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Autonomous learning of nonlocal stochastic neuron dynamics.

Tyler E Maltba1, Hongli Zhao2, Daniel M Tartakovsky3

  • 1Department of Statistics, UC Berkeley, Berkeley, CA 94720 USA.

Cognitive Neurodynamics
|May 23, 2022
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Summary
This summary is machine-generated.

This study introduces novel methods to model neuronal dynamics driven by complex noise. These techniques accurately capture neuron behavior, improving our understanding of neural information processing.

Keywords:
Colored noiseEquation learningMethod of distributionsNonlocalStochastic neuron model

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Area of Science:

  • Computational Neuroscience
  • Stochastic Processes
  • Information Theory

Background:

  • Neuronal dynamics are influenced by random noise, often modeled by stochastic differential equations.
  • The probability density function (PDF) characterizes neuron state distributions and information-theoretic quantities.
  • Existing models struggle with biologically realistic, correlated (colored) noise, requiring closure approximations.

Purpose of the Study:

  • To develop and test new methods for closing PDF equations for neurons driven by colored noise.
  • To accurately model neuronal responses to complex, biologically relevant noise sources.
  • To calculate information-theoretic measures in neuronal models with colored noise.

Main Methods:

  • Proposed two closure methods: nonlocal large-eddy-diffusivity and data-driven sparse regression.
  • Applied methods to stochastic leaky integrate-and-fire and FitzHugh-Nagumo (FHN) neuron models.
  • Utilized sine-Wiener processes to simulate correlated noise.

Main Results:

  • Successfully implemented and tested the proposed closure approximations for neuronal PDF equations.
  • Demonstrated the ability to calculate mutual information and total correlation for the FHN neuron under colored noise.
  • Validated the effectiveness of the novel closure techniques in capturing neuronal dynamics.

Conclusions:

  • The developed closure methods provide accurate descriptions of neuronal dynamics driven by colored noise.
  • These advancements enhance the modeling of neural information processing in more biologically realistic scenarios.
  • The study offers improved tools for analyzing neural responses to complex stimuli.