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.

Theory of elasticity and electric polarization effects in the group-III nitrides

In this work, the properties of strained tetrahedrally bonded materials are explored theoretically, with special focus on group-III nitrides. In order to do so, a multiscale approach is taken: accurate quantitative calculations of material properties are carried out in a quantum first-principles frame, for small systems. These properties are then extrapolated and empirical methods are employed to make predictions for larger systems, such as alloys or nanostructures. We focus our attention on elasticity and electric polarization in semiconductors. These quantities serve as input for the calculation of the optoelectronic properties of these systems. Regarding the methods employed, our first-principles calculations use highly- accurate density functional theory (DFT) within both standard Kohn-Sham and generalized (hybrid functional) Kohn-Sham approaches. We have developed our own empirical methods, including valence force field (VFF) and a point-dipole model for the calculation of local polarization and local polarization potential. Our local polarization model gives insight for the first time to local fluctuations of the electric polarization at an atomistic level. At the continuum level, we have studied composition-engineering optimization of nitride nanostructures for built-in electrostatic field reduction, and have developed a highly efficient hybrid analytical-numerical staggered-grid computational implementation of continuum elasticity theory, that is used to treat larger systems, such as quantum dots.

Language legislation in Ireland and the United Kingdom: Exploring the gaps between theory and practice

The central objective in this thesis is to explore the gaps between the normative justifications advanced for language rights and language legislative protection and the effective realisation of those rights and legislative provisions in practice. This objective is achieved by examining the scope and application of language rights and legislative provisions within language legislation in Ireland and the United Kingdom. Drawing on Canadian jurisprudence advocating for language rights to be recognised as “purposeful”, the thesis considers the extent to which Ireland and the United Kingdom have limited the acceptance of positive obligations as they relate to the provision of language services in the public sphere. In arguing that language rights are distinct in nature, the thesis suggests that in order for language rights to be effectively realised, an approach to language rights and language legislation more generally must be underpinned by a substantive vision of equality, otherwise language rights and legislative provisions merely amount to symbolic recognition and vacuous rhetoric as opposed to being substantive and enabling rights and provisions. Having said that, the thesis also recognises and elucidates the practical difficulties that arise in the realisation of language rights and language legislative provisions and in doing so seeks to stimulate further dialogue about the nature and limits of language rights and language legislation.

Accommodating interruptions: a grounded theory of young people with asthma

Background: Accommodating Interruptions is a theory that emerged in the context of young people who have asthma. A background to the prevalence and management of asthma in Ireland is given to situate the theory. Ireland has the fourth highest incidence of asthma in the world, with almost one in five Irish young people having asthma. Although national and international asthma management guidelines exist it is accepted that the symptom control of asthma among the young people population is poor. Aim: The aim of this research is to investigate the lives of young people who have asthma, to allow for a deeper understanding of the issues affecting them. Methods: This research was undertaken using a Classic Grounded Theory approach. It is a systematic approach to allowing conceptual emergence from data in generating a theory that explains behaviour in resolving the participant’s main concern. The data were collected through in-depth interviews with young people aged 11-16 years who had asthma for over one year. Data were also collected from participant diaries. Constant comparative analysis, theoretical coding and memo writing were used to develop the theory. Results: The theory explains how young people resolve their main concern of being restricted, by maximizing their participation and inclusion in activities, events and relationships in spite of their asthma. They achieve this by accommodating interruptions in their lives in minimizing the effects of asthma on their everyday lives. Conclusion: The theory of accommodating interruptions explains young people’s asthma management behaviours in a new way. It allows us to understand how and why young people behave the way they do in order minimise the effect of asthma on their lives. The theory adds to the body of knowledge on young people with asthma and challenges some viewpoints regarding their behaviours.

Moral shielding: A grounded theory of integrity maintenance in multidisciplinary teams

Using a classic grounded theory methodology (CGT), this study explores the phenomenon of moral shielding within mental health multidisciplinary teams (MDTS). The study was located within three catchment areas engaged in acute mental health service practice. The main concern identified was the maintenance of a sense of personal integrity during situational binds. Through theoretical sampling thirty two practitioners, including; doctors, nurses, social workers, occupational therapists, counsellors and psychologists, where interviewed face to face. In addition, emergent concepts were identified through observation of MDTs in clinical and research practice. Following a classic grounded theory methodology, data collection and analysis occurred simultaneously. A constant comparative approach was adopted and resulted in the immergence of three sub- core categories; moral abdication, moral hinting and pseudo-compliance. Moral abdication seeks to re-position within an event in order to avoid or deflect the initial obligation to act, it is a strategy used to remove or reduce moral ownership. Moral gauging represents the monitoring of an event with the goal of judging the congruence of personal principles and commitments with that of other practitioners. This strategy is enacted in a bid to seek allies for the support of a given moral position. Pseudo-compliance represents behaviour that hides desired principles and commitments in order to shield them from challenge. This strategy portrays agreement with the dominant position within the MDT, whilst holding a contrary position. It seeks to preserve a reservoir of emotional energy required to maintain a sense of personal integrity. Practitioners who were successful in enacting moral shielding were found to not experience significant emotional distress associated with the phenomenon of moral distress; suggesting that these practitioners had found mechanisms to manage situational binds that threatened their sense of personal integrity.

From the demise of theory to its resurgence. A retrospective on the postmodern turn to rethink the 'desire for narrative' and the sublime untimeliness of emancipation

Cultural Marxist Theory, commonly known as theory, enjoyed a moment of extraordinary success in the 1970s, when the works of leading post-war French philosophers were published in English. After relocating to Anglophone academia, however, theory disavowed its original concerns and lost its ambition to understand the world as a whole, becoming the play of heterogeneities associated with postcolonialism, multiculturalism and identity politics, commonly referred to as postmodern theory. This turn, which took place during a period that seemed to have spelt the death of Marxism, the 1990s, induced many of its supporters to engage in an ongoing funeral wake designating the merits of theory and dreaming its resurgence. According to them, had theory been resurrected in historical circumstances completely different from those which had led to its rise, it would have never reacquired the significance that had originally connoted it. This thesis demonstrates how theory has survived its demise and entirely regained its prominence in our socio-political context marked by the effects of the latest crisis of capitalism and by the global threat of terrorisms rooted in messianic eschatologies. In its current form theory does no longer need to show allegiance to certain intellectual stances or political groupings in order to produce important reformulations of the projects it once gave life to. Though less overtly radical and epistemologically bounded, theory remains a necessary form of enquiry justified by the political commitment which originated it in the first place. Its voice continues to speak to us about justice ‘where it is not yet, not yet there, where it is no longer’ (Derrida, 1993, XVIII).