Efficient computation of transient solutions of the chemical master equation based on uniformization and quasi-Monte Carlo

Journal of Chemical Physics

Volumn 128, Issue 15, 2008, Pages

  Hellander, Andreas ^a  

^a UPPSALA UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

MONTE CARLO METHODS; POISSON DISTRIBUTION; PROBABILITY DENSITY FUNCTION; PROBLEM SOLVING;

BIOCHEMICAL REACTION NETWORKS; CHEMICAL MASTER EQUATION; TRANSIENT SOLUTIONS;

MARKOV PROCESSES;

ALGORITHM; ARTICLE; CHEMICAL MODEL; CHEMICAL STRUCTURE; COMPUTER SIMULATION; MONTE CARLO METHOD; STATISTICAL MODEL;

ALGORITHMS; COMPUTER SIMULATION; MODELS, CHEMICAL; MODELS, MOLECULAR; MODELS, STATISTICAL; MONTE CARLO METHOD;

EID: 42449098178     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2897976     Document Type: Article

References (37)

1. M. Thattai and A. van Oudenaarden, Proc. Natl. Acad. Sci. U.S.A. 98, 8614 (2001).
2. S. Engblom, Division of Scientific Computing, Department of Information Technology, Uppsala University, Technical Report No. 36, 2006 http://www.it.uu.se/research/publications/reports/2006-036/.
3. M. Hegland, C. Burden, L. Santoso, S. MacNamara, and H. Booth, J. Comput. Appl. Math. 205, 708 (2005).
4. B. Munsky and M. Khammash, J. Chem. Phys. 124, 044104 (2006).
5. P. Sjöberg, P. Lötstedt, and J. Elf, Comput. Visualization Sci. (in press).
6. J. Zhang, L. T. Watson, and Y. Cao, Department of Computer Science, Virginia Tech, Technical Report No. TR-07-31, 2008 (http://eprints.cs.vt.edu/ archive/00000992/01/IETSB07.pdf).
7. D. T. Gillespie, J. Comput. Phys. 22, 403 (1976).
8. Y. Cao, D. Gillespie, and L. Petzold, J. Comput. Phys. 206, 395 (2005).
9. Y. Cao, D. T. Gillespie, and L. R. Petzold, J. Chem. Phys. 122, 014116 (2005).
10. W. E. D. Liu and E. Vanden-Eijnden, J. Chem. Phys. 123, 194107 (2005).
11. D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001).
12. E. L. Haseltine and J. B. Rawlings, J. Chem. Phys. 117, 6959 (2002).
13. A. Hellander and P. Lötstedt, J. Comput. Phys. 227, 127 (2008).
14. H. Salis and Y. Kaznessis, J. Chem. Phys. 122, 054103 (2005).
15. A. Lipshtat, J. Chem. Phys. 126, 184103 (2007).
16. R. E. Haddad, C. Ĺcot, and P. L'Ecuyer, in Monte Carlo and Quasi Monte Carlo Methods 2006, edited by, A. Keller, S. Heinrich, and, H. Neiderriter, (Springer, Berlin, 2008), pp. 413-429.
17. C. Ĺcot and B. Tuffin, in Monte Carlo and Quasi Monte Carlo Methods 2002, edited by, H. Neiderriter, (Springer-Verlag, Berlin, 2002).
18. C. Ĺcot and B. Tuffin, Monte Carlo Meth. Appl. 10, 337 (2004).
19. P. L'Ecuyer, C. Ĺcot, and B. Tuffin, Monte Carlo and Quasi-Monte Carlo Methods 2004 (Springer, Berlin, Heidelberg, 2007), pp. 331-342, edited by, H. Neiderriter, and, D. Talay,.
20. D. M. Nicol and P. Heidelberger, ACM SIGSIM Simulation Digest 23, 11 (1993).
21. S. Streltsov and P. Vakili, Proceedings of the 1992 Winter Simulation Conference, 1993 (unpublished), pp. 430-436.
22. S. Streltsov and P. Vakili, Discrete Event Dyn. Syst. 6, 159 (1996).
23. A. P. van Moorsel and W. H. Sanders, IEEE Trans. Reliab. 46, 430 (1997).
24. M. A. Gibson and J. Bruck, J. Phys. Chem. 104, 1876 (2000).
25. Y. Cao, H. Li, and L. Petzold, J. Chem. Phys. 121, 4059 (2004).
26. J. M. McCollum, G. D. Peterson, C. D. Cox, M. L. Simpson, and N. F. Samtova, Comput. Biol. Chem. 30, 39 (2005).
27. H. Li and L. Petzold, Department of Computer Science, University of California, Santa Barbara, 2006, http://www.engineering.ucsb.edu/cse/Files/ ldm0513.pdf (unpublished).
28. A. Jensen, Skand. Aktuarietidskr. 36, 87 (1953).
29. N. M. V. Dijk, Adv. Appl. Probab. 22, 749 (1990).
30. B. L. Fox and P. W. Glynn, Commun. ACM 31, 440 (1988).
31. R. E. Caflisch, Acta Numerica 7, 1 (1998).
32. C. Lemiuex and P. L'Ecuyer, in Lecture Notes in Computer Science (Springer, New York, 2001), 2073.
33. T. A. Standish, Data Structures in Java (Addison-Wesley, Reading, MA, 1998).
34. H. S. Hong and F. J. Hickernell, ACM Trans. Math. Softw. 29, 95 (2003).
35. B. N. Kholodenko, Eur. J. Biochem. 267, 1583 (2000).
36. B. Bromley, J. Parallel Distrib. Comput. 38, 101 (1995).
37. A. P. van Moorsel and W. H. Sanders, ORSA Commun. Stat. Stoch. Models 10, 619 (1994).