학술논문
A linear algorithm for computing Polynomial Dynamical System
Document Type
Working Paper
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Subject
Language
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 Gr\"obner 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.
Comment: 11 pages, 3 figures
Comment: 11 pages, 3 figures