PARALLEL, INTERCONNECTED NEURONS 



15 



eralization of the mechanism just discussed, consider the following 

 (cf. Rashevsky, 1938, chap. xxii). The neurons N„ and N 22 are ex- 

 citatory, originating, respectively, at s 1 and s 2 , terminating, respec- 

 tively, at s\ and s' 2 . The neurons N 12 and AT. 21 are inhibitory, originat- 

 ing, respectively, at s x and s 2 , terminating, respectively, at s' 2 and s\ . 

 Let us restrict ourselves here to a range of intensities over which the 

 linear approximations to the functions </> and y> are adequate. Then, 

 stimuli Si and S 2 being applied at s 3 and s 2 , we have 



<*i — «n (Si — /in) + a 21 (S 2 — h 21 ), 

 a 2 = ai2 (Si — /i-i 2 ) + a 22 (S 2 — /l 22 ) , 



(1) 



when the quantities within the parentheses are all positive. When 

 any of these quantities within parentheses is negative, however, the 

 term is deleted. The conditions for the excitation of 2v\ and N 2 are, 

 respectively, a 1 > h x and <t 2 > h? . 



A geometric representation of these conditions is easily obtained 

 on the (Si , S 2 ) -plane. The graph of the relation <ti = h x is a broken 

 line consisting of a single vertical ray of abscissa h xl + hja xi extend- 

 ing downward to infinity from the ordinate hz X , and a ray extending 

 up and to the right with slope -a n /a 21 . Note that this slope is posi- 

 tive, since, N 21 being inhibitory, a 2] is negative. Then the region de- 

 fined by o-i > hi is that to the right of and below the broken line. Like- 

 wise the region defined by or 2 > Ju consists of those points above and 

 to the left of a certain broken line which consists of a horizontal ray 

 extending to the left, and a ray of positive slope. If these regions 

 overlap (Figure 3), it is possible to have both N x and N 2 acting simul- 

 taneously. Otherwise it is not possible. 



Figure 3 



These regions necessarily overlap if the determinant of the co- 

 efficients in equation (1) is positive: 



