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Neural circuits and neuronal pools are two of the main structures found in the nervous system. Neural circuits are networks of neurons that work together to carry out a specific task or process. They consist of interconnected neurons and glial cells, which provide structural and metabolic support.
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Using Neuron Spiking Activity to Trigger Closed-Loop Stimuli in Neurophysiological Experiments
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Using Neuron Spiking Activity to Trigger Closed-Loop Stimuli in Neurophysiological Experiments

Published on: November 12, 2019

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

Jonathan D Touboul1, Olivier D Faugeras

  • 1NeuroMathComp Laboratory, INRIA, Sophia Antipolis, France. jonathan.touboul@sophia.inria.fr

Journal of Computational Neuroscience
|April 19, 2011
PubMed
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Spiking neural networks exhibit Markovian properties in their spike times, allowing prediction of future activity solely from past spike trains. This simplifies network analysis by focusing on event times rather than complex membrane potentials.

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Area of Science:

  • Computational Neuroscience
  • Artificial Intelligence
  • Complex Systems

Background:

  • Spiking neural networks (SNNs) encode information in precise spike timing.
  • Understanding the temporal dynamics of SNNs is crucial for their application.
  • Current models often rely on detailed membrane potential dynamics.

Purpose of the Study:

  • To investigate the Markovian nature of spike train sequences in stochastic neural networks.
  • To develop an event-based description for analyzing SNN activity.
  • To determine if network activity can be described solely by spike times.

Main Methods:

  • Introduction of an event-based description for noisy integrate-and-fire neuron networks.
  • Analysis of spike times as a Markov chain.
  • Derivation of transition probabilities based on interspike interval distributions.

Main Results:

  • Demonstrated that firing times in these networks form a Markov chain.
  • Established a relationship between transition probability and interspike interval distribution.
  • Explicitly derived transition probabilities for various integrate-and-fire models.

Conclusions:

  • The event-based description provides a simplified, Markovian view of SNN activity.
  • This framework is applicable to diverse neural network configurations, including those with synaptic noise and refractory periods.
  • The findings facilitate a more tractable analysis of complex spiking neural network dynamics.