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A Linear Algebra Approach for Detecting Binomiality of Steady State Ideals of Reversible Chemical Reaction Networks

Abstract : Motivated by problems from Chemical Reaction Network Theory, we investigate whether steady state ideals of reversible reaction networks are generated by binomials. We take an algebraic approach considering, besides concentrations of species, also rate constants as indeterminates. This leads us to the concept of unconditional binomiality, meaning binomiality for all values of the rate constants. This concept is different from conditional binomiality that applies when rate constant values or relations among rate constants are given. We start by representing the generators of a steady state ideal as sums of binomials, which yields a corresponding coefficient matrix. On these grounds, we propose an efficient algorithm for detecting unconditional binomiality. That algorithm uses exclusively elementary column and row operations on the coefficient matrix. We prove asymptotic worst case upper bounds on the time complexity of our algorithm. Furthermore, we experimentally compare its performance with other existing methods.
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https://hal.archives-ouvertes.fr/hal-02977486
Contributor : Thomas Sturm Connect in order to contact the contributor
Submitted on : Sunday, October 25, 2020 - 9:58:25 AM
Last modification on : Saturday, October 16, 2021 - 11:26:09 AM

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Hamid Rahkooy, Ovidiu Radulescu, Thomas Sturm. A Linear Algebra Approach for Detecting Binomiality of Steady State Ideals of Reversible Chemical Reaction Networks. Computer Algebra in Scientific Computing: 22nd International Workshop - CASC 2020, pp.492-509, 2020, ⟨10.1007/978-3-030-60026-6_29⟩. ⟨hal-02977486⟩

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