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Bootstrap Percolation in Living Neural Networks

Journal of Statistical Physics volume 141, pages 459–475 (2010)Cite this article

Abstract

Recent experimental studies of living neural networks reveal that their global activation induced by electrical stimulation can be explained using the concept of bootstrap percolation on a directed random network. The experiment consists in activating externally an initial random fraction of the neurons and observe the process of firing until its equilibrium. The final portion of neurons that are active depends in a non linear way on the initial fraction. The main result of this paper is a theorem which enables us to find the final proportion of the fired neurons, in the asymptotic case, in the case of random directed graphs with given node degrees as the model for interacting network. This gives a rigorous mathematical proof of a phenomena observed by physicists in neural networks.

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Authors and Affiliations

  1. INRIA – École Normale Supérieure, Paris, France

    Hamed Amini

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  1. Hamed Amini
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Correspondence to Hamed Amini.

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Amini, H. Bootstrap Percolation in Living Neural Networks. J Stat Phys 141, 459–475 (2010). https://doi.org/10.1007/s10955-010-0056-z

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  • DOI: https://doi.org/10.1007/s10955-010-0056-z

Keywords

  • Bootstrap percolation
  • Phase transition
  • Random graphs
  • Neural networks