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Chapter 5
Future Work
Each of the model reduction techniques presented in the previous chapters prompt
a number of questions about improving their efficiency and functionality, as well as
about how to optimize certain parameters. However, rather than enumerate many
small details, I will focus on two concerns. The first is a way to include more realistic
biophysics in the model and the second is a possible way to improve the performance
of the models which use the POD and DEIM.
5.1 Modeling Synaptic Inputs via Receptors
Synaptic inputs can be modeled more accurately by kinetic equations than by
alpha functions or similar conductance time courses (Destexhe et al., 1994). In the
cell, synaptic input occurs when a presynaptic neuron releases neurotransmitter into
the synaptic cleft. Neurotransmitter activates receptors on the synapse, allowing ions
to flow into the cell and thus induce changes in voltage. These processes are efficiently
modeled by (usually) first-order differential equations that dictate the fraction r of
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