Gröbner basis techniques for certain problems in coding and systems theory

There is much common ground between the areas of coding theory and systems theory. Fitzpatrick has shown that a Göbner basis approach leads to efficient algorithms in the decoding of Reed-Solomon codes and in scalar interpolation and partial realization. This thesis simultaneously generalizes and simplifies that approach and presents applications to discrete-time modeling, multivariable interpolation and list decoding. Gröbner basis theory has come into its own in the context of software and algorithm development. By generalizing the concept of polynomial degree, term orders are provided for multivariable polynomial rings and free modules over polynomial rings. The orders are not, in general, unique and this adds, in no small way, to the power and flexibility of the technique. As well as being generating sets for ideals or modules, Gröbner bases always contain a element which is minimal with respect tot the corresponding term order. Central to this thesis is a general algorithm, valid for any term order, that produces a Gröbner basis for the solution module (or ideal) of elements satisfying a sequence of generalized congruences. These congruences, based on shifts and homomorphisms, are applicable to a wide variety of problems, including key equations and interpolations. At the core of the algorithm is an incremental step. Iterating this step lends a recursive/iterative character to the algorithm. As a consequence, not all of the input to the algorithm need be available from the start and different "paths" can be taken to reach the final solution. The existence of a suitable chain of modules satisfying the criteria of the incremental step is a prerequisite for applying the algorithm.

Uniformly convergent finite element and finite difference methods for singularly perturbed ordinary differential equations

This thesis is concerned with uniformly convergent finite element and finite difference methods for numerically solving singularly perturbed two-point boundary value problems. We examine the following four problems: (i) high order problem of reaction-diffusion type; (ii) high order problem of convection-diffusion type; (iii) second order interior turning point problem; (iv) semilinear reaction-diffusion problem. Firstly, we consider high order problems of reaction-diffusion type and convection-diffusion type. Under suitable hypotheses, the coercivity of the associated bilinear forms is proved and representation results for the solutions of such problems are given. It is shown that, on an equidistant mesh, polynomial schemes cannot achieve a high order of convergence which is uniform in the perturbation parameter. Piecewise polynomial Galerkin finite element methods are then constructed on a Shishkin mesh. High order convergence results, which are uniform in the perturbation parameter, are obtained in various norms. Secondly, we investigate linear second order problems with interior turning points. Piecewise linear Galerkin finite element methods are generated on various piecewise equidistant meshes designed for such problems. These methods are shown to be convergent, uniformly in the singular perturbation parameter, in a weighted energy norm and the usual L2 norm. Finally, we deal with a semilinear reaction-diffusion problem. Asymptotic properties of solutions to this problem are discussed and analysed. Two simple finite difference schemes on Shishkin meshes are applied to the problem. They are proved to be uniformly convergent of second order and fourth order respectively. Existence and uniqueness of a solution to both schemes are investigated. Numerical results for the above methods are presented.

Becoming a CEO: an exploration of the theory and practice of effective organisational leadership

This Thesis is an exploration of potential enhancement in effectiveness, personally, professionally and organisationally through the use of Theory as an Apparatus of Thought. Enhanced effectiveness was sought by the practitioner (Subject), while in transition to becoming Chief Executive of his organization. The introduction outlines the content and the structure of the University College Cork DBA. Essay One outlines what Theory is, what Adult Mental Development is and an exploration of Theories held in the Authors past professional practice. Immunity to change is also reflected on. Essay Two looks at the construct of the key Theories used in the Thesis. Prof. Robert Kegan’s Theory of Adult Mental Development was used to aid the generation of insight. The other key Theories used were The Theory of The Business, Theory of the Co‐operative and a Theory of Organisational Leadership. Essay Three explores the application of the key Theories in a professional setting. The findings of the Thesis were that the subject was capable of dealing with increased environmental complexity and uncertainty by using Theory as an Apparatus of Thought, which in turn enhanced personal, professional and organisational effectiveness. This was achieved by becoming more aware of the Theories held by the practitioner, the experiences from the application of those Theories, which then led to greater insight. The author also found that a detailed understanding of the Theory of the Business and a Theory of Leadership would support any new CEO in the challenging early part of their tenure.

Thomas Wolfe and the genre question: Beyond the "charge of autobiography"

The North Carolinian author Thomas Wolfe (1900‐1938) has long suffered under the “charge of autobiography,” which lingers to this day in critical assessments of his work. Criticism of Wolfe is frequently concerned with questions of generic classification, but since the 1950s, re‐assessments of Wolfe’s work have suggested that Wolfe’s “autobiographical fiction” exhibits a complexity that merits further investigation. Strides in autobiographical and narrative theory have prompted reconsiderations of texts that defy the artificial boundaries of autobiography and fiction. Wolfe has been somewhat neglected in the canon of American fiction of his era, but deserves to be reconsidered in terms of how he engages with the challenges and contradictions of writing about or around the self. This thesis investigates why Wolfe’s work has been the source of considerable critical discomfort and confusion with regard to the relationship between Wolfe’s life and his writing. It explores this issue through an examination of elements of Wolfe’s work that problematise categorisation. Firstly, it investigates the concept of Wolfe as “storyteller.” It explores the motivations and philosophies that underpin Wolfe’s work and his concept of himself as a teller of tales, and examines aspects of Wolfe’s writing process that have their roots in medieval traditions of the memorisation and recitation of tales. The thesis then conducts a detailed examination of how Wolfe describes the process of transforming his memory into narrative through writing. The latter half of the thesis examines narrative techniques used by Wolfe, firstly analysing his extensive use of the iterative and pseudo‐iterative modes, and then his unusual deployment of narrators and focalization. This project sheds light on elements of Wolfe’s approach to writing and narrative strategies that he employs that have previously been overlooked, and that have created considerable critical confusion with regard to the supposedly “autobiographical” genesis of his work.

The political and economic context of Keynes’s 1933 Finlay lecture: transforming a business practitioner’s ways of knowing

This thesis is structured in the format of a three part Portfolio of Exploration to facilitate transformation in my ways of knowing to enhance an experienced business practitioner’s capabilities and effectiveness. A key factor in my ways of knowing, as opposed to what I know, is my exploration of context and assumptions. By interacting with my cultural, intellectual, economic, and social history, I seek to become critically aware of the biographical, historical, and cultural context of my beliefs and feelings about myself. This Portfolio is not exclusively for historians of economics or historians of ideas but also for those interested in becoming more aware of how these culturally assimilated frames of reference and bundles of assumptions that influence the way they perceive, think, decide, feel and interpret their experiences in order to operate more effectively in their professional and organisational lives. In the first part of my Portfolio, I outline and reflect upon my Portfolio’s overarching theory of adult development; the writings of Harvard’s Robert Kegan and Columbia University’s Jack Mezirow. The second part delves further into how meaning-making, the activity of how one organises and makes sense of the world and how meaning-making evolves to different levels of complexity. I explore how past experience and our interpretations of history influences our understandings since all perception is inevitably tinged with bias and entrenched ‘theory-laden’ assumptions. In my third part, I explore the 1933 inaugural University College Dublin Finlay Lecture delivered by economist John Maynard Keynes. My findings provide a new perspective and understanding of Keynes’s 1933 lecture by not solely reading or relying upon the text of the three contextualised essay versions of his lecture. The purpose and context of Keynes’s original longer lecture version was quite different to the three shorter essay versions published for the American, British and German audiences.

The study of molecular variation in Atlantic salmon (Salmo salar L.) and brown trout (Salmo trutta L.)

Polymorphic microsatellite DNA loci were used here in three studies, one on Salmo salar and two on S. trutta. In the case of S. salar, the survival of native fish and non-natives from a nearby catchment, and their hybrids, were compared in a freshwater common garden experiment and subsequently in ocean ranching, with parental assignment utilising microsatellites. Overall survival of non-natives was 35% of natives. This differential survival was mainly in the oceanic phase. These results imply a genetic basis and suggest local adaptation can occur in salmonids across relatively small geographic distances which may have important implications for the management of salmon populations. In the first case study with S trutta, the species was investigated throughout its spread as an invasive in Newfoundland, eastern Canada. Genetic investigation confirmed historical records that the majority of introductions were from a Scottish hatchery and provided a clear example of the structure of two expanding waves of spread along coasts, probably by natural straying of anadromous individuals, to the north and south of the point of human introduction. This study showed a clearer example of the genetic anatomy of an invasion than in previous studies with brown trout, and may have implications for the management of invasive species in general. Finally, the genetics of anadromous S. trutta from the Waterville catchment in south western Ireland were studied. Two significantly different population groupings, from tributaries in geographically distinct locations entering the largest lake in the catchment, were identified. These results were then used to assign very large rod caught sea trout individuals (so called “specimen” sea trout) back to region of origin, in a Genetic Stock Identification exercise. This suggested that the majority of these large sea trout originated from one of the two tributary groups. These results are relevant for the understanding of sea trout population dynamics and for the future management of this and other sea trout producing catchments. This thesis has demonstrated new insights into the population structuring of salmonids both between and within catchments. While these chapters look at the existence and scale of genetic variation from different angles, it might be concluded that the overarching message from this thesis should be to highlight the importance of maintaining genetic diversity in salmonid populations as vital for their long-term productivity and resilience.

“Something isn’t right here”: American exceptionalism and the creative nonfiction of the Vietnam War

In this thesis, I argue that few attempts were as effective in correcting the exceptionalist ethos of the United States than the creative nonfiction written by the veterans and journalists of the Vietnam War. Using critical works on creative nonfiction, I identify the characteristics of the genre that allowed Paul John Eakin to call it ‘a special kind of fiction.’ I summarise a brief history of creative nonfiction to demonstrate how it became a distinctly American form despite its Old World origins. I then claim that it was the genre most suited to the kind of ideological transformation that many hoped to instigate in U.S. society in the aftermath of Vietnam. Following this, the study explores how this “new” myth-making process occurred. I use Tim O’Brien’s If I Die in a Combat Zone and Philip Caputo’s A Rumor of War to illustrate how autobiography/memoir was able to demonstrate the detrimental effect that America’s exceptionalist ideology was having on its population. Utilising narrative and autobiographical theory, I contend that these accounts represented a collective voice which spoke for all Americans in the years after Vietnam. Using Neil Sheehan’s A Bright Shining Lie and C.D.B. Bryan’s Friendly Fire, I illustrate how literary journalism highlighted the hubris of the American government. I contend that while poiesis is an integral attribute of creative nonfiction, by the inclusion of extraneous bibliographic material, authors of the genre could also be seen as creating a literary context predisposing the reader towards an empirical interpretation of the events documented within. Finally, I claim that oral histories were in their essence a synthesis of “everyman” experiences very much in keeping with the American zeitgeist of the early Eighties. Focussing solely on Al Santoli’s Everything We Had, I demonstrate how such polyphonic narratives personalised the history of the Vietnam War.