The name is absent

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veloped a branchwise orthogonalization algorithm that improves the accuracy of the
POD÷DEIM system, and a snapshot elimination algorithm that removes snapshots
that provide little information. Using these techniques together, spike times can be
accurately computed to within 2 ms with coincidence factors Γ ≥ 0.9 for a broad
class of realistic neurons, and simulation times can decrease by a factor of nearly 10.

While these model reduction techniques perform very well in isolation, together
they can be even more effective. The Reduced Strong-Weak (RSW) model incorpo-
rates a reduced linear system to model regions with weak (linear) dynamics while
using a POD+DEIM system to model the dynamics of strong (nonlinear) regions.
This method is still under development, so the main contribution of this thesis is
to present the theory and derivation for this model. However, I have also offered
computational evidence that the RSW model can be more accurate than the linear
or nonlinear reduced models individually.

Until now, model reduction of realistic spiking neurons was not robust to inputs
nor faithful to the spatial description of the cell. In this thesis I have developed
and implemented multiple techniques that satisfy these two requirements and out-
perform all current model reduction efforts on such cells. These results demonstrate
that hidden within the complicated dendritic structure there exists a low-dimensional
subspace that describes the neuronal dynamics. This knowledge is important not only
because neuronal simulations can be drastically accelerated, but also because it en-
courages exploration into model reduction for other complex systems in the brain.

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