Editing Warren Sturgis McCulloch (section)

=== Neural network modelling ===
In the 1943 paper McCulloch and Pitts attempted to demonstrate that a [[Turing machine]] program could be implemented in a finite network of ''formal'' [[neuron]]s (in the event, the Turing Machine contains their model of the brain, but the converse is not true<ref>see: S.C. Kleene, "Representations of Events in Nerve Nets and Finite Automata"</ref>), that the neuron was the base logic unit of the brain. In the 1947 paper they offered approaches to designing "nervous nets" to recognize visual inputs despite changes in orientation or size.

From 1952 McCulloch worked at the Research Laboratory of Electronics at MIT, working primarily on [[neural network (biology)|neural network]] modelling. His team examined the visual system of the [[frog]] in consideration of McCulloch's 1947 paper, discovering that the eye provides the brain with information that is already, to a degree, organized and interpreted, instead of simply transmitting an image.

With Roberto Moreno-Díaz, he studied a formalized problem of memory. Given that neural networks can story memory by a pattern of oscillations in a circle, they studied the number of possible oscillation patterns that can be sustained by some neural network with <math>N</math> neurons. This came out to be <math>K(N) = \binom{2^N}{k}\sum_{k=1}^{2^N-1} k!</math> (Schnabel, 1966).<ref>Schnabel, C. P. J. ''Number of Modes of Oscillation of a Net of N Neurons''. Quarterly Progress Report No. 80, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Mass., January 15, 1966. P. 253.</ref> Also, they proved a universality theorem, in that for each <math>N</math>, there exists a neural network (possibly with more than <math>N</math> neurons) with <math>\log_2 K(N)</math> binary inputs, such that, for any oscillation pattern realizable by some neural network with <math>N</math> neurons, there exists a binary input for this universal network such that it exhibits the same pattern.<ref>Moreno-Díaz, R. ''Realizability of a Neural Network Capable of All Possible Modes of Oscillation''. Quarterly Progress Report No. 82, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Mass., July 15, 1966. Pp. 280-285.</ref><ref>Moreno-Díaz, R., and W. S. McCulloch. "''Circularities in nets and the concept of functional matrices''." ''Biocibernetics of the Central Nervous System, Little, Brown and Company, Boston'' (1969): 145-151.</ref><ref>{{Cite journal |last1=Moreno-Díaz |first1=Roberto |last2=Moreno-Díaz |first2=Arminda |date=2007-04-01 |title=On the legacy of W.S. McCulloch |url=https://www.sciencedirect.com/science/article/abs/pii/S0303264706002152 |journal=Biosystems |series=BIOCOMP 2005: Selected papers presented at the International Conference - Diffusion Processes in Neurobiology and Subcellular Biology |volume=88 |issue=3 |pages=185–190 |doi=10.1016/j.biosystems.2006.08.010 |bibcode=2007BiSys..88..185M |issn=0303-2647}}</ref>