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Chapter 3
Nonlinear Model Reduction
This chapter, like the previous one, follows almost verbatim from another paper by
Kellems, Chaturantabut, Sorensen, and Cox, which has been published in the Journal
of Computational Neuroscience (Kellems et al., 2010), which is used here, with some
modifications, with kind permission from Springer ScienceTBusiness Media: Journal
of Computational Neuroscience, Morphologically accurate reduced order modeling of
spiking neurons, published online March 19, 2010, A. R. Kellems, S. Chaturantabut,
D. C. Sorensen, and S. J. Cox, copyright Springer ScienceTBusiness Media, LLC
2010.
Here we extend the results of our previous work to reproduce the full nonlinear
behavior of morphologically accurate models by applying two model reduction tech-
niques. The first reduces the number of state variables, while the second reduces
the complexity of the nonlinear term by interpolating at a small number of dendritic
locations. These techniques preserve the spatial precision of synaptic input while
reproducing the global voltage dynamics, including both subthreshold and spiking
behaviors.