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.

Legal regulation of the software "patentable subject matter" requirement in the US and in Europe: The need for certainty, predictability and uniformity

This thesis critically investigates the divergent international approaches to the legal regulation of the patentability of computer software inventions, with a view to identifying the reforms necessary for a certain, predictable and uniform inter-jurisdictional system of protection. Through a critical analysis of the traditional and contemporary US and European regulatory frameworks of protection for computer software inventions, this thesis demonstrates the confusion and legal uncertainty resulting from ill-defined patent laws and inconsistent patent practices as to the scope of the “patentable subject matter” requirement, further compounded by substantial flaws in the structural configuration of the decision-making procedures within which the patent systems operate. This damaging combination prevents the operation of an accessible and effective Intellectual Property (IP) legal framework of protection for computer software inventions, capable of securing adequate economic returns for inventors whilst preserving the necessary scope for innovation and competition in the field, to the ultimate benefit of society. In exploring the substantive and structural deficiencies in the European and US regulatory frameworks, this thesis develops to ultimately highlight that the best approach to the reform of the legal regulation of software patentability is two-tiered. It demonstrates that any reform to achieve international legal harmony first requires the legislature to individually clarify (Europe) or restate (US) the long-standing inadequate rules governing the scope of software “patentable subject matter”, together with the reorganisation of the unworkable structural configuration of the decision-making procedures. Informed by the critical analysis of the evolution of the “patentable subject matter” requirement for computer software in the US, this thesis particularly considers the potential of the reforms of the European patent system currently underway, to bring about certainty, predictability and uniformity in the legal treatment of computer software inventions.