English

Multiscale Computations on Neural Networks: From the Individual Neuron Interactions to the Macroscopic-Level Analysis

Computational Engineering, Finance, and Science 2015-05-13 v1 Numerical Analysis Neurons and Cognition

Abstract

We show how the Equation-Free approach for multi-scale computations can be exploited to systematically study the dynamics of neural interactions on a random regular connected graph under a pairwise representation perspective. Using an individual-based microscopic simulator as a black box coarse-grained timestepper and with the aid of simulated annealing we compute the coarse-grained equilibrium bifurcation diagram and analyze the stability of the stationary states sidestepping the necessity of obtaining explicit closures at the macroscopic level. We also exploit the scheme to perform a rare-events analysis by estimating an effective Fokker-Planck describing the evolving probability density function of the corresponding coarse-grained observables.

Keywords

Cite

@article{arxiv.0903.2641,
  title  = {Multiscale Computations on Neural Networks: From the Individual Neuron Interactions to the Macroscopic-Level Analysis},
  author = {Konstantinos G. Spiliotis and Constantinos I. Siettos},
  journal= {arXiv preprint arXiv:0903.2641},
  year   = {2015}
}