Abstract
We present an improvement of a method that aims at detecting important dynamical structures in complex systems, by identifying subsets of elements that show tight and coordinated interactions among themselves, while interplaying much more loosely with the rest of the system. Such subsets are estimated by means of a Relevance Index (RI), which is normalized with respect to a homogeneous system, usually described by independent Gaussian variables, as a reference. The strategy presented herein improves the way the homogeneous system is conceived from a theoretical viewpoint. Firstly, we consider the system components as dependent and with equal pairwise correlations, which implies a non-diagonal correlation matrix of the homogeneous system. Then, we generate the components of the homogeneous system according to a multivariate Bernoulli distribution, by exploiting the NORTA method, which is able to create samples of a desired random vector, given its marginal distributions and its correlation matrix. The proposed improvement on the RI method has been applied to three different case studies, obtaining better results compared with the traditional method based on the homogeneous system with independent Gaussian variables.
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Notes
- 1.
- 2.
In details, \(L_b(t)\) = \(L_a(t-1)\) and \(L_c(t)\) = \(L_b(t-1)\).
- 3.
data not shown.
- 4.
Notice that, in case of a perfect copy, the action of excluding a particular variable and including another one leads to groups having the same \(T_{c}\) value.
References
Balakrishnan, V.: Graph Theory. McGraw Hill, New York (1997)
Balduzzi, D., Tononi, G.: Integrated information in discrete dynamical systems: motivation and theoretical framework. PLOS Comput. Biol. 4(6), 1–18 (2008)
Barrett, A.B., Seth, A.K.: Practical measures of integrated information for time-series data. PLOS Comput. Biol. 7(1), 1–18 (2011)
Bazzi, M., Porter, M.A., Williams, S., McDonald, M., Fenn, D.J., Howison, S.D.: Community detection in temporal multilayer networks, with an application to correlation networks. Multiscale Model. Simul. 14(1), 1–41 (2016)
Bossomaier, T., Barnett, L., Harré, M.: Information and phase transitions in socio-economic systems. Complex Adapt. Syst. Model. 1(1), 9 (2013)
Cario, M.C., Nelson, B.L.: Modeling and generating random vectors with arbitrary marginal distributions and correlation matrix. Technical report (1997)
Cover, T., Thomas, A.: Elements of Information Theory, 2nd edn. Wiley, New York (2006)
Cross, M.C., Hohenberg, P.C.: Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851–1112 (1993)
Filisetti, A., Villani, M., Roli, A., Fiorucci, M., Poli, I., Serra, R.: On some properties of information theoretical measures for the study of complex systems. In: Pizzuti, C., Spezzano, G. (eds.) WIVACE 2014. CCIS, vol. 445, pp. 140–150. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-12745-3_12
Gershenson, C., Fernandez, N.: Complexity and information: measuring emergence, self-organization, and homeostasis at multiple scales. Complex 18(2), 29–44 (2012)
Johnson, J.: Hypernetworks in the Science of Complex Systems. Imperial College Press, London (2013)
Kauffman, S.: The Origins of Order. Oxford University Press, Oxford (1993)
Kivelä, M., Arenas, A., Barthelemy, M., Gleeson, J.P., Moreno, Y., Porter, M.A.: Multilayer networks. J. Complex Netw. 2(3), 203–271 (2014)
Lewis, T.G.: Network Science: Theory and Applications. Wiley, Hoboken (2009)
Mansy, S., Schrum, J., Krishnamurthy, M., Tobe, S., Trecol, D., Szostak, J.: Template-directed synthesis of a genetic polymer in a model protocell. Nature 454, 122 (2008)
Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69, 026113 (2004)
Nuño, E., Cutululis, N.: A heuristic for the synthesis of credible operating states in the presence of renewable energy sources. In: 2016 International Conference on Probabilistic Methods Applied to Power Systems (PMAPS), pp. 1–7, October 2016
Pearl, J.: Causality: Models, Reasoning, and Inference. Cambridge University Press, New York (2000)
Prokopenko, M., Boschetti, F., Ryan, A.J.: An information-theoretic primer on complexity, self-organization, and emergence. Complexity 15(1), 11–28 (2009)
Prokopenko, M., Lizier, J.T., Obst, O., Wang, X.R.: Relating fisher information to order parameters. Phys. Rev. E 84, 041116 (2011)
Roli, A., Villani, M., Caprari, R., Serra, R.: Identifying critical states through the relevance index. Entropy 19(2), 73 (2017)
Sani, L., et al.: Efficient search of relevant structures in complex systems. In: Adorni, G., Cagnoni, S., Gori, M., Maratea, M. (eds.) AI*IA 2016. LNCS (LNAI), vol. 10037, pp. 35–48. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-49130-1_4
Sani, L., Lombardo, G., Pecori, R., Fornacciari, P., Mordonini, M., Cagnoni, S.: Social relevance index for studying communities in a facebook group of patients. In: Sim, K., Kaufmann, P. (eds.) EvoApplications 2018. LNCS, vol. 10784, pp. 125–140. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-77538-8_10
Serra, R., Villani, M., Semeria, A.: Genetic network models and statistical properties of gene expression data in knock-out experiments. J. Theor. Biol. 227(1), 149–157 (2004)
Shalizi, C.R., Camperi, M.F., Klinkner, K.L.: Discovering functional communities in dynamical networks. In: Airoldi, E., Blei, D.M., Fienberg, S.E., Goldenberg, A., Xing, E.P., Zheng, A.X. (eds.) ICML 2006. LNCS, vol. 4503, pp. 140–157. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-73133-7_11
Silvestri, G., et al.: Searching relevant variable subsets in complex systems using k-means PSO. In: Pelillo, M., Poli, I., Roli, A., Serra, R., Slanzi, D., Villani, M. (eds.) WIVACE 2017. CCIS, vol. 830, pp. 308–321. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78658-2_23
Sporns, O., Tononi, G., Edelman, G.: Theoretical neuroanatomy: relating anatomical and functional connectivity in graphs and cortical connection matrices. Cereb. Cortex 10(2), 127–141 (2000)
Tononi, G., McIntosh, A., Russel, D., Edelman, G.: Functional clustering: identifying strongly interactive brain regions in neuroimaging data. Neuroimage 7, 133–149 (1998)
Tononi, G., Sporns, O., Edelman, G.M.: A measure for brain complexity: relating functional segregation and integration in the nervous system. Proc. Natl. Acad. Sci. 91(11), 5033–5037 (1994)
Vicari, E., et al.: GPU-based parallel search of relevant variable sets in complex systems. In: Rossi, F., Piotto, S., Concilio, S. (eds.) WIVACE 2016. CCIS, vol. 708, pp. 14–25. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-57711-1_2
Villani, M., Filisetti, A., Benedettini, S., Roli, A., Lane, D., Serra, R.: The detection of intermediate-level emergent structures and patterns. In: Miglino, O. et al. (ed.) Advances in Artificial Life, ECAL 2013, pp. 372–378. The MIT Press (2013). http://mitpress.mit.edu/books/advances-artificial-life-ecal-2013
Villani, M., et al.: A relevance index method to infer global properties of biological networks. In: Pelillo, M., Poli, I., Roli, A., Serra, R., Slanzi, D., Villani, M. (eds.) WIVACE 2017. CCIS, vol. 830, pp. 129–141. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78658-2_10
Villani, M., et al.: An iterative information-theoretic approach to the detection of structures in complex systems. Complexity 2018, 15 (2018). https://doi.org/10.1155/2018/3687839. Article ID 3687839
Wang, X., Lizier, J., Prokopenko, M.: Fisher information at the edge of chaos in random boolean networks. Artif. Life 17(4), 315–329 (2011)
Xie, W., Nelson, B.L., Barton, R.R.: Statistical uncertainty analysis for stochastic simulation with dependent input models. In: Proceedings of the Winter Simulation Conference, pp. 674–685 (2014)
Xu, X., Yan, Z.: Probabilistic load flow evaluation with hybrid Latin hypercube sampling and multiple linear regression. In: 2015 IEEE Power Energy Society General Meeting, pp. 1–5, July 2015
Zubillaga, D., et al.: Measuring the complexity of self-organizing traffic lights. Entropy 16(5), 2384–2407 (2014). http://www.mdpi.com/1099-4300/16/5/2384
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Sani, L. et al. (2019). An Improved Relevance Index Method to Search Important Structures in Complex Systems. In: Cagnoni, S., Mordonini, M., Pecori, R., Roli, A., Villani, M. (eds) Artificial Life and Evolutionary Computation. WIVACE 2018. Communications in Computer and Information Science, vol 900. Springer, Cham. https://doi.org/10.1007/978-3-030-21733-4_1
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