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From this we obtain with eq. (69) the stimulus matrix
1
-
a
0
-
a
-
a
1
-
a
0
S
=
,
4
0
-
a
1
-
a
-
a
0
-
a
1
which inverted gives the following response matrix:
12
-
a
2
a
2
a
2
a
12
-
a
2
a
2
a
2
1
4
=
.
2
a
2
a
1
-
2
a
2
a
a
2
a
2
a
1
-
2
a
2
The characteristic determinant is
Da
=14
2
with the two roots
a
=±
2
. Hence, the system becomes unstable, whenever
the interaction coefficient
a
approaches +
2
(facilitation) or -
2
(inhibition).
We are now in a position to write all responses r(
j
) in terms of the stimuli
s(
i
). For the response of the first element we have
◊
()
=-
(
)
D
r
112
a
2
s
++ +
a
s
2
s s
2
a
s
4
,
1
2
3
the others are obtained by cyclic rotation of indices or directly from
R
n
.
For uniform stimulation of all elements, s(
i
) =s
o
for all
i
, the uniform
response is
1
12
a
r
=
s
,
o
o
-
which clearly depends upon the sign of the interaction coefficient, giving
increased or decreased responses for facilitation or inhibition respectively.
If uniform stimulation is maintained for
e
2
,
e
3
,
e
4
(s
2
=s
3
=s
4
=s
o
), but
element
e
1
is stimulated by a (±) superposition of s* (s
1
=s
o
+s*), and all
stimuli and responses are expressed in terms of uniform stimulus and
response we have
()
=+
o
r
r
i
s
s
*
1
b
i
o
12
12
-
+
a
a
2
a
2
12
a
2
b
=
,
bb
==
+
,
b
=
.
1
2
4
3
12
a
+
a
The quadratic terms for
a
in the numerator of
b
1
and
b
3
show clearly the
effect of “double negation” by “inhibition of inhibition”, for these terms are
independent of the sign of
a
.
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