Singular Boolean networks: Semi-tensor product approach

被引：0
作者：
JunE Feng
Juan Yao
Peng Cui
机构：
[1] Shandong University,School of Mathematics
[2] Shandong University,School of Control Science and Engineering
来源：
Science China Information Sciences | 2013年 / 56卷
关键词：
admissible initial value; normalization problem; semi-tensor product; singular Boolean network;
D O I：
暂无
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学科分类号：
摘要：
Singular Boolean networks are introduced in this paper. Via semi-tensor product of matrices and the matrix expression of logical functions, two kinds of the condensed algebraic expressions of singular Boolean networks are obtained. The normalization problem of singular Boolean networks is addressed; that is, under what condition singular Boolean networks can be converted into normal Boolean networks with algebraic restrictions. Then one sufficient condition and one necessary and sufficient condition are derived for the normalization problem. Furthermore, the solvability of singular Boolean networks is discussed and the concept of admissible initial values of singular Boolean networks is presented. Finally, fixed points and cycles of singular Boolean networks are also investigated.
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页码：1 / 14
页数：13
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共 39 条
[1]  
Kauffman S(1969)Metabolic stability and epigenesis in randomly constructed genetic nets J Theor Biol 22 437-467
[2]  
Davison E H(2002)A genomic regulatory network for development Science 295 1669-1678
[3]  
Rast J P(2002)A model of transcriptional regulatory networks based on biases in the observed regulations rules Complexity 7 23-40
[4]  
Oliveri P(2007)How to infer gene networks from expression profiles Mol Syst Biol 3 1-10
[5]  
Harris S E(2005)Number and length of attractors in a critical kauffman model with connectivity one Phys Rev Lett 94 088701-2387
[6]  
Sawhill B K(2006)Optimal infinite-horizon control for probabilistic Boolean networks IEEE Trans Signal Process 54 2375-2258
[7]  
Wuenche A(2010)A linear representation dynamics of Boolean networks IEEE Trans Automat Control 55 2251-1667
[8]  
Bansal M(2009)Controllability and observability of Boolean control networks Automatica 45 1659-69
[9]  
Belcastro V(2010)Realization of Boolean control networks Automatica 46 62-156
[10]  
Ambesi-Impiobato A(2011)Stability and stabilization of Boolean networks Int J Robust Nonlinear Control 21 134-10
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