Bursting Activity in Weakly Electric Fish - Computational Neuroscience: A Comprehensive Approach - page 224

to the right of the threshold, q, yields the probability of correct detection, P D .The
right tail of the distribution P corresponds to the probability of false

alarms, P FA . By varying the threshold value, q, P D can be determined as a func-
tion of P FA . The resulting curves are called ROC curves ( Figure 8.7c) . The larger
the area under a given curve the better is the detection performance. However, false
alarms are not the only kind of error that can occur. The second type of error happens
when a spike is missed because the corresponding projection value is below thresh-
old ( P

( h f , ( s ) | r = 0 )

q

to the left of q). Therefore, a measure of the misclassification
error has to incorporate both, the probability of false alarms and the probability of
missed events: P E =

( h f , ( s ) | r = 1 )

q

. The best classification performance of an
ideal observer corresponds to the minimum of the plot of P E versus P FA ( Figure 8.7d) .
As is evident from Figure 8.7b, the probability distribution of stimulus projections
for burst spikes is more clearly separated from the distribution of stimuli preceding a
spikeless bin than is the one for isolated or all spikes. Consequently, the ROC curve
for burst spikes rises more steeply than the one for isolated spikes and all spikes
(Figure 8.7c) yielding the lowest misclassification errors (Figure 8.7d). The superior
feature extraction performance of burst spikes was typical for all cells studied so far
in the CMS and LS of the weakly electric fish, Eigenmannia (overall 133 pyramidal
cells [40, 68, 69, 86]).
When the same analysis was applied to spike trains of primary afferents, they con-
sistently performed worse than pyramidal cells ( Figure 8.7e) [86] suggesting that
information is filtered in different ways at the first two stages of electrosensory pro-
cessing. Feature extraction analysis also revealed differences in performance be-
tween cells recorded in different maps of the ELL. Cells from the CMS displayed
lower misclassification errors than cells from the LS ( Figure 8.7f) [86]. This find-
ing correlates well with the different behavioral significance attributed to the two
maps. The CMS has been shown by lesion experiments [85] to be necessary and
sufficient for JAR behavior, which is known to involve the correlation of up- and
downstrokes in stimulus amplitude with advances or delays in EOD phase [52]. The
LS, on the other hand, was shown to be necessary and sufficient for the processing
of electrocommunicatory signals [85], which may involve a more complex analysis
of the electrosensory input.
Recently, the analysis of electrosensory information transmission was extended
to simultaneously recorded spike trains of pairs of pyramidal cells with overlapping
receptive fields [68]. Cross-correlation analysis showed that correlations in spike
timing between cells of the same type (two E-units or two I-units) were broad (tens
of milliseconds) and were not caused by shared synaptic input, but were induced by
the independent coupling of both cells to the stimulus. Feature extraction analysis
demonstrated that spikes of two nearby cells occurring within a coincidence time
window of 5 to 10 ms significantly improved the reliability of feature extraction
compared to burst spikes of the individual neurons ( Figure 8.8b, c ). Interestingly,
a large fraction of the coincident spikes occurred in bursts (for a coincidence time
window of 5 ms, 63

0 . 5 [ P FA +( 1 − P D )]

standard deviation; see Figure 8.8a) . This finding
supports the thesis that coincident bursts of spikes may constitute the most reliable
neural code [76]. The similar time scales of the typical intraburst interspike interval

± 15%, mean ±