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<p>Canonical Correlation Analysis (CCA) is one of the multivariate statistical methods that can be used to find relationship between two sets of variables. I highlighted challenges in analyzing high-dimensional data with CCA. Recently, Sparse CCA (SCCA) methods have been proposed to identify sparse linear combinations of two sets of variables with maximal correlation in the context of high-dimensional data. In my thesis, I compared three different SCCA approaches. I evaluated the three approaches as well as the classical CCA on simulated datasets and illustrated the methods with publicly available genomic and proteomic datasets.</p> / Master of Science (MSc)

In this dissertation, we study the existence and multiplicity of positive solutions to classes of one-dimensional singular p-Laplacian problems with nonlinear and intergral boundary conditions when the reaction termis p-superlinear or p-sublinear at infinity. In the p-superlinear case, we prove the existence of a large positive solution when a parameter is small and if, in addition, the reaction term satisfies a concavity-like condition at the origin, the existence of two positive solutions for a certain range of the parameter. In the p-sublinear case, we establish the existence of a large positive solution when a parameter is large. We also investigate the number of positive solutions for the general PHI-Laplacian with nonlinear boundary conditions when the reaction term is positive. Our results can be applied to the challenging infinite semipositone case and complement or extend previous work in the literature.Our approach depends on Amann's fixed point in a Banach space, degree theory, and comparison principles.

To assess the long-term performance of a solar thermal system, mathematical models that accurately capture the effects of heat transfer within and interactions between individual components are required. For solar domestic hot water systems, the components can include the solar collectors, storage tanks, heat exchangers, pumps, and associated piping. In addition, weather data and demand profiles are also required. Simplified models for each component are needed to reduce the computational time required to run long-term simulations. The simplified models, however, must also be sufficiently accurate in order to provide meaningful system-level results. Accurate prediction of the temperature profiles in the storage tanks of these systems is important since the temperature within the tank has a large impact on the efficiency of the entire system. TRNSYS, which is a commercial code commonly used for such simulations, contains a variety of different one-dimensional storage tank models. Previous research has indicated that these models have deficiencies in predicting experimental data. Therefore, this thesis is focussed on the analysis of the tank modelling used in TRNSYS. Results of this thesis show that the poor predictions are a result of numerical diffusion due to insufficient grid resolution. The correct theoretical profiles could be obtained by using a large number of nodes. However, this would lead to a significant increase in computational time. Alternative modelling strategies were also developed using analytical techniques to more accurately predict the temperature profiles within a storage tank while keeping a relatively low computational cost. Different models were created which considered the different mixing mechanisms present in a storage tank, such as increasing inlet temperatures with time, heat losses to the surroundings, tank wall heat conduction, and inlet jet mixing. / Thesis / Master of Applied Science (MASc)

<p> The objective of this thesis was to undertake an uncertainty analysis on the outputs from a two-dimensional hydrodynamic model. The analysis utilized an application of the Resource Management Associates' RMA2 model for the Upper St. Lawrence River in Ontario, Canada. Two uncertainty analysis methods, First-Order Second Moment (FOSM) and Monte Carlo analysis, are applied to calculate the uncertainty in water levels and velocities computed by the model.</p> <p> Both uncertainty analysis methods can be applied together with two-dimensional hydrodynamic modelling, but based on the findings of this work, the FOSM method is preferred. First, FOSM estimates of uncertainty are slightly larger than those obtained using Monte Carlo analysis. Thus, FOSM provides a conservative estimate of the uncertainty, a positive characteristic. Second, the FOSM method is simpler to apply than Monte Carlo analysis, requiring less information to describe the model inputs, fewer model executions and computations to calculate the uncertainty. Third, FOSM provides an immediate indication of the primary contributors to the uncertainty in the output, where Monte Carlo analysis requires additional effort to do the same.</p> <p> The model input that contributed the most to the uncertainty in the model outputs is the bottom resistance represented in RMA2 using Manning's n. The uncertainty in Manning's n is large and the model is sensitive to the parameter. As a result, a significant amount of uncertainty in the model outputs is contributed by this parameter.</p> <p> Uncertainty analysis is a practical addition to the two-dimensional hydrodynamic modelling process. The effort required to complete an uncertainty analysis using the FOSM method is minimal and the resulting insight is meaningful. It provides information to the model developer, quantifying how good the model actually is. It also provides a measure of the accuracy of the model for future model users or clients using hydrodynamic modelling outputs.</p> / Thesis / Master of Applied Science (MASc)