The name is absent

41

the neuron’s output is now more oscillatory, but the reduced system’s accuracy is
unchanged (Figure 2.7E-F).

Computing the BT matrices required about 72 seconds, while the 30 ms simulation
required only 0.02 seconds. At first glance this appears expensive when compared to
the nonlinear and quasi-active simulation times, both requiring about 1.3 seconds.
However, the BT matrix computation is a one-time cost, since these matrices can
now be reused to facilitate simulation with their associated morphology.

In fact, it can be seen that the decay of the normalized Hankel singular values
almost directly corresponds with the numerical accuracy achieved, as Figure 2.8 il-
lustrates on a more realistic neuron. This result is not surprising, however, given
that an error bound exists for BT model reduction (Antoulas and Sorensen, 2001).
Therefore, the normalized Hankel singular values may be used as a reliable guide to
achieving any desired numerical accuracy compared to the quasi-active system.

2.5.2 Application to Synaptic Scaling

An immediate application for such low-dimensional systems is to accurately quan-
tify how synaptic input scales with distance to the soma, also known as “dendritic
democratization” (Magee and Cook, 2000) (Hausser, 2001) (Timofeeva et al., 2008).
One standard form of synaptic input is an alpha function, which describes the input

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