66 MATHEMATICAL BIOPHYSICS OF THE CENTRAL NERVOUS SYSTEM 

 P(RO) = 



(15) 



-Si+7»/(<H3) °° oo oo 



f Piti) j P(C 2 ) dC 2 dCi + J p(Ci) J P(C a ) #.dk, 



-oo ^(fi+Si)/a+/i/a-S 2 -Si+7i/(<H3) a(£i+Si)//3-ft/0-S2 



P(Otf) = 



(16) 



-8 1+ h/(a-p) a(£i-:S,)/0-fi/|3-S 2 oo oo 



j p(Ci) Jp(C 2 )^C 2 ^C 1 +J 2>(Ci) JV(C 2 )<#3<#i, 



-oo -oo -Si+fe/(o-|3) /3(fi+S!)/a+Va-S2 



-S 1+ 7i/(a-(3) (3(fi+S 1 )/a+ft/a-S 2 



P(00)=J 2?(d) J"p(C*)#»#i. (17) 



-oo a(£i+Si)/0-/!/0-S 2 



Other expressions for P(RR) and for P{00) can be obtained by 

 interchanging- subscripts. These four P's are functions of S x and S 2 

 whose values are experimentally determinable; their sum is unity so 

 that only three are independent. If p(C) is given they depend upon 

 the parameters a , /5 and h; if the distribution 29(C) is assumed to be 

 normal there is an additional parameter, the standard deviation. Pear- 

 son's tables of tetrachorics can be utilized for determining these para- 

 meters from the empirical frequencies. The quantities S t and S 2 are 

 not the intensities of the external stimuli but some monotonic func- 

 tions of these; however, at the near-threshold level it is permissible 

 to regard these functions as linear. 



In the preceding paragraphs we have considered the case of two 

 stimuli simultaneously presented to the organism, with two alterna- 

 tive responses permitted. In chapter vi we considered the case where 

 a response may follow the sudden increase in the intensity of a stim- 

 ulus previously maintained at a constant level. We turn now to a 

 process of more complex form in which each of a group of stimuli 

 differing only in intensity elicits a distinct response. This involves 

 absolute discrimination though a similar mechanism may be at work 

 when relative discrimination occurs. The important point to notice is 

 that an increase in the intensity of the stimulus does not merely 

 change the strength of the response or bring into activity additional 

 elements, but may so alter the response that none of the elements 

 involved before the change is included among those active after the 

 change. 



Consider the net of Figure 5 which is a parallel interconnected 

 structure containing also circuits (Householder, 1939b). Let an affer- 



