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119

∆r = 1 μτn, the discretized cell consists of N = 1501 compartments, and the strong
and weak parts have
Ns = 481 and Nw = 1019 compartments, respectively. I ran
two different simulation sets, one with the MIG ion channel model and one with the
MIG-P model. I ran 20 simulations of 1000 ms each using the full, POD⅛DEIM,
and RSW models. For each simulation I applied 1000 step current inputs lasting
0 5 ms and having amplitudes of 0-250 pA to random locations. I computed the
performance statistics for both reduced models against the full model, and these
results are summarized in Table 4.2.

Note that when the MIG-P model is used, the RSW system is significantly more
accurate at smaller reduced system sizes than the POD+DEIM system is. While the
RSW system’s timings are worse compared to the POD+DEIM system’s, the RSW
code is not yet optimized. Therefore I believe that, as mentioned in §4.1.3, with a
better implementation the RSW system’s timings should scale similarly to those of
the POD÷DEIM system. Also worth noting is that for the MIG-P model, the RSW
system of size
ks = 40 achieves a Γ that is about 0.1 higher than that of the best
POD÷DEIM system
(kv = 60). Hence I hypothesize that when the weak part of the
neuron consists of dendrites with mainly passive conductances, the RSW model will
perform better than if there are active conductances present, even if these active ones
have very little effect on the voltage dynamics.



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