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Dynamical Systems and Stochastic Programming: To Ordinary Differential Equations and Back

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Transactions on Computational Systems Biology XI

Part of the book series: Lecture Notes in Computer Science ((TCSB,volume 5750))

Abstract

In this paper we focus on the relation between models of biological systems consisting of ordinary differential equations (ODE) and models written in a stochastic and concurrent paradigm (sCCP stochastic Concurrent Constraint Programming). In particular, we define a method to associate a set of ODE’s to an sCCP program and a method converting ODE’s into sCCP programs. Then we study the properties of these two translations. Specifically, we show that the mapping from sCCP to ODE’s preserves rate semantics for the class of biochemical models (i.e. chemical kinetics is maintained) and we investigate the invertibility properties of the two mappings. Finally, we concentrate on the question of behavioral preservation, i.e if the models obtained applying the mappings have the same dynamics. We give a convergence theorem in the direction from ODE’s to sCCP and we provide several well-known examples in which this property fails in the inverse direction, discussing them in detail.

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Author information

Authors and Affiliations

  1. Dept. of Mathematics and Computer Science, University of Trieste, Italy

    Luca Bortolussi

  2. Dept. of Mathematics and Computer Science, University of Udine, Italy

    Alberto Policriti

  3. Applied Genomics Institute (IGA), Udine, Italy

    Alberto Policriti

Authors
  1. Luca Bortolussi
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  2. Alberto Policriti
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Editor information

Editors and Affiliations

  1. Centre for Computational and Systems Biology, The Microsoft Research - University of Trento, Piazza Manci, 17, 38050, Povo, (TN), Italy

    Corrado Priami

  2. Department of Information Technologies, Åbo Akademi University, FI-20520, Turku, Finland

    Ralph-Johan Back

  3. Computational Biomodelling Laboratory, Turku Center for Computer Science, FIN-20520, Turku, Finland

    Ion Petre

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© 2009 Springer-Verlag Berlin Heidelberg

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Bortolussi, L., Policriti, A. (2009). Dynamical Systems and Stochastic Programming: To Ordinary Differential Equations and Back. In: Priami, C., Back, RJ., Petre, I. (eds) Transactions on Computational Systems Biology XI. Lecture Notes in Computer Science(), vol 5750. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04186-0_11

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  • DOI: https://doi.org/10.1007/978-3-642-04186-0_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04185-3

  • Online ISBN: 978-3-642-04186-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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