Skip to main content
SpringerLink
Log in

On global properties of neuronal interaction

  • Published:
Biological Cybernetics Aims and scope Submit manuscript

Abstract

Rate-coded interaction between neurons is governed by a nonlinear equation, of which the McCulloch-Pitts model for a neural network and the Hartline-Ratliff model of lateral inhibition are special limiting cases. Feature detection is treated as a variational problem and conditions are derived on the connections between neurons at a trigger feature. Perturbations from continual back-ground activity are examined as a possible means for coding and processing information.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Anderson, J. A.: A simple neural network generating an interacting memory. Math. Biosci.14, 197–220 (1972)

    Google Scholar 

  • Bennett, M. V. L. (Ed.): Synaptic transmission and neuronal interaction. New York: Raven Press 1974

    Google Scholar 

  • Cowan, J. D.: Stochastic models of neuroelectric activity. In: Rice, S., Light, J., Freed, K. (Eds.): Proceedings of the international union of pure and applied physics conference on statistical mechanics, pp. 109–127. Chicago: University of Chicago Press 1971

    Google Scholar 

  • Dunford, N., Schwartz, J. T.: Linear operators, Part I. General theory. New York: Interscience 1958

    Google Scholar 

  • Hartline, H. K., Ratliff, F.: Inhibitory interaction of receptor units in the eye of the Limulus. J. gen. Physiol.40, 357–376 (1957)

    Google Scholar 

  • Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer 1966

    Google Scholar 

  • Kohonen, T.: Correlation matrix memories. IEEE Trans. Computers21, 353–366 (1972)

    Google Scholar 

  • McCulloch, W. S., Pitts, W. H.: A logical calculus of ideas immanent in nervous activity. Bull. math. Biophys.5, 115–133 (1943)

    Google Scholar 

  • Moore G. P., Perkel, D. H., Segundo J. P.: Statistical analysis and functional interpretation of neuronal spike data. Ann. Rev. Phys.28, 493–522 (1966)

    Google Scholar 

  • Nirenberg, L.: Topics in nonlinear functional analysis. New York: Courant Institute of Mathematical Sciences 1974

    Google Scholar 

  • Perkel, D. H., Bullock, T. H.: Neural coding. Neurosci. Res. Progr. Bull.6, No. 3 (1968)

  • Smart, D. R.: Fixed point theorems. Cambridge: Cambridge University Press 1974

    Google Scholar 

  • Stein, R. B.: The frequency of nerve action potentials generated by applied currents. Proc. roy. Soc. Ser. B167, 64–86 (1967)

    Google Scholar 

  • Stein, R. B., Leung, K. V., Oguztoreli, M. N., Williams, D. W.: Properties of small neural networks. Kybernetik14, 223–230 (1974)

    Google Scholar 

  • Steinbuch, K.: Die Lernmatrix, Kybernetik1, 36–45 (1961)

    Google Scholar 

  • Wilson, H. R., Cowan, J. D.: Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J.12, 1–24 (1972)

    Google Scholar 

Download references

Author information

Author notes

  1. T. J. Sejnowski

    Present address: Joseph Henry Laboratories, Princeton University, 08540, Princeton, N.J., USA

Authors and Affiliations

  1. Department of Physics, University of California at Santa Barbara, USA

    T. J. Sejnowski

  2. Dept. of Physics Joseph Henry Laboratories, Princeton University, P.O. Box 708, 08540, Princeton, N.J., USA

    T. J. Sejnowski

Authors
  1. T. J. Sejnowski
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sejnowski, T.J. On global properties of neuronal interaction. Biol. Cybernetics 22, 85–95 (1976). https://doi.org/10.1007/BF00320133

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00320133

Keywords

Search

Navigation