Matrix Approach to Simplify Boolean Networks
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- 英文论文题名：Matrix Approach to Simplify Boolean Networks
- 论文作者：Jumei Yue ; Yongyi Yan ; Zhihong Zhang ; Shuqiang Li
- 英文论文作者：Jumei Yue ; Yongyi Yan ; Zhihong Zhang ; Shuqiang Li ; College of Agricultural Engineering ; Henan University of Science and Technology ; College of Information Engineering ; Henan University of Science and Technology
- 年：2017
- 作者机构：College of Agricultural Engineering,Henan University of Science and Technology;College of Information Engineering,Henan University of Science and Technology;
- 英文论文关键词：Boolean networks ; semi-tensor product ; Boolean control network ; matrix approach
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 语种：英文
- 分类号：O157.5
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：1795k
- 原文格式：D
- 会议级别：全国
摘要
The state space of Boolean networks grows exponentially with the number of nodes; this makes it hard to analyze large-scale Boolean networks. This paper aims to simplify Boolean networks mathematically by aid of a new matrix analysis tool, called semi-tensor product of matrices proposed in recent years. The simplification method contains two steps. First, delete the gene nodes that their dynamics are independent on their evolutions directly. Second, use the logic functions of the deleted nodes to replace the corresponding variables in the logic functions of other gene nodes that their dynamics are depend on themselves directly and the deleted nodes in the step 1. We prove that the reduced networks share some common key dynamics with the original networks such as the steady states, attractors and topological structure.
The state space of Boolean networks grows exponentially with the number of nodes; this makes it hard to analyze large-scale Boolean networks. This paper aims to simplify Boolean networks mathematically by aid of a new matrix analysis tool, called semi-tensor product of matrices proposed in recent years. The simplification method contains two steps. First, delete the gene nodes that their dynamics are independent on their evolutions directly. Second, use the logic functions of the deleted nodes to replace the corresponding variables in the logic functions of other gene nodes that their dynamics are depend on themselves directly and the deleted nodes in the step 1. We prove that the reduced networks share some common key dynamics with the original networks such as the steady states, attractors and topological structure.
The state space of Boolean networks grows exponentially with the number of nodes; this makes it hard to analyze large-scale Boolean networks. This paper aims to simplify Boolean networks mathematically by aid of a new matrix analysis tool, called semi-tensor product of matrices proposed in recent years. The simplification method contains two steps. First, delete the gene nodes that their dynamics are independent on their evolutions directly. Second, use the logic functions of the deleted nodes to replace the corresponding variables in the logic functions of other gene nodes that their dynamics are depend on themselves directly and the deleted nodes in the step 1. We prove that the reduced networks share some common key dynamics with the original networks such as the steady states, attractors and topological structure.
引文
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[21]J.Feng,H.Lv,D.Cheng,Multiple fuzzy relation and its application to coupled fuzzy control.Asian Journal of Control,15(5):1313-1324,2013.
[22]F.Li,Feedback control design for the complete synchronisation of two coupled Boolean networks.International Journal of Systems Science,47(12):2996-3003,2015.
[23]D.Cheng,F.He,H.Qi,et al.,Modeling,analysis and control of networked evolutionary games.IEEE Transactions on Automatic Control,60(9):2402-2415,2015.
[24]H.Qi,Y.Wang,T.Liu,et al.,Vector space structure of finite evolutionary games and its application to strategy profile convergence.Journal of Systems Science and Complexity,29(3):602-628,2016.
[25]X.Xu,Y.Hong,Leader-following consensus of multi-agent systems over finite fields.ar Xiv preprint ar Xiv:14051906,2014.
[26]Y.Yan,Z.Chen,Z.Liu,Semi-tensor product approach to controlliability and stabilizability of finite automata.Journal of Systems Engineering and Electronics,26(1):134-141,2015.
[27]Z.Liu,Y.Wang,H.Li,Controllability of Context Sensitive Probabilistic Mix-Valued Logical Control Networks with Constraints.Asian Journal of Control,17(1):246-254,2015.
[28]J.Lu,J.Zhong,D.W.Ho,et al.,On Controllability of Delayed Boolean Control Networks.SIAM Journal on Control and Optimization,54(2):475-494,2016.
[29]D.Cheng,Y.Dong,Semi-tensor product of matrices and its some applications to physics.Methods and Applications of Analysis,10(4):565-588,2003.
[30]D.Cheng,Some applications of semi-tensor product of matrices in algebra.Computers and Mathematics with Applications,52(6):1045-1066,2006.
[31]D.Cheng,H.Qi,Z.Li,Model construction of Boolean network via observed data.IEEE Transactions on Neural Networks,22(4):525-536,2011.
[2]H.Y.Lee,K.H.Cho,Abstract B2-28:The development of an individualized Boolean network model for targeted anticancer therapy of glioblastoma.Cancer Research,75(22Supplement 2):B2-28-B22-28,2015.
[3]N.K.Soni,N.Thukral,Y.Hasija.Personalized Medicine in the Era of Genomics.Handbook of Research on Computational Intelligence Applications in Bioinformatics.IGI Global.2016:296-327.
[4]M.Davidich,S.Bornholdt,Boolean network model predicts cell cycle sequence of fission yeast.Plo S one,3(2):1672-1679,2008.
[5]Q.Zhao,A remark on"Scalar equations for synchronous Boolean networks with biological Applications".IEEETransactions on Neural Networks,16(6):1715-1716,2005.
[6]A.Saadatpour,I.Albert,R.Albert,Attractor analysis of asynchronous Boolean models of signal transduction networks.Journal of Theoretical Biology,266(4):641-656,2010.
[7]A.Saadatpour,R.Albert,T.C.Reluga,A reduction method for Boolean network models proven to conserve attractors.SIAM journal on applied dynamical systems,12(4):1997-2011,2013.
[8]A.Veliz-Cuba,B.Aguilar,F.Hinkelmann,et al.,Steady state analysis of Boolean molecular network models via model reduction and computational algebra.BMCbioinformatics,15(1):1,2014.
[9]J.Za?udo,R.Albert,An effective network reduction approach to find the dynamical repertoire of discrete dynamic networks.Chaos:An Interdisciplinary Journal of Nonlinear Science,23(2):102-111,2013.
[10]A.Veliz-Cuba,A.S.Jarrah,R.Laubenbacher,Polynomial algebra of discrete models in systems biology.Bioinformatics,26(13):1637-1643,2010.
[11]I.Ivanov,E.Dougherty,Reduction mappings between probabilistic Boolean networks.EURASIP Journal on Applied Signal Processing,2004(125-131),2004.
[12]D.Cheng,H.Qi,Y.Zhao.An Introduction to Semi-tensor Product of Matrices and Its Applications.Singapore:World Scientific Publishing Co.Pte.Ltd.,2012.
[13]Y.Liu,L.Sun,J.Lu,et al.,Feedback Controller Design for the Synchronization of Boolean Control Networks.IEEETransactions on Neural Networks and Learning Systems,27(9):1991-1996,2015.
[14]Y.Zou,J.Zhu,Cycles of periodically time-variant Boolean networks.Automatica,51:175-179,2015.
[15]D.Cheng,H.Qi,T.Liu,et al.,A note on observability of Boolean control networks.Systems and Control Letters,87:76-82,2016.
[16]H.Li,Y.Wang,L.Xie,Output tracking control of Boolean control networks via state feedback:Constant reference signal case.Automatica,59:54-59,2015.
[17]D.Laschov,M.Margaliot,On Boolean control networks with maximal topological entropy.Automatica,50(11):2924-2928,2014.
[18]D.Cheng,H.Qi,A linear representation of dynamics of Boolean networks.IEEE Transactions on Automatic Control,55(10):2251-2258,2010.
[19]Y.Yan,Z.Chen,J.Yue,et al.,STP approach to model controlled automata with application to reachability analysis of DEDS.Asian Journal of Control,18(6):2027-2036,2016.
[20]E.Fornasini,M.Valcher,Fault detection analysis of Boolean control networks.IEEE Trans on Automatic Control,60(10):2734-2739,2015.
[21]J.Feng,H.Lv,D.Cheng,Multiple fuzzy relation and its application to coupled fuzzy control.Asian Journal of Control,15(5):1313-1324,2013.
[22]F.Li,Feedback control design for the complete synchronisation of two coupled Boolean networks.International Journal of Systems Science,47(12):2996-3003,2015.
[23]D.Cheng,F.He,H.Qi,et al.,Modeling,analysis and control of networked evolutionary games.IEEE Transactions on Automatic Control,60(9):2402-2415,2015.
[24]H.Qi,Y.Wang,T.Liu,et al.,Vector space structure of finite evolutionary games and its application to strategy profile convergence.Journal of Systems Science and Complexity,29(3):602-628,2016.
[25]X.Xu,Y.Hong,Leader-following consensus of multi-agent systems over finite fields.ar Xiv preprint ar Xiv:14051906,2014.
[26]Y.Yan,Z.Chen,Z.Liu,Semi-tensor product approach to controlliability and stabilizability of finite automata.Journal of Systems Engineering and Electronics,26(1):134-141,2015.
[27]Z.Liu,Y.Wang,H.Li,Controllability of Context Sensitive Probabilistic Mix-Valued Logical Control Networks with Constraints.Asian Journal of Control,17(1):246-254,2015.
[28]J.Lu,J.Zhong,D.W.Ho,et al.,On Controllability of Delayed Boolean Control Networks.SIAM Journal on Control and Optimization,54(2):475-494,2016.
[29]D.Cheng,Y.Dong,Semi-tensor product of matrices and its some applications to physics.Methods and Applications of Analysis,10(4):565-588,2003.
[30]D.Cheng,Some applications of semi-tensor product of matrices in algebra.Computers and Mathematics with Applications,52(6):1045-1066,2006.
[31]D.Cheng,H.Qi,Z.Li,Model construction of Boolean network via observed data.IEEE Transactions on Neural Networks,22(4):525-536,2011.