The name is absent

IOO

branching patterns, such as Purkinje neurons (Stuart et al., 2008). However, cells such
as pyramidal neurons with branching patterns that are organized into two distinct
dendritic tufts are better suited for success with the reduced strong-weak model.

Here I derive the strong-weak model and its reduction, and I demonstrate that it
improves upon the spike-capturing accuracy of the reduced model that uses only the
POD and DEIM techniques. First I begin with the derivation for a uniform fiber in
order to more clearly show the changes that occur, and then I generalize the derivation
to apply to any morphology.

4.1 Constructing the Strong-Weak Model

I begin with the simplest morphology, a uniform fiber of radius a and length £.
Using an ion channel model that yields weakly excitable distal dendrites (see Table
B.3), we identify the transition location xτ on the fiber at which we say the voltage
behavior transitions from strong (active) to weak (quasi-active). The method to
identify æʃ is to be determined, but once we have it we can partition the fiber into
two separate fibers, one strong (from x = 0 to x = xτ) and one weak (from x = xγ
to x = £), which join at the point xγ, as shown in Figure 4.1.

The absolute voltages of each fiber will be denoted V_s and V_w, while the voltages
with respect to rest will be denoted v_s and v_w. Similarly, Vp and υτ will denote the

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