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Effective non-universality of the quorum percolation model on directed graphs with Gaussian in-degree

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  • Renault, Renaud
  • Monceau, Pascal
  • Bottani, Samuel
  • Métens, Stéphane

Abstract

We investigate a model derived from bootstrap percolation on a directed random graph with Gaussian in-degree useful in describing the collective behavior of dissociated neuronal networks. By developing a continuous version of the model, we were able to provide accurate values of the critical thresholds and exponents associated with the occurrence of a giant cluster. As a main result, it turns out that the values of the exponents calculated over a numerical accessible range covering more than two orders of magnitude below the critical point exhibit a slight dependence upon the connectivity of the graph.

Suggested Citation

  • Renault, Renaud & Monceau, Pascal & Bottani, Samuel & Métens, Stéphane, 2014. "Effective non-universality of the quorum percolation model on directed graphs with Gaussian in-degree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 352-359.
    • Handle: RePEc:eee:phsmap:v:414:y:2014:i:c:p:352-359
    DOI: 10.1016/j.physa.2014.07.028
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    References listed on IDEAS

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    1. K. L. Majumder & G. P. Bhattacharjee, 1973. "The Incomplete Beta Integral," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 22(3), pages 409-411, November.
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    Cited by:

    1. Fardet, Tanguy & Bottani, Samuel & Métens, Stéphane & Monceau, Pascal, 2018. "Effects of inhibitory neurons on the quorum percolation model and dynamical extension with the Brette–Gerstner model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 98-109.

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