In this dissertation we discuss two problems. In the first part, we consider the problem of computing a few extreme eigenvalues of a symmetric definite generalized eigenvalue problem or a few extreme singular values of a large and sparse matrix. The standard method of choice of computing a few extreme eigenvalues of a large symmetric matrix is the Lanczos or the implicitly restarted Lanczos method. These methods usually employ a shift-and-invert transformation to accelerate the speed of convergence, which is not practical for truly large problems. With this in mind, Golub and Ye proposes an inverse-free preconditioned Krylov subspace method, which uses preconditioning instead of shift-and-invert to accelerate the convergence. To compute several eigenvalues, Wielandt is used in a straightforward manner. However, the Wielandt deflation alters the structure of the problem and may cause some difficulties in certain applications such as the singular value computations. So we first propose to consider a deflation by restriction method for the inverse-free Krylov subspace method. We generalize the original convergence theory for the inverse-free preconditioned Krylov subspace method to justify this deflation scheme. We next extend the inverse-free Krylov subspace method with deflation by restriction to the singular value problem. We consider preconditioning based on robust incomplete factorization to accelerate the convergence. Numerical examples are provided to demonstrate efficiency and robustness of the new algorithm. In the second part of this thesis, we consider the so-called subspace clustering problem, which aims for extracting a multi-subspace structure from a collection of points lying in a high-dimensional space. Recently, methods based on self expressiveness property (SEP) such as Sparse Subspace Clustering and Low Rank Representations have been shown to enjoy superior performances than other methods. However, methods with SEP may result in representations that are not amenable to clustering through graph partitioning. We propose a method where the points are expressed in terms of an orthonormal basis. The orthonormal basis is optimally chosen in the sense that the representation of all points is sparsest. Numerical results are given to illustrate the effectiveness and efficiency of this method.

In English the personal pronouns are morphologically marked for grammatical number, whilst the third-person singular pronouns are also obligatorily marked for gender. As a result, the use of any singular animate antecedent coindexed with a third-person pronoun forces a choice between he and she, whether or not the biological sex of the intended referent is known. This forced choice of gender, and the corresponding lack of a gender-neutral third-person singular pronoun where gender is not formally marked, is the primary focus of this thesis. I compare and contrast the use of the two main candidates for epicene status, singular they and generic he, which are found consistently opposed in the wider literature. Using corpus-based methods I analyse current epicene usage in written British English, and investigate which epicene pronouns are given to language-acquiring children in their L1 input. I also consider current prescriptions on epicene usage in grammar texts published post-2000 and investigate whether there is any evidence that language-external factors impact upon epicene choice. The synthesis of my findings with the wider literature on epicene pronouns leads me to the conclusion that, despite the restrictions imposed on the written pronoun paradigm evident in grammatical prescriptivism, singular they is the epicene pronoun of British English.

Birds are a key environmental asset and this is recognised through comprehensive legislation and policy ensuring their protection and conservation. Many species are active at night and surveys are required to understand the implications of proposed developments such as towers and reduce possible conflicts with these structures. Night vision devices are commonly used in nocturnal surveys, either to scope an area for bird numbers and activity, or in remotely sensing an area to determine potential risk. This thesis explores some practical and theoretical approaches that can improve the accuracy, confidence and efficiency of nocturnal bird surveillance. As image intensifiers and thermal imagers have operational differences, each device has associated strengths and limitations. Empirical work established that image intensifiers are best used for species identification of birds against the ground or vegetation. Thermal imagers perform best in detection tasks and monitoring bird airspace usage. The typically used approach of viewing bird survey video from remote sensing in its entirety is a slow, inaccurate and inefficient approach. Accuracy can be significantly improved by viewing the survey video at half the playback speed. Motion detection efficiency and accuracy can be greatly improved through the use of adaptive background subtraction and cumulative image differencing. An experienced ornithologist uses bird flight style and wing oscillations to identify bird species. Changes in wing oscillations can be represented in a single inter-frame similarity matrix through area-based differencing. Bird species classification can then be automated using singular value decomposition to reduce the matrices to one-dimensional vectors for training a feed-forward neural network.

This thesis is about the politics and the possibilities of aetiology. Firstly, the possibilities. Does an infectious disease have one, single pathogenic cause or many, interacting causes? In the medical microbiological sciences, there is no definitive answer, one way or another, to this question: there, the conditions of aetiological possibility exist in a curious tension. Ever since the birth of the 'germ theory of disease' and the concomitant birth of the singular aetiological object, these conditions have allowed for the co-existence of a very different, and far less well understood kind of object: the multifactorial object. That SARS was caused by one, singular viral agent, a coronavirus (CoV), is now entrenched as microbiological fact. And yet, the curious thing about SARS is that the history of the 2003 outbreak is littered with moments at which the possibility of the multifactorial object presented itself to, and was actively considered by, medical microbiologists. So how did we get here - to SARS-CoV, an infectious disease that could be understood and storied in this, the most singular of ways? And what happened along the way to deny the multifactorial aetiological object any kind of existence at all? In an attempt to grapple with these questions, the thesis seeks to recover the possibility of the multifactorial object through a deep, ethnomethodological reading of the moments at which it flared up precise/y as a possibility for medical microbiologists investigating the outbreak. What emerges from that recovery operation is a sense that the multifactorial object was never actually ruled out or disproved in any way, but rather, was vanished. Put another way, the suggestion is that various medical microbiological practices and interventions, whilst establishing singularity, were serving, at the same time, to create an illusion of multifactorality's non-existence; an illusion behind which the issue of multifactorality, its possibility, could be discarded without ever having to be resolved, one way or the other. In the closing sections of this thesis a move is made towards suggesting that SARS-Co V, the singular disease, was the product of a choice-, a choice that was made to explore one aetiological possibility at the expense of another. And that is where the politics comes in. For if politics, the realm of the political, can be taken to arise in situations where various possibilities exist but not all possibilities can be chosen, then it follows that what this thesis provides is an opportunity to foreground the politics bound up with the practical doing of aetiology. As a result, and based on the experience of attempting to recover the vanished multifactorial object from the 2003 SARS outbreak, the thesis concludes with an attempt to inhabit the present in such a way as to make it possible to think, in a little more detail, about where aetiology, as understood by medical microbiologists, might be heading in the future: might recent shifts in practical, everyday, seemingly innocuous microbiological technique, have begun to make it easier to coax the multifactorial object out into a space of visibility? Might those shifts actually herald the crossing of an epistemological threshold in the medical sciences? And might the conditions of aetiological possibility be changing, and changing in ways that would drastically alter what it meant to speak of a 'disease', an 'infection' and a 'pathogen'?

The world is slowly moving into increased human-robot interaction where both humans and robots can co-exist in the same domain. For the robot to be able to operate effectively in a man’s designed environment, it becomes necessary to model the robot with human capabilities as humans are seen as more capable. Replicating human becomes a huge challenge due to numerous degrees-of-freedom (DOFs) that human possess resulting into too many variables and nonlinear equations. Other challenges do occur like singularities.   In this thesis, the singularity challenge of a redundant humanoid arm is explored while maintaining a simple 7 DOF serial chain structure. As opposed to the 30 DOF human arm, a simpler 7 DOF humanoid arm is adopted and studied to eliminate the singularity challenges. The singularity problem mainly comes from the elbow and the spherical joints at the shoulder and wrist. A step-by-step review of available inverse kinematics techniques is made with more focus on the iterative Jacobian-based methods. A step-by-step approach is adopted so as to identify the source of singularities while using the iterative Jacobian-based techniques that are able to handle the nonlinearities of the equations.   The Singular Value Filtering (SVF) technique coupled with Selectively Damped Least Squares (SDLS) is employed. Without any restrictions to the stretch of the arm or end-effector pose, the method demonstrates, in conjunction with Euler angle singularity avoidance method, the elimination of singularity problems. This is achieved with no adjustment to kinematic model of the manipulator.

Considerando germes de hipersuperfícies em \'C POT.n+1\' com conjunto singular de dimensão s, Massey em [14] introduz um conjunto de (s+1) números chamados de números de Lê. Estes números se mostram como a generalização natural do número de Milnor para singularidades isoladas. O principal objetivo deste trabalho é mostrar como estes números são obtidos e que os números de Lê de uma hipersuperfície singular estão relacionados com os números de Lê de uma certa sequência de hipersuperfícies singulares \'X IND.0\',...,\'X IND.s-1\' que se aproxima da singularidade original de tal forma que os conjuntos críticos de seus termos \'X IND.i\' têm dimensão i. Essas relações são dadas pelas fórmulas de Lê-Iomdine. / For any germ of hypersurface in \'C POT. n+1\' with singular set of dimension s, Massey in [14] introduces a set of (s+1) numbers called Lê numbers. These numbers are a natural generalization of the Milnor number for isolated singularity hypersurfaces. The main goal of this work is to show how to obtain these numbers and to show the Lê numbers of a singular hypersurface are related with the the Lê numbers of a sequence of singular hypersurfaces \'X IND.0\',...,\'X IND.s-1\' which approach the original singularity in such a way that the critical set of each \'X IND.i\' has dimension i. These relationship are given by the Lê-Iomdine formulas.

Neste trabalho,apresentamos um breve compêndio sobre o estudo topológico das fibras de Milnor. Abordamoso caso clássico, estudado por J. Milnor, e a generalização apresentada por Lê D. T. para o caso de germes de funções analíticas definidas em variedades singulares. Nestas duas situações, os resultados principais tratam de germes de funções com singularidades isoladas / In this work, we present a brief compendium about the topological study of J. Milnor fibers. We address the classic case, studied by Milnor, and the generalization presented by Lê D. T. for the case of germs of analytic functions defined on singular varieties. In both situations, the main results deal with germs of functions with isolated singularities

National security needs dictate the development of new radar systems capable of identifying and tracking exoatmospheric threats to aid our defense. These new radar systems feature reduced noise floors, electronic beam steering, and ultra-wide bandwidths, all of which facilitate threat discrimination. However, in order to identify missile attributes such as RF reflectivity, distance, and velocity, many existing processing algorithms rely upon narrow bandwidth assumptions that break down with increased signal bandwidth. We present a fresh investigation into these algorithms for removing bandwidth limitations and propose novel state-space and direct-data factoring formulations such as * the multidimensional extension to the Eigensystem Realization Algorithm, * employing state-space models in place of interpolation to obtain a form which admits a separation and isolation of solution components, * and side-stepping the joint diagonalization of state transition matrices, which commonly plagues methods like multidimensional ESPRIT. We then benchmark our approaches and relate the outcomes to the Cramer-Rao bound for the case of one and two adjacent reflectors to validate their conceptual design and identify those techniques that compare favorably to or improve upon existing practices.

Frequency estimation plays an important role in many digital signal processing applications. Many areas have benefited from the discovery of the Fast Fourier Transform (FFT) decades ago and from the relatively recent advances in modern spectral estimation techniques within the last few decades. As processor and programmable logic technologies advance, unconventional methods for rapid frequency estimation in white Gaussian noise should be considered for real time applications. In this thesis, a practical hardware implementation that combines two known frequency estimation techniques is presented, implemented, and characterized. The combined implementation, using the well known FFT and a less well known modern spectral analysis method known as the Direct State Space (DSS) algorithm, is used to demonstrate and promote application of modern spectral methods in various real time applications, including Electronic Counter Measure (ECM) techniques.

This thesis explores the evolution plural verbal -s ("People thinks he is guilty") and zero 3rd singular ("He think he is guilty") in data from two sources on Southern English: The Linguistic Atlas of the Gulf States (LAGS) and The Linguistic Atlas of the Middle and South Atlantic States (LAMSAS). The research questions that underlie this study consider (1) the demographic association of plural verbal -s and zero 3rd singular, (2) the maintenance of each form, (3) the constraints on their use, and (4) the origins of -s variability. The atlas data suggest the following for plural verbal -s: (1) it has a British source, (2) it was present in both African American Vernacular English (AAVE) and early Southern White English (SWE), and (3) there were different grammatical constraints on its use in AAVE and SWE. Data for zero 3rd singular -s suggest this form (1) did not have a British source and (2) that it has historically been an AAVE feature.