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a
=
Iω
−
kω
+
a
n
(13)
In this case the presynaptic rule is expressed in terms of
a
as:
ω
=
ξ
[
a
−
a
n
+
k
]
+
(
a
−
ω
)
(14)
ω
yielding fig 3.d, which is consistent with the property of metaplasticity of the
LTD threshold.
3.2 Biological Plausibility of the Probabilistic Version of
Presynaptic Rule
In previous sections, we simplified the mathematical description of a neuron by
making the assumption of linearity in neuron activation function. In this section,
Fig. 3.
Metaplasticity and the ABS rule according to the incremental version of presy-
naptic equation. (a) LTP threshold metaplasticity according to Eq. 9: the different
curves are obtained for different values of synaptic weight
ω
. (b) LTP threshold meta-
plasticity considering heterosynaptic influence according to Eq. 11. (c) ABS theory
according to presynaptic rule incremental version in equation 12. Presynaptic activ-
ity is shown in the horizontal axis and the curves are obtained for different values of
a
n
. The weight was
ω
=0
.
5 (d) Metaplasticity of the LTD threshold according to
equation 14.
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