The name is absent

56

that such an investigation is indeed warranted.

In particular, we apply a multi-site IAF mechanism to the forked neuron subject
to the same input streams that generated Figure 2.14. Since there are 3 branches and
a soma, we set p = 4 and designate as observables the voltages at the soma and the
midpoints of each branch. Threshold values are V⅛ = 22 mV at the leaf midpoints,
½h = ɪθ mV at the root midpoint, and V⅛ = 14 mV at the soma (these values
were chosen after manual trial-and-error). Using the same discretization as in §2.7.1,
IRKA computes a reduced model with к = 40 that is accurate to nearly 5 digits, and
hence A_fc ∈ R⁴⁰×⁴⁰, B_fc ∈ R⁴⁰×⁶°¹, and C_fc ∈ R⁴×⁴⁰.

Using the same input patterns as above, we find a significant increase in the accu-
racy of the spiking behavior (see Figure 2.16) with very little change in computational
cost. For the strong input case we match 56% of the actual spikes and have only a
15% mismatch rate. For the weak input case, we get 65% matched with 13% mis-
matched. The coincidence factor improves in both cases: from 0.43 to 0.73 for the
“weak” input case, and from 0.52 to 0.66 for the “strong” input case. Moreover,
the difference in simulation time was negligible when compared to the thresholding
mechanism of §2.7.1.

Table 2.1: A multi-site variable-threshold IAF mechanism improves spike-capturing accu-
racy.

Input scheme A^z_nonIi_n A^z_red_uced % Matched % Mismatched Γ

1250 weak      136     101       64.7           12.9       0.73

250 strong      582     385       56.2           15.1       0.66

<<   63   64   65   66   67   68   69   >>

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