Language and coherent neural amplification in hierarchical systems: Renormalization and the dual information source of a generalized spatiotemporal stochastic resonance

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 10, Issue 2, 2000, Pages 493-502

  Wallace, Rodrick ^a,b  

^a NEW YORK STATE PSYCHIATRIC INSTITUTE   (United States)

^b PISCS Inc   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034134397     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127400000335     Document Type: Article

References (31)

1. Ash, R. [1990] Information Theory (Dover, NY).
2. Binney, J., Dowrick, N., Fisher, A. & Newman, M. [1995] The Theory of Critical Phenomena; An Introduction to the Renormalization Group (Oxford Science Publications, Oxford).
3. Braiman, Y., Linder, J. & Ditto, W. [1995] "Taming spatiotemporal chaos with disorder," Nature 378, p. 465.
4. Cramer, H. [1938] "Sur un nouveau theoreme-limite de la theorie des probabilities," in Actualities Scientifiques et Industrielles, No. 736 in Colloque consacre al la theorie des probabilities (Hermann, Paris), pp. 5-23.
5. Deco, G. & Schurmann, B. [1998] "Stochastic resonance in the mutual information between input and output spike trains of noisy central neurons," Physica D117, 276-282.
6. Dembo, A. & Zeitouni, O. [1998] Large Deviations: Techniques and Applications, 2nd edition (Springer-Verlag NY).
7. Dykman, M., Luchinsky, D., McClintock, P. & Smelyansky, V. [1996] "Corrals and critical behavior of the distribution of fluctuational paths," Phys. Rev. Lett. 77, 5229-5232.
8. Elger, C. & Lehnertz, K. [1998] "Seizure prediction by nonlinear time series analysis of brain electrical activity," European J. Neurosci. 10, 786-789.
9. Ellis, R. [1985] Large Deviations and Statistical Mechanics (Springer-Ver lag, NY).
10. Gammaitoni, A., Hanggi, P., Jung, P. & Marchesoni, F. [1998] "Stochastic resonance," Rev. Mod. Phys. 70, 223-287.
11. Godivier, X. & Chapeau-Blondeau, F. [1998] "Stochastic resonance in the information capacity of a nonlinear dynamic system," Int. J. Bifurcation and Chaos 8, 581-589.
12. Granovetter, M. [1973] "The strength of weak ties," Am. J. Social. 78, 1360-1380.
13. Heneghan, C., Chow, C., Collins, J., Imhoff, T., Lowen, S. & Teich, M. [1996] "Information measures quantifying aperiodic stochastic resonance," Phys. Rev. A54, 2366-2377.
14. Iasemidis, L. & Sackellares, J. [1996] "Chaos theory and epilepsy," The Neurosci. 2, 118-126.
15. Khinchine, A. [1957] The Mathematical Foundations of Information Theory (Dover, NY).
16. Lindenmayer, A. [1971] "Developmental systems without cellular interactions, their languages and grammars," J. Theoret. Biol. 30, 455-484.
17. Linder, J., Meadows, B. & Ditto, W. [1995] "Array enhanced stochastic resonance and spatiotemporal synchronization," Phys. Rev. Lett. 75, 3-6.
18. Linder, J., Meadows, B., Ditto, W., Inchiosa, M. & Bulsara, A. [1996] "Scaling laws for spatiotemporal synchronization and array enhanced stochastic resonance," Phys. Rev. A53, 2081-2086.
19. Martinerie, J., Adam, C., Le Van Quyen, M., Baulac, M., Clemenceau, S., Renault, B. & Varela, F. [1998] Nature Medicine 4, 1173-1176.
20. McCauley, L. [1993] Chaos, Dynamics and Fractals: An Algorithmic Approach to Deterministic Chaos (Cambridge University Press, Cambridge).
21. McClintock, J. & Luchinsky, D. [1999] "Glorious noise," The New Scientist 161(2168), 36-39.
22. Nieman, A., Shulgin, B., Anishchenko, V., Ebeling, W., Schimansky-Geier, L. & Freund, J. [1996a] "Dynamical entropies applied to stochastic resonance," Phys. Rev. Lett. 76, 4299-4302.
23. Nieman, A., Shulgin, B., Anishchenko, V., Ebeling, W., Schimansky-Gier, L. & Freund, J. [1996b] "Correction," Phys. Rev. Lett. 77, p. 4851.
24. Onsager, L. & Machlup, S. [1953] "Fluctuations and irreversible processes," Phys. Rev. 91, 1501-1512.
25. Schimansky-Gier, L., Freund, J., Siewert, U. & Nieman, A. [1996] "Stochastic resonance: Informational aspects and distributed systems," ICND-96 book of abstracts.
26. Waddington, C. [1972] "Epilogue," Towards a Theoretical Biology 4: Essays, ed. Waddington, C. (Aldine.Atherton, Chicago).
27. Wallace, R. & Wallace, R. G. [1998] "Information theory, scaling laws and the thermodynamics of evolution," J. Theoret. Biol. 192, 545-559.
28. Wallace, R. & Wallace, R. G. [1999] "Organisms, organizations and interactions: An information theory approach to biocultural evolution," Biosystems 51, 101-119.
29. Wilson, K. [1971] "Renormalization group and critical phenomena. I. Renormalization group and the Kadanoff scaling picture," Phys. Rev. B4, 3174-3183.
30. Zurek, W. [1985] "Cosmological experiments in superfluid helium?" Nature 317, 505-508.
31. Zurek, W. [1996] "The shards of broken symmetry," Nature 382, 296-298.