2006/03/13 by Maria A. Avino-Diaz, Avino-Diaz, Maria A.
Biochemistry, Genetics and Molecular Biology · Mathematics · #00A71 #03C60 #Bioinformatics and Genomic Networks #Dynamical Systems (math.DS) #FOS: Biological sciences #FOS: Mathematics #Gene Regulatory Network Analysis #Genomics (q-bio.GN) #Microbial Metabolic Engineering and Bioproduction #Probability (math.PR) #math.DS #math.PR #msc:00A71 #msc:03C60 #q-bio.GN
paper · pdf · doi:10.48550/arxiv.math/0603291
arxiv created 2006/03/13 · openalex publication_date 2006/03/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study finite dynamical systems with n functions acting on the same set X, and probabilities assigned to these functions, that it is called Probabilistic Regulatory Gene Networks (PRN. his concept is the same or a natural generalization of the concept Probabilistic Boolean Networks (PBN), introduced by I. Shmulevich, E. Dougherty, and W. Zhang, particularly the model PBN has been using to describe genetic networks and has therapeutic applications. In PRNs the most important question is to describe the steady states of the systems, so in this paper we pay attention to the idea of transforming a network to another without lost all the properties, in particular the probability distribution. Following this objective we develop the concepts of homomorphism and ε-homomorphism of probabilistic regulatory networks, since these concepts bring the properties from one networks to another. Projections are special homomorphisms, and they always induce invariant subnetworks that contain all cycles and steady states in the network.