Stahl675 bmp

THE EOLE OF MODELS IN THEORETICAL BIOLOGY 199

B. Artificial Neeve Networks

A long series of works pertaining to the modeling of “brain logie” was initiated by the historie paper of McCulloch and Pitts (1943), which largely disregarded neurophysiological or biochemical aspects of neuron function and used a specialized form of Boolean logie to represent a “logical neuron” as a simple mathematical operator, capable of being assembled into large networks. This modeling concept played an im-portant role in the later development of digital computers, particularly in the hands of John von Neumann. Computers are “models of the brain” in a certain sense and it is very important to notę that although numerous neurophysiological similarity criteria are not applicable to them, they are partial models in regard to performance scores for solu-tion of certain types of problems. A partial model may be held to exist if even one well-defined mathematical invariant property can be attributed to both the model and prototype. A Computer can represent many dif-ferent kiDds of brain function, and the brain may function in many different ways, so the similarity invariants are nonuniąue for these models.

Neurons have been modeled in the sense of creating fairly smali unitized physical analogs, such as “neuromimes” of Harmon (1964), which may or may not simulate observed electrical membranę activity of the real neuron. Morę commonly, they have been modeled in a morę phenomenological sense by networks of simple logical units (MacKay, 1960; Sears and Khanna, 1963; Guinn, 1963). A symposium volume entitled “Neural Theory and Modeling” (Reiss et dl., 1964) is available, but does not, in generał, discuss similarity invariants in a systematic manner.

Representation of complex neurophysiological events by networks of elementary neurons is implied in the above approach. Uttley (1962) describes a probabilistic model in which there occurs learned association of simultaneous sensory inputs. McCulloch et al. (1962) use the basie McCulloch-Pitts neuron concept to create a model logical network which is highly resistant to errors arising from random low-level damage to individual units. An entirely phenomenological approach to nervous system modeling is proposed by Mesarovic (1964), who would have neurons behave like living “goal-seeking automata” and Miller (1964), who compares a pigeon’s eye with military radar eąuipment.

In the Soviet Union automata and algorithm theory has been used to describe neuromuscular coordination. Gel’fand et al. (1962, 1963) at-