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.

Achieving continuous professional development in higher education

Traditional higher education technology emphasizes knowledge transmission. In contrast, the Community platform presented in this paper follows a social approach that interleaves knowledge delivery with social and professional skills development, engaging with others, and personal growth. In this paper, we apply learning and complex adaptive systems theory to motivate and justify a continuous professional development model that improves higher education outcomes such as placement. The paper follows action design research (ADR) as the research method to propose and evaluate design principles.

Counterstories: who counts as lesbian?

Coming out midlife is a profound and life‐changing experience—it is an experience of self‐shattering that entails the destabilisation of identity, and of family relationships. Entailing a displacement from social insider to outsider, it is a difficult, but also exhilarating, journey of self, and sexual, discovery. This thesis is an examination of the experiences of nine women who undertook that journey. This dissertation is very much a search for understanding—for understanding how one can be lesbian, and how one can not have known, following a lifetime of heterosexual identification—as well as a search for why those questions arise in the first place. I argue that the experience of coming out midlife exposes the fundamental ambiguity of sexuality; and has a significance that ranges beyond the particularity of the participants’ experiences and speaks to the limitations of the hegemonic sexual paradigm itself. Using the theoretical lens of three diverse conceptual approaches—the dynamic systems theory of sexual fluidity; liminality; and narrative identity—to illuminate their transition, I argue that the event of coming out midlife should be viewed not merely as an atypical experience, but rather we should ask what such events can tell us about women’s sexuality in particular, and the sexual paradigm more generally. I argue that women who come out midlife challenge those dominant discourses of sexuality that would entail that women who come out midlife were either in denial of their “true” sexuality throughout their adult lives; or that they are not really lesbian now. The experiences of the women I interviewed demonstrate the inadequacy of the sexual paradigm as a framework within which to understand and research the complexity of human sexuality; they also challenge hegemonic understandings of sexuality as innate and immutable. In this thesis, I explore that challenge.

Quantum behavior in mesoscopic systems

In this thesis I present the work done during my PhD. The Thesis is divided into two parts; in the first one I present the study of mesoscopic quantum systems whereas in the second one I address the problem of the definition of Markov regime for quantum system dynamics. The first work presented is the study of vortex patterns in (quasi) two dimensional rotating Bose Einstein condensates (BECs). I consider the case of an anisotropy trapping potential and I shall show that the ground state of the system hosts vortex patterns that are unstable. In a second work I designed an experimental scheme to transfer entanglement from two entangled photons to two BECs. This work is meant to propose a feasible experimental set up to bring entanglement from microscopic to macroscopic systems for both the study of fundamental questions (quantum to classical transition) and technological applications. In the last work of the first part another experimental scheme is presented in order to detect coherences of a mechanical oscillator which is assumed to have been previously cooled down to the quantum regime. In this regime in fact the system can rapidly undergo decoherence so that new techniques have to be employed in order to detect and manipulate their states. In the scheme I propose a micro-mechanical oscillator is coupled to a BEC and the detection is performed by monitoring the BEC with a negligible back-action on the cantilever. In the second part of the thesis I give a definition of Markov regime for open quantum dynamics. The importance of such definition comes from both the mathematical description of the system dynamics and from the understanding of the role played by the environment in the evolution of an open system. In the Markov regime the mathematical description can be simplified and the role of the environment is a passive one.

The contribution of enterprise systems to core capabilities: the case of asset lifecycle management in the utilities sector

The desire to obtain competitive advantage is a motivator for implementing Enterprise Resource Planning (ERP) Systems (Adam & O’Doherty, 2000). However, while it is accepted that Information Technology (IT) in general may contribute to the improvement of organisational performance (Melville, Kraemer, & Gurbaxani, 2004), the nature and extent of that contribution is poorly understood (Jacobs & Bendoly, 2003; Ravichandran & Lertwongsatien, 2005). Accordingly, Henderson and Venkatraman (1993) assert that it is the application of business and IT capabilities to develop and leverage a firm’s IT resources for organisational transformation, rather than the acquired technological functionality, that secures competitive advantage for firms. Application of the Resource Based View of the firm (Wernerfelt, 1984) and Dynamic Capabilities Theory (DCT) (Teece and Pisano (1998) in particular) may yield insights into whether or not the use of Enterprise Systems enhances organisations’ core capabilities and thereby obtains competitive advantage, sustainable or otherwise (Melville et al., 2004). An operational definition of Core Capabilities that is independent of the construct of Sustained Competitive Advantage is formulated. This Study proposes and utilises an applied Dynamic Capabilities framework to facilitate the investigation of the role of Enterprise Systems. The objective of this research study is to investigate the role of Enterprise Systems in the Core Dynamic Capabilities of Asset Lifecycle Management. The Study explores the activities of Asset Lifecycle Management, the Core Dynamic Capabilities inherent in Asset Lifecycle Management and the footprint of Enterprise Systems on those Dynamic Capabilities. Additionally, the study explains the mechanisms by which Enterprise Systems sustain the Exploitability and the Renewability of those Core Dynamic Capabilities. The study finds that Enterprise Systems contribute directly to the Value, Exploitability and Renewability of Core Dynamic Capabilities and indirectly to their Inimitability and Non-substitutability. The study concludes by presenting an applied Dynamic Capabilities framework, which integrates Alter (1992)’s definition of Information Systems with Teece and Pisano (1998)’s model of Dynamic Capabilities to provide a robust diagnostic for determining the sustained value generating contributions of Enterprise Systems. These frameworks are used in the conclusions to frame the findings of the study. The conclusions go on to assert that these frameworks are free - standing and analytically generalisable, per Siggelkow (2007) and Yin (2003).

Correlations in low dimensional quantum systems

In this thesis I present the work done during my PhD in the area of low dimensional quantum gases. The chapters of this thesis are self contained and represent individual projects which have been peer reviewed and accepted for publication in respected international journals. Various systems are considered, the first of which is a two particle model which possesses an exact analytical solution. I investigate the non-classical correlations that exist between the particles as a function of the tunable properties of the system. In the second work I consider the coherences and out of equilibrium dynamics of a one-dimensional Tonks-Girardeau gas. I show how the coherence of the gas can be inferred from various properties of the reduced state and how this may be observed in experiments. I then present a model which can be used to probe a one-dimensional Fermi gas by performing a measurement on an impurity which interacts with the gas. I show how this system can be used to observe the so-called orthogonality catastrophe using modern interferometry techniques. In the next chapter I present a simple scheme to create superposition states of particles with special emphasis on the NOON state. I explore the effect of inter-particle interactions in the process and then characterise the usefulness of these states for interferometry. Finally I present my contribution to a project on long distance entanglement generation in ion chains. I show how carefully tuning the environment can create decoherence-free subspaces which allows one to create and preserve entanglement.

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.

Theory of the electronic and optical properties of dilute bismide alloys

Dilute bismide alloys, containing small fractions of bismuth (Bi), have recently attracted interest due to their potential for applications in a range of semiconductor devices. Experiments have revealed that dilute bismide alloys such as GaBixAs1−x, in which a small fraction x of the atoms in the III-V semiconductor GaAs are replaced by Bi, exhibit a number of unusual and unique properties. For example, the band gap energy (E g) decreases rapidly with increasing Bi composition x, by up to 90 meV per % Bi replacing As in the alloy. This band gap reduction is accompanied by a strong increase in the spin-orbit-splitting energy (ΔSO) with increasing x, and both E g and ΔSO are characterised by strong, composition-dependent bowing. The existence of a ΔSO > E g regime in the GaBixAs1−x alloy has been demonstrated for x ≳10%, a band structure condition which is promising for the development of highly efficient, temperature stable semiconductor lasers that could lead to large energy savings in future optical communication networks. In addition to their potential for specific applications, dilute bismide alloys have also attracted interest from a fundamental perspective due to their unique properties. In this thesis we develop the theory of the electronic and optical properties of dilute bismide alloys. By adopting a multi-scale approach encompassing atomistic calculations of the electronic structure using the semi-empirical tight-binding method, as well as continuum calculations based on the k•p method, we develop a fundamental understanding of this unusual class of semiconductor alloys and identify general material properties which are promising for applications in semiconductor optoelectronic and photovoltaic devices. By performing detailed supercell calculations on both ordered and disordered alloys we explicitly demonstrate that Bi atoms act as isovalent impurities when incorporated in dilute quantities in III-V (In)GaAs(P) materials, strongly perturbing the electronic structure of the valence band. We identify and quantify the causes and consequences of the unusual electronic properties of GaBixAs1−x and related alloys, and our analysis is reinforced throughout by a series of detailed comparisons to the results of experimental measurements. Our k•p models of the band structure of GaBixAs1−x and related alloys, which we derive directly from detailed atomistic calculations, are ideally suited to the study of dilute bismide-based devices. We focus in the latter part of the thesis on calculations of the electronic and optical properties of dilute bismide quantum well lasers. In addition to developing an understanding of the effects of Bi incorporation on the operational characteristics of semiconductor lasers, we also present calculations which have been used explicitly in designing and optimising the first generation of GaBixAs1−x-based devices.