Biomedical Engineering Reference
In-Depth Information
scale than changes in firing rates and only depend on the average firing rates, we can
further simplify Equation (11.2) to
r
out
∑
i
w
i
r
in
(
t
)=
G
(
t
)
−
θ
.
(11.4)
i
This simplification is however not appropriate when we consider plasticity rules that
depend on spike time later in this chapter. Computationally, the simplest rule that
follows from Hebb's idea is probably
)
dt
=
(
dw
i
t
r
out
r
in
i
(
t
)
(
t
)
.
(11.5)
w
We will drop the '(t)' term in subsequent equations and the reader should note that
all these entities represent functions in time. After plugging in Equation (11.4), we
have
dw
i
dt
=
∑
j
w
j
r
i
j
r
in
G
,
(11.6)
w
i
If we average over a long time, we can write the rule as
dw
i
dt
=
∑
j
G
w
j
Q
ij
,
(11.7)
w
r
i
j
(
r
in
i
where
Q
ij
(
represents the average correlation between the inputs
over the training sets. If this rule is applied for a long enough time, the weight vectors
would pick out the principal eigenvector of the correlation matrix of the inputs the
neuron experienced [62].
t
)=
<
t
)
(
t
)
>
11.2 Spike-timing dependent plasticity
More recently, many studies have focused on spike-timing dependent plasticity rules
(STDP). These rules are inspired by recent studies that have tested the role of tim-
ing in synaptic plasticity by directly controling the timing of pre- and postsynaptic
spikes. Markram et al. [51], using dual intracellular recordings, found that if neuron
A repeatedly fired 10ms before neuron B, the connection from neuron A to neuron
B was strengthened. However, if neuron A consistently fired 10 ms after neuron B,
the connection was weakened. Time separations of 100ms between pre- and post-
synaptic spikes were ineffective in inducing synaptic plasticity. Similar results have
been found in hippocampal slice [21, 49], hippocampal culture [21], somatosensory
cortical slice [26], and visual cortical slice [78]. Zhang et. al. [101], working with
an
in vivo
preparation of the optic tectum of frogs, have documented the relation-
ship between changes in synaptic strength and relative timing in great detail. Earlier
studies done with field recordings suggest essentially the same rule
[36, 46]. An
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