The name is absent

71

provides accurate results for the reduced system.

For the purpose of analyzing spiking behavior, we need only consider the voltage
traces from one site (namely, the soma). It is easy to obtain this voltage v_soma from the
reduced system via (3.11), but computing the full matrix-vector product at each time
step becomes expensive. However, noting that v_soma = U(j_soma, : )v, it is clear that
performing this inner product is much cheaper. Thus we can accelerate the reduced
system by saving voltage data at different temporal resolutions: a fine resolution for
the soma, and a coarse one everywhere else. For instance, saving the somatic potential
every r_s time-steps and saving all other potentials every r_c time-steps, where r_s < r_c,
will reduce the computational expense of (3.11) while still giving the detail we desire
at the soma. In this chapter, all timings reflect the use of r_s = 1 and r_c = 10.

3.3 Results on Simplified Morphologies

3.3.1 Straight Fiber

Consider a uniform fiber that is 1 mm long with N — 1401 compartments with
HH kinetics. We generate a reduced model using 200 snapshots over 10 ms (solving
(3.5)-(3.8) with ∆i = 0.01 ms) for both the POD and DEIM bases by applying
a suprathreshold step current of 500 pA for 1 ms at the distal end. This choice
of stimulus location permits the action potential to traverse the whole fiber, thus
providing a sufficiently rich set of snapshots from which to build the reduced system
(see Figure 3.1 A). Computing the singular values for the POD and DEIM snapshot

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