Hybrid dynamics of stochastic programs

Theoretical Computer Science

Volumn 411, Issue 20, 2010, Pages 2052-2077

  Bortolussi, Luca ^a   Policriti, Alberto ^b,c  

^a UNIVERSITY OF TRIESTE   (Italy)

^b UNIVERSITY OF UDINE   (Italy)

^c Institute of Applied Genomics   (Italy)

Author keywords

Discreteness; Dynamical systems; Hybrid automata; Robustness; Stochastic concurrent constraint programming

Indexed keywords

APPROXIMATION TECHNIQUES; CIRCADIAN CLOCK; CONCURRENT CONSTRAINT PROGRAMMING; CONTINUOUS TIME MARKOV CHAIN; DYNAMICAL EVOLUTION; HYBRID AUTOMATA; HYBRID AUTOMATONS; HYBRID DYNAMICS; REPRESSILATOR; SEMANTIC MODEL; STOCHASTIC PROCESS ALGEBRAS; STOCHASTIC SEMANTICS;

COMPUTER PROGRAMMING; CONSTRAINT THEORY; DYNAMICAL SYSTEMS; MARKOV PROCESSES; ORDINARY DIFFERENTIAL EQUATIONS; ROBOTS; SEMANTICS; STOCHASTIC SYSTEMS; TRANSLATION (LANGUAGES);

AUTOMATA THEORY;

EID: 77950459132     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2010.02.008     Document Type: Article

References (51)

1. R. Alur, C. Belta, F. Ivancic, V. Kumar, M. Mintz, G. Pappas, H. Rubin, J. Schug, Hybrid modeling and simulation of biomolecular networks, in: Proceedings of Fourth International Workshop on Hybrid Systems: Computation and Control, in: LNCS, vol. 2034, 2001, pp. 19-32.
2. Alfonsi A., Cances E., Turinici G., Di Ventura B., and Huisinga W. Adaptive simulation of hybrid stochastic and deterministic models for biochemical systems. Proceedings of ESAIM vol. 14 (2005) 1-13
3. Antoniotti M., Policriti A., Ugel N., and Mishra B. Model building and model checking for biochemical processes. Cell Biochemistry and Biophysics 38 3 (2003) 271-286
4. A. Aziz, V. Singhal, F. Balarin, R. Brayton, A. Sangiovanni-Vincentelli, Verifying continuous time markov chains. in: Proceedings of CAV96, 1996.
5. Blossey R., Cardelli L., and Phillips A. Compositionality, stochasticity and cooperativity in dynamic models of gene regulation. HFPS Journal 2 1 (2008) 17-28
6. L. Bortolussi, S. Fonda, A. Policriti, Constraint-based simulation of biological systems described by molecular interaction maps, in: Proceedings of IEEE conference on Bioinformatics and Biomedicine, BIBM 2007, 2007.
7. M.L. Bujorianu, J. Lygeros, General stochastic hybrid systems: Modeling and optimal control. In Proceedings of 43rd IEEE Conference on Decision and Control, CDC 2004, 2004, pp. 182-187.
8. M.L. Bujorianu, J. Lygeros, Theoretical foundations of stochastic hybrid systems, in: Proceedings XVI Int. Symp. on Math. Theory of Networks and Systems, MTNS 2004, 2004.
9. L. Bortolussi, Stochastic concurrent constraint programming, in: Proceedings of 4th International Workshop on Quantitative Aspects of Programming Languages, QAPL 2006, in: ENTCS, vol. 164, 2006, pp. 65-80.
10. L. Bortolussi, A master equation approach to differential approximations of stochastic concurrent constraint programming, in: Proceedings of the Sixth Workshop on Quantitative Aspects of Programming Languages, QAPL 2008, in: ENTCS, vol. 220, 2008, pp. 163-180.
11. L. Bortolussi, A. Policriti, Stochastic concurrent constraint programming and differential equations, in: Proceedings of Fifth Workshop on Quantitative Aspects of Programming Languages, QAPL 2007, in: ENTCS, vol. 167, 2007.
12. Bortolussi L., and Policriti A. Hybrid systems and biology: Continuous and discrete modeling for systems biology. Formal Methods for Computational Systems Biology. LNCS vol. 5016 (2008), Springer-Verlag 424-448 Chapter
13. L. Bortolussi, A. Policriti, Hybrid approximation of stochastic concurrent constraint programming, in: Proceeding of IFAC 2008, 2008.
14. L. Bortolussi, A. Policriti, The importance of being (a little bit) discrete, in: Proceedings of FBTC'08, 2008.
15. Bortolussi L., and Policriti A. Modeling biological systems in concurrent constraint programming. Constraints 13 1 (2008)
16. Bortolussi L., and Policriti A. Hybrid dynamics of stochastic π-calculus. Mathematics in Computer Science 2 3 (2009) 465-491
17. L. Bortolussi, A. Policriti, Hybrid semantics of stochastic programs with dynamic reconfiguration, in: Proceedings of CompMod, 2009.
18. L. Bortolussi, A. Policriti, Stochastic programs and hybrid automata for (biological) modeling, in: Proceedings of CiE 2009, 2009.
19. Batt G., Yordanov B., Belta C., and Weiss R. Robustness analysis and tuning of synthetic gene networks. Bioinformatics 23 18 (2007) 2415-2422
20. Calzone L., Fages F., and Soliman S. Biocham: An environment for modeling biological systems and formalizing experimental knowledge. Bioinformatics 22 (2006) 1805-1807
21. Seattle CompBio Group, Institute for Systems Biology. Dizzy home page.
22. Calder M., Gilmore S., and Hillston J. Modelling the influence of rkip on the erk signalling pathway using the stochastic process algebra PEPA. Transactions on Computational Systems Biology 4230 (2006) 1-23
23. Davis M.H.A. Markov Models and Optimization (1993), Chapman & Hall
24. Elowitz M.B., and Leibler S. A synthetic oscillatory network of transcriptional regulators. Nature 403 (2000) 335-338
25. Gibson M., and Bruck J. Efficient exact simulation of chemical systems with many species and many channels. Journal Physical Chemistry 104 9 (2000) 1876-1889
26. Gonze D., Halloy J., and Gaspard P. Biochemical clocks and molecular noise: Theoretical study of robustness factors. Journal of Chemical Physics 116 12 (2002) 10997-11010
27. Geisweiller N., Hillston J., and Stenico M. Relating continuous and discrete pepa models of signalling pathways. Theoretical Computer Science 404 1-2 (2008) 97-111
28. Gillespie D.T. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. Journal of Computational Physics 22 (1976)
29. Gillespie D.T. Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry 81 25 (1977)
30. Gillespie D. The chemical langevin equation. Journal of Chemical Physics 113 1 (2000) 297-306
31. Goldbeter A. Computational approaches to cellular rhythms. Nature 420 (2002) 238-245
32. Ghosh R., and Tomlin C. Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modelling: Delta-notch protein signalling. IEEE Systems Biology 1 1 (2004) 170-183
33. T. A. Henzinger, The theory of hybrid automata, in: LICS'96: Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science, 1996.
34. Henzinger T.A., Ho P.H., and Wong-Toi H. Hytech: A model checker for hybrid systems. Software Tools for Technology Transfer 1 (1997) 110-122
35. J. Hillston, Fluid flow approximation of PEPA models, in: Proceedings of the Second International Conference on the Quantitative Evaluation of Systems, QEST05, 2005.
36. Haseltine E.L., and Rawlings J.B. Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics. Journal of Chemical Physics 117 15 (2002)
37. Kurtz T., and Ethier S. Markov Processes - Characterisation and Convergence (1986), Wiley
38. Kitano H. Computational systems biology. Nature 420 (2002) 206-210
39. Kwiatkowska M., Norman G., and Parker D. Probabilistic symbolic model checking with prism: A hybrid approach. International Journal on Software Tools for Technology Transfer 6 2 (2004) 128-142
40. Kurtz T.G. Solutions of ordinary differential equations as limits of pure jump markov processes. Journal of Applied Probability 7 (1970) 49-58
41. McAdams H.H., and Arkin A. Stochastic mechanisms in gene expression. Proceedings of the National Academy of Sciences 94 (1997) 814-819
42. Prism home page. http://www.cs.bham.ac.uk/~dxp/prism/.
43. Müller S., Hofbauer J., Endler L., Flamm C., Widder S., and Schuster P. A generalized model of the repressilator. Journal of Mathematical Biology 53 (2006) 905-937
44. N.A. Neogi, Dynamic partitioning of large discrete event biological systems for hybrid simulation and analysis, in: Proceedings of 7th International Workshop on Hybrid Systems: Computation and Control, HSCC 2004, in: LNCS, vol. 2993, 2004, pp. 463-476.
45. Norris J.R. Markov Chains (1997), Cambridge University Press
46. Pahle J. Biochemical simulations: Stochastic, approximate stochastic and hybrid approaches. Brief Bioinformatics 10 1 (2009) 53-64
47. Priami C., Regev A., Shapiro E.Y., and Silverman W. Application of a stochastic name-passing calculus to representation and simulation of molecular processes. Information Processing Letters 80 1 (2001) 25-31
48. Ross S.M. Stochastic Processes (1996), Wiley, New York
49. Saraswat V.A. Concurrent Constraint Programming (1993), MIT press
50. Vilar J.M.G., Yuan~Kueh H., Barkai N., and Leibler S. Mechanisms of noise resistance in genetic oscillators. Proceedings of the National Academy of Sciences 99 9 (2002) 5991
51. Wilkinson D.J. Stochastic Modelling for Systems Biology (2006), Chapman & Hall