From processes to ODEs by chemistry

IFIP International Federation for Information Processing

Volumn 273, Issue , 2008, Pages 261-281

  Cardelli, Luca ^a  

^a MICROSOFT RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHEMICAL REACTIONS; COMPUTER SCIENCE; ORDINARY DIFFERENTIAL EQUATIONS; RANDOM PROCESSES;

COLLECTIVE BEHAVIOR; COMPOSITIONAL MAPPING; DIRECT MAPPING; IT SUPPORTS; PARAMETRIC FORMS; STEPPING STONE; STOCHASTIC PROCESS ALGEBRAS;

MAPPING;

EID: 48249136571     PISSN: 15715736     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-0-387-09680-3_18     Document Type: Conference Paper

References (30)

1. R. Blossey, L. Cardelli, A. Phillips: A Compositional Approach to the Stochastic Dynamics of Gene Networks. Transactions on Computational Systems Biology IV, LNCS 3939, 99-122. Springer 2006.
2. W.E. Boyce, R.C. DiPrima. Elementary Differential Equations and Boundary Value Problems, 5th ed. New York:WIley, p. 494, 1992.
3. M. Bernardo, L. Donatiello, R. Gorrieri. MPA: A Stochastic Process Algebra. Technical Report UBLCS-94-10, University of Bologna, Laboratory of Computer Science. 1994
4. P. Buchholz. Markovian Process Algebra: Composition and Equivalence. In Proc. PAPM '94, Erlangen (Germany), 11-30, 1994.
5. M. Calder, S. Gilmore, J. Hillston: Automatically Deriving ODEs from Process Algebra Models of Signalling Pathways. Proc. Computational Methods in Systems Biology 2005, pp 204-215.
6. L. Cardelli: On Process Rate Semantics. Theoretical Computer Science 391(3) 190-215, Elsevier, 2008. DOI: .
7. N. Chabrier, M. Chiaverini, V. Danos, F. Fages and V. Schchter. Modeling and querying biomolecular interaction networks. Theoretical Computer Science, 2004.
8. M. Dam: On the Decidability of Process Equivalences for the pi-Calculus. Theoretical Computer Science 183, 215-228, 1997.
9. A. Funahashi, N. Tanimura, M. Morohashi, H. Kitano. CellDesigner: A process diagram editor for gene-regulatory and biochemical networks, BIOSILICO, 1:159-162, 2003.
10. D.T. Gillespie. Exact Stochastic Simulation of Coupled Chemical Reactions. Journal of Physical Chemistry 81, 2340-2361. 1977.
11. D.T. Gillespie: The chemical Langevin equation. Journal of Chemical Physics 113(1), 297-306, 2000.
12. H. Hermanns: Interactive Markov Chains. Springer LNCS, vol 2428, 2002.
13. H. Hermanns, M. Rettelbach. Syntax, Semantics, Equivalences, and Axioms for MTIPP. Proc. of PAPM '94, Erlangen (Germany), pp 71-87. 1994.
14. N. Gtz, H. Hermanns, U. Herzog, V. Mertsiotakis, M. Rettelbach. Stochastic Process Algebras: Constructive Specification Techniques Integrating Functional, Performance and Dependability. In Baccelli and Mitrani (eds): Quantitative Modelling in Parallel Systems. Chapter 1, Springer 1995.
15. J. Hillston. A compositional approach to performancemodelling. Cambridge University Press, 1996.
16. J. Hillston: Fluid flow approximation of PEPA models. In Proceedings of the Second International Conference on the Quantitative Evaluation of Systems, 33-43. IEEE Press, 2005.
17. A. Hinton, M. Kwiatkowska, G. Norman, D. Parker. PRISM: A Tool for Automatic Verification of Probabilistic Systems. In H. Hermanns, J. Palsberg (Eds.): Proc. TACAS'06. Springer LNCS 3920, 441-444, 2006.
18. F. Horn, R. Jackson. General mass action kinetics. Arch. Rational Mech. Anal. 47, 81-116, 1972.
19. W.O. Kermack, A.G. McKendrick: A Contribution to the Mathematical Theory of Epidemics. Proc. Roy. Soc. Lond. A 115, 700-721, 1927.
20. H. Kitano: A graphical notation for biochemical networks. BioSilico 1(5): 169-76. 2003.
21. R. Milner: Communicating and Mobile Systems: The p-Calculus. Cambridge University Press, 1999.
22. R. Norman, C. Shankland. Developing the Use of Process Algebra in the Derivation and Analysis of Mathematical Models of Infectious Disease. Proc. Computer Aided Systems Theory - EUROCAST 2003. Springer LNCS 2809, 404-414, 2003.
23. A. Phillips, L. Cardelli: A Correct Abstract Machine for the Stochastic Picalculus. Proc. BioConcur'04.
24. C. Priami. Stochastic p-calculus. The Computer Journal, 38, 578-589, 1995.
25. C. Priami, A. Regev, E. Shapiro, W. Silverman: Application of a stochastic namepassing calculus to representation and simulation of molecular processes. Information Processing Letters 80, 25-31. 2001.
26. A. Regev. Computational systems biology: A calculus for biomolecular knowledge. Ph.D. Thesis, Tel Aviv University, 2002.
27. A. Regev, E. Shapiro. Cellular abstractions: Cells as computation. Nature 419 343. 2002.
28. The Mathworks: Matlab. http://www.mathworks.com.
29. J.M.G. Vilar, H.Y. Kueh, N. Barkai, S. Leibler: Mechanisms of noise-resistance in genetic oscillators. PNAS 99(9) 5988-5992. 2002.
30. O. Wolkenhauer, M. Ullah, W. Kolch, K. Cho. Modelling and simulation of intracellular dynamics: Choosing an appropriate framework. IEEE Transactions on NanoBioscience 3, 200-207. 2004.