2018/10/08 by Abdeljaoued-Tej, Ines, BenKahla, Alia, Haddad, Ghassen +1
#FOS: Biological sciences #FOS: Mathematics #Molecular Networks (q-bio.MN) #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.1810.04069
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.