Let M_k^2 be the complete, simply connected, Riemannian 2-manifold of constant curvature k ± 0. Let E be a closed, simply connected subspace of M_k^2 with the property that every two points in E are connected by a rectifi able path in E. We show that E is CAT(k) under the induced path metric.

This dissertation investigates the interactive or joint influence of autocorrelative processes (autoregressive-AR, moving average-MA, and autoregressive moving average-ARMA) and sample weights present in a longitudinal panel data set. Specifically, to what extent are the sample estimates influenced when autocorrelation (which is usually present in a panel data having correlated observations and errors) and sample weights (complex sample design feature used in longitudinal data having multi-stage sampling design) are modeled versus when they are not modeled or either one of them is taken into account. The current study utilized a Monte Carlo simulation design to vary the type and magnitude of autocorrelative processes and sample weights as factors incorporated in growth or latent curve models to evaluate the effect on sample latent curve estimates (mean intercept, mean slope, intercept variance, slope variance, and intercept slope correlation). Various latent curve models with weights or without weights were specified with an autocorrelative process and then fitted to data sets having either the AR, MA or ARMA process. The relevance and practical importance of the simulation results were ascertained by testing the joint influence of autocorrelation and weights on the Early Childhood Longitudinal Study for Kindergartens (ECLS-K) data set which is a panel data set having complex sample design features. The results indicate that autocorrelative processes and weights interact with each other as sources of error to a statistically significant degree. Accounting for just the autocorrelative process without weights or utilizing weights while ignoring the autocorrelative process may lead to bias in the sample estimates particularly in large-scale datasets in which these two sources of error are inherently embedded. The mean intercept and mean slope of latent curve models without weights was consistently underestimated when fitted to data sets having AR, MA or ARMA process. On the other hand, the intercept variance, intercept slope, and intercept slope correlation were overestimated for latent curve models with weights. However, these three estimates were not accurate as the standard errors associated with them were high. In addition, fit indices, AR and MA estimates, parsimony of the model, behavior of sample latent curve estimates, and interaction effects between autocorrelative processes and sample weights should be assessed for all the models before a particular model is deemed as most appropriate. If the AR estimate is high and MA estimate is low for a LCAR model than the other models that are fitted to a data set having sample weights and the fit indices are in the acceptable cut-off range, then the data set has a higher likelihood of having an AR process between the observations. If the MA estimate is high and AR estimate is low for a LCMA model than the other models that are fitted to a data set having sample weights and the fit indices are in the acceptable cut-off range, then the data set has a higher likelihood of having an MA process between the observations. If both AR and MA estimates are high for a LCARMA model than the other models that are fitted to a data set having sample weights and the fit indices are in the acceptable cut-off range, then the data set has a higher likelihood of having an ARMA process between the observations. The results from the current study recommends that biases from both autocorrelation and sample weights needs to be simultaneously modeled to obtain accurate estimates. The type of autocorrelation (AR, MA or ARMA), magnitude of autocorrelation, and sample weights influences the behavior of estimates and all the three facets should be carefully considered to correctly interpret the estimates especially in the context of measuring growth or change in the variable(s) of interest over time in large-scale longitudinal panel data sets.

Evaluating the resilience of transportation infrastructures, including bridges, roads, and tunnels, is a critical aspect of ensuring the ongoing functionality and reliability of urban or regional areas in the face of various disruptive events. Such infrastructures are susceptible to a range of disruptions which can have significant impacts on their ability to function effectively. Resilience refers to the capacity of an infrastructure or a system to withstand and recover from these disruptions. This research presents a framework to evaluate the resilience surface for assessing the resilience of various transportation infrastructure components. This comprehensive approach involves several steps. First, the framework identifies unique damage configurations by performing a fragility analysis. This analysis allows for a better understanding of how susceptible the infrastructure is to different hazards. Next, the framework focuses on the restoration of the affected infrastructure by developing recovery curves for each identified damage configuration. This is done by taking into account relevant restoration data and considering the specific characteristics of each configuration. Additionally, the framework acknowledges the inherent uncertainty that exists within various aspects of infrastructure resilience assessment. These uncertainties include hazard intensity, modeling uncertainty, and the restoration process itself. By incorporating these uncertainties into the framework, a more accurate and reliable assessment can be achieved. The utility of this framework is demonstrated through its application to a real-world case study involving a highway bridge located in Canada. The goal of this research is to offer decision-makers a valuable tool for evaluating the resilience of transportation infrastructure. This can contribute to more robust and reliable transportation infrastructures, capable of withstanding and recovering from a wide range of disruptive events. / Thesis / Master of Applied Science (MASc) / Resilience quantification of infrastructures is the assessment and measurement of their ability to withstand and recover from disruptive events. However, there is a significant research gap in this field, with limited studies and standardized methodologies available. This research presented a framework to quantify the hazard resiliency of infrastructures through development of resilience surface. The framework and the procedure were then numerically tested on a real bridge in Canada as a case study.

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Robotic-assisted segmentectomy is a pulmonary resection procedure that is emerging as an alternative to lobectomy for the treatment of early-stage lung cancer tumours less than 2 cm in maximal diameter. Segmentectomy offers better lung function after surgery by only removing a few segments of the lobe that contain the tumour, and sparing remaining healthy lung tissue. As tumours are being more frequently detected in their early-stages, segmentectomy has gained considerable attention for its potential as a primary treatment option for suspected nodules less than 3 cm in maximal diameter. However, there is a reluctance in adopting segmentectomy due to technical challenges while performing the operation, and the lack of high-quality prospective data compared to lobectomy, which is the current standard of care. From a technical standpoint, segmentectomy is difficult to perform because the pulmonary lines that separate segments, or intersegmental planes, are invisible. This poses a challenge for the operating surgeon in determining where to resect the lung tissue to obtain adequate margin distance from the tumour. Near-infrared mapping (NIF) with indocyanine green dye (ICG) is a recent advancement in robotic-assisted segmentectomy that provides a complete delineation of the intersegmental plane. Previous work at our center has also shown that this technique was associated with an increase in the oncological margin distance compared to the surgeons’ initially estimated resection line. Given that segmentectomy is associated with a learning curve, we evaluated whether this was observed due to our early experience in robotic-assisted segmentectomy, and hypothesized that the added benefit of ICG would diminish as more cases were performed. In Chapter 2, we used a temporal analysis to monitor surgeon experience over time, and found that the clinical utility of NIF mapping diminished after approximately 42 cases with ICG, and the surgeon began to identify the location of the intersegmental plane more accurately and consistently without ICG injection since. The second barrier in the adoption of segmentectomy is the lack of high quality-prospective data. Current evidence pertaining to the effectiveness of segmentectomy in terms of cancer-related outcomes is inconclusive and difficult to generalize to the current lung cancer population. In Chapter 3, we performed a secondary analysis of a prospectively collected database of participants who underwent robotic-assisted segmentectomy or lobectomy for tumours less than 3 cm. The oncological efficacy of segmentectomy can be evaluated by the measuring the number of lymph node stations sampled intraoperatively and rates of nodal upstaging, and comparing these outcomes to pulmonary lobectomy. These are important surrogate outcomes that can be readily evaluated, and have been shown to predict overall survival after lung resection. We observed that these outcomes, including overall survival, were similar between patients who underwent segmentectomy and lobectomy for tumours less than 3 cm. While these findings were consistent for patients that underwent segmentectomy for tumours between 2 and 3 cm, recurrence-free survival was found to be significantly lower after segmentectomy compared to lobectomy. In conclusion, the clinical utility of near-infrared mapping diminishes over time, which is indicative of an improved ability to perform robotic-assisted segmentectomy as more cases were attempted. Second, adequate lymph node evaluation can be expected after segmentectomy, reducing the likelihood of missing positive lymph nodes. Although patients who underwent segmentectomy for tumours greater than 2 cm may be at a greater risk of experiencing recurrence compared to lobectomy, this population did not experience any reductions in overall survival. / Thesis / Master of Health Sciences (MSc)

The yields of xenon and krypton from the neutron- induced fission of Am241 and Am242 have been measured with a mass spectrometer. This was accomplished by irradiating samples of Am241 for different lengths of time so that the effect of the growth of highly fissionable Am242 could be determined. These studies reveal that both the degree of fine structure in the mass yield curve and the fission-product charge distribution are dependent on the energy of the incident neutrons. This has not been previously observed for any fissioning nuclide. These studies also reveal effects of the 50-neutron shell and of the neutron-proton ratio of the fissioning nuclide on the mass yield curve. / Thesis / Doctor of Philosophy (PhD)

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