Abstract
A model build with an ensemble of identical, noisy, integrate-and-fire oscillators with messages interchange has been studied to find out regimes in which the collective behavior is stable at mesoscopic level. We have found for our model a range in the strength of messages for which the system settles into a periodic synchronic behavior that only depends on structural parameters: the number of units in the ensemble and the time taken by the message to arrive from the sender to the receiving unit. This type of periodic and synchronic firing pattern could be relevant for information processing since it is independent of the detailed dynamics of units making up the ensemble. The periodic pattern is drive by passing messages and it, remains stable even under severe noise affecting the evolution of isolated units.
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References
C. von der Malsburg: The Correlation Theory of Brain Function. Internal Report, Max-Planck-Institute of Biophysical Chemistry, Gottingen, West Germany, (1981).
C. von der Malsburg and W. Schneider: A Neural Cocktail-partty Processor. Biol. Cybern. Vol 54, pp. 29–40, (1986)
W. Singer and C.M. Gray: Visual Feature Integration and the Temporal correlation Hypothesis. Annu Rev Neurosci, Vol 18, pp 555–586.
C.M. Gray, P. König, A.K. Engel and W. Singer: Stimulus-Specific Neuronal Oscillations in Cat Visual Cortex Exhibit Inter-Columnar Synchronization Which Reflects Global Stimulus Properties. Nature, Vol. 388, pag 334 (1989)
Renato E. Mirollo and Steven H. Strogatz: Synchronization of Pulse-Coupled Biological Oscillators. SIAM J. Appl. Math. Vol. 50. N? 6, pp. 1645–1662, (December 1990).
Y. Kuramoto: Chemical oscillations, Waves and Turbulence. Springer-Verlag, Berlin, (1984).
C.J. Pérez, A. Corral, A. Díaz-Guilera, K. Chistensen, and A. Arenas: On Self-Organized Criticallity and Synchronization in Lattice Models of Coupled Dynamical Systems. Int. J. Mod. Phys, Vol 10, pp. 1111–, (1996).
H.D.I. Abarbanel, M.I. Rabinovich, A. Selverston, M.V. Bazhenov, R. Huerta, L.L. Rubchinsky, y M.M. Sushchik: The synchronization of Neural Assemblies. Uspekhi Fizicheskih Nauk Vol 166, No 4, pp. 1–28, (1996).
V. López, J.A. Sigüenza, J.R. Dorronsoro and S. Carrillo-Menendez: Stochastic Specificity in Neural Interaction. Proceedings ICANN 93 pp 196–199. Eds. S. Gielen and B. Kappen Springer Verlag, (1993).
Paul M. Hofman, Francisco B. Rodríguez, Juan A. Sigüenza, Vicente López, Santiago Carrillo-Menendez: A Simple Probabilistic Neural Model Producing Multimodal ISHs, in LNCS 930 pp. 166–173 Mira-Sandoval (Eds.) From Natural to Artificial Neural Computation, Springer Verlag, IWANN95.
Francisco B. Rodríguez and Vicente López: Stability and Hebbian Learning in Populations of Probabilistic Neurons, in LNCS 1240 pp. 433–442 Mira, Moreno-Díaz, Cabestany (Eds.) From Neuroscience to technology, Springer Verlag, IWANN97.
W. Feller: An Introduction to Probability Theory and Its Applications. Vol. I, Ed. J. Wiley and Sons.
Fred Rieke, David Warland, Rob de Ruyter van Steveninck, and Willian Bialek: Spikes: Exploring the Neural Code. A Bradford Book. The MIT Press Cambridge, Massachusetts, London, England (1997).
J. Buck: Synchronous Rhythmic Flashing of Fireflies. II. Quart. Rev. Biol. Vol 63, pp 265–289, (1988).
T. J. Walker: Acoustic Synchrony: Two Mechanisms in the Snowy Tree Cricket. Science, Vol. 166, pp 891–894, (1969).
Hiroshi Fujii, Hiroyuki Ito, Kazuyuki Aihara, Natsuhiro Ichinose, and Minoru Tsukada: Dynamical Cell Assembly Hypothesis—Theoretical Possibility of Spatio-Temporal Coding in the Cortex. Neural Networks, Vol. 9, No 8, pp. 1303–1350, (1996).
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Rodríguez, F.B., López, V. (1999). Periodic and synchronic firing in an ensemble of identical stochastic units: Structural stability. In: Mira, J., Sánchez-Andrés, J.V. (eds) Foundations and Tools for Neural Modeling. IWANN 1999. Lecture Notes in Computer Science, vol 1606. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098193
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DOI: https://doi.org/10.1007/BFb0098193
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