References

  1. R. Alfieri, E. Bartocci, E. Merelli & L. Milanesi (2011): Modeling the cell cycle: From deterministic models to hybrid systems. Biosystems 105, pp. 34–40, doi:10.1016/j.biosystems.2011.03.002.
  2. V. Baldazzi, P. T. Monteiro, M. Page, D. Ropers, J. Geiselmann & H. Jong (2011): Qualitative Analysis of Genetic Regulatory Networks in Bacteria. Understanding the Dynamics of Biological Systems, pp. 111–130, doi:10.1007/978-1-4419-7964-3-6.
  3. G. Batt, H. De Jong, M. Page & J. Geiselmann (2008): Symbolic reachability analysis of genetic regulatory networks using discrete abstractions. Automatica 44(4), pp. 982–989, doi:10.1016/j.automatica.2007.08.004.
  4. K.W. Chu, Y. Deng & J. Reinitz (1999): Parallel Simulated Annealing by Mixing of States 1. Journal of Computational Physics 148(2), pp. 646–662, doi:10.1006/jcph.1998.6134.
  5. A. Csikász-Nagy, D. Battogtokh, K. C. Chen, B. Novák & J. J. Tyson (2006): Analysis of a generic model of eukaryotic cell-cycle regulation. Biophysical Journal 90(12), pp. 4361–4379, doi:10.1529/biophysj.106.081240.
  6. G. B. Dantzig, A. Orden & P. Wolfe (1955): The generalized simplex method for minimizing a linear form under linear inequality restraints. Pacific Journal of Mathematics 5(2), pp. 183–195, doi:10.2140/pjm.1955.5.183.
  7. M. Di Bernardo (2008): Piecewise-smooth dynamical systems: theory and applications. Springer Verlag, doi:10.1007/978-1-84628-708-4.
  8. S. Drulhe, G. Ferrari-Trecate & H. de Jong (2008): The switching threshold reconstruction problem for piecewise-affine models of genetic regulatory networks. IEEE Transactions on Automatic Control 53, pp. 153–165, doi:10.1109/TAC.2007.911326.
  9. A. N. Gorban & O. Radulescu (2008): Dynamic and static limitation in reaction networks, revisited. In: David West Guy B. Marin & Gregory S. Yablonsky: Advances in Chemical Engineering - Mathematics in Chemical Kinetics and Engineering, Advances in Chemical Engineering 34. Elsevier, pp. 103–173, doi:10.1016/S0065-2377(08)00003-3.
  10. Radu Grosu, S Mitra, Pei Ye, Emilia Entcheva, IV Ramakrishnan & Scott A Smolka (2007): Learning cycle-linear hybrid automata for excitable cells. In: Hybrid Systems: Computation and Control. Springer, pp. 245–258, doi:10.1007/978-3-540-71493-4_21.
  11. Jimmy Lam & Jean-Marc Delosme (1988): An efficient simulated annealing schedule: derivation. Yale University, New Haven, Connecticut, Technical Report 8816, doi:10.1.1.74.4461.
  12. P. Lincoln & A. Tiwari (2004): Symbolic systems biology: Hybrid modeling and analysis of biological networks. Hybrid Systems: Computation and Control, pp. 147–165, doi:10.1007/978-3-540-24743-2-44.
  13. B. Mishra (2009): Intelligently deciphering unintelligible designs: algorithmic algebraic model checking in systems biology. Journal of The Royal Society Interface 6(36), pp. 575–597, doi:10.1098/rsif.2008.0546.
  14. V. Noel, D. Grigoriev, S. Vakulenko & O. Radulescu: Tropicalization and tropical equilibrations of chemical reactions. Contemporary Mathematics, in press; arXiv : 1303.3963.
  15. V. Noel, D. Grigoriev, S. Vakulenko & O. Radulescu (2012): Tropical geometries and dynamics of biochemical networks. Application to hybrid cell cycle models. Electronic Notes in Theoretical Computer Science 284, pp. 75–91, doi:10.1016/j.entcs.2012.05.016.
  16. V. Noel, S. Vakulenko & O. Radulescu (2010): Piecewise smooth hybrid systems as models for networks in molecular biology. In: Proceedings of JOBIM 2010. Jobim, Montpellier.
  17. V. Noel, S. Vakulenko & O. Radulescu (2011): Algorithm for identification of piecewise smooth hybrid systems: application to eukaryotic cell cycle regulation. Lecture Notes in Computer Science 6833, pp. 225–236, doi:10.1007/978-3-642-23038-7-20.
  18. Vincent Noel, Dima Grigoriev, Sergei Vakulenko & Ovidiu Radulescu (2012): Hybrid models of the cell cycle molecular machinery. Electronic Proceedings in Theoretical Computer Science 92, pp. 88–105, doi:10.4204/EPTCS.92.7.
  19. R. Porreca, S. Drulhe, H. Jong & G. Ferrari-Trecate (2008): Structural identification of piecewise-linear models of genetic regulatory networks. Journal of Computational Biology 15(10), pp. 1365–1380, doi:10.1089/cmb.2008.0109.
  20. O. Radulescu, A. N. Gorban, A. Zinovyev & A. Lilienbaum (2008): Robust simplifications of multiscale biochemical networks. BMC systems biology 2(1), pp. 86, doi:10.1186/1752-0509-2-86.
  21. D. Ropers, V. Baldazzi & H. de Jong (2011): Model reduction using piecewise-linear approximations preserves dynamic properties of the carbon starvation response in Escherichia coli. IEEE/ACM Transactions on Computational Biology and Bioinformatics 8(1), pp. 166–181, doi:10.1109/TCBB.2009.49.
  22. Alexander Orden Savageau, M. A. anGeorge Bernard Dantzig & E. O. Philip Wolfed Voit (1987): Recasting nonlinear differential equations as S-systems: a canonical nonlinear form. Mathematical biosciences 87(1), pp. 83–115, doi:10.1016/0025-5564(87)90035-6.
  23. R. Singhania, R. M. Sramkoski, J. W. Jacobberger & J. J. Tyson (2011): A hybrid model of mammalian cell cycle regulation. PLoS computational biology 7(2), pp. e1001077, doi:10.1371/journal.pcbi.1001077.
  24. P. Ye, E. Entcheva, SA Smolka & R. Grosu (2008): Modelling excitable cells using cycle-linear hybrid automata. Systems Biology, IET 2(1), pp. 24–32, doi:10.1049/iet-syb:20070001.
Comments and questions to: eptcs@eptcs.org
For website issues: webmaster@eptcs.org