Stochastic process semantics for dynamical grammars

Annals of Mathematics and Artificial Intelligence

Volumn 47, Issue 3-4, 2006, Pages 329-395

  Mjolsness, Eric ^a   Yosiphon, Guy ^a  

^a Ringgold Standard Institution Informatics   (United States)

Author keywords

Dynamical systems; Machine learning; Multiscale modeling; Operator algebra; Probabilistic inference; Stochastic processes

Indexed keywords

EID: 33847413751     PISSN: 10122443     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10472-006-9034-1     Document Type: Conference Paper

References (52)

1. Mjolsness, E.: Stochastic process semantics for dynamical grammar syntax: an overview. In: Ninth International Symposium on Artificial Intelligence and Mathematics, Fort Lauderdale, Florida, 4-6 January 2006
2. Preston, C.J.: Spatial birth-and-death processes. Bull. Int. Statist. Inst. 46(2), 371-391 (1977)
3. Lange, K.: Applied Probability. Section 9.6. Springer, Berlin Heidelberg New York (2004)
4. Snyder, D.L., Miller, M.I.: Random Point Processes in Time and Space. Wiley, New York (1991)
5. Athreyea, K.B., Ney, P.E.: Branching Processes. Dover, New York (1972)
6. Engel, K., Nagel, R.: One-parameter Semigroups for Linear Evolution Equations. Springer Graduate Texts in Mathematics 194, New York (2000)
7. Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Francisco (1988)
8. Nodelman, U., Shelton, C., Koller, D.: Continuous time Bayesian networks. In: Proceedings of the Eighteenth Conference on Uncertainty in Artificial Intelligence (UAI), pp. 378-387. Morgan Kaufmann, San Francisco (2002)
9. Dean, T., Kanazawa, K.: A model for reasoning about persistence and causation. Comput. Intell. 5, 142-150 (1989)
10. Sanghai, S., Domingos, P., Weld, D.: Relational dynamic Bayesian networks. J. Artif. Intell. Res. 24, 759-797 (2005)
11. Milch, B., Marthi, B., Russell, S., Sontag, D.: BLOG: probabilistic models with unknown objects. In: Proceedings of the 19th International Joint Conference on Artificial Intelligence, pp. 1352-1359 (2005)
12. St-Aubin, R., Friedman, J., Mackworth, A.K.: A formal mathematical framework for modeling probabilistic hybrid systems. In: Ninth International Symposium on Artificial Intelligence and Mathematics, Fort Lauderdale, Florida, 4-6 January 2006
13. Prusinkiewicz, P., Lindenmeyer, A.: The Algorithmic Beauty of Plants. Springer, Berlin Heidelberg New York (1990)
14. Giavitto, J., Michel, O.: MGS: a programming language for the transformations of topological collections. LaMI - Universite d' Evry Val d'Essonne. Technical Report 61-2001. Cited in May 2001
15. Prusinkiewicz, P., Hammel, M.S., Mjolsness, E.: Animation of plant development. Comput. Graph. SIGGRAPH '93, 351-360 (1993)
16. Mjolsness, E., Sharp, D.H., Reinitz, J.: A Connectionist Model of Development. J. Theor. Biol. 152(4), 429-454 (1991)
17. Phillips, A., Cardelli, L.: A Correct Abstract Machine for the Stochastic Pi-calculus, http://lucacardelli.name/Bibliography.htm Cited Sep 2006 (2006)
18. Petri, C.A.: Kommunikation mit Automaten. Dissertation, University of Bonn (1962)
19. Jensen, K.: Coloured Petri Nets I, II, III. Springer, Berlin Heidelberg New York (1997)
20. Genrich, H.: Predicate/Transition nets. Advances in Petri nets : APN 1, 208-247. (1986)
21. Haas, P.J.: Stochastic Petri Nets. Springer, Berlin Heidelberg New York (2006)
22. van Kampen, N.G.: Stochastic Processes in Physics and Chemistry. North-Holland, Amsterdam, The Netherlands (1981)
23. Reed, M., Simon, B.: Methods of Modern Mathematical Physics: Functional Analysis I. Academic, New York (1972)
24. Mattis, D.C., Glasser, M.L.: The uses of quantum field theory in diffusion-limited reactions. Rev. Mod. Phys. 70, 979-1001 (1998)
25. McLachlan, R.I., Quispel, G.R.: Splitting methods. Acta Numer. 11, 341-434 (2002)
26. Hatano, N., Suzuki, M.: Finding Exponential Product Formulas of Higher Orders. http://arxiv.org/pdf/math-ph/0506007. Cited in 2 Jun 2005 (2005)
27. Hall, B.C.: Lie Groups, Lie Algebras, and Representations: An Elementary Introduction, pp. 63-76. Springer, Berlin Heidelberg New York (2003)
28. Müser, M.H.: The path-integral Monte Carlo approach of rigid linear molecules in three dimensions. Mol. Simul. 17(131) (1996)
29. Dyson, F.: Phys. Rev. 75, 486 (1949)
30. Risken, H.: The Fokker-Planck Equation. Springer, Berlin Heidelberg New York (1984)
31. Gillespie, D.J.: A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 2, 403-434 (1976)
32. Shachter, R.: Evaluating influence diagrams. Oper. Res. 33, 871-882 (1986)
33. Kanazawa, Koller, D., Russell, S.: Stochastic simulation algorithms for dynamic probabilistic networks. In: Proceedings of Uncertainty in Artificial Intelligence 95. http://citeseer.ist.psu.edu/kanazawa95stochastic.html (1995)
34. Mjolsness, E.: Variable-Structure Systems from Graphs and Grammars. UC Irvine School of Information and Computer Sciences, Irvine. U CI ICS TR# 05-09, http://computableplant.ics.uci.edu/papers/ vbl-Struct_GG_TR.pdf (2005)
35. Ghahramani, Z.: Non-parametric Bayesian methods. In: The 21st Conference on Uncertainty in Artificial Intelligence (UAI2005), University of Edinburgh, Edinburgh, Scotland, July 26th-July 29th 2005. http://www.gatsby.ucl.ac.uk/ ~zoubin/talks/uai05tutorial-b.pdf. Cited in Sep 06 (2006)
36. Geman, S., Geman, D.: Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6, 721-741 (1984)
37. MacQueen, J.B.: Some methods for classification and analysis of multivariate observations. In: Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability (1967)
38. Dempster, A., Laird, N., Rubin, D.: Maximum likelihood from incomplete data via the EM algorithm. J.R. Stat. Soc. Series B, 1-38 (1977)
39. Hart, C., et al.: A mathematical and computational framework for quantitative comparison and integration of large-scale gene expression data. Nucleic Acids Res. 33, 2580-2594 (2005)
40. Jönsson, H., et al.: An auxin-driven polarized transport model for phyllotaxis. Proc. Natl. Acad. Sciences USA, 103(5), 1633-1638. Retrieved 13 January 2006 from http://www.pnas.org/cgi/content/abstract/103/5/1633(2006)
41. Federl, P., Prusinkiewicz, P.: Solving differential equations in developmental models of multicellular structures expressed using L-systems. In: Bubak, M., van Albada, G., Sloot, P., Dongarra, J. (eds.) Proceedings of Computational Science. ICCS 2004, II. Lecture Notes in Computer Science, vol. 3037, pp. 65-72. Springer, Berlin Heidelberg New York (2004)
42. Jacquez, J.A., Simon, C.P.: The stochastic SI model with recruitment and deaths. I. Comparison with the closed SIS model. Math. Biosci. 11.7, 77-125 (1993)
43. Cenzer, D., Marek, V.W., Remmel, J.B.: Using logic programs to reason about infinite sets. In: Eighth International Symposium on Artificial Intelligence and Mathematics, http://rutcor.rutgers.edu/~amai/aimath04/accepted. html (2004)
44. Cuny, J., Ehrig, H., Engels, G., Rozenberg, G.: Graph Grammars and their Applications to Computer Science. Springer, Berlin Heidelberg New York (1994)
45. Mjolsness, E.: Symbolic neural networks derived from stochastic grammar domain models. In: Sun, R., Alexandre, R. (eds.) Connectionist Symbolic Integration. Erlbaum, Mahwah, NJ (1997)
46. Bhan, A., Mjolsness, E.: Static and dynamic models of biological networks. Complexity 11(6), 57-63 (2006)
47. Turing, A.M.: The chemical basis of morphogenesis. Phil. Trans. Roy. Soc. Lond. B237, 37-72 (1952)
48. Gor, V., Bacarian, T., Elowitz, M., Mjolsness, E.: Tracking cell signals in fluorescent images. In: Computer Vision Methods for Bioinformatics (CVMB) workshop, at Computer Vision and Pattern Recognition (CVPR). http://computableplant.ics.uci.edu/CVPR-2005.pdL Cited in June 2005
49. Shapiro, B.E., et al.: Cellerator: extending a computer algebra system to include biochemical arrows for signal transduction simulations. Bioinformatics 19, 671-618 (2003)
50. Fracchia, F.D.: Integrating lineage and interaction for the visualization of cellular structures. In: Cuny, J., Ehrig, H., Engels, G., Rozenberg, G. (eds.) Graph Grammars and Their Application
51. to Computer Science. Fifth International Workshop, Lecture Notes in Computer Science 1073, pp. 521-535. Springer, Berlin Heidelberg New York (1996)
52. Soloveichik, D., Cook, M., Winfree, E., Bruck, J. : Computation with Finite Stochastic Chemical Reaction Networks, manuscript (2006)