Nonstationary stochastic resonance viewed through the lens of information theory

European Physical Journal B

Volumn 69, Issue 1, 2009, Pages 29-35

  Goychuk, I ^a   Hanggi P ^a  

^a UNIVERSITY OF AUGSBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL THEORY; FINITE DURATION; INFORMATION TRANSFERS; INFORMATION-CARRYING SIGNALS; INPUT SIGNAL; KULLBACK-LEIBLER INFORMATION; NONSTATIONARY; STOCHASTIC INTENSITY; STOCHASTIC RESONANCES; THROUGH THE LENS;

BIOLOGICAL SYSTEMS; INFORMATION THEORY; RESONANCE;

RANDOM PROCESSES;

EID: 67649498393     PISSN: 14346028     EISSN: 14346036     Source Type: Journal    
DOI: 10.1140/epjb/e2009-00049-y     Document Type: Article

References (62)

1. R. Benzi, A. Sutera, A. Vulpiani, J. Phys. A 14, L453 (1981);
2. C. Nicolis, G. Nicolis, Tellus 33, 225 (1981)
3. L. Gammaitoni, P. Hänggi, P. Jung, F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998)
4. V.S. Anishchenko, A.B. Neiman, F. Moss, L. Schimansky-Geier, Sov. Phys. Usp. 42, 7 (1999)
5. P. Hänggi, Chem. Phys. Chem. 3, 285 (2002)
6. R. Löfstedt, S.N. Coppersmith, Phys. Rev. E 49, 4821 (1994);
7. M. Grifoni, M. Sassetti, P. Hänggi, U. Weiss, Phys. Rev. E 52, 3596 (1995);
8. M. Grifoni, P. Hänggi, Phys. Rev. Lett. 76, 1611 (1996);
9. M. Grifoni, P. Hänggi, Phys. Rev. E 54, 1390 (1996);
10. M. Grifoni, L. Hartmann, S. Berchtold, P. H änggi, Phys. Rev. E 53, 5890 (1996);
11. M. Grifoni, L. Hartmann, S. Berchtold, P. Hänggi, Phys. Rev. E 56, 6213 (1997);
12. I. Goychuk, P. Hänggi, Phys. Rev. E 59, 5137 (1999)
13. R.B. Alley, S. Anadakrishnan, P. Jung, Paleoceanography 16, 190 (2001);
14. A. Ganopolski, S. Rahmstorf, Phys. Rev. Lett. 88, 038501 (2002)
15. G. Schmid, I. Goychuk, P. Hänggi, Europhys. Lett. 56, 22 (2001)
16. J.A. Freund, L. Schimansky Geier, P. Hänggi, Chaos 13, 225 (2003)
17. L.B. Kiss, A. Ambrózy, in Noise in Physical Systems and 1/f Noise - 1985, edited by A. D'Amico, P. Mazzetti (North-Holland, Amsterdam, 1986), pp. 501-504
18. B.D. Hughes, Random Walks and Random Environments (Clarendon Press, Oxford, 1995), Vol. 1
19. C. Shannon, Bell System Technical J. 27, 379 (1948);
20. C. Shannon, Bell System Technical J. 27, 623 (1948);
21. C. Shannon, Proc. IRE 37, 10 (1949)
22. P. Jung, P. Hänggi, Europhys. Lett. 8, 505 (1989)
23. P. Jung, P. Hänggi, Phys. Rev. A 44, 8032 (1991);
24. P. Jung, P. H änggi, Phys. Rev. A 41, 2977 (1990)
25. J. Casado-Pascual, C. Denk, J. Gomez-Ordonez, M. Morillo, P. Hänggi, Phys. Rev. E 67, 036109 (2003)
26. K. Loerincz, Z. Gingl, L.B. Kiss, Phys. Lett. A 224, 63 (1996);
27. P. Hänggi, M. Inchiosa, D. Fogliatti, A. Bulsara, Phys. Rev. E 62, 6155 (2000);
28. J. Casado-Pascual, J. Gomez-Ordonez, M. Morillo, P. Hänggi, Phys. Rev. Lett. 91, 210601 (2003);
29. J. Casado-Pascual, J. Gomez-Ordonez, M. Morillo, P. Hänggi, Phys. Rev. E 68, 061104 (2003)
30. F. Rieke, D. Warland, R. de Ruyter van Steveninck, W. Bialek, Spikes: Exploring the Neural Code (MIT Press, Cambridge, MA, 1997)
31. W. Bialek, A. Zee, J. Stat. Phys. 59, 103 (1990);
32. W. Bialek, M. DeWeese, F. Rieke, D. Warland, Physica 200, 581 (1993);
33. M. DeWeese, W. Bialek, Nuovo Cimento D 17, 733 (1995)
34. J.J. Collins, C.C. Chow, T.T. Imhoff, Nature (London) 376, 236 (1995);
35. A.R. Bulsara, A. Zador, Phys. Rev. E 54, R2185 (1996);
36. J.E. Levin, J.P. Miller, Nature (London) 380, 165 (1996);
37. I. Goychuk, P. Hanggi, New J. Phys. 1, 14 (1999);
38. L.B. Kish, G.P. Harmer, D. Abbott, Fluct. Noise Lett. 1, L13 (2001)
39. S. Kullback, R.A. Leibler, Ann. Math. Stat. 22, 79 (1951);
40. S. Kullback, Information Theory and Statistics (Wiley, New York, 1959)
41. D.J.C. MacKay, Information theory, Inference, and Learning Algorithms (Cambridge University Press, New York, 2003)
42. A. Neiman, B. Shulgin, V. Anishchenko, W. Ebeling, L. Schimansky-Geier, J. Freund, Phys. Rev. Lett. 76, 4299 (1996)
43. I. Goychuk, P. Hanggi, Phys. Rev. E 61, 4272 (2000)
44. I. Goychuk, Phys. Rev. E 64, 021909 (2001)
45. N.G. Van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1992)
46. K. Wiesenfeld, D. Pierson, E. Pantazelou, Ch. Dames, F. Moss, Phys. Rev. Lett. 72, 2125 (1994)
47. S.M. Bezrukov, I. Vodyanoy, Nature (London) 37 8, 362 (1995);
48. S.M. Bezrukov, I. Vodyanoy, Nature (London) 385, 319 (1997);
49. S.M. Bezrukov, I. Vodyanoy, Chaos 8, 557 (1998)
50. C. Koch, Biophysics of Computation. Information Processing in Single Neurons (Oxford University Press, New York, 1999)
51. M. Gopalakrishnan, P. Borowski, F. Juelicher, M. Zapotocky, Phys. Rev. E 76, 021904 (2007)
52. A. Skupin, M. Falcke, Genome Informatics 18, 44 (2007)
53. I. Goychuk, P. Hanggi, Phys. Rev. E 69, 021104 (2004)
54. s (t) is not a renewal process, i.e. the signal induces correlations among the interspike intervals in the corresponding averaged process. This is the reason why it was not possible thus far to find an exact expression for the rate of mutual information for this model. For weak Gaussian signals the Shannon-Pinsker formula for the transinformation rate [11,16,18,32] provides but a valid approximation [17] which serves as a lower bound [33] for the mutual information
55. M.S. Pinsker, Dokl. Akad. Nauk SSSR 99, 213 (1954) (in Russian); M.S. Pinsker, Information and Information Stability of Random Variables and Processes (Holden-Day, San Francisco, 1964)
56. P.P. Mitra, J.B. Stark, Nature (London) 411, 1027 (2001)
57. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 2nd edn. (McGraw-Hill Book Company, New York, 1984)
58. Z. Gingl, L.B. Kiss, F. Moss, Europhys. Lett. 29, 191 (1995)
59. C.C. Chow, J.A. White, Biophys. J. 71, 3013 (1996)
60. P. Gaspard, X.-J. Wang, Phys. Rep. 235, 292 (1993)
61. D.M. MacKay, W.S. McCulloch, Bull. Math. Biophys. 14, 127 (1952)
62. S.B. Lowen, M.C. Teich, Phys. Rev. Lett. 63, 1755 (1989)