The complex problem of metrication of highway design, construction and maintenance has been the subject of a number of studies and pilot projects carried out by the Federal Highway Administration (F.H.W.A.) of the United States and the Roads and Transportation Association of Canada. Through a research grant, the FHWA of the U.S.A. assigned the Ohio Department of Transportation, the Illinois Department of Transportation and the Oregon Highway Division to design, construct, and maintain these metric projects. The author has reviewed the experience and conclusions of these studies and the problems encountered in the pilot projects relative to the design, survey, contracting, construction, signing, and public reactions to the metrication process. In the conclusions to this review, the author questions some of the recommendations of these studies, specifically in the area of curvature and station definition, notation convention, and the concept of dual signing. In these and other areas recommended guidelines for highway metrication are proposed. Finally, the author presents a set of equations and computer generated tables for highway design and layout in metric incorporating the flexibility of 10, 20, 40, and 100 metre station and curvature definition.

This bachelor's thesis discusses from an ergodic-theoretical perspective the "metric functional analysis" that Anders Karlsson and others have developed in the recent years. We introduce a new symbolic calculus for metric functionals which includes a notion of the adjoint of a nonexpansive map. Using these tools we revisit many central results, including Karlsson's spectral principle and its stronger form for star-shaped spaces due to Gaubert and Vigeral, as well as the multiplicative ergodic theorem of Karlsson-Ledrappier.

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The Multidimensional Quality Metrics (MQM) framework is a new system for creating customized translation quality assessment and evaluation metrics designed to fit specific translation needs. In this study I test the viability of MQM to determine whether the framework in its current state is ready for implementation as a quality assessment framework in the translation industry. Other contributions from this study include: (1) online software for designing and using metrics based on the MQM framework; (2) a survey of the typical, real-world quality assessment and evaluation practices of language service providers in the translation industry; and (3) a measurement scale for determining the viability of translation quality assessment and evaluation frameworks such as MQM. The study demonstrates that the MQM framework is a viable solution when it comes to the validity and practicality of creating translation quality metrics for the translation industry. It is not clear whether those metrics can be used reliably without extensive training of qualified assessors on the use of MQM metrics.

This thesis presents new theorems in homotopy theory, in particular it generalizes a theorem of Saharon Shelah. We employ a technique used by Janusz Pawlikowski to show that certain Peano continua have a least nontrivial homotopy group that is finitely presented or of cardinality continuum. We also use this technique to give some relative consistency results.

<p>This thesis is concerned with the problem of characterizing the orbits of certain probability density functions under the action of the Euclidean group. Our motivating application is the recognition of a point configuration where the coordinates of the points are measured under noisy conditions. Consider a random variable X in R^d with probability density function ρ(x). Let x₁ and x₂ be independent random samples following ρ(x). Define ∆ as the squared Euclidean distance between x₁ and x₂. It has previously been shown that two distributions ρ(x) and ρ(x) consisting of Dirac delta distributions in generic positions that have the same respective distributions of ∆ are necessarily related by a rigid motion. That is, there exists some rigid motion g in the Euclidean group E(d) such that ρ(x) = ρ(g · x) for all x ∈ R^d . To account for noise in the measurements, we assume X is a random variable in R^d whose density is a k-component mixture of Gaussian distributions with means in generic position. We further assume that the covariance matrices of the Gaussian components are equal and of the form Σ = σ²1_d with  0 ≤ σ² ∈ R. In Theorem 3.1.1 and Theorem 3.2.1, we prove that, when σ² is known, generic k-component Gaussian mixtures are uniquely reconstructible up to a rigid motion from the density of ∆. A more general formulation is proven in Theorem 3.2.3. Similarly, when σ² is unknown, we prove in Theorem 4.1.1 and Theorem 4.1.2 that generic equally-weighted k-component Gaussian mixtures with k = 1 and k = 2 are uniquely reconstructible up to a rigid motion from the distribution of ∆. There are at most three non-equivalent equally weighted 3-component Gaussian mixtures up to a rigid motion having the same distribution of ∆, as proven in Theorem 4.1.3. In Theorem 4.1.4, we present a test to check if, for a given k and d, the number of non-equivalent equally-weighted k-component Gaussian mixtures in R^d having the same distribution of ∆ is at most (k choose 2) + 1. Numerical computations showed that distributions with k = 4, 5, 6, 7 such that d ≤ k −2 and (k, d) = (8, 1) pass the test, and thus have a finite number of reconstructions up to a rigid motion. When σ² is unknown and the mixture weights are also unknown, we prove in Theorem 4.2.1 that there are at most four non-equivalent 2-component Gaussian mixtures up to a rigid motion having the same distribution of ∆. </p>

In the field of control theory, optimal performance is generally defined as the best possible controlled performance given a static, unchangeable plant system. However, principled design of the underlying system can make designing effective controllers easier and dramatically improve the final control performance beyond what any finely tuned controller could achieve alone. This work develops performance metrics for serial robot arms which help guide the design and optimization of the structure of the arm to achieve greater final performance. First, a kinematic (motion-based) metric called the Actuator Independence Metric (AIM) measures the uniqueness of the movement capabilities of the different joints in a robot arm. Arms which are optimized with respect to the AIM exhibit a greater freedom of movement. In particular, it is shown that the AIM score of a robot correlates strongly with their ability to find solutions to the Inverse Kinematics problem, and that redundant arms with a high AIM score have more useful null-spaces with significant ability to change configuration while maintaining a fixed end-effector pose. Second, a dynamic metric called the Acceleration Radius is explored. The acceleration radius measures the maximum acceleration which a robot arm is capable of generating in any direction. An efficient algorithm for calculating the acceleration radius is developed which exploits the geometry of the mapping from joint torques to acceleration. A design optimization is carried out to demonstrate how the acceleration radius predicts the dynamic movement capabilities of robot arms. It is shown that arms which are optimal with respect to the acceleration radius can follow faster paths through a task space. The metrics developed in this thesis can be used to create customized robot arm designs for specific tasks, which will exhibit desirable control performance.

The growing popularity of photovoltaic (PV) generation systems leads to an increase in the number of residential and commercial grid-tied PV systems that interconnect to the distribution circuit. This affects the characteristics of the distribution circuit; for example, the assumption that the voltage profile of a radial line decreases down-stream becomes invalid because of the addition of the PV system on the line. This poses new challenges when setting the parameters of voltage regulating devices. Add to that the fact that PV systems are intermittent, especially on cloudy days, which make the line even more difficult to regulate, and the number of switching occurrences of the regulating devices increases, thus accelerating wear-and-tear to the utility’s equipment. The objective of this thesis is to develop an index which qualitatively indicates the impact of PV system(s) on operation, efficiency, reliability, and lifetime of voltage regulation equipment. Tests on the proposed index will be performed on several cases including circuits containing state-of-the art methods that integrate PV systems with minimum impact to utility equipment. Investigation of methods to further mitigate equipment wear by selecting the best interconnect point on the circuit will also be conducted to test the proposed index. The development and validation of the proposed index will entail power system modeling and simulation of distributed generation using PSCAD. The proposed index resulted from this study will provide a useful tool to allow utility companies pick the optimum locations for distributed generation to minimize their negative impact on the distribution lines as well as to determine the need for extra mitigation equipment.

<p> This thesis is both classically and abstractly oriented in a geometrical sense. The discussion is centred around the motion distance.</p> <p> In the first chapter, the concept of a regular set is defined and discussed. The idea of a regular set is a natural generalization of equilateral triangles and regular tetrahedra in Euclidean spaces.</p> <p> In chapter two, two kinds of scalar multiplication associated with metric spaces are studied.</p> <p> In chapter three, the concept of distance is abstracted to a level where it loses most of its structure. This abstraction is then examined.</p> <p> In chapter four, generalized metric spaces are examined. These are specializations of the abstract spaces of chapter three.</p> / Thesis / Doctor of Philosophy (PhD)