The name is absent

113

With this partition in place, it is necessary to reorder the branches in the strong
and weak parts. This means that we assign local branch indices according to decreas-
ing dendritic depth with respect to a specific reference point. For the strong part
the soma is the reference point, and for the weak system it is the transition point
xτ- This reordering allows for construction of a coupled “Hines” matrix for which
Gaussian Elimination can efficiently be used. As a consequence of the reordering, the
transition point xτ lies at the proximal end of branch β_w = B_w in the local ordering of
the weak part, but xτ lies at the distal end of branch β_s ∈ [1, B_s]. Thus the absolute
voltages for the strong and weak parts of branch bτ in the local indexing are denoted
by Vβ_s,s and Vβ_w,_w> and the radii of these components are denoted by aρ_s,_s and ap_w>_w.

The boundary conditions, initial conditions, and soma conditions for the strong-
weak model are the same as those given in (2.19)-(2.26), but we must include condi-
tions at the transition point to account for the strong-weak coupling. The voltage at
the transition point xτ is given by

V_τ(t) = Vρ_sts(xτ,t) = Vρ_wtiυ(xτ,t), Vτ(t) = Vτ(t)-Vt- (4.18)

We assume that the dendritic radii are not discontinuous in space, and thus continuity
of current at the transition point requires

∂_xVβ_s,_s(x_τ,t) = ∂_xυ_0wrw(x_τ,t).

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