Computation in Neural Nets - Understanding Understanding: Essays on Cybernetics and Cognition - page 45

this out, we propose to investigate what happens as pulses, with various
frequencies, pass over various fibers.

3.1.2. Asynchronism

Assume that along each fiber X i travels a periodic chain of rectangular
pulses with universal pulse width D t (see fig. 14), but with time intervals t i
varying from fiber to fiber. The probability that fiber X i activates its synap-
tic junctions at an arbitrary instant of time is clearly

duration of pulse
duration of pulse interval

D
t

t

(20)

p = = ,

i

i

or, replacing the periodic pulse interval on fiber X i by the frequency f i ,
we have

pf

=D,

t (21)

i

for the probability that X i 's synaptic junctions are activated, and the
probability

q =- 1 p (22)

i i

that they are inactivated. The probability of a particular input state X ( x 1 ,
x 2 ,..., x N ) which is characterized by the distribution of “ones” and “zeros”
of the input values x i , and which may be represented by an N -digit binary
number

0

££ - X 2

N

1 ,

(23)

N

 2

i - 1

Xx = , x = 0 1 , , (24)

i i

1

is given by the Bernoulli product

FIGURE 14. Schematic of pulse width,
pulse interval and refractory period.