The name is absent

95

maintain an implicit time-stepping scheme, (3.21) implies that we must compute
U^τdiag(G(t))U, where G(t) is the input synaptic conductance to each compartment.
When many synaptic inputs are present, this becomes an expensive double-matrix
product which can dominate the total simulation time. If alpha functions are used
to model synaptic events, we can decrease the number of active inputs via a shutoff
mechanism, thus greatly accelerating this computation. In fact, shutoff mechanisms
can be analogously implemented for any decaying synaptic conductance time course.

Alpha functions have a characteristic form

g(t~> =              (ɪ -                                (3.27)

where τ is the time constant and g is the maximal conductance. Now we assume that
the synaptic event is inactive after some shutoff time, t_θff, at which g(t_off) = ε and
g^,(toff) < 0 for some small tolerance ε. The truncated alpha function can then be
implemented as

{g(j'}ι An — < Aff

(3.28)

0, otherwise.

Shutoff mechanisms can significantly speed up simulations when many synaptic
inputs are used. For example, for cell AR-l-20-04-A with N = 2233, k_v = Kj = 60,
and 500 inputs with g = 2 nS and τ = 1, we observe a speed-up in calculating the
double-matrix product from 30 seconds to 3.3 seconds when the shutoff tolerance
ε = 10~⁴ is used. Now the reduced system is much more competitive with the full

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