tailieunhanh - Báo cáo hóa học: " Research Article Fixed Points in Discrete Models for Regulatory Genetic Networks"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Fixed Points in Discrete Models for Regulatory Genetic Networks | Hindawi Publishing Corporation EURASIP Journal on Bioinformatics and Systems Biology Volume 2007 Article ID 97356 8 pages doi 2007 97356 Research Article Fixed Points in Discrete Models for Regulatory Genetic Networks Dorothy Bollman 1 Omar Colon-Reyes 1 and Edusmildo Orozco2 1 Departament of Mathematical Sciences University of Puerto Rico Mayaguez PR 00681 USA 2 Department of Computer Science University of Puerto Rico Rio Piedras San Juan PR 00931-3355 USA Received 1 July 2006 Revised 22 November 2006 Accepted 20 February 2007 Recommended by Tatsuya Akutsu It is desirable to have efficient mathematical methods to extract information about regulatory iterations between genes from repeated measurements of gene transcript concentrations. One piece of information is of interest when the dynamics reaches a steady state. In this paper we develop tools that enable the detection of steady states that are modeled by fixed points in discrete finite dynamical systems. We discuss two algebraic models a univariate model and a multivariate model. We show that these two models are equivalent and that one can be converted to the other by means of a discrete Fourier transform. We give a new more general definition of a linear finite dynamical system and we give a necessary and sufficient condition for such a system to be a fixed point system that is all cycles are of length one. We show how this result for generalized linear systems can be used to determine when certain nonlinear systems monomial dynamical systems over finite fields are fixed point systems. We also show how it is possible to determine in polynomial time when an ordinary linear system defined over a finite field is a fixed point system. We conclude with a necessary condition for a univariate finite dynamical system to be a fixed point system. Copyright 2007 Dorothy Bollman et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use .