zbMATH — the first resource for mathematics

Realization of Boolean control networks. (English) Zbl 1214.93031
Summary: Based on the linear expression of the dynamics of Boolean networks, a coordinate transformation of Boolean variables is defined. It follows that the state space coordinate transformation for the dynamics of Boolean networks is revealed. Using it, the invariant subspace for a Boolean control network is defined. Then the structure of a Boolean control network is analyzed, and the controllable and observable normal forms and the Kalman decomposition form are presented. Finally the realization problem, including minimum realization, of Boolean control networks is investigated.

93B15 Realizations from input-output data
93E03 Stochastic systems in control theory (general)
93B17 Transformations
93B10 Canonical structure
Full Text: DOI
[1] Akutsu, T.; Hayashida, M.; Ching, W.; Ng, M.K., Control of Boolean networks: hardness results and algorithms for tree structured networks, Journal of theoretical biology, 244, 670-679, (2007)
[2] Albert, R.; Othmer, H.G., The topology and signature of the regulatory interactions predict the expression pattern of the segment polarity genes in drospphila melanogaster, Journal of theoretical biology, 223, 1, 1-18, (2003)
[3] Cheng, D. (2007.). Semi-tensor product of matrices and its applications — A survey. In Proc. ICCM (pp. 641-668) vol. 3
[4] Cheng, D., Input-state approach to Boolean networks, IEEE transactions on neural networks, 20, 3, 512-521, (2009)
[5] Cheng, D.; Qi, H., Controllability and observability of Boolean control networks, Automatica, 45, 7, 1659-1667, (2009) · Zbl 1184.93014
[6] Cheng, D., & Qi, H. (2009b). A linear representation of dynamics of Boolean networks, IEEE Transactions on Automatic Control. (in press, Preprint: http://lsc.amss.ac.cn/ dcheng/preprint)
[7] Davidson, E.; Rast, J.; Oliveri, P.; Ransick, A.; Calestani, C.; Yuh, C., A genomic regulatory network for development, Science, 295, 5560, 1669-1678, (2002)
[8] Farrow, C.; Heidel, J.; Maloney, H.; Rogers, J., Scalar equations for synchronous Boolean networks with biological applications, IEEE transactions on neural networks, 15, 2, 348-354, (2004)
[9] Huang, S., Regulation of cellular states in Mammalian cells from a genomewide view, (), 181-220
[10] Huang, S.; Ingber, I., Shape-dependent control of cell growth, differentiation, and apoptosis: switching between attractors in cell regulatory networks, Experimental cell research, 261, 91-103, (2000)
[11] Kauffman, S.A., Metabolic stability and epigenesis in randomly constructed genetic nets, Journal of theoretical biology, 22, 437-467, (1969)
[12] Rade, L.; Westergren, B., Mathematics handbook for science and engineering, (1998), Studentlit-teatur Sweden
[13] Robert, F., Discrete iterations: A metric study (J. rokne, trans.), (1986), Springer-Verlag Berlin
[14] Wonham, W., Linear multivariable control: A geometric approach, (1979), Springer Berlin · Zbl 0424.93001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.