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.

History, revolution and the British popular novel: historical fiction in the romantic age

“History, Revolution and the British Popular Novel” takes as its focus the significant role which historical fiction played within the French Revolution debate and its aftermath. Examining the complex intersection of the genre with the political and historical dialogue generated by the French Revolution crisis, the thesis contends that contemporary fascination with the historical episode of the Revolution, and the fundamental importance of history to the disputes which raged about questions of tradition and change, and the meaning of the British national past, led to the emergence of increasingly complex forms of fictional historical narrative during the “war of ideas.” Considering the varying ways in which novelists such as Charlotte Smith, William Godwin, Mary Robinson, Helen Craik, Clara Reeve, John Moore, Edward Sayer, Mary Charlton, Ann Thomas, George Walker and Jane West engaged with the historical contexts of the Revolution debate, my discussion juxtaposes the manner in which English Jacobin novelists inserted the radical critique of the Jacobin novel into the wider arena of history with anti-Jacobin deployments of the historical to combat the revolutionary threat and internal moves for socio-political restructuring. I argue that the use of imaginative historical narrative to contribute to the ongoing dialogue surrounding the Revolution, and offer political and historical guidance to readers, represented a significant element within the literature of the Revolution crisis. The thesis also identifies the diverse body of historical fiction which materialised amidst the Revolution controversy as a key context within which to understand the emergence of Scott’s national historical novel in 1814, and the broader field of historical fiction in the era of Waterloo. Tracing the continued engagement with revolutionary and political concerns evident in the early Waverley novels, Frances Burney’s The Wanderer (1814), William Godwin’s Mandeville (1816), and Mary Shelley’s Valperga (1823), my discussion concludes by arguing that Godwin’s and Shelley’s extension of the mode of historical fiction initially envisioned by Godwin in the revolutionary decade, and their shared endeavour to retrieve the possibility enshrined within the republican past, appeared as a significant counter to the model of history and fiction developed by Walter Scott in the post-revolutionary epoch.

The Viking age glass beads of Ireland and their North Atlantic context

Hitherto, the majority of studies which have included the discussion of Viking glass beads have mainly focused on the assemblages from individual sites, with limited use of known parallels. Exceptions to this include recent publications regarding the Icelandic material and Callmer’s 1977 catalogue of the finds from mainland Scandinavia, now over thirty years old. Analysis of these finds from Ireland was, for the most part, non-existent. The aim of this research is to address this lack of analysis within Ireland, while incorporating the wider context of the beads within the Viking North Atlantic. The research thus examines the use of glass beads of diagnostically Scandinavian manufacture and import found in Ireland, particularly in relation to their context and distribution. The history of research from Ireland as well as from across the Viking world is considered and explored throughout the thesis, with critique of methods and discussions used. Focussed analysis of both published and unpublished material detailing artefacts from Scandinavia (especially Vestfold), Britain, Iceland, the Faroe Islands and L’Anse aux Meadows is presented within the thesis in order to provide the greater picture for the core section of the thesis, the glass beads found in Ireland. Three appendices are included within Volume 2, databases of the glass beads under discussion from Ireland, the Vestfold region graves in Norway and the topsoil finds from the Kaupang trading place, also located within Vestfold. These appendices therefore represent the first-hand analysis of glass beads by the author. In total, this research represents the most up-to-date analysis of Viking glass beads from Ireland and presents a new look at the patterns of use, trade and interpersonal contact that affected the everyday lives of individuals living within Viking Age Ireland.

Epidemiology and comparative analysis of Yersinia in Ireland

Yersiniosis is an acute or chronic enteric zoonosis caused by enteropathogenic Yersinia species. Although yersiniosis is predominantly associated with gastroenteric forms of infection, extraintestinal forms are often reported from the elderly or patients with predisposing factors. Yersiniosis is often reported in countries with cold and mild climates (Northern and Central Europe, New Zealand and North of Russian Federation). The Irish Health Protection Surveillance Centre (HPSC) currently records only 3-7 notified cases of yersiniosis per year. At the same time pathogenic Yersinia enterocolitica is recovered from pigs (main source of pathogenic Y. enterocolitica) at the levels similar to that observed in Yersinia endemic countries. Introduction of Yersinia selective culture procedures may increase Yersinia isolation rates. To establish whether the small number of notifications of human disease was an underestimate due to lack of specific selective culture for Yersinia we carried out a prospective culture study of faecal samples from outpatients with diarrhoea, with additional culture of appendix and throat swabs. Higher levels of anti-Yersinia seroprevalence than yersiniosis notification rates in endemic countries suggests that most yersiniosis cases are unrecognised by culture. Subsequently, in addition to a prospective culture study of clinical specimens, we carried out serological screening of Irish blood donors and environmental screening of human sewage. Pathogenic Yersinia strains were not isolated from 1,189 faeces samples, nor from 297 throat swabs, or 23 appendix swabs. This suggested that current low notification rates in Ireland are not due to the lack of specific Yersinia culture procedures. Molecular screening detected a wider variety of Y. enterocolitica-specific targets in pig slurry than in human sewage. A serological survey for antibodies against Yersinia YOP (Yersinia Outer Proteins) proteins in Irish blood donors found antibodies in 25%, with an age-related trend to increased seropositivity, compatible with the hypothesis that yersiniosis may have been more prevalent in Ireland in the recent past. Y. enterocolitica is a heterogeneous group of microorganisms that comprises strains with different degree of pathogenicity. Although non-pathogenic Y. enterocolitica lack conventional virulence factors, these strains can be isolated from patients with diarrhoea. Insecticidal Toxin Complex (ITC) and Cytolethal Distending Toxins can potentially contribute to the virulence of non-pathogenic Y. enterocolitica in the absence of other virulence factors. We compared distribution of ITC and CDT loci among pathogenic and non-pathogenic Y. enterocolitica. Additionally, to demonstrate potential pathogenicity of non-pathogenic Y. enterocolitica we compared their virulence towards Galleria mellonella larvae (a non-mammalian model of human bacterial infections) with the virulence of highly and mildly pathogenic Y. enterocolitica strains. Surprisingly, virulence of pathogenic and non-pathogenic Y. enterocolitica in Galleria mellonella larvae observed at 37°C did not correlate with their pathogenic potential towards humans. Comparative phylogenomic analysis detects predicted coding sequences (CDSs) that define host-pathogen interactions and hence providing insights into molecular evolution of bacterial virulence. Comparative phylogenomic analysis of microarray data generated in Y. enterocolitica strains isolated in the Great Britain from humans with diarrhoea and domestic animals revealed high genetic heterogeneity of these species. Because of the extensive human, animal and food exchanges between the UK and Ireland the objective of this study was to gain further insight into genetic heterogeneity and relationships among clinical and non-clinical Y. enterocolitica strains of various pathogenic potential isolated in Ireland and Great Britain. No evidence of direct transfer of strains between the two countries was found.

Copper mining in Ireland during the later Bronze Age

Accepted Version

SDC: Scalable description coding for adaptive streaming media

Video compression techniques enable adaptive media streaming over heterogeneous links to end-devices. Scalable Video Coding (SVC) and Multiple Description Coding (MDC) represent well-known techniques for video compression with distinct characteristics in terms of bandwidth efficiency and resiliency to packet loss. In this paper, we present Scalable Description Coding (SDC), a technique to compromise the tradeoff between bandwidth efficiency and error resiliency without sacrificing user-perceived quality. Additionally, we propose a scheme that combines network coding and SDC to further improve the error resiliency. SDC yields upwards of 25% bandwidth savings over MDC. Additionally, our scheme features higher quality for longer durations even at high packet loss rates.