Applied Modeling and Quantitative Methods

Research and development activities conducted at universities and firms fuel economic growth

and play a key role in the process of innovation. Specifically, prior research has investigated the

widespread university-to-firm research development path and concluded that universities are

better suited for early stage of research while firms are better positioned for later stages. This

thesis aims to present a novel explanation for the pervasive university-to-firm research

development path. The model developed uses game theory to visualize and analyze interactions

between a firm and university under different strategies. The results reveal that as academic

research signals knowledge it helps attract tuition paying students. Generating these tuition

revenues is facilitated by university research discoveries, which, once published, a firm can build

upon to make new innovative products. In an environment of weak intellectual property rights,

moreover, the university-to-firm research development path enables firms to bypass the hefty

costs that are involved in basic research activities. The model also provides a range of solution

scenarios where a university and firm may find it viable to initiate a research line.

Author Keywords: Game theory, Intellectual property rights, Nash equilibrium, Research and development, University to-firm research path

A comparison of two high performance computing clusters running on AWS and Sharcnet was done to determine which scenarios yield the best performance. Algorithm complexity ranged from O (n) to O (n3). Data sizes ranged from 195 KB to 2 GB. The Sharcnet hardware consisted of Intel E5-2683 and Intel E7-4850 processors with memory sizes ranging from 256 GB to 3072 GB. On AWS, C4.8xlarge instances were used, which run on Intel Xeon E5-2666 processors with 60 GB per instance. AWS was able to launch jobs immediately regardless of job size. The only limiting factors on AWS were algorithm complexity and memory usage, suggesting a memory bottleneck. Sharcnet had the best performance but could be hampered by the job scheduler. In conclusion, Sharcnet is best used when the algorithm is complex and has high memory usage. AWS is best used when immediate processing is required.

Author Keywords: AWS, cloud, HPC, parallelism, Sharcnet

While existing models of emotional intelligence (EI) generally recognize the importance of social competencies (SC), there is a tendency in the literature to narrow the focus to competencies that pertain to the self. Given the experiential and perceptual differences between self- vs. other-oriented emotional abilities, this is an important limitation of existing EI models and assessment tools. This thesis explores the psychometric properties of a multidimensional model for SC. Chapter 1 describes the evolution of work on SCs in modern psychology and describes the multidimensional model of SC under review. Chapter 2 replicates this model across a variety of samples and explores the model's construct validity via basic personality and EI constructs. Chapter 3 further explores the predictive validity of the SC measure within a group of project managers and several success and wellness variables. Chapter 4 examines potential applications for the model and suggestions for further research.

Author Keywords: emotional intelligence, project management, social competency, work readiness

The time-dependent Gross-Pitaevskii Equation, describing the movement of parti-

cles in quantum mechanics, may not be solved analytically due to its inherent non-

linearity. Hence numerical methods are of importance to approximate the solution.

This study develops a discrete scheme in time and space to simulate the solution

defined in a finite domain by using the Crank-Nicolson difference method and Sinc

Collocation Methods (SCM), respectively. In theory and practice, the time discretiz-

ing system decays errors in the second-order of accuracy, and SCMs are decaying

errors exponentially. A new SCM with a unique boundary treatment is proposed

and compared with the original SCM and other similar numerical techniques in time

costs and numerical errors. As a result, the new SCM decays errors faster than the

original one. Also, to attain the same accuracy, the new SCM interpolates fewer

nodes than the original SCM, which saves computational costs. The new SCM is

capable of approximating partial differential equations under different boundary con-

ditions, which can be extensively applied in fitting theory.

Author Keywords: Crank-Nicolson difference method, Gross-Pitaevskii Equation, Sinc-Collocation methods

Higher education is important. It enhances both individual and social welfare by improving productivity, life satisfaction, and health outcomes, and by reducing rates of crime. Universities play a critical role in providing that education. Because academic institutions face resource constraints, it is thus important that they deploy resources in support of student success in the most efficient ways possible. To inform that efficient deployment, this research analyzes institutional data reflecting undergraduate student performance to identify predictors of student success measured by GPA, rates of credit accumulation, and graduation rates. Using methods of cluster analysis and machine learning, the analysis yields predictions for the probabilities of individual success.

Author Keywords: Educational data mining, Students' academic performance modelling

This thesis presents an exploration of the requirements for and development of a software tool to calculate Certified Emission Reduction (CERs) credits for afforestation and reforestation projects conducted under the Clean Development Mechanism (CDM). We examine the relevant methodologies and tools to determine what is required to create a software package that can support a wide variety of projects involving a large variety of data and computations. During the requirements gathering, it was determined that the software package developed would need to support the ability to enter and edit equations at runtime. To create the software we used Java for the programming language, an H2 database to store our data, and an XML file to store our configuration settings. Through these choices, we can build a cross-platform software solution for the purpose outlined above. The end result is a versatile software tool through which users can create and customize projects to meet their unique needs as well as utilize the features provided to streamline the management of their CDM projects.

Author Keywords: Carbon Emissions, Climate Change, Forests, Java, UNFCCC, XML

This thesis proposes an agro-ecological zoning (AEZ) methodology of southern Ontario for the characterization and mapping of agro-ecological zones during the historical term (1981-2010), and their shifts into the long-term (2041-2070) projected climate period. Agro-ecological zones are homogenous areas with a unique combination of climate, soil, and landscape features that are important for crop growth. Future climate variables were derived from Earth System Models (EMSs) using a high emission climate forcing scenario from the Intergovernmental Panel on Climate Change 5th Assessment Report. The spatiotemporal shifts in agro-ecological zones with projected climate change are analyzed using the changes to the length of growing period (LGP) and crop heat units (CHU), and their manifestation in agro-climatic zones (ACZ). There are significant increases to the LGP and CHU into the long-term future. Two historical ACZs exist in the long-term future, and have decreased in area and shifted northward from their historical locations.

Author Keywords: Agro-climatic Zones, Agro-ecological Zones, Agro-ecological Zoning, Climate Change, Crop Heat Units, Length of Growing Period

Volatility modelling is an important task in the financial markets. This paper first evaluates the range-based DCC-CARR model of Chou et al. (2009) in modelling larger systems of assets, vis-à-vis the traditional return-based DCC-GARCH. Extending Colacito, Engle and Ghysels (2011), range-based volatility specifications are then employed in the first-stage of DCC-MIDAS conditional covariance estimation, including the CARR model of Chou et al. (2005). A range-based analog to the GARCH-MIDAS model of Engle, Ghysels and Sohn (2013) is also proposed and tested - which decomposes volatility into short- and long-run components and corrects for microstructure biases inherent to high-frequency price-range data. Estimator forecasts are evaluated and compared in a minimum-variance portfolio allocation experiment following the methodology of Engle and Colacito (2006). Some consistent inferences are drawn from the results, supporting the models proposed here as empirically relevant alternatives. Range-based DCC-MIDAS estimates produce efficiency gains over DCC-CARR which increase with portfolio size.

Author Keywords: asset allocation, DCC MIDAS, dynamic correlations, forecasting, portfolio risk management, volatility

In this thesis, we study modelling with non-linear ordinary differential equations, and the existence of positive solutions for Boundary Value Problems (BVPs). These problems have wide applications in many areas. The focus is on the extensions of previous work done on non-linear second-order differential equations with boundary conditions involving first-order derivative. The contribution of this thesis has four folds. First, using a fixed point theorem on order intervals, the existence of a positive solution on an interval for a non-local boundary value problem is obtained. Second, considering a different boundary value problem that consists of the first-order derivative in the non-linear term, an increasing solution is obtained by applying the Krasnoselskii-Guo fixed point theorem. Third, the existence of two solutions, one solution and no solution for a BVP is proved by using fixed point index and iteration methods. Last, the results of Green's function unify some methods in studying the existence of positive solutions for BVPs of nonlinear differential equations. Examples are presented to illustrate the applications of our results.

Author Keywords: Banach Space, Boundary Value Problems, Differential Equations, Fixed Point, Norm, Positive Solutions

With wide applications in many fields such as engineering, physics, chemistry, biology and social sciences, semi-linear equations have attracted great interests of researchers from various areas. In the study of existence of solutions for such class of equations, a general and commonly applied method is the compression cone method for fixed-point index. The main idea is to construct a cone in an ordered Banach space based on the linear part so that the nonlinear part can be examined in a relatively smaller region.

In this thesis, a new class of cone is proposed as a generalization to previous work. The construction of the cone is based on properties of both the linear and nonlinear part of the equation. As a result, the method is shown to be more adaptable in applications. We prove new results for both semi-linear integral equations and algebraic systems.

Applications are illustrated by examples. Limitations of such new method are also discussed.

Keywords: Algebraic systems; compression cone method; differential equations; existence of solutions; fixed point index; integral equations; semi-linear equations.

Author Keywords: algebraic systems, differential equations, existence of solutions, fixed point index, integral equations, semi-linear equations