CHAINS OF NEURONS IN STEADY-STATE ACTIVITY 11 



by more than Hi that N t is in a state of maximal activity. Then (cf. 

 Pitts, 1942a) : 



A. Let there be an odd number of inhibitory neurons between Si and 

 Sj . Then if, for given S i+1 , • • • , Sj , it can occur that both N% and ZV, 

 are inactive, or that both are in maximal activity, s j+1 is inaccessible 

 to Si , and a fortiori, s n to s . 



B. Let there be an even number of inhibitory neurons, or none, be- 

 tween Si and Sj . Then if, for given Si +1 , • • • , S, ■ , it can occur that Nj 

 is at rest while Ni is in maximal activity, or that Nj is in maximal 

 activity while Ni is at rest, s, +1 is inaccessible to s ; , and a fortiori, 

 s n x>o Sq . 



Consider case A, the first alternative. Making Ni active could 

 decrease, but could not increase, the activity of Nj and hence could 

 not initiate activity in Nj . Similarly in the second alternative, dimin- 

 ishing the activity of Ni could increase, but could not decrease that of 

 Ni , and since Nj is already in maximal activity, the resulting a can 

 not be further increased. Analogous considerations apply to case B. 



Accessibility is denned only with reference to a given distribu- 

 tion of the stimulation, supposedly fixed, applied at all synapses of 

 the chain except at the origin. However, if, the distribution being 

 fixed, s n is accessible to s , then, still with the same applied distribu- 

 tion, rj n is a linear function of t] when ^ lies between certain limits, 

 and elsewhere rj n is constant. Now each rji defined the excess of the 

 total stimulation at Si over the threshold hi of Ni . Hence if 



Vi = rji + hi 



is the total stimulation, yi is a linear function of y when y lies be- 

 tween suitable limits. This is the property postulated of single neu- 

 rons for this discussion. To get an explicit representation, let 



E = a,,-! (S n -! — /&„-i) + • • • + a n _ a a„_ 2 • • • a t (S x — h^) 



- a„_i • • • a h , (9) 



A Ct n _i 0C n _2 ■ • • (Xo . 



Then for suitable y' and y" we have 



y n = S n + 3 + Ay' when y fl = V' , 



y n = S n + S + Ay when y' < y < y" , (10) 



y n = S n + S + Ay" when y ^ y" . 



The quantities E , y and y" depend upon the applied stimulation. The 

 A does not. 



With reference to the steady-state dependence of <r upon S , the 

 properties of a chain of neurons are seen to be very similar to those 

 of a single neuron. This is true especially in the case when a constant 



