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Unambiguous reconstruction of network structure using avalanche dynamics

Timothée Leleu1,2 and Kazuyuki Aihara2

  • 1Center for Emergent Matter Science, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
  • 2Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan

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Phys. Rev. E 91, 022804 – Published 5 February, 2015

DOI: https://doi.org/10.1103/PhysRevE.91.022804

Abstract

A robust method for inferring the structure of networks is presented based on the one-to-one correspondence between the expected composition of cascades of bursts of activity, called crackling noise or avalanches, and the weight matrix. Using a model of neuronal avalanches as a paradigmatic example, we derive this correspondence exactly by calculating the closed-form expression of the joint probability distribution of avalanche sizes obtained by counting separately the number of elements active in each subnetwork during avalanches.

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Phys. Rev. E 91, 022804– Published 5 February, 2015
  • Received 9 July 2014
  • Revised 14 December 2014

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