High Integrated Information in Complex Networks Near Criticality

  • Xerxes D. Arsiwalla
  • Paul F. M. J. Verschure
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9886)


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.


Network dynamics Complexity measures Information theory 


  1. 1.
    Arsiwalla, X.D., Betella, A., Martínez, E., Omedas, P., Zucca, R., Verschure, P.: The dynamic connectome: a tool for large scale 3d reconstruction of brain activity in real time. In: Rekdalsbakken, W., Bye, R., Zhang, H. (eds.) 27th European Conference on Modeling and Simulation (ECMS), Alesund, Norway (2013)Google Scholar
  2. 2.
    Arsiwalla, X.D., Dalmazzo, D., Zucca, R., Betella, A., Brandi, S., Martinez, E., Omedas, P., Verschure, P.: Connectomics to semantomics: addressing the brain’s big data challenge. Procedia Comput. Sci. 53, 48–55 (2015)CrossRefGoogle Scholar
  3. 3.
    Arsiwalla, X.D., Verschure, P.: Computing information integration in brain networks. In: Wierzbicki, A., Brandes, U., Schweitzer, F., Pedreschi, D. (eds.) NetSci-X 2016. LNCS, vol. 9564, pp. 136–146. Springer, Heidelberg (2015). doi:10.1007/978-3-319-28361-6_11 CrossRefGoogle Scholar
  4. 4.
    Arsiwalla, X.D., Verschure, P.F.: Integrated information for large complex networks. In: The 2013 International Joint Conference on Neural Networks (IJCNN), pp. 1–7. IEEE (2013)Google Scholar
  5. 5.
    Arsiwalla, X.D., Zucca, R., Betella, A., Martinez, E., Dalmazzo, D., Omedas, P., Deco, G., Verschure, P.: Network dynamics with brainx3: a large-scale simulation of the human brain network with real-time interaction. Front. Neuroinf. 9(2) (2015). http://www.frontiersin.org/neuroinformatics/10.3389/fninf.2015.00002/abstract
  6. 6.
    Balduzzi, D., Tononi, G.: Integrated information in discrete dynamical systems: motivation and theoretical framework. PLoS Comput. Biol. 4(6), e1000091 (2008)CrossRefGoogle Scholar
  7. 7.
    Barrett, A.B., Barnett, L., Seth, A.K.: Multivariate granger causality and generalized variance. Phys. Rev. E 81(4), 041907 (2010)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Barrett, A.B., Seth, A.K.: Practical measures of integrated information for time-series data. PLoS Comput. Biol. 7(1), e1001052 (2011)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Betella, A., Bueno, E.M., Kongsantad, W., Zucca, R., Arsiwalla, X.D., Omedas, P., Verschure, P.F.: Understanding large network datasets through embodied interaction in virtual reality. In: Proceedings of the 2014 Virtual Reality International Conference, p. 23. ACM (2014)Google Scholar
  10. 10.
    Betella, A., Cetnarski, R., Zucca, R., Arsiwalla, X.D., Martinez, E., Omedas, P., Mura, A., Verschure, P.: BrainX3: embodied exploration of neural data. In: Virtual Reality International Conference (VRIC 2014), Laval, France (2014)Google Scholar
  11. 11.
    Deco, G., Ponce-Alvarez, A., Mantini, D., Romani, G.L., Hagmann, P., Corbetta, M.: Resting-state functional connectivity emerges from structurally and dynamically shaped slow linear fluctuations. J. Neurosci. 33(27), 11239–11252 (2013)CrossRefGoogle Scholar
  12. 12.
    Oizumi, M., Albantakis, L., Tononi, G.: From the phenomenology to the mechanisms of consciousness: integrated information theory 3.0. PLoS Comput. Biol. 10(5), e1003588 (2014)CrossRefGoogle Scholar
  13. 13.
    Omedas, P., Betella, A., Zucca, R., Arsiwalla, X.D., Pacheco, D., Wagner, J., Lingenfelser, F., Andre, E., Mazzei, D., Lanatá, A., Tognetti, A., de Rossi, D., Grau, A., Goldhoorn, A., Guerra, E., Alquezar, R., Sanfeliu, A., Verschure, P.: XIM-engine: a software framework to support the development of interactive applications that uses conscious and unconscious reactions in immersive mixed reality. In: Proceedings of the 2014 Virtual Reality International Conference, VRIC 2014, p. 26. ACM (2014)Google Scholar
  14. 14.
    Orlandi, J.G., Soriano, J., Alvarez-Lacalle, E., Teller, S., Casademunt, J.: Noise focusing and the emergence of coherent activity in neuronal cultures. Nat. Phys. 9(9), 582–590 (2013)CrossRefGoogle Scholar
  15. 15.
    Tononi, G.: An information integration theory of consciousness. BMC Neurosci. 5(1), 42 (2004)CrossRefGoogle Scholar
  16. 16.
    Tononi, G., Sporns, O.: Measuring information integration. BMC Neurosci. 4(1), 31 (2003)CrossRefGoogle Scholar
  17. 17.
    Tononi, G., Sporns, O., Edelman, G.M.: A measure for brain complexity: relating functional segregation and integration in the nervous system. Proc. Nat. Acad. Sci. 91(11), 5033–5037 (1994)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Xerxes D. Arsiwalla
    • 1
  • Paul F. M. J. Verschure
    • 1
    • 2
  1. 1.Synthetic Perceptive Emotive and Cognitive Systems (SPECS) Lab, Center of Autonomous Systems and NeuroroboticsUniversitat Pompeu FabraBarcelonaSpain
  2. 2.Institució Catalana de Recerca i Estudis Avançats (ICREA)BarcelonaSpain

Personalised recommendations