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Reduced Order Modeling for Optimization of Large Scale Dynamical Systems
This thesis compares different techniques for applying reduced order modeling to PDE constrained optimization and develops a new method based on recent work by Dihlmann and Haasdonk. Model reduction techniques have been ...
Adaptive Reduction of Large Spiking Neurons
This thesis develops adaptive reduction approaches for various models of large spiking neurons. Most neurons are like dendritic trees with many branches, and they communicate by nonlinear spiking behaviors. However, with ...
Moment Matching and Modal Truncation for Linear Systems
While moment matching can effectively reduce the dimension of a linear, time-invariant system, it can simultaneously fail to improve the stable time-step for the forward Euler scheme. In the context of a semi-discrete ...
The Neural Computations of Spatial Memory from Single Cells to Networks
Studies of spatial memory provide valuable insight into more general mnemonic functions, for by observing the activity of cells such as place cells, one can follow a subject’s dynamic representation of a changing environment. ...