time neural network model with spiking neurons: II: dynamics with noise.

1. Precise spike synchronization in monkey motor cortex involved in preparation for movement.

2. Rate coding versus temporal order coding: what the retinal ganglion cells tell the visual cortex.

3. Generalized integrate-and-fire models of neuronal activity approximate spike trains of a detailed model to a high degree of accuracy.

4. Spike-frequency adaptation separates transient communication signals from background oscillations.

5. Spontaneous dynamics of asymmetric random recurrent spiking neural networks.

6. Weak pairwise correlations imply strongly correlated network states in a neural population.

7. The impulses produced by sensory nerve-endings: Part II. The response of a Single End-Organ.

8. Optimality model of unsupervised spike-timing-dependent plasticity: synaptic memory and weight distribution.

Review 9. The spikes trains probability distributions: a stochastic calculus approach.

10. Prediction of spatiotemporal patterns of neural activity from pairwise correlations.

1. A Markovian event-based framework for stochastic spiking neural networks.

2. Gibbs distribution analysis of temporal correlations structure in retina ganglion cells.

3. Statistics of spike trains in conductance-based neural networks: Rigorous results.

4. A Markov model for the temporal dynamics of balanced random networks of finite size.

5. Phase transitions and self-organized criticality in networks of stochastic spiking neurons.

6. PRANAS: A New Platform for Retinal Analysis and Simulation.

7. A Spiking Neuron and Population Model Based on the Growth Transform Dynamical System.

8. Noise Helps Optimization Escape From Saddle Points in the Synaptic Plasticity.

9. Retinal Processing: Insights from Mathematical Modelling.