Biomedical Engineering Reference
In-Depth Information
Noise shaping has been observed in the sen-
sory system of the electric fish that detects the
perturbation of the ambient electric field. The
intensity of the receptive field directly modu-
lates the firing rate of the afferent neurons. The
firing rates are synchronized where spikes with
long interspike intervals follow spikes with
short interspike intervals. This correlation
between the interspike intervals leads to a noise-
shaping effect, as shown in Figure 2.6 d, where
the noise is shifted out of the input stimuli [34] .
The role of synaptic weights W ij in noise shaping
is not yet understood. These network parameters
have to be learned and their values are critical for
the successful exploitation of noise shaping and
stochastic resonance. Synaptic learning and
adaptation are the topics of the next section.
spikes. The increase or decrease in the strength
of the synapse ( W ) depends on whether the pre-
synaptic spike arrives before or after the post-
synaptic spike and the time duration between
the pre- and postsynaptic spikes as illustrated in
Figure 2.7 . If the presynaptic spike were gener-
ated at time t j and the postsynaptic spike were
generated at time t i , then one form of STDP can
be mathematically expressed as
W ij ( t ) sgn( t ) e | t | ,
(2.6)
where Δ t = t j t i , sgn( · ) denotes the sign of its
argument, whereas A and τ refer to the ampli-
tude and time parameters of the synapse,
respectively. Depending on the retention time
of the synapse, increase of weight is referred as
the short-term potentiation (STP) or long-term
potentiation (LTP). Similarly, the decrease of
weight is referred to as the short-term depres-
sion (STD) or long-term depression (LTD).
Equation (2.6) is the time-domain representa-
tion of the Hebbian rule
2.4 L EARNING AND ADAPTAT ION
The primary mechanism of learning and
adaptation in the nervous system is the spike-
time-dependent plasticity (STDP). Although
different models have been reported for describ-
ing STDP, all of them agree on the causal
relationship between the pre- and postsynaptic
W ij [ n ]=η y i [ n ] x j [ n ] ,
(2.7)
where x i [ n ] and y j [ n ] are the pre- and postsynap-
tic signal amplitudes, respectively, and n denotes
the learning-rate parameter. The causality in
Preneuron
Pre j
Postneuron
Post i
LTP:
Pre before post
Ganglion cell in
ampullary afferent
of electric fish
t j - t i
0
LTD:
Post before pre
-40 0 40
ms
t pre - t post
t pre : Time of electron organ discharge
t post : Time of stimulus
(a)
(b)
FIGURE 2.7
(a) STDP and (b) plasticity in electric fish. Part (b) is adapted from Ref. 35 .
 
Search WWH ::




Custom Search