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those that are activated by e p . Since this is obviously an almost impossible
task, the procedure is usually reversed. One enters a particular fiber e q of
a higher nucleus, and establishes, by stimulation of elements e p , which one
of these activates e q . In this way it is the receptor field which is established,
rather than the action field. However, considering the geometrical con-
straints so far introduced, it is easy to see that, with the exception of the
anti-symmetric action function, action function K ( p , q ) and “receptor func-
tion” G ( q , p ) are identical:
GK
GK
GK
=
=
=-
,
,
S
S
r
r
(91)
.
a
a
For more relaxed geometrical constraints the expressions relating receptor
function and action function may be more complex, but are always easy to
establish.
It may have been noticed that a variety of structural properties of net-
works have been discussed without any reference to a particular action
function. Although the actual computational labor involved to obtain
stimulus-response relationships in action nets is far less than in interaction
nets, the machinery is still clumsy if nets are of appreciable sophistication.
Instead of demonstrating this clumsiness in some examples, we postpone
the discussion of such nets. In the next paragraph the appropriate mathe-
matical apparatus to bypass this clumsiness will be developed. Presently,
however, we will pick an extremely simple action net, and explore to a full
extent the conceptual machinery so far presented with the inclusion of
various examples of operation modalities of the network's constituents.
Example: Binomial Action Function
Fig. 25a represents our choice. It is a one-dimensional periodic action net
with unit periodicity, its predominant feature being lateral inhibition. The
universal action function and receptor function of this network are quickly
found by inspection and are drawn in fig. 25b and c respectively. Obviously,
these functions are symmetric, hence
*
(
) =
*
(
) =
*
(
) =
*
()
Gqp K pq K xu
,
,
-
K
D
1
1
1
1
= () ()
D
2
1
,
1
+
D
i.e.,
-=-
+=
- +
1
,
D
D
D
1
,
Ï
Ô
Ô
() =
K 1
*
D
2
,
0
,
1
,
1
,
everywhere else K 1 = 0.
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