Mathematical Psychology and Psychophysiology

By Stephen Grossberg | Go to book overview

manifestations of one such principle: automatic self-tuning by competitive networks. My other chapter in the book illustrates some applications of a second principle: gating properties of chemical transmitters. A third principle is reviewed elsewhere ( Grossberg [ 1971], [ 1974], [ 1978b]): pattern learning and growth properties by networks containing fast (STM) and slow (LTM) feedback interactions. These several principles are joined together to generate adaptive resonances and reset operations in the service of global code development and error-correction.

Various other articles in this book have probed aspects of these concepts from several experimental and theoretical perspectives. Thus the principles are starting to enjoy the multiple emergence that often characterizes major conceptual progress in a science. We are, happily, approaching an era when it will be appropriate to identify a small number of laws on which the brain sciences can be based. It is imperative that we not confuse the invariant structure of these laws with the endless list of minor experimental or numerical variations that can draw both experimental and theoretical neuroscience to the brink of conceptual solipsism. A law must be identified before it can be classified, just as a single Schrödinger or Laplace equation can be identified despite its appearance in a vast number of physically distinct examples. The possibility of achieving such coherence is vested in mathematics for the brain sciences no less than for science in general.


REFERENCES

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Bloomfield T. M., 1969. Behavioral contrast and the peak shift, Animal Discrimination Learning ( R. M. Gilbert and N. S. Sutherland, eds.), Academic Press, New York.

Boring E. G., 1950. A history of experimental psychology, 2nd ed., Appleton-Century-Crofts, New York.

Campbell L. and W. Garnett, 1882. The life of James Clerk Maxwell, Macmillan, London.

Cornsweet T. N., 1970. Visual perception, Academic Press, New York.

Carpenter G. A., 1981. Normal and abnormal signal patterns in nerve cells, these PROCEEDINGS.

Dev P. 1975. Computer simulation of a dynamic visual perception model, Internat. J. Man-Machine Studies 7, 511-528.

Eigen M. and P. Schuster, 1978. The hypercycle: A principle of natural self-organization. B. The abstract hypercycle, Naturwissenschaften 65, 7-41.

Ellias S. A. and S. Grossberg, 1975. Pattern formation, contrast control, and oscillations in the short term memory of shunting on-center off-surround networks, Biol. Cybernet. 20, 69-98.

Freeman W. J., 1975. Mass action in the nervous system, Academic Press, New York.

_____, 1979. Nonlinear gain mediating cortical stimulus-response relations, Biol. Cybernet. 33, 237-247.

_____, 1980. EEG analysis gives model of neuronal template-matching mechanism for sensory search with olfactory bulb, Biol. Cybernet. 35, 221-234.

_____, 1981. A neural mechanism for generalization over equivalent stimuli in the olfactory system, these PROCEEDINGS.

Geman S., 1981. The law of large numbers in neural modelling, these PROCEEDINGS.

Glass L. and E. Switkes, 1976. Pattern recognition in humans: Correlations which cannot be perceived, Perception 5, 67-72.

Graham N., 1981. The visual system does a crude Fourier analysis of patterns, these PROCEEDINGS.

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