Applications of Finite Fields to Dynamical Systems and Reverse Engineering Problems
动力系统
2007-05-23 v1 环与代数
定量方法
摘要
We present a mathematical model: dynamical systems over finite sets (DSF), and we show that Boolean and discrete genetic models are special cases of DFS. In this paper, we prove that a function defined over finite sets with different number of elements can be represented as a polynomial function over a finite field. Given the data of a function defined over different finite sets, we describe an algorithm to obtain all the polynomial functions associated to this data. As a consequence, all the functions defined in a regulatory network can be represented as a polynomial function in one variable or in several variables over a finite field. We apply these results to study the reverse engineering problem.
引用
@article{arxiv.math/0603369,
title = {Applications of Finite Fields to Dynamical Systems and Reverse Engineering Problems},
author = {Maria A. Avino-Diaz and Edward Green and Oscar Moreno},
journal= {arXiv preprint arXiv:math/0603369},
year = {2007}
}