Abstract
In the study of complex networks, simple local heterogeneous interactions favor highly complicated and non-linear dynamics. In this paper, we take advantage of recent advances presented by Rosas et al [Physical Review E, 100, 032305] to capture the fundamentals of dynamics: high-order interdependencies. In particular, the phase diagram of Random Boolean Networks is described in terms of the information shared between multiple nodes. We found that the critical point between ordered and chaotic regimes is well defined by a balance between redundancy and synergy, for both normal and scale-free topologies. In addition, particular network structures are identified that characterize the behavior of high-order interdependencies in each dynamic regime.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
It should be noted that this result is of a statistical nature, since it is possible to find chaotic networks in the predicted stable regime and vice versa.
- 2.
Being in fact the only structure capable of achieving this, since the union set of attractors corresponds precisely to two fixed points with maximum Hamming distance.
References
Aldana, M.: Boolean dynamics of networks with scale-free topology. Phys. D 185, 45–66 (2003)
Brillouin, L.: The negentropy principle of information. J. Appl. Phys. 24, 1152–1163 (1953)
Derrida, B., Pomeau, Y.: Random networks of automata: a simple annealed approximation. Europhys. Lett. 1, 45–49 (2007)
Drossel, B.: Random boolean networks. In: Reviews of Nonlinear Dynamics and Complexity, Vol. 1, Ed. H.G. Schuster, Wiley (2008)
Gates, A.J., Rocha, L.M.: Control of complex networks requires both structure and dynamics. Sci. Rep. 6(1), 1–11 (2016)
Griffith, V., Koch, C.: Quantifying synergistic mutual information. In: Guided Self-Organization: Inception. Springer (2014)
James, R., Ellison, C., Crutchfield, J.P.: Anatomy of a bit: information in a time series observation. Chaos 21, 037109 (2011)
Kauffman, S.A.: Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. Biol. 22, 437–467 (1969)
Kim, J.R., Yoon, Y., Cho, K.H.: Coupled feedback loops form dynamic motifs of cellular networks. Biophys. J. 94, 359–365 (2008)
Kwon, Y.K., Cho, K.H.: Coherent coupling of feedback loops: a design principle of cell signaling networks. Bioinformatics 24, 1926–1932 (2008)
Langton, C.G.: Computation at the edge of chaos: phase transitions and emergent computation. Phys. D 42, 12–37 (1990)
Le, D.H., Kwon, Y.K.: A coherent feedforward loop design principle to sustain robustness of biological networks. Bioinformatics 29, 630–637 (2013)
Lizier, J., Prokopenko, M., Zomaya, A.: The information dynamics of phase transitions in random boolean networks. In Proceedings of 11th International Conference on the Simulation and Synthesis of Living Systems (ALife XI). MIT Press (2008)
Lloyd-Price, J., Gupta, A., Ribeiro, A.S.: Robustness and information propagation in attractors of random boolean networks. PLoS One 7(7), e42018 (2012)
Marques-Pita, M., Rocha, L.: Canalization and control in automata networks: body segmentation in Drosophila melanogaster. PLoS One 8(3), e55946 (2013)
Oosawa, C., Savageau, M.A.: Effects of alternative connectivity on behavior of randomly constructed Boolean networks. Phys. D 170, 143–161 (2002)
Philipp, R., Di Paolo, E.A.: The circular topology of rhythm in asynchronous random Boolean networks. Biosystems 73, 141–152 (2004)
Ribeiro, A., Kauffman, S.A., Lloyd-Price, J., Samuelsson, B., Socolar, J.: Mutual information in random Boolean models of regulatory networks. Phys. Rev. E 77, 011901 (2008)
Richard, A.: Positive and negative cycles in Boolean networks. J. Theor. Biol. 463, 67–76 (2019)
Rosas, F., Mediano, P., Gastpar, M., Jensen, H.: Quantifying high-order interdependencies via multivariate extensions of the mutual information. Phys. Rev. E 100, 032305 (2019)
Williams, P.L., Beer, R.D.: Nonnegative decomposition of multivariate information. arXiv preprint arXiv:1004.2515 (2010)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Orellana, S., Moreira, A. (2021). Multivariate Information in Random Boolean Networks. In: Benito, R.M., Cherifi, C., Cherifi, H., Moro, E., Rocha, L.M., Sales-Pardo, M. (eds) Complex Networks & Their Applications IX. COMPLEX NETWORKS 2020 2020. Studies in Computational Intelligence, vol 943. Springer, Cham. https://doi.org/10.1007/978-3-030-65347-7_49
Download citation
DOI: https://doi.org/10.1007/978-3-030-65347-7_49
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-65346-0
Online ISBN: 978-3-030-65347-7
eBook Packages: EngineeringEngineering (R0)