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(ii) Antisymmetric Interaction
As a final example of a distributed interaction function which sets the whole
system into action when stimulated only by that most local stimulus, the
Dirac delta function, we suggest an antisymmetric one-dimensional inter-
action function
() = sin
2
D
x
K
D
.
x
D
x
This function inhibits to the left (D<0) and facilitates to the right (D x > 0).
It is, in a sense, a close relative to the one-directional action-interaction
function of the quadrupole chain (fig. 21) discussed earlier. We apply to this
network at one point x a strong stimulus:
() = ()
x
d
x
.
The response is of the form
sin
x
() = () -
(
)
rd
x
x
a
cos
xa
-
,
x
a and a being constants.
Before concluding this highly eclectic chapter on some properties of com-
puting networks it is to be pointed out that a general theory of networks
that compute invariances on the set of all stimuli has been developed by
Pitts and McCulloch (1947). Their work has to be consulted for further
expansion and deeper penetration of the cases presented here.
5. Some Properties of Network Assembles
In this approach to networks we first considered nets composed of distin-
guishable elements. We realized that in most practical situations the indi-
vidual cell cannot be identified and we developed the notions of acting and
interacting cell assemblies whose identity was associated only with geo-
metrical concepts. The next logical step is to drop even the distinguishabil-
ity of individual nets and to consider the behavior of assemblies of nets.
Since talking about the behavior of such systems makes sense only if they
are permitted to interact with other systems—usually called the “environ-
ment”—this topic does not properly belong to an article confined to net-
works and, hence, has to be studied elsewhere (Pask, 1966). Nevertheless,
a few points may be made, from the network point of view, which illumi-
nate the gross behavior of large systems of networks in general.
We shall confine ourselves to three interrelated points that bear on the
question of stability of network assemblies. Stability of network structures
can be understood in essentially three different ways. First, in the sense, of
a constant or periodic response density within the system despite various
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