Neurons, Dynamics and Computation

FEB 01, 1994

Brains have long been regarded as biological computers. But how do these collections of neurons perform computations?

John J. Hopfield

The question “How does it work?” is the motivation of many physicists. Condensed matter physics, chemical physics and nuclear physics can all be thought of as descriptions of the relation between structure and properties. The components of a biological system have functional properties that are particularly relevant to the operation of the system. Thus it is especially important in biology to understand the relation between structure and function. Such understanding can be sought at the level of the molecule, the cell, the organ, the organism or the social group.

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References

1. J. J. Hopfield, in Evolutionary Trends in the Physical Sciences, M. Suzuki, R. Kubo, eds., Springer‐Verlag, New York (1991), p. 295.
2. E. R. Kandel, J. H. Schwartz, Principles of Neural Science, 3rd ed., Appleton & Lange, Norwalk, Conn. (1991), p. 19.
3. D. Junge, Nerve and Muscle Excitation, Sinauer, Sunderland, Mass. (1981), p. 115, discusses some of the complications of the biophysics of this process.
4. J. Hertz, A. Krogh, R. G. Palmer, Introduction to the Theory of Neural Computation, Addison Wesley, Redwood City, Calif. (1991), p. 16.
5. M. F. Bear, L. N. Cooper, F. F. Ebner, Science 237, 42 (1987).https://doi.org/SCIEAS
6. See, for example, G. Dreyfus, in Applications of Neural Networks, H. G. Schuster, ed., VCH, New York (1992), p. 35.
7. While these equations are in common use, they have evolved somewhat, and do not have a sharp original reference. See, however, H. R. Wilson, J. D. Cowan, Biophys. J. 12, 1 (1972); https://doi.org/BIOJAU
and W. Gerstner, J. L. van Hemmen, Network 3, 139 (1992).https://doi.org/NWRKEA
8. J. J. Hopfield, Proc. Natl. Acad. Sci. USA 79, 2554 (1982)
J. J. Hopfield, 81, 3088 (1984).https://doi.org/PNASA6 , Proc. Natl. Acad. Sci. U.S.A.
9. E. Domany, J. L. van Hemmen, K. Schulten, eds., Models of Neural Networks, Springer‐Verlag, New York (1991).
10. J. J. Hopfield, D. G. Tank, Biol. Cybern. 52, 141 (1985). https://doi.org/BICYAF
Y. Takefuji, Neural Network Parallel Computing Kluwer Boston (1992).
11. W. J. Freeman, Sci. Am., February 1991, p. 78.
12. R. Eckhorn, R. Bauer, W. Jordan, M. Brosch, W. Kruse, M. Munk, H. J. Reitboeck, Biol. Cybern. 60, 121 (1988).https://doi.org/BICYAF
13. C. M. Gray, W. Singer, Proc. Natl. Acad. Sci. USA 86, 1698 (1989).https://doi.org/PNASA6
14. Y. Kuramoto, Physica D 50, 15 (1991). https://doi.org/PDNPDT
R. E. Mirollo, S. H. Strogatz, SIAM J. Appl. Math 50, 1645 (1990).
L. F. Abbott, C. Vanvreeswijk, Phys. Rev. E 48, 1483 (1993).https://doi.org/PLEEE8
15. M. Tsodyks, I. Mitkov, H. Sompolinsky, Phys. Rev. Lett. 71, 1280 (1993).https://doi.org/PRLTAO
16. R. Burridge, L. Knopoff, Bull. Seismol. Soc. Am. 57, 341 (1967).https://doi.org/BSSAAP
17. Z. Olami, H. J. S. Feder, K. Christensen, Phys. Rev. Lett. 68, 1244 (1992).https://doi.org/PRLTAO
18. P. Bak, C. Tang, J. Geophys. Res. 94, 15, 635 (1989).https://doi.org/JGREA2

More about the authors

John J. Hopfield, California Institute of Technology, Pasadena, California.