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3.3.2.4 Branch-Ortho and V-Slim Implementation
We can efficiently apply both Branch-Ortho and V-Slim if we consider the struc-
ture of the snapshots. The initial set 5 is likely to have a significant number of
inactive snapshots, because of either delay due to onset of the stimulus or of the de-
cay back to rest after hyperpolarization. We call the set of active snapshots from this
initial set the global active zone, <Sgιobab since it defines when any part of the neuron
is active. Applying Branch-Ortho to the global active zone will produce a smaller
orthogonalized snapshot set than applying it to all of S, so it is natural to use V-Slim
on S to obtain ¾obai before applying Branch-Ortho.
Once the orthogonalized snapshot set is in hand, we apply V-Slim again to find
the local active zone for each route, that is, the set of snapshots in Cj that are active
for route j. The local active zone is often significantly smaller than Cj because an
individual route is not active during all of the global active zone, but rather it could
be inactive when other routes are active (due to travel time of the action potential
or different dendritic lengths). Thus applying V-Slim to the orthogonalized snapshot
set filters out these unnecessary local snapshots and can drastically reduce the size
of the final snapshot set.
Thus our implementation of Branch-Ortho and V-Slim uses a 3-step process. First
we apply V-Slim with a tolerance εgιobaj to S to obtain the global active zone, ⅜obaι∙
Next we run Branch-Ortho with Cj = 5gιobaι to obtain 5. Finally, we apply V-Slim
with a tolerance of ɛiɑeaɪ tθ <5, which effectively isolates the local active zones for each