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A Linear Algorithm For Computing Polynomial Dynamical Systems

Abstract : Computation biology helps to understand all processes in organisms from interaction of molecules to complex functions of whole organs. Therefore, there is a need for mathematical methods and models that deliver logical explanations in a reasonable time. For the last few years there has been a growing interest in biological theory connected to finite fields: the algebraic modeling tools used up to now are based on Gröbner bases or Boolean group. Let n variables representing gene products, changing over the time on p values. A Polynomial dynamical system (PDS) is a function which has several components; each one is a polynom with n variables and coefficient in the finite field Z/pZ that model the evolution of gene products. We propose herein a method using algebraic separators, which are special polynomials abundantly studied in effective Galois theory. This approach avoids heavy calculations and provides a first Polynomial model in linear time.
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https://hal.archives-ouvertes.fr/hal-01890698
Contributor : Ines Abdeljaoued-Tej <>
Submitted on : Monday, October 8, 2018 - 8:23:53 PM
Last modification on : Friday, January 8, 2021 - 5:34:03 PM
Long-term archiving on: : Wednesday, January 9, 2019 - 4:17:54 PM

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  • HAL Id : hal-01890698, version 1

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Ines Abdeljaoued-Tej, Alia Benkahla, Ghassen Haddad, Annick Valibouze. A Linear Algorithm For Computing Polynomial Dynamical Systems. 2018. ⟨hal-01890698⟩

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