Axis Mapping: The Estimation of Surface Orientations and its Applications in Vehicle Localization and Structural Geology

The map representation of an environment should be selected based on its intended application. For example, a geometrically accurate map describing the Euclidean space of an environment is not necessarily the best choice if only a small subset its features are required. One possible subset is the orientations of the flat surfaces in the environment, represented by a special parameterization of normal vectors called axes. Devoid of positional information, the entries of an axis map form a non-injective relationship with the flat surfaces in the environment, which results in physically distinct flat surfaces being represented by a single axis. This drastically reduces the complexity of the map, but retains important information about the environment that can be used in meaningful applications in both two and three dimensions. This thesis presents axis mapping, which is an algorithm that accurately and automatically estimates an axis map of an environment based on sensor measurements collected by a mobile platform. Furthermore, two major applications of axis maps are developed and implemented. First, the LiDAR compass is a heading estimation algorithm that compares measurements of axes with an axis map of the environment. Pairing the LiDAR compass with simple translation measurements forms the basis for an accurate two-dimensional localization algorithm. It is shown that this algorithm eliminates the growth of heading error in both indoor and outdoor environments, resulting in accurate localization over long distances. Second, in the context of geotechnical engineering, a three-dimensional axis map is called a stereonet, which is used as a tool to examine the strength and stability of a rock face. Axis mapping provides a novel approach to create accurate stereonets safely, rapidly, and inexpensively compared to established methods. The non-injective property of axis maps is leveraged to probabilistically describe the relationships between non-sequential measurements of the rock face. The automatic estimation of stereonets was tested in three separate outdoor environments. It is shown that axis mapping can accurately estimate stereonets while improving safety, requiring significantly less time and effort, and lowering costs compared to traditional and current state-of-the-art approaches.

Essays on Firm Heterogeneity with Empirical Applications in Economic History and Agricultural Economics

This thesis uses models of firm-heterogeneity to complete empirical analyses in economic history and agricultural economics. In Chapter 2, a theoretical model of firm heterogeneity is used to derive a statistic that summarizes the welfare gains from the introduction of a new technology. The empirical application considers the use of mechanical steam power in the Canadian manufacturing sector during the late nineteenth century. I exploit exogenous variation in geography to estimate several parameters of the model. My results indicate that the use of steam power resulted in a 15.1 percent increase in firm-level productivity and a 3.0-5.2 percent increase in aggregate welfare. Chapter 3 considers various policy alternatives to price ceiling legislation in the market for production quotas in the dairy farming sector in Quebec. I develop a dynamic model of the demand for quotas with farmers that are heterogeneous in their marginal cost of milk production. The econometric analysis uses farm-level data and estimates a parameter of the theoretical model that is required for the counterfactual experiments. The results indicate that the price of quotas could be reduced to the ceiling price through a 4.16 percent expansion of the aggregate supply of quotas, or through moderate trade liberalization of Canadian dairy products. In Chapter 4, I study the relationship between farm-level productivity and participation in the Commercial Export Milk (CEM) program. I use a difference-in-difference research design with inverse propensity weights to test for causality between participation in the CEM program and total factor productivity (TFP). I find a positive correlation between participation in the CEM program and TFP, however I find no statistically significant evidence that the CEM program affected TFP.

Supporting Metacognitive Development in Early Science Education: Exploring Elementary Teachers' Beliefs and Practices in Metacognition

Metacognition is the understanding and control of cognitive processes. Students with high levels of metacognition achieve greater academic success. The purpose of this mixed-methods study was to examine elementary teachers’ beliefs about metacognition and integration of metacognitive practices in science. Forty-four teachers were recruited through professional networks to complete a questionnaire containing open-ended questions (n = 44) and Likert-type items (n = 41). Five respondents were selected to complete semi-structured interviews informed by the questionnaire. The selected interview participants had a minimum of three years teaching experience and demonstrated a conceptual understanding of metacognition. Statistical tests (Pearson correlation, t-tests, and multiple regression) on quantitative data and thematic analysis of qualitative data indicated that teachers largely understood metacognition but had some gaps in their understanding. Participants’ reported actions (teaching practices) and beliefs differed according to their years of experience but not gender. Hierarchical multiple regression demonstrated that the first block of gender and experience was not a significant predictor of teachers' metacognitive actions, although experience was a significant predictor by itself. Experience was not a significant predictor once teachers' beliefs were added. The majority of participants indicated that metacognition was indeed appropriate for elementary students. Participants consistently reiterated that students’ metacognition developed with practice, but required explicit instruction. A lack of consensus remained around the domain specificity of metacognition. More specifically, the majority of questionnaire respondents indicated that metacognitive strategies could not be used across subject domains, whereas all interviewees indicated that they used strategies across subjects. Metacognition was integrated frequently into Ontario elementary classrooms; however, metacognition was integrated less frequently in science lessons. Lastly, participants used a variety of techniques to integrate metacognition into their classrooms. Implications for practice include the need for more professional development aimed at integrating metacognition into science lessons at both the Primary and Junior levels. Further, teachers could benefit from additional clarification on the three main components of metacognition and the need to integrate all three to successfully develop students’ metacognition.