Descriptions are given of different types of artificial synapses which have been developed to serve as operational units of an artificial neural processor. The synapses have an electrochemical action and emulate the essential functions of biological synapses, in particular in the transmission of an action potential and in the formation of memory by potentiation and sensitization. A synapse may transmit both steady and transient currents; a transient current follows a change in the potential difference across an electrolyte, which depends on the sign as well as the amplitude of the change of potential. A theory is given of the action of artificial synapses with cylindrical or rectangular geometry, and is made the basis of a mathematical model to simulate the current distribution in such devices. It is shown how the analysis of both steady and transient currents can be reduced to finding numerical solutions of Laplace's equation that satisfy the appropriate boundary condition on two different surfaces. Here the analysis is based on the theory of conformal transformations associated with functions of a complex variable, extended to a cylindrical (three-dimensional) geometry by a development of Whittaker's method. Analysis and results of numerical computation are given and illustrated to obtain the equipotentials and current lines of steady currents, and the time course of transient currents; these are in good qualitative agreement with those observed experimentally. An account is given of the way in which the artifical synapse may be developed and used as a unit that emulates the action of a functional unit of the cerebellum, or some other part of the animal cortex. A generalized neural network equation is obtained to simulate the action of an artificial neural processor consisting of such units; this is very similar in form to the equation proposed by the authors for the realistic simulation of the action of zones and areas of the animal cortex.

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