Biomedical Engineering Reference
In-Depth Information
1.2
0.5
A
1.1
1.0
0.0
B
0.9
1.2
0.5
1.
1
0.8
-0.5
0.0
1.
0
0.7
-50
0
50
0.
9
t
t
(ms)
post
pre
0.8
-0.5
0.7
-50
0
50
-
t
t
(ms)
post
pre
Figure 11.6
Correlation between pre- and postsynaptic action potentials before and after STDP.
The solid curves indicate the relative probability of a presynaptic spike occurring at
time
t
pre
when a postsynaptic spike occurs at time
t
post
. A correlation of one is the
value due solely to chance occurrences of such pairs. The dashed curves show the
STDP modification function from
Figure 11.1
. (A) Before STDP, the neuron is in
the unbalanced mode with large excess excitatory drive. There is only a small excess
of presynaptic spikes prior to a postsynaptic action potential. (B) After STDP, the
neuron is in the balanced mode. There
is a larger ex
cess of presynaptic spikes prior
to a postsynaptic action potential. Adapted with permission from [79].
11.4.5.2
Correlations with different time constants
We performed a simulation where 500 of the 1000 inputs were Poisson trains with a
fixed rate and the other 500 inputs were correlated with each other with the correla-
tion function
C
ij
r
in
2
e
−|
t
|/
τ
r
in
2
Q
ij
(
t
)=
+
+
δ
(
t
)
r
in
δ
,
(11.52)
c
ij
and
C
2
0
<
i
<
500
,
0
<
j
<
500
if
C
ij
=
(11.53)
0
otherwise
.
Therefore,
<
r
out
(
t
)
r
in
i
(
t
+
t
)
>
t
j
w
j
C
i
j
r
in
2
m
(
e
t
/
τ
−
e
t
/
τ
m
e
t
/
τ
[
)+
]
c
c
m
c
m
−
τ
+
τ
c
c
w
i
r
in
τ
e
t
/
τ
j
w
j
r
in
2
=
−
θ
r
in
+
G
+
∑
+
if
t
<
0
m
m
j
w
j
C
ij
r
in
2
m
e
t
/
τ
j
w
j
r
in
2
0
(11.54)
we plotted the average correlogram between the spike trains of the inputs and the
postsynaptic neuron from the simulations for
+
∑
if
t
≥
c
m
+
τ
c
=
20
ms
in
Figure 11.7A
. We have
also plotted in thin dotted line the mirror image of the portion
of the correla
tion
curve for
t
pre
−
t
post
>
0 for visual guidance. The correlograms display a 'spike' of
c
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