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High Integrated Information in Complex Networks Near Criticality

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Artificial Neural Networks and Machine Learning – ICANN 2016 (ICANN 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9886))

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Abstract

Integrated information has recently been proposed as an information-theoretic measure of a network’s dynamical complexity. It aims to capture the amount of information generated by a network as a whole over and above that generated by the sum of its parts when the network transitions from one dynamical state to another. Several formulations of this measure have been proposed, with numerical schemes for computing network complexity. In this paper, we approach the problem analytically. We compute the integrated information of weighted networks with stochastic dynamics. Our formulation makes use of the Kullback-Leibler divergence between the multi-variate distribution on the set of network states versus the corresponding factorized distribution over its parts. Using Gaussian distributions, we compute analytic results for several prototypical network topologies. Our findings show that operating near the edge of criticality is favorable for a high rate of information integration in complex dynamical networks. This observation is consistent across network topologies. We discuss the implication of these results for biological and communication networks.

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Notes

  1. 1.

    For the case of asymmetric weights, the entries of the covariance matrix cannot be explicitly expressed as a matrix equation. However, they may still be solved by Jordan decomposition of both sides of the Lyapunov equation.

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Acknowledgments

This work has been supported by the European Research Council’s CDAC project: “The Role of Consciousness in Adaptive Behavior: A Combined Empirical, Computational and Robot based Approach” (ERC-2013-ADG 341196).

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Authors and Affiliations

  1. Synthetic Perceptive Emotive and Cognitive Systems (SPECS) Lab, Center of Autonomous Systems and Neurorobotics, Universitat Pompeu Fabra, Barcelona, Spain

    Xerxes D. Arsiwalla & Paul F. M. J. Verschure

  2. Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona, Spain

    Paul F. M. J. Verschure

Authors
  1. Xerxes D. Arsiwalla
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  2. Paul F. M. J. Verschure
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Corresponding author

Correspondence to Xerxes D. Arsiwalla .

Editor information

Editors and Affiliations

  1. University of Lausanne, Lausanne, Switzerland

    Alessandro E.P. Villa

  2. University of Lausanne, Lausanne, Switzerland

    Paolo Masulli

  3. Universitat Politécnica de Catalunya, Terrrassa, Spain

    Antonio Javier Pons Rivero

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Arsiwalla, X.D., Verschure, P.F.M.J. (2016). High Integrated Information in Complex Networks Near Criticality. In: Villa, A., Masulli, P., Pons Rivero, A. (eds) Artificial Neural Networks and Machine Learning – ICANN 2016. ICANN 2016. Lecture Notes in Computer Science(), vol 9886. Springer, Cham. https://doi.org/10.1007/978-3-319-44778-0_22

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  • DOI: https://doi.org/10.1007/978-3-319-44778-0_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44777-3

  • Online ISBN: 978-3-319-44778-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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