Computation in Neural Nets - Understanding Understanding: Essays on Cybernetics and Cognition - page 65

As a final example we show the far-reaching influence of a local pertur-
bation in a mixed net which consists of a linear array of quadrupoles as
above with an inhibitory interaction coefficient of a =-0.3, and where each
quadrupole is actively connected to its neighbor on one side, but passively
connected to its neighbor on the other side (see fig. 21). Elements which
actively connect quadrupoles transmit their full response to their neighbors.
A unit stimulus is applied to element e 1 in the first quadrupole only. The
resulting response is plotted next to each element, the length of bars
representing intensity.
This example may again be taken as an instance of the principle “action
by contagion” which we met earlier in a mixed interaction net (sea-urchin).
In this case, however, the local perturbation spreads in the form of a decay-
ing oscillation.
The discussion of interaction in nets composed of discrete linear elements
has shown thus far two serious deficiencies. The first deficiency is clearly
the insurmountable difficulty in handling efficiently even simple net con-
figurations. We shall see later that this difficulty can be circumvented at
once, if the individuality of elements is dropped and only the activity of ele-
ments associated with an infinitesimal region in space is taken into conside-
ration. The powerful apparatus developed in the theory of integral
equations will take most of the burden in establishing the response func-
tion, given a stimulus function and an interaction function.
FIGURE 21. Responses in a mixed
action-interaction network after a
single stimulus is applied to the
NW element in the first interacting
quadrupole.