We examine the problem of staffing refreshment stations at a long distance road race. A race is modeled as a mixed queueing network in which the required number of servers at each service station has to be estimated. Two models to represent the progress of runners along a long distance road race course are developed. One model is a single-class model that allows a road race manager to staff service stations assuming the runners are identical to those in some historical dataset. Another model is a multi-class simulation model that allows a road race manager to simulate a race of any number of runners, classified based on their running pace into different runner classes. Both the single-class model and the multi-class model include estimates for the rates at which the runners arrive at specified locations along the course. The arrival rates, combined with assumed service rates, allow us to base staffing decisions on the Erlang loss formula or a lesser known staffing rule that gives a lower bound for the required number of servers. We develop a staffing strategy that we call the Peak Arrival Staffing Bound (PASB), which is based on this staffing bound. The PASB and the Erlang loss formula are implemented in the single-class model and the multi-class simulation model. By way of numerical experiments, we find that the PASB is numerically stable and can be used to get staffing results regardless of the traffic intensity. This finding is in contrast to the Erlang loss formula, which is known to become numerically unstable and overflows when the traffic intensity exceeds 171. We compare numerical results of the PASB and the Erlang loss formula with a blocking probability level of 5% and find that when iii the traffic intensity is high, staffing results based on the PASB are more conservative than staffing results based on the Erlang loss formula. As the traffic intensity gets lower, we find that staffing results based on the PASB are similar to staffing results based on the Erlang loss formula. These findings suggest that the PASB can be a valuable tool to aid race directors in making staffing decisions for races of all traffic intensities

Athletes complete a balance of training loads and rest periods, risking overtraining when this balance favors excessive training. Diagnostic biomarkers have been suggested but a clear diagnostic method is not available. This preliminary study's objective was to use data standardization to improve an electronic nose's (enose) discrimination model for athletes' breathprints after cumulative and acute training loads. Collegiate long distance runners were observed throughout competitive training seasons. Prolonged training effects were observed through Profile of Mood States (POMS) surveys and blood and breath samples collected at the beginning (Pre-Study) and end of the training season (Post-Study). Immediate training effects were observed for one low (LI) and one high (HI) intensity acute training load. Subjects provided blood and breath samples before the LI (BSR) and HI (BLR), completed the training load, and provided blood and breath samples after each training load (ASR; ALR). Blood was analyzed for antioxidant enzymes (catalase, glutathione peroxidase, and glutathione reductase). Breath samples were analyzed with a Cyranose® 320 (C320) enose. Age, gender, and training loads affected oxidative states, with the HI having more effect than the LI. Mood profiles indicated healthy and successful athletes. Neither POMS nor blood parameters suggested overtrained athletes. The C320 successfully discriminated between breathprints of athletes correlating to the training loads. Direct data standardization through carbon dioxide as a baseline sensor purge correctly classified 100 percent of the data through linear discriminant analysis (LDA). Indirect data standardization by subtracting Pre-Study data from the subsequent data classes (e.g. BSR) correctly classified 96 percent of the data. An LDA on the combined blood parameters correctly classified 61.9 percent of the data. The blood analyses required invasive sample collections and involved procedures that took a long time (hours). In comparison, the best C320 model correctly classified 96 percent of the data and required less invasive sample collections, simple analysis, and short result times (minutes). Evidence suggested the C320 will provide a simple and noninvasive method for clinically diagnosing the onset of overtraining. The unit is small, handheld, rapid, and noninvasive so it could also be used on- site to provide immediate feedback for training optimization. / Ph. D.

Athletic performance is improved by increasing training loads but it is difficult to determine an athlete's response to a training load and the amount of stress incurred. This makes athletes susceptible to overtraining, leading to decreased performance levels, due to physical exhaustion and oxidative stress. Past studies have observed a myriad of biomarkers without conclusively identifying a clinically specific marker for overtraining due to oxidative stress. These methods require invasive testing and lengthy result times, making real-time adjustments of training programs to prevent overtraining difficult. The use of an electronic nose (enose) as a non-invasive evaluation tool will provide immediate feedback on training stress, allowing for real-time training adjustments for performance optimization. Two long distance runners (one male and one female) completed a pilot study. Both performed a short run and the female performed a long run. Blood samples were collected from each athlete before and after each run and analyzed for catalase and GPx activity. Breath samples were also collected before and after each run and analyzed by an enose. Multivariate analyses of combined blood data yielded better results than individual analyses. Although data was limited for this pilot study, canonical discriminant analyses (CDA) showed separation between before and after run and between short and long run breath samples. Cross validations also found up to a 77.8 percent prediction accuracy for the enose. Results indicate an enose is feasible for detecting changes in the breath occurring after physically demanding exercise perhaps due to oxidative stress incurred during the exercise. / Master of Science

First demonstrated by Isaac Newton in his prism experiment, angular dispersion (AD) is a prevalent effect in optics where each wavelength in a pulsed field propagates at a different angle. Angular dispersion occurs after a collimated pulse traverses a diffractive or dispersive device and, as a result, helps modify the group velocity of a pulse in free space and introduces group-velocity dispersion into the freely propagating wave packet. These are essential ingredients in group-velocity matching and dispersion cancellation in various optical settings. With 300 years of development, it was only recently that a new class of angular dispersion materialized as non-differentiable AD. This non-differentiable AD has also been studied under the moniker space-time wave packets (STWP) and has shown to be propagation-invariant and possess arbitrary group velocity. In this dissertation, I will study (1) the underpinning theory of how non-differentiable AD allows for an optical field to break the pre-conceived notions of group velocity, group velocity dispersion (GVD), and pulse front tilt for on-axis propagation through analytical and experimental demonstrations. From these developments, I will (2) apply these concepts of non-differentiable AD to dispersive materials. I will validate these analytical predictions through experiments showing that propagation-invariant wave packets can also be supported in normal and anomalous media. Moreover, I will prove, through the use of non-differentiable AD, that the dispersive properties of a material can be overwritten to produce arbitrary group velocity and GVD characteristics. With this new information on propagation-invariant fields in dispersive materials, I will (3) exhibit new classes of optical fields that were previously theorized but never synthesized in dispersive materials, such as the X- to O- transition in anomalous GVD materials, which will be connected to the de-Broglie-Mackinnon wave packet and particle wave packets. To address the propagation invariance of non-differentiable AD, I will (4) demonstrate the STWP propagation throughout a kilometer in a turbulent environment and develop a new Rayleigh length for the STWP. Finally, I will (5) establish the consequences of discretization on the non-differentiable AD and produce a new form of the Talbot effect in which the temporal and spatial degrees of freedom are interlocked along with independent spatial and temporal Talbot effects in free space.

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The issue of protecting a fiber communication system is of considerable concern mainly because of the fiber's capability of carrying a large amount of traffic. In this study, we are concerned with the role of topology in relation to the survivability and network cost. Studying three simple network topologies, the ring, hub and mesh topologies, the ring topology is found to have many advantages for high capacity communication systems. Combinations of the simple network topologies may be used to combine the advantages of each topology. A toroidal grid topology, which combines advantages of ring and mesh topologies, is described and evaluated. Analytic results shows that the toroidal grid achieves survivability with lower incremental costs compared to the ring topology. The analytical results are limited to simple geometric and uniform traffic models. A computer program is developed to analyze the performance of more realistic networks. The computer results show that the length of a network system is a major factor affecting the cost of the network. The idea of having a multiply interconnected ring system appears to be an attractive topology for long-distance applications. / Master of Science

The purpose of this study was to determine why South African long-distance runners start and continue to run long distances, what perceived psychological benefits and negative effects they experience as a result of their involvement in the sport, and what thoughts and emotions are associated with the runner's high. Questionnaires were sent to 2 000 1992 Two Oceans Marathon participants and 777 responded. Results show that South African long-distance runners start running chiefly for physical fitness and health reasons, and continue for these reasons as well as psychological benefit reasons. As a result of their involvement in the sport, they experience psychological benefits such as a positive mood, positive self-image and positive mental outlook. When unable to run, these benefits are reversed. They also experience negative effects such as relationship problems because of long-distance running. Many thoughts and emotions are associated with the runner's high, but most define it as an euphoric feeling / Art History, Visual Arts & Musicology / M.A. (Psychology)