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Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks
Published on: March 2, 2015
Dynamic finite size effects in spiking neural networks
Michael A Buice1, Carson C Chow
1Laboratory of Biological Modeling, NIDDK, NIH, Bethesda, Maryland, United States of America. mabuice@mail.clm.utexas.edu
Plos Computational Biology
|January 30, 2013
Summary
We developed a new method to analyze the dynamics of spiking neural networks. This approach allows for precise calculations of network statistics, even in finite-sized systems.
Area of Science:
- Computational neuroscience
- Statistical physics
Background:
- Analyzing large-scale neural networks is complex.
- Existing models often rely on infinite-neuron approximations.
Purpose of the Study:
- To develop a formalism for computing network statistics in finite-sized spiking neural networks.
- To provide a method for perturbative expansion using inverse system size as a small parameter.
Main Methods:
- Utilized a neuron population density obeying a conservation law analogous to the Klimontovich equation.
- Recasted the moment hierarchy into a functional probability distribution.
- Employed statistical field theory methods for perturbative computations.
Main Results:
- Derived the complete mean-field theory for neural network dynamics.
- Calculated the lowest-order second moment corrections for physiologically relevant quantities.
- Demonstrated a method for finite-size corrections in neural network analysis.
Conclusions:
- The developed formalism enables accurate computation of network statistics in finite systems.
- The method offers a way to go beyond mean-field approximations.
- This approach is adaptable for perturbative expansions in various parameters.
