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With this expression we have arrived at the desired relation that gives
the response density at any point in
L
2
for any stimulus density distribution
in layer
L
1
, if the distributed action function
K
is specified.
In order to make any suggestions as to the form of this distributed action
function, it is necessary to enliven the formalism used so far with physio-
logically tangible concepts. This we shall do presently. At the moment we
adopt some simplifying notations. First, we may in various instances refer
to cell assemblies distributed along surfaces (
A
) or along lines (
D
). In these
cases we shall not change symbols for s and r, although all densities refer
in these cases to units of length. This may be permissible because the units
will be clear from context. Second, we shall adopt for the discussion of gen-
eralities vector representation for the localization of our points of interest
and introduce the point vector
r
. Discrimination of layers will be done by
subscripts. We have the following correspondences:
transmitting “layer”:
x
,
y
,
z
;
r
1
;
D
1
;
A
1
;
V
2
;
collecting “layer”:
u
,
v
,
w
;
r
2
;
D
2
;
A
2
;
V
2
.
The physiological significance of the distributed action function
K
(
r
1
,
r
2
)
will become evident with the aid of figs. 29 and 30. Fig. 29a—or 29b—shows
a linear array of neurons in a small interval of length d
x
about a point
x
in
layer
L
1
. These neurons give rise to a number of axons
N
x
, some of which,
say,
N
x
(
u
1
), are destined to contact in the collecting layer
L
2
with elements
located in the vicinity of
u
1
; others, say,
N
x
(
u
2
), will make contact with ele-
ments located at
u
2
, and so on:
FIGURE 29. Departure of fibers in the transmitting layer of an action network of cell
assemblies.
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