Pollanen, Marco

This thesis is focused on studying the population dynamics of a predator-prey system in a patchy environment, taking anti-predation responses into consideration. Firstly, we conduct mathematical analysis on the equilibrium solutions of the system. Using techniques from calculus we show that particular steady state solutions exist when the parameters of the system meet certain criteria. We then show that a further set of conditions leads to the local stability of these solutions. The second step is to extend the existing mathematical analysis by way of numerical simulations. We use octave to confirm the previous results, as well as to show that more complicated dynamics can exist, such as stable oscillations. We consider more complex and meaningful functions for nonlinear dispersal between patches and nonlinear predation, and show that the proposed model exhibits behaviours we expect to see in a population model.

Author Keywords: Anti-predation response, Asymptotic stability, Dispersal, Patch model, Population dynamics, Predator-prey

Universities produce a significant and increasing share of basic research that is later commercialized by firms. We argue that the university's prominence as a producer of basic research is the result of a differential efficiency in research production that cannot be replicated by firms or individual agents - teaching. By using research accomplishments to signal knowledge and attract tuition-paying students, universities are uniquely positioned to undertake certain types of research projects. However, in a market for innovation without patent rights, a significant and increasing number of basic research projects, that are social welfare improving, cannot be initiated by firms or universities. The extension of patent rights to university-generated research elegantly redresses this issue and leaves us to ponder important questions about the future of our innovation-driven economies.

Author Keywords: Innovation, Intellectual Property Rights, Research, Science Technology and Innovation Policy

In the context of Real-Time Bidding (RTB) the machine learning problems of

imbalanced classes and model selection are investigated. Synthetic Minority Oversampling Technique (SMOTE) is commonly used to combat imbalanced classes but a shortcoming is identified. Use of a distance threshold is identified as a solution and testing in a live RTB environment shows significant improvement. For model selection, the statistical measure Critical Success Index (CSI) is modified to add emphasis on recall. This new measure (CSI-R) is empirically compared with other measures such as accuracy, lift, efficiency, true skill score, Heidke's skill score and Gilbert's skill score. In all cases CSI-R is shown to provide better application to the RTB industry.

Author Keywords: imbalanced classes, machine learning, online advertising, performance measures, real-time bidding, SMOTE

This paper investigates the effect of listing a stock on the S&P 500 Index on the stock's volatility, using various econometrics models: GARCH and EGARCH. The study mainly addresses three issues; firstly, it analyzes stock volatility in two sub-periods, secondly, it determines whether the announcement can account for the fluctuations in the price of the stock, and finally, it investigates the change in the stock's variance. After isolating the effects of external and industry shock by using the returns on the S&P 500 Index as a proxy, the author finds evidence of structural change in the volatility of stocks after that stock is added to the index. Additionally, the existence of a dominant symmetric effect, which captures the response of volatility to news, indicate that following the onset of including the stock on the index, information flowing into the market increased. However, the rate at which old news is captured in price falls. The empirical evidence also suggests that on average a stocks variance falls and that the announcement to list a stock on the index has little effect on the stock's price.

Author Keywords: EGARCH, GARCH, S&P 500 Index, Symmetric Effect, Volatility

The digital typesetting of mathematics can present many challenges to users, especially those of novice to intermediate experience levels. Through a series of experiments, we show that two models used to represent mathematical structure in these typesetting applications, the 1-dimensional structure based model and the 2-dimensional freeform model, cause interference with users' working memory during the process of transcribing mathematical content. This is a notable finding as a connection between working memory and mathematical performance has been established in the literature. Furthermore, we find that elements of these models allow them to handle various types of mathematical notation with different degrees of success. Notably, the 2-dimensional freeform model allows users to insert and manipulate exponents with increased efficiency and reduced cognitive load and working memory interference while the 1-dimensional structure based model allows for handling of the fraction structure with greater efficiency and decreased cognitive load.

Author Keywords: mathematical cognition, mathematical software, user experience, working memory

Medication used to treat human illness is one of the greatest developments in human history. In Canada, prescription drugs have been developed and made available to treat a wide variety of illnesses, from infections to heart disease and so on. Records of prescription drug fulfillment at coarse Canadian geographic scales were obtained from Health Canada in order to track the use of these drugs by the Canadian population.

The obtained prescription drug fulfillment records were in a variety of inconsistent formats, including a large selection of years for which only paper tabular records were available (hard copies). In this work, we organize, digitize, proof and synthesize the full available data set of prescription drug records, from paper to final database. Extensive quality control was performed on the data before use. This data was then analyzed for temporal and spatial changes in prescription drug use across Canada from 1990-2013.

In addition, one of major research areas in environmental epidemiological studies is the study of population health risk associated with exposure to ambient air pollution. Prescription drugs can moderate public health risk, by reducing the drug user's physiological symptoms and preventing acute health effects (e.g., strokes, heart attacks, etc.). The cleaned prescription drug data was considered in the context of a common model to examine its influence on the association between air pollution exposure and various health outcomes. Since, prescription drug data were available only at the provincial level, a Bayesian hierarchical model was employed to include the prescription drugs as a covariate at regional level, which were then combined to estimate the association at national level. Although further investigations are required, the study results suggest that the prescription drugs influenced the air pollution related public health risk.

Author Keywords: Data, Error checking, Population health, Prescriptions

Health literature has long noted a positive correlation between health and levels of education. Two competing theories have been advanced to explain this phenomenon: (1) education "causes" health by allowing individuals to process complex information and act on it; and, (2) education and health are merely correlated through some third underlying characteristic.

Determining which of these two theories is correct is of importance to public policy. But that task is empirically difficult because, from the standard, static perspective, the theories are observationally equivalent.

We exploit a way in which the two theories have different implications regarding the sort of behaviour we should observe over time. We use smoking as a measure of health behaviour and find that smoking rates between "high" and "low" educated individuals expand when information is hard to process, and then contract as it becomes more easily processable. This approach is then repeated using physical activity as a measure of health-related behaviour to address limitations of the smoking model.

Our novel approach to estimating the differences in the behavioural responses to changes in the processability of health-related information, across education groups, provides strong evidence in support of the view that education and health are causally linked.

Author Keywords: applied statistics, education, health economics, public health, public policy, smoking

In this thesis, we explore the application of the Sinc-Collocation method to an oceanography model. The model of interest describes a wind-driven current with depth-dependent eddy viscosity and is formulated in two different systems; a complex-velocity system and a real-value coupled system. In general, the Sinc-based methods excel over other traditional numerical methods due to their exponentially decaying errors, rapid convergence and handling problems in the presence of singularities at end-points. In addition, the Sinc-Collocation approach that we utilize exploits first derivative interpolation, whose integration is less sensitive to numerical errors. We present several model problems to demonstrate the accuracy, and stability of the method. We compare the approximate solutions determined by the Sinc-Collocation technique with exact solutions and also with those obtained by the Sinc-Galerkin approach in earlier studies. Our findings indicate that the method we utilized outperforms those used in past studies.

Author Keywords: Boundary Value Problems, Eddy Viscosity, Oceanography, Sinc Numerical Methods, Wind-Driven Currents

In this thesis, a new sinc-collocation method based upon derivative interpolation is developed for solving linear and nonlinear boundary value problems involving differential as well as integro-differential equations. The sinc-collocation method is chosen for its ease of implementation, exponential convergence of error, and ability to handle to singularities in the BVP. We present a unique method of treating boundary conditions and introduce the concept of the stretch factor into the conformal mappings of domains. The result is a method that achieves great accuracy while reducing computational cost. In most cases, the results from the method greatly exceed the published results of comparable methods in both accuracy and efficiency. The method is tested on the Blasius problem, the Lane-Emden problem and generalised to cover Fredholm-Volterra integro-differential problems. The results show that the sinc-collocation method with derivative interpolation is a viable and preferable method for solving nonlinear BVPs.

Author Keywords: Blasius, Boundary Value Problem, Exponential convergence, Integro-differential, Nonlinear, Sinc

Little is actually known about how people cognitively process and integrate information when solving complex mathematical problems. In this thesis, eye-tracking was used to examine how people read and integrate information from mathematical symbols and complex formula, with eye fixations being used as a measure of their current focus of attention. Each participant in the studies was presented with a series of stimuli in the form of mathematical problems and their eyes were tracked as they worked through the problem mentally. From these examinations, we were able to demonstrate differences in both the comprehension and problem-solving, with the results suggesting that what information is selected, and how, is responsible for a large portion of success in solving such problems. We were also able to examine how different mathematical representations of the same mathematical object are attended to by students.

Author Keywords: eye-tracking, mathematical notation, mathematical representations, problem identification, problem-solving, symbolism