Radio frequency interference (RFI) mitigation enables radio astronomical observation in frequency bands that are shared with many modern satellite and ground based devices by filtering out the interference in corrupted bands. The present work documents the development of a beamformer (spatial filter) equipped with RFI mitigation capabilities. The beamformer is intended for systems with antenna arrays designed for large bandwidths. Because array data post processing on large bandwidths would require massive memory space beyond feasible limits, there is a need for a RFI mitigation system capable of doing processing on the data as it arrives in real-time; storing only a data reduced result into long term memory. The real-time system is designed to be implemented on both the FLAG phased array feed (PAF) on the Green Bank telescope in West Virginia, as well as future radio astronomy projects. It will also serve as the anti-jamming component in communications applications developed for the United States office of naval research (ONR). Implemented on a graphical processing unit (GPU), this beamformer demonstrates a working single step filter using nVidia's CUDA technology, technology with high-speed parallelism that makes real-time RFI mitigation possible.

Automated Face Recognition is the process of determining a subject's identity from digital imagery of their face without user intervention. The term in fact encompasses two distinct tasks; Face Verficiation is the process of verifying a subject's claimed identity while Face Identification involves selecting the most likely identity from a database of subjects. This dissertation focuses on the task of Face Verification, which has a myriad of applications in security ranging from border control to personal banking. Recently the use of 3D facial imagery has found favour in the research community due to its inherent robustness to the pose and illumination variations which plague the 2D modality. The field of 3D face recognition is, however, yet to fully mature and there remain many unanswered research questions particular to the modality. The relative expense and specialty of 3D acquisition devices also means that the availability of databases of 3D face imagery lags significantly behind that of standard 2D face images. Human recognition of faces is rooted in an inherently 2D visual system and much is known regarding the use of 2D image information in the recognition of individuals. The corresponding knowledge of how discriminative information is distributed in the 3D modality is much less well defined. This dissertations addresses these issues through the use of decompositional techniques. Decomposition alleviates the problems associated with dimensionality explosion and the Small Sample Size (SSS) problem and spatial decomposition is a technique which has been widely used in face recognition. The application of decomposition in the frequency domain, however, has not received the same attention in the literature. The use of decomposition techniques allows a map ping of the regions (both spatial and frequency) which contain the discriminative information that enables recognition. In this dissertation these techniques are covered in significant detail, both in terms of practical issues in the respective domains and in terms of the underlying distributions which they expose. Significant discussion is given to the manner in which the inherent information of the human face is manifested in the 2D and 3D domains and how these two modalities inter-relate. This investigation is extended to cover also the manner in which the decomposition techniques presented can be recombined into a single decision. Two new methods for learning the weighting functions for both the sum and product rules are presented and extensive testing against established methods is presented. Knowledge acquired from these examinations is then used to create a combined technique termed Log-Gabor Templates. The proposed technique utilises both the spatial and frequency domains to extract superior performance to either in isolation. Experimentation demonstrates that the spatial and frequency domain decompositions are complimentary and can combined to give improved performance and robustness.

Phased array feeds (PAFs) are a promising new technology for astronomical radio telescopes. While PAFs have been used in other fields, the demanding sensitivity and calibration requirements in astronomy present unique new challenges. This dissertation presents some of the first astronomical PAF results demonstrating the lowest noise temperature and highest sensitivity at the time (66 Kelvin and 3.3 m^2/K, respectively), obtained using a narrowband (425 kHz bandwidth) prototype array of 19 linear co-polarized L-band dipoles mounted at the focus of the Green Bank 20 Meter Telescope at the National Radio Astronomy Observatory (NRAO) in Green Bank, West Virginia. Results include spectral line detection of hydroxyl (OH) sources W49N and W3OH, and some of the first radio camera images made using a PAF, including an image of the Cygnus X region. A novel array Y-factor technique for measuring the isotropic noise response of the array is shown along with experimental measurements for this PAF. Statistically optimal beamformers (Maximum SNR and MVDR) are used throughout the work. Radio-frequency interference (RFI) mitigation is demonstrated experimentally using spatial cancelation with the PAF. Improved RFI mitigation is achieved in the challenging cases of low interference-to-noise ratio (INR) and moving interference by combining subspace projection (SP) beamforming with a polynomial model to track a rank 1 subspace. Limiting factors in SP are investigated including sample estimation error, subspace smearing, noise bias, and spectral scooping; each of these factors is overcome with the polynomial model and prewhitening. Numerical optimization leads to the polynomial subspace projection (PSP) method, and least-squares fitting to the series of dominant eigenvectors over a series of short term integrations (STIs) leads to the eigenvector polynomial subspace projection (EPSP) method. Expressions for the gradient, Hessian, and Jacobian are given for use in numerical optimization. Results are given for simulated and experimental data, demonstrating deeper beampattern nulls by 6 to 30dB. To increase the system bandwidth toward the hundreds of MHz bandwidth required by astronomers for a fully science-ready instrument, an FPGA digital backend is introduced using a 64-input analog-to-digital converter running at 50 Msamp/sec and the ROACH processing board developed at the University of California, Berkeley. International efforts to develop digital back ends for large antenna arrays are considered, and a road map is proposed for development of a hardware correlator/beamformer at BYU using three ROACH boards communicating over 10 gigabit Ethernet.

Numerical methods are often required to solve chemical problems, either to verify theoretical models or to access information that is not readily available experimentally. This thesis deals with both situations, though in differing levels of detail. A major component of this thesis is devoted to developing new methods to determine a full eigendecomposition of the matrices derived from "low temperature" unimolecular master equations. When transient behaviour is of interest achieving relative accuracy for more than just the eigenvector corresponding to the smallest eigenvalue is of central importance. Three new methods are presented. The first is based on a weighted implementation of subspace projection methods, in this case explored for the well-known Arnoldi method. This weighted inner product subspace projection methodology is demonstrated to

Numerical methods are often required to solve chemical problems, either to verify theoretical models or to access information that is not readily available experimentally. This thesis deals with both situations, though in differing levels of detail. A major component of this thesis is devoted to developing new methods to determine a full eigendecomposition of the matrices derived from "low temperature" unimolecular master equations. When transient behaviour is of interest achieving relative accuracy for more than just the eigenvector corresponding to the smallest eigenvalue is of central importance. Three new methods are presented. The first is based on a weighted implementation of subspace projection methods, in this case explored for the well-known Arnoldi method. This weighted inner product subspace projection methodology is demonstrated to

Numerical methods are often required to solve chemical problems, either to verify theoretical models or to access information that is not readily available experimentally. This thesis deals with both situations, though in differing levels of detail. A major component of this thesis is devoted to developing new methods to determine a full eigendecomposition of the matrices derived from "low temperature" unimolecular master equations. When transient behaviour is of interest achieving relative accuracy for more than just the eigenvector corresponding to the smallest eigenvalue is of central importance. Three new methods are presented. The first is based on a weighted implementation of subspace projection methods, in this case explored for the well-known Arnoldi method. This weighted inner product subspace projection methodology is demonstrated to

Numerical methods are often required to solve chemical problems, either to verify theoretical models or to access information that is not readily available experimentally. This thesis deals with both situations, though in differing levels of detail. A major component of this thesis is devoted to developing new methods to determine a full eigendecomposition of the matrices derived from "low temperature" unimolecular master equations. When transient behaviour is of interest achieving relative accuracy for more than just the eigenvector corresponding to the smallest eigenvalue is of central importance. Three new methods are presented. The first is based on a weighted implementation of subspace projection methods, in this case explored for the well-known Arnoldi method. This weighted inner product subspace projection methodology is demonstrated to