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

Hamid Rahkooy 1, 2 Ovidiu Radulescu 3 Thomas Sturm 2, 1, 4
1 MOSEL - Proof-oriented development of computer-based systems
LORIA - FM - Department of Formal Methods
2 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
MPII - Max-Planck-Institut für Informatik, Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
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-03017913
Contributor : Thomas Sturm Connect in order to contact the contributor
Submitted on : Saturday, November 21, 2020 - 5:25:11 PM
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. 2020. ⟨hal-03017913⟩

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