THE GENERAL NEURAL NET 33 



synapse. But if any synapse is the origin of only one and the termi- 

 nus of only one neuron, the two neurons constitute a chain, and after 

 the E is determined for this chain, this synapse requires no further 

 consideration. Again, let a neuron N form a synapse with two or 

 more neurons N x , N 2 , • • • . The results are the same if we suppose N 

 replaced by two or more neurons N7, N 2 ', • •• , with identical prop- 

 erties all originating at the origin of N , but N* forming a synapse 

 with N x alone, 2VY with iV 2 alone, ••• (Pitts, 1942b). Thus the only 

 synapses requiring separate consideration are those at which two 

 or more neurons terminate. Each of the synapses of the set under 

 consideration is the terminus of two or more chains which originate 

 at other synapses of the set, and, the distribution of stimulation be- 

 ing fixed, each chain is characterized by the values of its set of four 

 parameters. In case the terminus of any of these chains is inacces- 

 sible from its origin, the a which it produces is calculable indepen- 

 dently of the value of y at its origin, and we may delete this chain 

 and add this a to the 5 at the terminus. If there happens to be only 

 one other chain terminating there, this can be combined with the 

 chain or the chains originating there and the synapse dropped out 

 of the set being considered. We therefore suppose that each synapse 

 is accessible to the origin of every chain which terminates there. 

 There is also the possibility that when the S applied at any synapse 

 is increased by the maximum a that can be produced together by all 

 the chains which terminate there, this is still below the y', or that 

 the S increased by the minimal a of all together is above the y" of 

 some chain which originates there. If so, the a produced by this 

 chain can be calculated at once, the result added to the S applied 

 there, and the chain deleted. It is clear, of course, that these dele- 

 tions, which are made possible by the inaccessibility of one synapse 

 to another, will be different for different distributions of stimulation. 



Having performed these simplifications, we suppose, before pass- 

 ing on to the most general case, that only one synapse remains. The 

 resulting net, which consists of a number of circuits all joined at a 

 single common synapse, we shall call a rosette (Pitts, 1943a), and 

 the common synapse, we shall call its center. Now if the conduction- 

 time is not the same around all these circuits, we may nevertheless, 

 with sufficient accuracy, regard these times as commensurable, and 

 we shall use their common measure as the time-unit. Let n be the 

 number of circuits, and let //, be the conduction-time of the i-th circuit. 



Now consider the contributions of the i-th chain to the stimulus 

 y at s at any time. If y(t) is the total stimulus at time t , then the 

 contribution at time t + m is 



Si + Aiy(t) when y{ ^y(t) ^yj', 



