Statistical Analysis of Random Symmetric Positive Definite Matrices Via Eigen-Decomposition

The work in this dissertation is motivated by applications in the analysis of imaging data, with an emphasis on diffusion tensor imaging (DTI), a modality of MRI used to non-invasively map the structure of the brain in living subjects. In the DTI model, the local movement of water molecules within a small region of the brain is summarized by a 3-by-3 symmetric positive-definite (SPD) matrix, called a diffusion tensor. Diffusion tensors can be uniquely associated with three-dimensional ellipsoids which, when plotted, provide an image of the brain. We are interested in analyzing diffusion tensor data on the eigen-decomposition space because the eigenvalues and eigenvectors of a diffusion tensor describe the shape and orientation of its corresponding ellipsoid, respectively. One of the major contributions of this dissertation is the creation of the first statistical estimation framework for SPD matrices using the eigen-decomposition-based scaling-rotation (SR) geometric framework from Jung et al (2015). In chapter 3, we define the set of sample scaling-rotation means of a sample of SPD matrices, propose a procedure for approximating the sample SR mean set, provide conditions under which this procedure will provide a unique solution, and provide conditions guaranteeing consistency and a Central Limit Theorem for the sample SR mean set. Our procedure for approximating the sample SR mean can also be extended to compute a weighted SR mean, which can be useful for smoothing DTI data or interpolation to improve image resolution. In chapter 4, we present moment-based hypothesis tests concerning the eigenvalue multiplicity pattern of the mean of a sample of diffusion tensors which can be used to classify the mean as one of four possible shapes: isotropic, prolate, oblate, or triaxial. The derivations of these test procedures lead to the creation of consistent estimators of the eigenvalues of the mean diffusion tensor. In the final chapter, we present a mixture distribution framework which can be used to model the variability of SPD matrices on the eigen-decomposition space, and an accompanying likelihood based estimation procedure which can be used for estimation of parameters of interest or inference via likelihood ratio tests

A Comparison of Anaerobic Power Tests using Cycle Ergometry and Non-motorized Treadmill Ergometry at Optimized Loads

International Journal of Exercise Science 16(4): 1293-1305, 2023. The purpose of this study was to compare performance markers derived from a 30-second maximal bout on a cycle ergometer (CE) and non-motorized treadmill (NMT) under optimized loads. Recreationally active participants (n = 40) volunteered for the study. Force-velocity tests on the CE and NMT were used to determine optimal resistance for peak power (PP) production. The remaining visits were randomized and counterbalanced, with a single 30-second maximal test on CE or NMT to assess PP, mean power (MP), fatigue index (FI), over the course of the 30-second test, and maximum heart rate (HRmax) and blood lactate (BLa-) taken 1-minute post. Results were that PP and MP were higher (P\u3c0.05) on CE compared to NMT for both sexes. FI did not differ among males (P=0.201) whereas females showed higher FI (P=0.002) on the CE. HRmax and BLa- were higher (P\u3c0.05) after NMT for both sexes. There was no difference for optimal braking force on NMT between males (16.65±4.49%BW) and females (14.30±3.10%BW) (P=0.061). CE optimal torque factor was higher for males (0.78±0.16 Nm/kg) compared to females (0.62±0.14 Nm/kg) (P=0.001). Overall, CE produced higher power output using optimized loads in recreationally active males and females, while NMT test resulted in a higher HRmax andBLa- concentration. These tests for anaerobic power, when performed with optimized loads, produced different results for several variables, therefore these modalities should not be considered interchangeable. Practitioners should consider which modality best mimics the activities of the person being tested when selecting a protocol

Carbohydrate Rinse Fails to Enhance Cycling Performance or Alter Metabolic and Autonomic Recovery in Recreational Cyclists

The purpose of the study was to examine the effects of carbohydrate (CHO) mouth rinsing on autonomic and metabolic recovery as well as cycling performance. Ten male recreational cyclists (age = 30 ± 6 years, VO2peak = 54.5 ± 8.1 mL·kg-1·min-1) completed a randomized, double-blind, placebo-controlled, crossover designed study. A CHO or a placebo (PLA) rinse was administered every 12.5% of a work to completion trial (75%Wmax). Heart rate variability (lnRMSSD), the respiratory exchange ratio, and plasma epinephrine, norepinephrine, insulin, glucose, free fatty acids (FFA), and lactate were measured pre- and post-exercise. The CHO rinse did not improve time to completion of the test trial (CHO: 4108 ± 307 s, PLA: 4176 ± 374 s, p = 0.545). Further, the CHO rinse did not impact autonomic recovery, as measured by lnRMSSD (p = 0.787) and epinephrine (p = 0.132). Metabolic biomarkers were also unaffected by the CHO rinse, with no differences observed in responses of FFA (p = 0.064), lactate (p = 0.302), glucose (p = 0.113) or insulin (p = 0.408). Therefore, the CHO mouth rinse does not reduce the acute sympathetic response following strenuous exercise and does not result in improvements in cycling time to completion

Thomas H. Moore House

Prepared by the Fall 2013 Conservation of Historic Building Materials class. This Historic Structure Report contains historical context, building chronology, physical descriptions, current conditions assessment, and recommended treatment and use for the historic property. The purpose of this report is to provide a current assessment of the condition of the property, recommendations for needed repairs and options for future consideration.https://scholarworks.gsu.edu/history_heritagepreservation/1030/thumbnail.jp

High-Frequency (>100 GHz) and High-Speed (<1 ps) Electronic Devices

Contains an introduction, reports on three research projects and a list of publications.Advanced Research Projects Agency Contract MDA972-90-C-0021National Aeronautics and Space Administration Grant NAG2-693National Aeronautics and Space Administration Contract 959705National Science Foundation/MRSEC Grant DMR 94-00334MIT Lincoln Laboratory Advanced Concept Program Contract BX-5464MIT Research Laboratory of Electronics Postdoctoral FellowshipRome Air Force Laboratory Graduate FellowshipU.S. Army Research Office Grant DAAL03-92-G-0251Hertz Foundation FellowshipU.S. Army Research Office/ASSERT Grant DAAH04-94-G-016