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.

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.

Variability in north temperate dung beetle assemblages at different spatial and temporal scales

This study examined the spatial and temporal variability of dung beetle assemblages across a variety of scales e.g. from the between-pad scale (examining the effects of dung size and type) to larger spatial scales encompassing southern Ireland. Dung beetle assemblage structure as sampled by dung pad cohort samples and dung baited pitfall trapping were compared. Generally, the rank order of abundance of dung beetle species was significantly correlated between pitfall catches and cohort pad samples. Across different dung sizes, in both pitfall catches and cohort pad samples, the relative abundance of species was frequently significantly different, but the rank order of abundance of dung beetle was usually significantly correlated. Considerable variations in pitfall catches at temporal scales of a few days appeared to be closely related to weather conditions and rotational grazing. However, despite considerable variation in absolute abundances between consecutive days of sampling, assemblage structure typically remained very similar. The relationship between dung pad size and dung beetle colonisation was investigated. In field experiments in which pads of different sizes (0.25 L, 0.5 L, 1.0 L and 1.5 L) were artificially deposited, there was a positive relationship between pad size and both biomass and number of beetles colonising dung pads and pitfall traps. In addition, with one exception, the field experiments indicated a general positive relationship between dung pad size and biomass density (dung beetle biomass per unit dung volume). A laboratory experiment indicated that pat residence times of A. rufipes were significantly correlated with dung pad size. Investigation of naturally-deposited cow dung pads in the field also indicated that both larval numbers and densities were significantly correlated with dung pad size. These results were discussed in the context of theory related to aggregation and coexistence of species, and resource utilisation by organisms in ephemeral, patchy resources. The colonisation by dung beetles of dung types from native herbivores (sheep, horse and cow) was investigated in field experiments. There were significant differences between the dung types in the chemical parameters measured, and there were significant differences in abundances of dung beetles colonising the dung types. Sheep dung was typically the preferred dung type. Data from these field experiments, and from published literature, indicated that dung beetle species can display dung type preferences, in terms of comparisons of both absolute and relative abundances. In addition, data from laboratory experiments indicate that both Aphodius larval production and pat residence times tended to be higher in those dung types which were preferred by adult Aphodius in the colonisation experiments. Data from dung-baited pitfall trapping (from this and another study) at several sites (up to 180 km distant) and over a number of years (between 1991 and 1996) were used to investigate spatial and temporal variation in dung beetle assemblage structure and composition (Aphodius, Sphaeridium and Geotrupes) across a range of scales in southern Ireland. Species richness levels, species composition and rank order of abundances were very similar between the assemblages. The temporal variability between seasons within any year exceeded temporal variability between years. DCA ordinations indicated that there was a similar level of variability between assemblage structure from the between-field (~1km) to regional (~180 km) spatial scales, and between year (6 years) temporal scales. At the biogeographical spatial scale, analysis of data from the literature indicated that there was considerable variability at this scale, largely due to species turnover.

The role of inflammatory mediators in the overactive and bladder pain syndromes

The Overactive Bladder (OAB) and Bladder Pain Syndrome (BPS) are debilitating disorders for which the pathophysiological mechanisms are poorly understood. Injury or dysfunction of the protective urothelial barrier layer, specifically the proteoglycan composition and number, has been proposed as the primary pathological characteristic of BPS. For OAB, the myogenic theory with dysfunction of the muscarinic receptors is the most reiterated hypothesis. For both over activity of the inflammatory response has been posited to play a major role in these diseases. We hypothesise that BPS and OAB are peripheral sensory disorders, with an increase in inflammatory mediators, such as cytokines and chemokines, which are capable of activating, either directly or indirectly, sensory nerve activity causing the disease. The aim of the PhD is to identify potential new therapeutic targets for the treatment of BPS and OAB. We used medium throughput quantitative gene expression analysis of 96 inflammation associated mediators to measure gene expression levels in BPS and OAB bladder biopsies and compared them to control samples. Then we created a novel animal model of disease by specific proteoglycan deglycosylation of the bladder mucosal barrier, using the bacterial enzymes Chondroitinase ABC and Heparanase III. These enzymes specifically remove the glycosaminoglycan side chains from the urothelial proteoglycan molecules. We tested role of the identified mediators in this animal model. In addition, in order to determine on which patients peripheral treatment strategies may work, we assessed the effect of local anaesthetics on patients with bladder pain. Gene expression analysis did not reveal a difference in inflammatory genes in the OAB versus control biopsies. However, several genes were upregulated in BPS versus control samples, from which two genes, FGF7 and CLL21 were correlated with patient clinical phenotypes for ICS/PI symptom and problem indices respectively. In order to determine which patients are likely to respond to treatment, we sought to characterise the bladder pain in BPS patients. Using urodynamics and local anaesthetics, we differentiated patients with peripherally mediated pain and patients with central sensitisation of their pain. Finally to determine the role of these mediators in bladder pain, we created an animal model of disease, which specifically replicates the human pathology: namely disruption in the barrier proteoglycan molecules. CCL21 led to an increase in painrelated behaviour, while FGF7 attenuated this behaviour, as measured by cystometry, spinal c-fos expression and mechanical withdrawal threshold examination. In conclusion, we have identified CCL21 and FGF7 as potential targets for the treatment of BPS. Manipulation of these ligands or their receptors may prove to be valuable previously unexploited targets for the treatment of BPS.