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All issues Volume 10 / No 3 (2015) Math. Model. Nat. Phenom., 10 3 (2015) 124-138 References
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Issue
Math. Model. Nat. Phenom.
Volume 10, Number 3, 2015
Model Reduction
Page(s) 124 - 138
DOI https://doi.org/10.1051/mmnp/201510310
Published online 22 June 2015
  1. T. Bogart, A.N. Jensen, D. Speyer, B. Sturmfels, R.R. Thomas. Computing tropical varieties. Journal of Symbolic Computation, 42 (1) (2007), 54–73. [CrossRef] [MathSciNet] [Google Scholar]
  2. B.L. Clarke. General method for simplifying chemical networks while preserving overall stoichiometry in reduced mechanisms. J. Phys. Chem., 97 (1992), 4066–4071. [CrossRef] [Google Scholar]
  3. E.M. Clarke, R. Enders, T. Filkorn, S. Jha. Exploiting symmetry in temporal logic model checking. Formal Methods in System Design, 9 (1-2) (1996), 77–104. [CrossRef] [Google Scholar]
  4. M. Einsiedler, M. Kapranov, D. Lind. Non-archimedean amoebas and tropical varieties. Journal für die reine und angewandte Mathematik (Crelles Journal), (601) (2006), 139–157. [Google Scholar]
  5. D. Eisenbud. Commutative Algebra with a View Toward Algebraic Geometry. Springer-Verlag, 1995. [Google Scholar]
  6. J. Feret, V. Danos, J. Krivine, R. Harmer, W. Fontana. Internal coarse-graining of molecular systems. Proceedings of the National Academy of Sciences, 106 (16) (2009), 6453–6458. [CrossRef] [Google Scholar]
  7. A.N. Gorban, I.V. Karlin. Invariant manifolds for physical and chemical kinetics, Lect. Notes Phys. 660. Springer, Berlin Heidelberg, 2005. [Google Scholar]
  8. A.N. Gorban, O. Radulescu. Dynamic and static limitation in reaction networks, revisited. In: D.W. Guy, B. Marin, G.S. Yablonsky, editors. Advances in Chemical Engineering – Mathematics in Chemical Kinetics and Engineering. vol. 34 of Advances in Chemical Engineering. Elsevier, 2008, 103–173. [Google Scholar]
  9. A.N. Gorban, O. Radulescu, A. Zinovyev. Asymptotology of chemical reaction networks. Chemical Engineering Science, 65 (7) (2010), 2310–2324. [CrossRef] [Google Scholar]
  10. D. Grigoriev, A. Weber. Complexity of solving systems with few independent monomials and applications to mass-action kinetics. In: V. P. Gerdt, W. Koepf, E.W. Mayr, E.V. Vorozhtsov, editors. Computer Algebra in Scientific Computing, vol. 7442 of Lecture Notes in Computer Science. Springer, Berlin Heidelberg, 2012, 143–154. [Google Scholar]
  11. A. Katok, B. Hasselblatt. Introduction to the Modern Theory of Dynamical Systems. Cambridge University Press, 1996. [Google Scholar]
  12. E.L. King, C.A. Altman. A schematic method of deriving the rate laws for enzyme-catalyzed reactions. J. Phys. Chem., 60 (1956), 1375–1378. [CrossRef] [Google Scholar]
  13. S.H. Lam, D.A. Goussis. The CSP method for simplifying kinetics. International Journal of Chemical Kinetics, 26 (4) (1994), 461–486. [Google Scholar]
  14. U. Maas, S.B. Pope. Simplifying chemical kinetics: intrinsic low-dimensional manifolds in composition space. Combustion and Flame, 88 (3) (1992), 239–264. [Google Scholar]
  15. D. Maclagan, B. Sturmfels. Introduction to tropical geometry. Graduate Studies in Mathematics, vol. 161, 2009. [Google Scholar]
  16. M.P. Millán, A. Dickenstein, A. Shiu, C. Conradi. Chemical reaction systems with toric steady states. Bulletin of mathematical biology, 74 (5) (2012), 1027–1065. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  17. V. Noel, D. Grigoriev, S. Vakulenko, O. Radulescu. Tropical geometries and dynamics of biochemical networks application to hybrid cell cycle models. In: Jérôme Feret and Andre Levchenko, editors, Proceedings of the 2nd International Workshop on Static Analysis and Systems Biology (SASB 2011), vol. 284 of Electronic Notes in Theoretical Computer Science. Elsevier, 2012, 75–91. [Google Scholar]
  18. V. Noel, D. Grigoriev, S. Vakulenko, O. Radulescu. Tropicalization and tropical equilibration of chemical reactions. In: G. Litvinov and S. Sergeev, editors, Tropical and Idempotent Mathematics and Applications, vol. 616 of Contemporary Mathematics. American Mathematical Soc., 2014, 261–277. [Google Scholar]
  19. O. Radulescu, A.N. Gorban, A. Zinovyev, A. Lilienbaum. Robust simplifications of multiscale biochemical networks. BMC systems biology, 2(1) (2008), 86. [CrossRef] [PubMed] [Google Scholar]
  20. O. Radulescu, A.N. Gorban, A. Zinovyev, V. Noel. Reduction of dynamical biochemical reactions networks in computational biology. Frontiers in Genetics, 3 (2012), 131. [CrossRef] [PubMed] [Google Scholar]
  21. S. Rao, A. van der Schaft, B. Jayawardhana. A graph-theoretical approach for the analysis and model reduction of complex-balanced chemical reaction networks. Journal of Mathematical Chemistry, 51 (9) (2013), 2401–2422. [CrossRef] [Google Scholar]
  22. C. Robinson. Dynamical systems: stability, symbolic dynamics and chaos. CRC Press, 1999. [Google Scholar]
  23. S.S. Samal, O. Radulescu, D. Grigoriev, H. Fröhlich, A. Weber. A Tropical Method based on Newton Polygon Approach for Algebraic Analysis of Biochemical Reaction Networks. In: Proceedings of the 9th European Conference on Mathematical and Theoretical Biology, 2014. [Google Scholar]
  24. M.A. Savageau, E.O. Voit. Recasting nonlinear differential equations as S-systems: a canonical nonlinear form. Mathematical biosciences, 87 (1) (1987), 83–115. [CrossRef] [Google Scholar]
  25. S. Soliman. Invariants and other structural properties of biochemical models as a constraint satisfaction problem. Algorithms for Molecular Biology, 7 (1) (2012), 15. [CrossRef] [Google Scholar]
  26. S. Soliman, F. Fages, O. Radulescu. A constraint solving approach to model reduction by tropical equilibration. Algorithms for Molecular Biology, 9 (1) (2014), 24. [CrossRef] [Google Scholar]
  27. D. Speyer, B. Sturmfels. The tropical grassmannian. Advances in Geometry, 4 (3) (2004), 389–411. [CrossRef] [MathSciNet] [Google Scholar]
  28. M.I. Temkin. Graphical method for the derivation of the rate laws of complex reactions. Dokl. Akad. Nauk SSSR, 165 (1965), 615–618. [Google Scholar]

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