A linear algorithm for computing Polynomial Dynamical System

TL;DR

This paper introduces a linear-time algorithm for constructing Polynomial Dynamical Systems (PDS) in computational biology, leveraging algebraic separators to efficiently model gene interactions over finite fields.

Contribution

It presents a novel linear-time method using algebraic separators for constructing PDS, improving computational efficiency over existing algebraic modeling techniques.

Findings

The method computes PDS in linear time.

Algebraic separators effectively model gene dynamics.

The approach reduces computational complexity significantly.

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.