tailieunhanh - Báo cáo hóa học: " Reduction Mappings between Probabilistic Boolean 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: Reduction Mappings between Probabilistic Boolean Networks | EURASIP Journal on Applied Signal Processing 2004 1 125-131 2004 Hindawi Publishing Corporation Reduction Mappings between Probabilistic Boolean Networks Ivan Ivanov Department of Electrical Engineering Texas A M University College Station TX 77843 USA Email ivanov@ Edward R. Dougherty Department of Electrical Engineering Texas A M University 3128 TAMU College Station TX 77843-3128 USA Email e-dougherty@ Received 11 April 2003 Revised 28 August 2003 Probabilistic Boolean networks PBNs comprise a model describing a directed graph with rule-based dependences between its nodes. The rules are selected based on a given probability distribution which provides a flexibility when dealing with the uncertainty which is typical for genetic regulatory networks. Given the computational complexity of the model the characterization of mappings reducing the size of a given PBN becomes a critical issue. Mappings between PBNs are important also from a theoretical point of view. They provide means for developing a better understanding about the dynamics of PBNs. This paper considers two kinds of mappings reduction and projection and their effect on the original probability structure of a given PBN. Keywords and phrases Boolean network genetic network graphical models projection reduction. 1. INTRODUCTION Given a set of genes the evolution of their expressions constitutes a dynamical system over time. Owing to the complexity of gene interaction and the paucity of data homogeneous transitions are customarily assumed. Many different gene-regulatory-network models have been proposed. Among deterministic dynamical systems perhaps the most attention has been given to the Boolean network model 1 2 3 . In this model gene expression is quantized to only two levels ON and OFF. The expression level state of a gene is functionally related via a logical rule to the expression states of some other genes. The Boolean network model has yielded insights into the overall behavior of

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