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A Fast and Effective Method to Identify Relevant Sets of Variables in Complex Systems

Author

Listed:
  • Gianluca D’Addese

    (Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, 41121 Modena, Italy)

  • Martina Casari

    (Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, 41121 Modena, Italy)

  • Roberto Serra

    (Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, 41121 Modena, Italy
    Institute for Advanced Studies, University of Amsterdam, 1012 WX Amsterdam, The Netherlands
    European Centre for Living Technology, 30123 Venice, Italy)

  • Marco Villani

    (Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, 41121 Modena, Italy
    European Centre for Living Technology, 30123 Venice, Italy)

Abstract

In many complex systems one observes the formation of medium-level structures, whose detection could allow a high-level description of the dynamical organization of the system itself, and thus to its better understanding. We have developed in the past a powerful method to achieve this goal, which however requires a heavy computational cost in several real-world cases. In this work we introduce a modified version of our approach, which reduces the computational burden. The design of the new algorithm allowed the realization of an original suite of methods able to work simultaneously at the micro level (that of the binary relationships of the single variables) and at meso level (the identification of dynamically relevant groups). We apply this suite to a particularly relevant case, in which we look for the dynamic organization of a gene regulatory network when it is subject to knock-outs. The approach combines information theory, graph analysis, and an iterated sieving algorithm in order to describe rather complex situations. Its application allowed to derive some general observations on the dynamical organization of gene regulatory networks, and to observe interesting characteristics in an experimental case.

Suggested Citation

  • Gianluca D’Addese & Martina Casari & Roberto Serra & Marco Villani, 2021. "A Fast and Effective Method to Identify Relevant Sets of Variables in Complex Systems," Mathematics, MDPI, vol. 9(9), pages 1-27, April.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:1022-:d:547305
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    References listed on IDEAS

    as
    1. Hiroaki Kitano, 2002. "Computational systems biology," Nature, Nature, vol. 420(6912), pages 206-210, November.
    2. Marco Villani & Luca La Rocca & Stuart Alan Kauffman & Roberto Serra, 2018. "Dynamical Criticality in Gene Regulatory Networks," Complexity, Hindawi, vol. 2018, pages 1-14, October.
    3. H. Jeong & B. Tombor & R. Albert & Z. N. Oltvai & A.-L. Barabási, 2000. "The large-scale organization of metabolic networks," Nature, Nature, vol. 407(6804), pages 651-654, October.
    4. Marco Villani & Laura Sani & Riccardo Pecori & Michele Amoretti & Andrea Roli & Monica Mordonini & Roberto Serra & Stefano Cagnoni, 2018. "An Iterative Information-Theoretic Approach to the Detection of Structures in Complex Systems," Complexity, Hindawi, vol. 2018, pages 1-15, November.
    Full references (including those not matched with items on IDEAS)

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