109
We define the reduced strong gating variables by
ws = Pws
and we approximate the strong nonlinear term N by applying the matrices obtained
from the DEIM as in (3.14). Substituting these into (4.17) and simplifying yields the
fully reduced strong-weak (RSW) system
∂t
ξ
CmV g
0
RN(U(:, z)vs, ws)
0J ɪ 1 Γ¾M
UτΦJ 2πα∆τ ∣UτIs(t)
where R ∈ JRfcsxfcs.
4.1.3 Results for the Reduced Strong-Weak Fiber
The uniform fiber is not morphologically interesting, but it can be used as a proof-
of-concept. Since the RSW model is only really useful for weakly excitable dendrites,
we apply the MIG channel model (Table B.3) to the fiber. I run 20 simulations of 1000
ms each with 1000 step current inputs, each lasting 0-2 ms and having amplitudes of
0-500 pA, applied to random locations on the fiber.
To assess the accuracy of this new method, I simulate the full system and two
RSW systems, with xj∙ located 500 μm and 400 lum, respectively, from the distal end,
and I compute the spike-capturing statistics as described in §3.3.1. I also simulate
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