Abstract
The author examines the connection between classical differential algebra of Ritt and Kolchin and differential algebraic models of biochemical systems-in particular, the models generated by S-system of Savageau. Several open problems of both biological and mathematical significance are proposed.
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References
Brockett, R.: Nonlinear Systems and Differential Geometry. Proceedings of the IEEE, 64 (1976): 61–72.
Carrá Ferro, G.: Gröbner Bases and Differential Ideals. Proceedings of AAECC-5, Lecture Notes in Computer Science, Springer-Verlag, (1987): 129–140.
Diop, S.: Elimination in Control Theory. Math. Control Signals Systems, 4 (1991): 17–32.
Forsman, K.: Constructive Commutative Algebra in Nonlinear Control Theory, Linköping Studies in Science and Technology, Dissertation, No. 261, Department of Electrical Engineering, Linköping University, Linköping, Sweden, 1992. 730
Gallo, G., Mishra, B., and Ollivier, F.: Some Constructions in Rings of Differential Polynomials. Proceedings of AAECC-9, Lecture Notes in Computer Science, Springer-Verlag, 539 (1991): 171–182.
Kolchin, E.R.: On the Basis Theorem for Differential Systems. Transactions of the AMS, 52 (1942): 115–127.
Mishra, B.: Computational Differential Algebra. Geometrical Foundations of Robotics, (Ed. Jon Selig), World-Scientific, Singapore, Lecture 8 (2000): 111–145.
Ritt, J. F.: Differential Equations from the Algebraic Standpoint, AMS Coloq. Publ. 14, New York 1932.
Seidenberg, A.: An Elimination Theory for Differential Algebra. University of California, Berkeley, Publications in Mathematics, 3 (1956): 31–65.
Savageau, M.A.: Biochemical System Analysis: A Study of Function and Design in Molecular Biology. Addison-Wesley, 1976. 725
Voit, E.O.: Computational Analysis of Biochemical Systems. Cambridge, 2000. 725, 727
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Mishra, B. (2002). A Symbolic Approach to Modeling Cellular Behavior. In: Sahni, S., Prasanna, V.K., Shukla, U. (eds) High Performance Computing — HiPC 2002. HiPC 2002. Lecture Notes in Computer Science, vol 2552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36265-7_70
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DOI: https://doi.org/10.1007/3-540-36265-7_70
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