logo

SCIENTIA SINICA Informationis, Volume 48 , Issue 9 : 1214-1226(2018) https://doi.org/10.1360/N112018-00038

Reconstruction of probabilistic Boolean networks

More info
  • ReceivedApr 21, 2018
  • AcceptedMay 30, 2018
  • PublishedAug 23, 2018

Abstract


Funded by

国家自然科学基金(61640315,61603125)

河南省高等学校青年骨干教师资助计划(2017GGJS-243)

河南省高等学校重点科研项目(18A110003,17A120001)

河南财经政法大学学术创新骨干支持计划和 河南财经政法大学青年拔尖人才资助计划(hncjzfdxqnbjrc201607)


Acknowledgment

感谢编委和审稿人对本文的初稿提出宝贵的修改意见和建议.


References

[1] Kauffman S A. Metabolic stability and epigenesis in randomly constructed genetic nets. J Theory Biol, 1969, 22: 437-467 CrossRef Google Scholar

[2] de Castro L N, von Zuben F J, de Deus J G A. The construction of a Boolean competitive neural network using ideas from immunology. Neurocomputing, 2003, 50: 51-85 CrossRef Google Scholar

[3] Pattison P E, Breiger R L. Lattices and dimensional representations: matrix decompositions and ordering structures. Social Networks, 2002, 24: 423-444 CrossRef Google Scholar

[4] Wang L, Tian Y, Du J M. Opinion dynamics in social networks, Sci Sin Inform, 2018, 48: 3--23. Google Scholar

[5] Wang Y Z, Zhang C H, Liu Z B. A matrix approach to graph maximum stable set and coloring problems with application to multi-agent systems. Automatica, 2012, 48: 1227-1236 CrossRef Google Scholar

[6] Hopfensitz M, Mussel C, Maucher M. Attractors in Boolean networks: a tutorial. Comput Stat, 2013, 28: 19-36 CrossRef Google Scholar

[7] Cheng D Z, Qi H S. A linear representation of dynamics of Boolean networks. IEEE Trans Autom Control, 2010, 55: 2251-2258 CrossRef Google Scholar

[8] Heidel J, Maloney J, Farrow C. Finding cycles in synchronous Boolean networks with applications to biochemical systems. Int J Bifurcat Chaos, 2003, 13: 535-552 CrossRef ADS Google Scholar

[9] Farrow C, Heidel J, Maloney J. Scalar equations for synchronous Boolean networks with biological applications. IEEE Trans Neural Netw, 2004, 15: 348-354 CrossRef PubMed Google Scholar

[10] Zhao Q C. A remark on “scalar equations for synchronous Boolean networks with biological applications". IEEE Trans Neural Netw 2005, 16: 1715--1716. Google Scholar

[11] Kitano H. Systems biology: a brief overview. Science, 2002, 295: 1662-1664 CrossRef PubMed ADS Google Scholar

[12] Shmulevich I, Dougherty E R, Kim S, et al. Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks. IEEE/ACM Trans Comput Biol Bioinf, 2002, 18: 261--274. Google Scholar

[13] Shmulevich I, Dougherty E R, Zhang W. From Boolean to probabilistic Boolean networks as models of genetic regulatory networks. Proc IEEE, 2002, 90: 1778-1792 CrossRef Google Scholar

[14] Shmulevich I, Dougherty E R, Zhang W. Gene perturbation and intervention in probabilistic Boolean networks. Bioinformatics, 2002, 18: 1319-1331 CrossRef Google Scholar

[15] Shmulevich I, Dougherty E R, Zhang W. Control of stationary behavior in probabilistic Boolean networks by means of structural intervention. J Biol Syst, 2002, 10: 431-445 CrossRef Google Scholar

[16] Datta A. External control in Markovian genetic regulatory networks. Mach Learn, 2003, 52: 169-191 CrossRef Google Scholar

[17] Cheng D Z, Qi H S, Zhao Y. An Introduction to Semi-Tensor Product of Matrices and Its Applications. Singapore: World Scientific Publishing, 2012. Google Scholar

[18] Cheng D Z, Qi H S. Semi-tensor Product of Matrix — Theory and Applications. Beijing: Science Press, 2007. Google Scholar

[19] Cheng D Z, Qi H S, Li Z Q. Analysis and Control of Boolean Networks — A Semi-tensor Product Approach. Berlin: Springer, 2011. Google Scholar

[20] Zhang X H, Han H X, Sun Z J. Alternative approach to calculate the structure matrix of Boolean network with semi-tensor product. IET Control Theory Appl, 2017, 11: 2048-2057 CrossRef Google Scholar

[21] Cheng D Z, Li Z Q, Qi H S. Realization of Boolean control networks. Automatica, 2010, 46: 62-69 CrossRef Google Scholar

[22] Fornasini E, Valcher M E. Observability, reconstructibility and state observers of Boolean control networks. IEEE Trans Autom Control, 2013, 58: 1390-1401 CrossRef Google Scholar

[23] Zhu Q X, Liu Y, Lu J Q. Observability of Boolean control networks. Sci China Inf Sci, 2018, 61: 092201 CrossRef Google Scholar

[24] Li F F. Pinning control design for the stabilization of Boolean networks. IEEE Trans Neural Netw Learn Syst, 2016, 27: 1585-1590 CrossRef Google Scholar

[25] Li H T, Wang Y Z, Xie L H. Output tracking control of Boolean control networks via state feedback: constant reference signal case. Automatica, 2015, 59: 54-59 CrossRef Google Scholar

[26] Bof N, Fornasini E, Valcher M E. Output feedback stabilization of Boolean control networks. Automatica, 2015, 57: 21-28 CrossRef Google Scholar

[27] Li H T, Wang Y Z. Minimum-time state feedback stabilization of constrained Boolean control networks. Asian J Control, 2016, 18: 1688-1697 CrossRef Google Scholar

[28] Cheng D Z. Disturbance decoupling of Boolean control networks. IEEE Trans Autom Control, 2011, 56: 2-10 CrossRef Google Scholar

[29] Yang M, Li R, Chu T G. Controller design for disturbance decoupling of Boolean control networks. Automatica, 2013, 49: 273-277 CrossRef Google Scholar

[30] Liu Y, Li B W, Lu J Q. Pinning control for the disturbance decoupling problem of Boolean networks. IEEE Trans Autom Control, 2017, 62: 6595-6601 CrossRef Google Scholar

[31] Li S J, Nicolau F, Respondek W. Multi-input control-affine systems static feedback equivalent to a triangular form and their flatness. Int J Control, 2016, 89: 1-24 CrossRef Google Scholar

[32] Lu J Q, Zhong J, Ho D W C. On controllability of delayed Boolean control networks. SIAM J Control Opt, 2016, 54: 475-494 CrossRef Google Scholar

[33] Zhong J, Lu J Q, Liu Y. Synchronization in an array of output-coupled Boolean networks with time delay. IEEE Trans Neural Netw Learn Syst, 2014, 25: 2288-2294 CrossRef PubMed Google Scholar

[34] Zhong J, Lu J Q, Huang T W. Synchronization of master-slave Boolean networks with impulsive effects: necessary and sufficient criteria. Neurocomputing, 2014, 143: 269-274 CrossRef Google Scholar

[35] Lu J Q, Zhong J, Huang C. On pinning controllability of Boolean control networks. IEEE Trans Autom Control, 2016, 61: 1658-1663 CrossRef Google Scholar

[36] Chen H W, Liang J L, Wang Z D. Pinning controllability of autonomous Boolean control networks. Sci China Inf Sci, 2016, 59: 070107 CrossRef Google Scholar

[37] Liu Y, Li B W, Lou J G. Disturbance decoupling of singular Boolean control networks. IEEE/ACM Trans Comput Biol Bioinf, 2016, 13: 1194-1200 CrossRef PubMed Google Scholar

[38] Lu J Q, Zhong J, Li L L. Synchronization analysis of master-slave probabilistic Boolean networks. Sci Rep, 2015, 5: 13437 CrossRef PubMed ADS Google Scholar

[39] Li R, Yang M, Chu T G. State feedback stabilization for probabilistic Boolean networks. Automatica, 2014, 50: 1272-1278 CrossRef Google Scholar

[40] Chen H W, Liang J L, Huang T W. Synchronization of arbitrarily switched Boolean networks. IEEE Trans Neural Netw Learn Syst, 2017, 28: 612-619 CrossRef PubMed Google Scholar

[41] Cheng D Z, Qi H S, Li Z Q. Model construction of Boolean network via observed data. IEEE Trans Neural Netw, 2011, 22: 525-536 CrossRef PubMed Google Scholar

[42] Chen X, Ching W K, Chen X S. Construction of probabilistic Boolean networks from a prescribed transition probability matrix: a maximum entropy rate approach. East Asian J Appl Math, 2011, 1: 132-154 CrossRef Google Scholar

[43] Jiang H, Chen X, Qiu Y S. On generating optimal sparse probabilistic Boolean networks with maximum entropy from a positive stationary distribution. East Asian J Appl Math, 2012, 2: 353-372 CrossRef Google Scholar

  •   

    Algorithm 1 概率布尔网络的重构

    Step 1 基于概率逻辑矩阵$L$, 计算第$i$个结点的概率逻辑矩阵 $M_i$, $i=1,2,\ldots,n$;Step 2 从 $M_i$构造$M_i^j$, $j=1,2,\ldots,\ell_i$和相应的概率$p_i^{j}$, $j=1,2,\ldots,\ell_i$, 使得 $$M_i=\mathop{\sum}\limits_{j=1}^{\ell_i}{\rm Pr}(f_i=f_i^j)M_i^j;$$ Step 3 从 $M_i^j$构造 $f_i^j$, $j=1,2,\ldots,\ell_i$.