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