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sonable. However, the state variables of the reduced system do not have apparent
biophysical significance until transformed into the observable y(t). This implies our
choice of rest as the reset value for ξ(t).
Using the forked neuron as our test case, we implement the IAF mechanism using
the non-uniform channel model. We discretized using h ≈ 1 μm so that the nonlinear
model had 3606 variables; IRKA computed a reduced model having only 10 variables.
First we simulate using the nonlinear system, and then we compare this to the output
from the reduced system simulation. The spikes generated from both systems are
compared to determine if there are any matches. A match is said to occur when the
reduced system’s spike occurs within τref ms before or after a spike in the nonlinear
system.
In order to quantify how well the mechanism captures spiking behavior, we com-
pute the coincidence factor Γ (Kistler et al., 1997) (Jolivet et al., 2006), defined as
Acoiric A^nonijn .ZVreducec∣ (τref∕T)
(Monlin + Meduced)(l ~ Monlin (ʃref/ɪɔ)/2 ’
(2.45)
where Moniin and Meduced are the number of spikes in the nonlinear and reduced
models, respectively, and T is the length of the simulation. The coincidence factor
measures how close the spike train from the reduced model approximates that of
the nonlinear model by comparing the number of coincident spikes, Moinc1 with the
number of coincident spikes occurring by chance. Γ is scaled to ensure that Γ = 1
implies the spike trains are equal and Γ = 0 implies the spike trains would occur