Computation in gene networks

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2055 LNCS, Issue , 2001, Pages 11-24

  Ben Hur, Asa ^a   Siegelmann, Hava T ^b  

^a BIOwulf Technologies   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANALOG COMPUTERS; BIOINFORMATICS; BIOLOGY; DIFFERENTIAL EQUATIONS; GENE EXPRESSION; MICROCONTROLLERS; PIECEWISE LINEAR TECHNIQUES; GENES;

BIOLOGICAL COMPUTING; BOUNDED TURING MACHINES; GENE NETWORKS; GENETIC REGULATORY NETWORKS; PIECEWISE LINEAR; PROTEIN CONCENTRATIONS;

TURING MACHINES;

EID: 84898852027     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45132-3_2     Document Type: Conference Paper

References (35)

1. M. A. Nielsen and I. L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2000.
2. L. Kari. DNA computing: the arrival of biological mathematics. The mathematical intelligencer, 19(2):24-40, 1997.
3. J. Hertz, A. Krogh, and R. Palmer. Introduction to the Theory of Neural Computation. Addison-Wesley, Redwood City, 1991.
4. C. Mead. Analog VLSI and Neural Systems. Addison-Wesley, 1989.
5. H. Lodish, A. Berk, S. L. Zipursky, P. Matsudaira, D. Baltimore, and J. Darnell. Molecular cell biology. W. H. Freemand and Company, 4th edition, 2000.
6. S. A. Kauffman. Metabolic stability and epigenesis in randomly connected nets. Journal of Theoretical Biology, 22:437, 1969.
7. D. Bray. Protein molecules as computational elements in living cells. Nature, 376:307-312, July 1995.
8. H. H. McAdams and A. Arkin. Simulation of prokaryotic genetic circuits. Annual Review of Biophysics and Biomolecular Structure, 27:199-224, 1998.
9. T. S. Gardner, C. R. Cantor, and J. J. Collins. Construction of a genetic toggle switch in E. coli. Nature, 403:339-342, January 2000.
10. M. B. Elowitz and S. Leibler. A synthetic oscillatory network of transcriptional regulators. Nature, 403:335-338, January 2000.
11. A. Arkin and J. Ross. Computational functions in biochemical reaction networks. Biophysical Journal, 67:560-578, 1994.
12. T. Mestl, E. Plahte, and S. W. Omholt. A mathematical framework for describing and analyzing gene regulatory networks. Journal of Theoretical Biology, 176:291-300, 1995.
13. L. Glass. Combinatorial and topological method in chemical kinetics. Journal of Chemical Physics, 63:1325-1335, 1975.
14. C. Papadimitriou. Computational Complexity. Addison-Wesley, Reading, Mass., 1995.
15. H. T. Siegelmann. Neural Networks and Analog Computation: Beyond the Turing Limit. Birkhauser, Boston, 1999.
16. H. T. Siegelmann, A. Roitershtein, and A. Ben-Hur. Noisy neural networks and generalizations. In Proceedings of the Annual Conference on Neural Information Processing Systems 1999 (NIPS*99). MIT Press, 2000.
17. W. Maass and P. Orponen. On the effect of analog noise in discrete time computation. Neural Computation, 10(5):1071-1095, 1998.
18. L. F. Landweber and L. Kari. The evolution of cellular computing: nature's solution to a computational problem. In Proceedings of the 4th DIMACS meeting on DNA based computers, pages 3-15, 1998.
19. L. Glass and J. S. Pasternack. Stable oscillations in mathematical models of biological control systems. Journal of Mathematical Biology, 6:207-223, 1978.
20. R. N. Tchuraev. A new method fo rthe analysis of the dynamics of the molecular genetic control systems. I. description of the method of generalized threshold models. Journal of Theoretical Biology, 151:71-87, 1991.
21. T. Mestl, R. J. Bagley, and L. Glass. Common chaos in arbitrarily complex feedback networks. Physical Review Letters, 79(4):653-656, 1997.
22. L. Glass and C. Hill. Ordered and disordered dynamics in random networks. Europhysics Letters, 41(6):599-604, 1998.
23. M. S. Branicky. Analog computation with continuous ODEs. In Proceedings of the IEEE Workshop on Physics and Computation, pages 265-274, Dallas, TX, 1994.
24. E. Asarin, O. Maler, and A. Pnueli. Reachability analysis of dynamical systems with piecewise-constant derivatives. Theoretical Computer Science, 138:35-66, 1995.
25. A. Saito and K. Kaneko. Geometry of undecidable systems. Prog. Theor. Phys., 99:885-890, 1998.
26. J. E. Hopcroft and J. D. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, 1979.
27. P. Koiran and C. Moore. Closed-form analytic maps in one and two dimensions can simulate universal Turing machines. Theoretical Computer Science, 210:217-223, 1999.
28. J. E. Lewis and L. Glass. Nonlinear dynamics and symbolic dynamics of neural networks. Neural Computation, 4:621-642, 1992.
29. P. Orponen. The computational power of discrete hopfield nets with hidden units. Neural Computation, 8:403-415, 1996.
30. P. Orponen. Computing with truly asynchronous threshold logic networks. Theoretical Computer Science, 174:97-121, 1997.
31. C. Moore. Generalized one-sided shifts and maps of the interval. Nonlinearity, 4:727-745, 1991.
32. J. P. Crutchfield and K. Young. Computation at the onset of chaos. In W. H. Zurek, editor, Complexity, Entropy and the Physics of Information, pages 223-269, Redwood City, CA, 1990. Addison-Wesley.
33. C. Moore. Queues, stacks, and transcendentality at the transition to chaos. Physica D, 135:24-40, 2000.
34. R. Edwards, H. T. Siegelmann, K. Aziza, and L. Glass. Symbolic dynamics and computation in model gene networks. in preparation.
35. J. Sima and P. Orponen. A continuous-time hopfield net simulation of discrete neural networks. Technical Report 773, Academy of Sciences of the Czech Republic, 1999.