Bio-PEPAd: A non-Markovian extension of Bio-PEPA

Theoretical Computer Science

Volumn 419, Issue , 2012, Pages 26-49

  Caravagna, Giulio ^a   Hillston, Jane ^b  

^a UNIVERSITY OF PISA   (Italy)

^b UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

Bio PEPA; DDEs; Delay as duration; DSSA; GSMPs; Non Markovian process algebra

Indexed keywords

BIO-PEPA; DDES; DELAY-AS-DURATION; DSSA; GSMPS; NON-MARKOVIAN PROCESS;

ALGEBRA; DIFFERENTIAL EQUATIONS; MARKOV PROCESSES; SEMANTICS; STOCHASTIC MODELS; STOCHASTIC SYSTEMS;

BIOLOGICAL SYSTEMS;

EID: 84855967684     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2011.11.028     Document Type: Article

References (43)

1. R. Barbuti, G. Caravagna, A. Maggiolo-Schettini, and P. Milazzo On the interpretation of delays in delay stochastic simulation of biological systems R. Back, I. Petre, E.P. de Vink, Proceedings of the 2nd Int. Workshop on Computational Models for Cell Processes, CompMod'09 EPTCS vol. 6 2009 17 29
2. R. Barbuti, G. Caravagna, A. Maggiolo-Schettini, and P. Milazzo Delay stochastic simulation of biological systems: a purely delayed approach Trans. Comp. Sys. Bio. XIII 6575 2011 61 84
3. R. Barbuti, G. Caravagna, A. Maggiolo-Schettini, P. Milazzo, and G. Pardini The Calculus of Looping Sequences M. Bernardo, P. Degano, G. Zavattaro, Formal Methods for Computational Systems Biology, SFM 2008 LNCS vol. 5016 2008 387 423
4. R. Barbuti, A. Maggiolo-Schettini, P. Milazzo, and G. Pardini Spatial calculus of looping sequences Int. Workshop From Biology to Concurrency and Back, FBTC'08 ENTCS 229 1 2008 21 39
5. M. Barrio, K. Burrage, A. Leier, and T. Tian Oscillatory regulation of Hes1: discrete stochastic delay modelling and simulation PLoS Comp. Bio. 2 9 2006
6. E. Beretta, T. Hara, W. Ma, and Y. Takeuchi Permanence of an SIR epidemic model with distributed time delays Tohoku Math. J. 54 2 2002 581 591 (Pubitemid 36177504)
7. Bio-PEPA web site http://biopepa.org/.
8. D. Bratsun, D. Volfson, L.S. Tsimring, and J. Hasty Delay-induced stochastic oscillations in gene regulation PNAS 102 41 2005 14593 14598 (Pubitemid 41457102)
9. M. Bravetti, Specification and analysis of stochastic real-time systems, Ph.D. Thesis, Universit di Bologna, 2002.
10. M. Bravetti, and R. Gorrieri The theory of interactive generalized semi-Markov processes Theoret. Comput. Sci. 282 1 2002 5 32 (Pubitemid 34715709)
11. M. Bravetti, M. Bernardo, and R. Gorrieri Towards performance evaluation with general distributions in process algebras Proc. of CONCUR'98 LNCS vol. 1466 1998 405 422 (Pubitemid 128125371)
12. G. Caravagna, Formal modeling and simulation of biological systems with delays, Ph.D. Thesis, Universit di Pisa, 2011.
13. G. Caravagna, and J. Hillston Modeling biological systems with delays in Bio-PEPA Proc. of the 4-th Workshop on Membrane Computing and Biologically Inspired Process Calculi, MeCBIC 2010 EPTCS vol. 40 2010 85 101
14. F. Ciocchetta, and J. Hillston Bio-PEPA: a framework for the modelling and analysis of biochemical networks Theoret. Comput. Sci. 410 3334 2009 3065 3084
15. F. Ciocchetta, and J. Hillston Calculi for biological systems M. Bernardo, P. Degano, G. Zavattaro, Formal Methods for Computational Systems Biology, SFM 2008 LNCS vol. 5016 2008 265 312
16. D.R. Cox The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables Proc. Cambridge Phil. Soc. 51 1955 433 440
17. R.V. Culshaw, and S. Ruan A Delay-differential equation model of HIV infection of CD4+ T-cells Math. Biosci. 165 2000 27 39 (Pubitemid 30305420)
18. P.R. D'Argenio, and J.-P. Katoen A theory of stochastic systems, part II: process algebra Inf. and Comp. 203 1 2005 39 74 (Pubitemid 41562144)
19. P.R. D'Argenio, J.-P. Katoen, E. Brinksma, A stochastic automata model and its algebraic approach, in: Proc. 5th Int. Workshop on Process Algebra and Performance Modeling, PAPM'97, CTIT technical reports series 9714, University of Twente, 1997, pp. 116.
20. V. Danos, J. Feret, W. Fontana, R. Harmer, and J. Krivine Rule-based modelling of cellular signalling Proc. of CONCUR'07 LNCS vol. 4703 2007 17 41
21. L. Dematt, C. Priami, and A. Romanel Modelling and simulation of biological processes in BlenX SIGMETRICS Perform. Eval. Rev. 35 4 2008 32 39
22. V. Galpin, and J. Hillston A semantic equivalence for Bio-PEPA based on discretisation of continuous values Theoret. Comput. Sci. 412 21 2011 2142 2161
23. R. German Performance Analysis of Communication Systems with NonMarkovian Stochastic Petri Nets 2000 John Wiley & Sons, Inc.
24. D. Gillespie Exact stochastic simulation of coupled chemical reactions J. Phys. Chem. 81 1977 2340
25. R.J. van Glabbeek, and F.W. Vaandrager Petri net models for algebraic theories of concurrency LNCS 259 1987 224 242
26. P.W. Glynn, On the role of generalized semi-markov processes in simulation output analysis, in: Proc. of the 15th Conference on Winter Simulation, Volume 1, 1983, pp. 3944.
27. J. Hillston A Compositional Approach to Performance Modelling 1996 Cambridge University Press
28. J. Heath, M. Kwiatkowska, G. Norman, D. Parker, and O. Tymchyshyn Probabilistic model checking of complex biological pathways Theoret. Comput. Sci. 391 2008 239 257
29. N. Lopez, and M. Nunez NMSPA: a non-Markovian model for stochastic processes T.-H. Lai, Proc. of ICDS 2000 2000 IEEE 33 40
30. J. Markovski, Real and stochastic time in process algebras for performance evaluation, Ph.D. Thesis, University of Eindhoven, 2008.
31. P. Milazzo, Qualitative and quantitative formal modeling of biological systems, Ph.D. Thesis, Universit di Pisa, 2007.
32. R. Milner, M. Toft, and R. Harper The Definition of Standard ML 1990 MIT Press
33. I. Mura, D. Prandi, C. Priami, and A. Romanel Exploiting non-Markovian bio-processes ENTCS 253 3 2009 83 98
34. L. Paulev, S. Youssef, M.R. Lakin, A. Phillips, A generic abstract machine for stochastic process calculi, in: Proceedings of the 8th International Conference on Computational Methods in Systems Biology CMSB vol. 10, 2010, pp. 4354.
35. M. Pedersen, and G. Plotkin A language for biochemical systems: design and formal specification Trans. Comp. Sys. Bio. XII 5945 3 2010 77 145
36. G. Plotkin The origins of structural operational semantics J. Log. Alg. Progr. 6061 2004 3 15
37. C. Priami Stochastic π-calculus The Comp. J. 38 7 1995 578 589
38. C. Priami, A. Regev, E. Shapiro, and W. Silverman Application of a stochastic name-passing calculus to representation and simulation of molecular processes Inform. Process. Lett. 80 2001 25 31 (Pubitemid 32833107)
39. A. Regev, E.M. Panina, W. Silverman, L. Cardelli, and E.Y. Shapiro Bioambients: an abstraction for biological compartments Theoret. Comput. Sci. 325 1 2004 141 167
40. A. Regev, W. Silverman, and E. Shapiro Representation and simulation of biochemical processes using the pi-calculus process algebra Pacific Symposium on Biocomputing, vol. 6 2001 World Scientic Press 459 470
41. Prism web site http://www.prismmodelchecker.org/.
42. M. Villasana, and A. Radunskaya A delay differential equation model for tumor growth J. Math. Biol. 47 2003 270 294 (Pubitemid 38272158)
43. F. Zhanga, Z. Lia, and F. Zhangc Global stability of an SIR epidemic model with constant infectious period Appl. Math. Comp. 199 1 2008 285 291