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.
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.
References
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)
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)
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
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)
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
Balduzzi, D., Tononi, G.: Integrated information in discrete dynamical systems: motivation and theoretical framework. PLoS Comput. Biol. 4(6), e1000091 (2008)
Barrett, A.B., Barnett, L., Seth, A.K.: Multivariate granger causality and generalized variance. Phys. Rev. E 81(4), 041907 (2010)
Barrett, A.B., Seth, A.K.: Practical measures of integrated information for time-series data. PLoS Comput. Biol. 7(1), e1001052 (2011)
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)
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)
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)
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)
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)
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)
Tononi, G.: An information integration theory of consciousness. BMC Neurosci. 5(1), 42 (2004)
Tononi, G., Sporns, O.: Measuring information integration. BMC Neurosci. 4(1), 31 (2003)
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)
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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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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