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Exploiting Variable Sparsity in Computing Equilibria of Biological Dynamical Systems by Triangular Decomposition

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Algorithms for Computational Biology (AlCoB 2021)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 12715))

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Abstract

Biological systems modeled as dynamical systems can be large in the number of variables and sparse in the interrelationship between the variables. In this paper we exploit the variable sparsity of biological dynamical systems in computing their equilibria by using sparse triangular decomposition. The variable sparsity of a biological dynamical system is characterized via the associated graph constructed from the polynomial set in the system. To make use of sparse triangular decomposition which has been proven to maintain the variable sparsity when a perfect elimination ordering of a chordal associated graph is used, we first study the influence of chordal completion on the variable sparsity for a large number of biological dynamical systems. Then for those systems which are both large and sparse, we compare the computational performances of sparse triangular decomposition versus ordinary one with experiments. The experimental results verify the efficiency gains in sparse triangular decomposition exploiting the variable sparsity.

This work was partially supported by the National Natural Science Foundation of China (NSFC 11971050) and Beijing Natural Science Foundation (Z180005).

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Notes

  1. 1.

    https://www.ebi.ac.uk/biomodels/.

  2. 2.

    http://odebase.cs.uni-bonn.de/.

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Authors and Affiliations

  1. LMIB–School of Mathematical Sciences, Beihang University, Beijing, 100191, China

    Wenwen Ju & Chenqi Mou

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  1. Wenwen Ju
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  2. Chenqi Mou
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Correspondence to Chenqi Mou .

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Editors and Affiliations

  1. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  2. University of Extremadura, Cáceres, Spain

    Miguel A. Vega-Rodríguez

  3. University of Montana, Missoula, MT, USA

    Travis Wheeler

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Ju, W., Mou, C. (2021). Exploiting Variable Sparsity in Computing Equilibria of Biological Dynamical Systems by Triangular Decomposition. In: Martín-Vide, C., Vega-Rodríguez, M.A., Wheeler, T. (eds) Algorithms for Computational Biology. AlCoB 2021. Lecture Notes in Computer Science(), vol 12715. Springer, Cham. https://doi.org/10.1007/978-3-030-74432-8_3

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  • DOI: https://doi.org/10.1007/978-3-030-74432-8_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-74431-1

  • Online ISBN: 978-3-030-74432-8

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