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Statistical mechanics for networks of analog neurons

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Statistical Mechanics of Neural Networks

Part of the book series: Lecture Notes in Physics ((LNP,volume 368))

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References

  1. T. Pynchon, Gravity's Rainbow, (The Viking Press, New York, 1973) p 664.

    Google Scholar 

  2. A.L. Hodgkin and A.F. Huxley, J. Physiol. 117, 500 (1952).

    Google Scholar 

  3. W.A. Little, Math. Biosci. 19, 101 (1974).

    Google Scholar 

  4. J.J. Hopfield, Proc. Natl. Acad. Sci. USA 79, 2554 (1982).

    Google Scholar 

  5. L.F. Abbott, Model Neurons: From Hodgkin-Huxley to Hopfield, these proceedings.

    Google Scholar 

  6. D.J. Amit, Modeling Brain Function — The World of Attractor Neural Networks, (Cambridge University Press, Cambridge, 1989).

    Google Scholar 

  7. P.Peretto, Biol. Cybern. 50, 51 (1984).

    Google Scholar 

  8. D.J. Amit, H. Gutfreund, and H. Sompolinsky, Phys. Rev. A 32, 1007 (1985); Phys. Rev. Lett. 55, 1530 (1986); Ann. Phys. (N.Y.) 173, 30 (1987).

    Google Scholar 

  9. E. Domany, J.L. van Hemmen, and K. Schulten (eds.), Physics of Neural Networks, (Springer, Heidelberg, 1990).

    Google Scholar 

  10. I. Kanter, Phys. Rev. A 37, 2739 (1988); see also the contribution of D. Bollé, these proceedings.

    Google Scholar 

  11. C. Meunier, D. Hansel, and A. Verga, J. Stat. Phys. 55, 859 (1989).

    Google Scholar 

  12. J. Yedidia, J. Phys. A 22, 2265 (1989).

    Google Scholar 

  13. H. Rieger, Thesis, Köln, (1989), unpublished.

    Google Scholar 

  14. S. Mertens, Storing p-state Patterns in a Network with Analog Neurons, this conference, and private communication.

    Google Scholar 

  15. J. Cook, J. Phys. A 22, 2257 (1989).

    Google Scholar 

  16. J. Stark and P. Bressloff J. Phys. A 23, 1633 (1990).

    Google Scholar 

  17. M.V. Tsodyks, Europhys. Lett. 7, 203 (1988).

    Google Scholar 

  18. C.M. Marcus and R.M. Westervelt, Phys. Rev. A 40, 501 (1989)

    Google Scholar 

  19. C.M. Marcus, F.M. Waugh, and R.M. Westervelt, Phys. Rev. A 41, 3355 (1990).

    Google Scholar 

  20. I. Kanter and H. Sompolinsky, Phys. Rev. A 35, 380 (1987).

    Google Scholar 

  21. F.M. Waugh, C.M. Marcus, and R.M. Westervelt, Phys. Rev. Lett. 64, 1986 (1990).

    Google Scholar 

  22. A. Treves, Graded-Response Neurons and Information Encodings in Auto-Associative Memories, Phys. Rev. A (1990), in press; see also Neural Networks in the Hippocampus Involved in Learning, these proceedings.

    Google Scholar 

  23. H. Rieger, Properties of Neural Networks with Multi-State Neurons, these proceedings.

    Google Scholar 

  24. J.J. Hopfield, Proc. Natl. Acad. Sci. 81 3088 (1984).

    Google Scholar 

  25. R. Kühn, S. Bös, and J.L. van Hemmen, Statistical Mechanics for Networks of Graded Response Neurons, submitted to Phys. Rev. A (1990).

    Google Scholar 

  26. J.J. Hopfield and D.W. Tank, Biol. Cybern. 52, 141 (1985); D.W. Tank and J.J. Hopfield, IEEE Transactions on Circuits and Systems Cas-33 533 (1986).

    Google Scholar 

  27. J.L. van Hemmen and R. Kühn, Collection Phenomena in Neural Networks, in Ref: 9. (Springer, Heidelberg, 1990).

    Google Scholar 

  28. S. Bös, to be published.

    Google Scholar 

  29. R. Graham and H. Haken, Z. Phys. 243 289 (1971).

    Google Scholar 

  30. R. Kühn et al., to be published.

    Google Scholar 

  31. M. Abeles Local Cortical Circuits, (Springer, Berlin, Heidelberg, New York, 1982); M. Abeles, E. Vaadia, and H. Bergman, Network 1, 13 (1990).

    Google Scholar 

  32. D. Amit and A. Treves Proc. Natl. Acad. Sci. USA 86, 7871 (1989); A. Treves and D.J. Amit, J. Phys. A 22, 2205 (1989).

    Google Scholar 

  33. N. Rubin and H. Sompolinsky, Neural Networks with Low Local Firing Rates, Europhys. Lett. (1990), in press.

    Google Scholar 

  34. H. Sompolinsky, in: Heidelberg Colloquium on Glassy Dynamics, J.L. van Hemmen and I. Moegenstern (eds.), (Springer, Heidelberg, 1987) p 485.

    Google Scholar 

  35. W. Kinzel, in: Heidelberg Colloquium on Glassy Dynamics, J.L. van Hemmen and I. Morgenstern (eds.), (Springer, Heidelberg, 1987) p 529.

    Google Scholar 

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Luis Garrido

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© 1990 Springer-Verlag

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Kühn, R. (1990). Statistical mechanics for networks of analog neurons. In: Garrido, L. (eds) Statistical Mechanics of Neural Networks. Lecture Notes in Physics, vol 368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3540532676_38

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  • DOI: https://doi.org/10.1007/3540532676_38

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