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transition location x?. Choosing a transition location that is too close to the soma
will cut out important active dendritic segments, but choosing xτ to be too far out in
the morphology may leave too many passive segments that are not well-approximated
in the strong part. My method for selecting this location has been by inspection of
the morphology. However, for a general-purpose implementation, this ought to be
algorithmic and should remove much of the burden of selection from the user. For
instance, a transition location selection algorithm could suggest candidate locations by
analyzing voltage data to determine where the voltage attenuates to a small fraction
of the amplitude of an action potential.
Multiple Transition Locations
Depending on the branching pattern of the morphology, it may make sense to
consider having multiple transition locations. This could occur if there are multiple
apical tufts, or if there is not a sufficiently long dendrite connecting the weak and
strong parts. If there are p transition points, then the complete weak system is really
a set of p smaller weak systems that are each coupled to the strong system but not
to each other, leading to a quasi-active matrix of the block diagonal form
Qi
(4.23)
Qp
where the matrices on the diagonal correspond to the individual small weak systems.
To compute the reduction of weak systems of this form, there are two options, both
of which incur extra computational cost and which alter the entries of the coupled
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