In this thesis, we discuss a new kind of polygon, which we call one-sided polygons. The shortest path between any pair of vertices of a one-sided polygon makes only left turns or right turns. We prove that the set of one-sided polygons is a superset of the star-shaped polygons and the spiral polygons. We also show that the set of one-sided polygons is a subset of the set of LR-visibility polygons. We present a linear time recognition algorithm for one-sided rectilinear polygons. We then discuss the searching of monotone and one-sided rectilinear polygons. We show that all one-sided polygons can be 1-searched and a search schedule can be given in linear time.

In this thesis, we discuss a new kind of polygon, which we call one-sided polygons. The shortest path between any pair of vertices of a one-sided polygon makes only left turns or right turns. We prove that the set of one-sided polygons is a superset of the star-shaped polygons and the spiral polygons. We also show that the set of one-sided polygons is a subset of the set of LR-visibility polygons. We present a linear time recognition algorithm for one-sided rectilinear polygons. We then discuss the searching of monotone and one-sided rectilinear polygons. We show that all one-sided polygons can be 1-searched and a search schedule can be given in linear time.

Parallel computing offers immense potential to solve large, complex scientific problems. Load imbalance is a major impediment in obtaining high performance by a parallel system. One principal form of parallelism found in scientific applications is data parallelism. Loops without dependencies are data parallel. During the execution of large parallel loops, computational requirements vary due to problem, algorithmic and systemic characteristics. These factors lead to load imbalance which in turn degrades the performance of an application. Over the years, a number of dynamic loop scheduling techniques have been proposed to address one or more of these factors. However, there is no single strategy that works well for different problem domains and system characteristics. Moreover, load balancing during runtime is complicated because of its need for dynamic data redistribution. Therefore, there is a distinct need to integrate the dynamic loop scheduling techniques into a single package and provide them as an application programming interface (API) to the application developer. In recent years, along this direction, a number of dynamic loop scheduling techniques have been integrated into the compiler technologies for shared memory environments. On the other hand, there is no such integrated approach for distributed memory applications. The purpose of this thesis is to present the design, implementation and effectiveness of an integrated approach:the dynamic loop scheduling techniques are integrated into a runtime system for distributed memory architectures. For this purpose, we choose the newly developed parallel runtime environment for multicomputer architecture (PREMA) with its main components: the data movement and control substrate (DMCS) and mobile object layer (MOL). This runtime system has recently been developed and has demonstrated to be one of the most competitive runtime systems for distributed memory architectures. The significance of this work is that the proposed API will enhance the performance of parallel applications by reducing the load imbalance among processors caused by a wide range of factors and will reduce the software developmental cost required for load balancing. With the integration of the scheduling capabilities into the runtime system, its applicability has been expanded. The performance of the API has been evaluated qualitatively and quantitatively. The overhead of the API has been studied analytically and measured experimentally. Three parallel benchmarks including scientific applications of general interest (N-body simulations, automatic quadrature routine and unstructured grid heat solver) were considered for experimentation purpose. Based on the experiments conducted, a cost improvement of up to 76% over the straight forward parallel benchmark has been obtained. For certain application characteristics, the overhead of the runtime system was found to be within 10% of the underlying messaging layer. These results demonstrate that, in large scientific applications it is possible and desirable to combine the rich functionality of a runtime system with the advantages of scheduling techniques to achieve high performance.

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P-values combination procedure for multiple statistical tests is a common data analysis method in many applications including bioinformatics. However, this procedure is nontrivial when input P-values are dependent. For the Fisher€™s combination procedure, a classic method is the Brown€™s Strategy [1, Brown,1975], which is based empirical moment-matching of gamma distribution. In this project, we address a more general family of weighting-andtruncation p-value combination procedures called TFisher. We first study how to extend Brown€™s Strategy to this problem. Then we make further development in two directions. First, instead of using the empirical polynomial model-fitting strategy to find moments, we developed an analytical calculation strategy based on asymptotic approximation. Second, instead of using the gamma distribution to approximate the null distribution of TFisher, we propose to use a mixed gamma distribution or a shifted-mixed gamma distribution. We focus on calculating the one-sided p-value for TFisher, especially the soft-thresholding version of TFisher. Simulations show that our methods much improve the accuracy than the traditional strategy.

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The physical properties of visible light and its interaction with matter create obstructions the human eye cannot explore. High energy radiation has been used as an alternative to visible light to penetrate these concealed regions and reveal their contents. However, traditional imaging techniques require a two-sided apparatus with a radiation source and a detector on opposite sides of the concealed object. One-sided imaging of concealed objects is made possible by a technique called backscatter imaging, utilizing high energy radiation. However, the signal produced by backscatter imaging is inherently weak, which makes in- terpretation di cult. One of the most promising techniques for recovering the weak signal is the coding and decoding provided by Coded Aperture Imaging (CAI). The purpose of this study was to create and test a coded aperture imaging system using backscattered x-rays. This would enable one-sided imaging of concealed objects and demonstrate whether a portable imaging system was feasible. The results obtained from conducting a computer simulation, visi- ble light experiments, and x-ray experiments proved that the process works, however, the x-ray ux levels required were too high for a portable system, based upon the current equipment available at UOIT. / UOIT

This report is a summarization and extension of previous work done by Dr. Efraim Armendariz, University of Texas at Austin, and Dr. Henry E. Heatherly, University of Lousiana Lafayette, on the topic of rings with commuting ideals. Some of these authors’ results are extended to one-sided ideals instead of two-sided ideals. Topics discussed include homomorphic images of rings with commuting left ideals, finite direct products of rings with commuting left ideals, rings of n x n matrices over a ring with commuting left ideals, constructing rings with commuting ideals using an idempotent, and simple rings with commuting ideals over polynomials in X. Examples are given to illustrate some properties of rings with commuting ideals. A short a discussion regarding the inclusion of ring theory in the secondary mathematics classroom is also included. / text