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List of Figures

2.1 Circuit diagram of a single integrate-and-fire cell............ 13

2.2 Hodgkin-Huxley gating variable functions ............... 14

2.3 Circuit diagram of the Hodgkin-Huxley cell .............. 15

2.4 Resonance properties of isopotential Hodgkin-Huxley cell....... 19

2.5 Demo neuron with labeling scheme................... 22

2.6 Morphologies used in quasi-active model reduction study....... 39

2.7 Forked neuron Balanced Truncation summary results......... 40

2.8 Converging accuracy for the quasi-active versus reduced system ... 42

2.9 Dendritic democratization in a forked neuron.............. 43

2.10 Dendritic democratization in a realistic neuron............. 44

2.11 Resonant frequency plots for forked neuron............... 47

2.12 Computation time and error for IRKA on cell AR-l-20-04-A..... 48

2.13 Computation time and error for IRKA on cell n408 .......... 50

2.14 Spike statistics for naïve quasi-integrate-and-fire reduced model ... 53

2.15 Soma potentials for quasi-integrate-and-fire reduced model...... 54

2.16 Raster diagrams for multi-site quasi-integrate-and-fire reduced model 55

3.1 POD and EIM description for Hodgkin-Huxley fiber ......... 72

3.2 Soma potentials for nonlinear reduction of HHA fiber......... 76

3.3 Illustration of the Branch-Ortho and V-Slim algorithms........ 78

3.4 DEIM points with and without branchwise orthogonalization..... 85

3.5 Somatic potentials for forked neuron with branch-ortho........ 86

3.6 Binary branching cell of depth 3 obeying Rall’s 3/2 power law .... 87

3.7 Accuracy of P0D+EIM reduced system for cell AR-1-20-04-A .... 88

3.8 P0D+EIM accuracy for multiple cells ................. 90

3.9 Dendritic voltage traces for cell AR-l-20-04-A with MIG channel model 92

3.10 P0D+EIM accuracy for multiple cells with MIG channel model ... 94

4.1 Strong-weak model schematic on fiber.................. 101

4.2 Strong-weak partitioning of a realistic cell ............... 112

4.3 Accuracy of RSW and P0D÷DEIM models for cell pl8........ 122

4.4 Dendritic voltage traces for cell pl8 with MIG channel model..... 123