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.

Police accountability in Ireland: an analysis of the problems posed by the legal, constitutional and political dimensions and how they might be addressed

The concept of police accountability is not susceptible to a universal or concise definition. In the context of this thesis it is treated as embracing two fundamental components. First, it entails an arrangement whereby an individual, a minority and the whole community have the opportunity to participate meaningfully in the formulation of the principles and policies governing police operations. Second, it presupposes that those who have suffered as victims of unacceptable police behaviour should have an effective remedy. These ingredients, however, cannot operate in a vacuum. They must find an accommodation with the equally vital requirement that the burden of accountability should not be so demanding that the delivery of an effective police service is fatally impaired. While much of the current debate on police accountability in Britain and the USA revolves around the issue of where the balance should be struck in this accommodation, Ireland lacks the very foundation for such a debate as it suffers from a serious deficit in research and writing on police generally. This thesis aims to fill that gap by laying the foundations for an informed debate on police accountability and related aspects of police in Ireland. Broadly speaking the thesis contains three major interrelated components. The first is concerned with the concept of police in Ireland and the legal, constitutional and political context in which it operates. This reveals that although the Garda Siochana is established as a national force the legal prescriptions concerning its role and governance are very vague. Although a similar legislative format in Britain, and elsewhere, have been interpreted as conferring operational autonomy on the police it has not stopped successive Irish governments from exercising close control over the police. The second component analyses the structure and operation of the traditional police accountability mechanisms in Ireland; namely the law and the democratic process. It concludes that some basic aspects of the peculiar legal, constitutional and political structures of policing seriously undermine their capacity to deliver effective police accountability. In the case of the law, for example, the status of, and the broad discretion vested in, each individual member of the force ensure that the traditional legal actions cannot always provide redress where individuals or collective groups feel victimised. In the case of the democratic process the integration of the police into the excessively centralised system of executive government, coupled with the refusal of the Minister for Justice to accept responsibility for operational matters, project a barrier between the police and their accountability to the public. The third component details proposals on how the current structures of police accountability in Ireland can be strengthened without interfering with the fundamentals of the law, the democratic process or the legal and constitutional status of the police. The key elements in these proposals are the establishment of an independent administrative procedure for handling citizen complaints against the police and the establishment of a network of local police-community liaison councils throughout the country coupled with a centralised parliamentary committee on the police. While these proposals are analysed from the perspective of maximising the degree of police accountability to the public they also take into account the need to ensure that the police capacity to deliver an effective police service is not unduly impaired as a result.

Principles and prejudice: The erosion of fairness in admissibility determinations relating to historic child sexual abuse trials in Ireland

This thesis interrogates the construction of fairness to the accused in historic child sexual abuse trials in Ireland. The protection of fairness is a requirement of any trial that claims to adhere to the rule of law. Historic child sexual abuse trials, in which the charges relate to events that are alleged to have taken place decades previously, present serious challenges to the ability of the trial process to safeguard fairness. They are a litmus test of the courts’ commitment to fairness. The thesis finds that in historic abuse trials fairness to the accused has been significantly eroded and that therefore the Irish Courts have failed to respect the core of the rule of law in these most serious of prosecutions. The thesis scrutinises two bodies of case law, both of which deal with the issue of whether evidence should reach the jury. First, it examines the decisions on applications brought by defendants seeking to prohibit their trial. The courts hearing prohibition applications face a dilemma: how to ensure the defendant is not put at risk of an unfair trial, while at the same time recognising that delay in reporting is a defining feature of these cases. The thesis traces the development of the prohibition case law and tracks the shifting interpretations given to fairness by the courts. Second, the thesis examines what fairness means in the superior courts’ decisions regarding the admissibility of the following kinds of evidence, each of which presents particular challenges to the ability of the trial to safeguard fairness: evidence of multiple complainants; evidence of recovered memories and evidence of complainants’ therapeutic records. The thesis finds that in both bodies of case law the Irish courts have hollowed out the meaning of fairness. It makes proposals on how fairness might be placed at the heart of courts’ decisions on admissibility in historic abuse trials. The thesis concludes that the erosion of fairness in historic abuse trials is indicative of a move away from the liberal model of criminal justice. It cautions that unless fairness is prioritised in historic child sexual abuse trials the legitimacy of these trials and that of all Irish criminal trials will be contestable.

Home, family and society: women of the Irish landed class, 1860-1914. A Munster case study

The thesis analyses the roles and experiences of female members of the Irish landed class (wives, sisters and daughters of gentry and aristocratic landlords with estates over 1,000 acres) using primary personal material generated by twelve sample families over an important period of decline for the class, and growing rights for women. Notably, it analyses the experiences of relatively unknown married and unmarried women, something previously untried in Irish historiography. It demonstrates that women’s roles were more significant than has been assumed in the existing literature, and leads to a more rounded understanding of the entire class. Four chapters focus on themes which emerge from the sources used and which deal with their roles both inside and outside the home. These chapters argue that: Married and unmarried women were more closely bound to the priorities of their class than their sex, and prioritised male-centred values of family and estate. Male and female duties on the property overlapped, as marriage relationships were more equal than the legislation of the time would suggest. London was the cultural centre for this class. Due to close familial links with Britain (60% of sample daughters married English men) their self-perception was British or English, as well as Irish. With the self-confidence of their class, these women enjoyed cultural and political activities and movements outside the home (sport, travel, fashion, art, writing, philanthropy, (anti-)suffrage, and politics). Far from being pawns in arranged marriages, women were deeply conscious of their marriage decisions and chose socially, financially and personally compatible husbands; they also looked for sexual satisfaction. Childbirth sometimes caused lasting health problems, but pregnancy did not confine wealthy women to an invalid state. In opposition to the stereotypical distant aristocratic mother, these women breastfed their children, and were involved mothers. However, motherhood was not permitted to impinge on the more pressing role of wife

Embodied sexualities: Exploring accounts of Irish women's sexual knowledge and sexual experiences, 1920-1970

This chapter explores the ways in which sexuality has been understood, embodied and negotiated by a cohort of Irish women through their lives. It is based on qualitative data generated as part of an oral history project on Irish women’s experiences of sexuality and reproduction during the period 1920–1970.1 The interviews, which were conducted with 21 Irish women born between 1914 and 1955, illustrate that social and cultural discourses of sexuality as secretive, dangerous, dutiful and sinful were central to these women’s interpretative repertoires around sexuality and gender. However, the data also contains accounts of behaviours, experiences and feelings that challenged or resisted prevailing scripts of sexuality and gender. Drawing on feminist conceptualisations of sexuality and embodiment (Holland et al., 1994; Jackson and Scott, 2010), this chapter demonstrates that the women’s sexual subjectivities were forged in the tensions that existed between normative sexual scripts and their embodied experiences of sexual desires and sexual and reproductive practices. While recollections of sexual desire and pleasure did feature in the accounts of some of the women, it was the difficulties experienced around sexuality and reproduction that were spoken about in greatest detail. What emerges clearly from the data is the confusion, anxiety and pain occasioned by the negotiation of external demands and internal desires and the contested, unstable nature of both cultural power and female resistance.

Problems with drawing lines: Theo-geographies of the Catholic parish in Ireland

While people in Catholic parishes in Ireland appear keenly aware of parish boundaries, these understandings are more often oral than cartographic. There is no digital map of all of the Catholic parishes in Ireland. However, the institutional Catholic Church insists that no square kilometre can exist outside of a parish boundary. In this paper, I explain a process whereby the Catholic parishes of Ireland were produced digitally. I will outline some of the technical challenges of digitizing such boundaries. In making these maps, it is not only a question of drawing lines but mapping people’s understanding of their locality. Through an example of one part of the digitisation project, I want to talk about how verifying maps with local people often complicates something which may have at first sight seemed simple. The paper ends on a comparison with how other communities of interest are territorialised in Ireland and elsewhere to draw out some broader theoretical and theological issues of concern.