The name is absent



96

system, as Table 3.10 illustrates. Compared to Table 3.6 the accuracy and speed-
ups in Table 3.11 are less, due to the fact that synaptic input is more complex than
current injection, but the reduced system is still very successful at capturing the cell’s
behavior.

Table 3.10: Alpha synapse shutoff mechanism (ε = 10 4) accelerates the reduced system
of neuron AR-l-20-04-A.

Type

Dimension

Sim. Time (sec)
Without shutoff

With shutoff

Full

N = 2233

115

115

Reduced

kv = kf = 60

41

15

Reduced

kv == kf = 90

73

32

Table 3.11: AR-l-20-04-A, N = 2233 (here kv = feʃ), 500 alpha synapses, HHA model.

kv

Speed-up

% Matched

% Mismatched

Γ

60

8.4×

86.6

22.8

0.807

75

5.9×

92.8

12.8

0.894

90

4.7×

93.9

15.1

0.886

105

3.6×

98.6

6.8

0.955

120

2.9×

98.6

5.9

0.961

3.6 Discussion

We have applied nonlinear model reduction techniques to morphologically realistic
cells in a way that preserves the input-output relationships while accurately reproduc-
ing the complete voltage dynamics. We approximate the voltage using a POD basis,
which reduces the number of state variables. Using the DEIM we build a set of spa-
tial interpolation points and basis vectors to reduce the complexity of the nonlinear



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