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.

First-principles calculation of carrier-phonon scattering in n-type Si1−xGex alloys

First-principles electronic structure methods are used to find the rates of inelastic intravalley and intervalley n-type carrier scattering in Si1-xGex alloys. Scattering parameters for all relevant Delta and L intra- and intervalley scattering are calculated. The short-wavelength acoustic and the optical phonon modes in the alloy are computed using the random mass approximation, with interatomic forces calculated in the virtual crystal approximation using density functional perturbation theory. Optical phonon and intervalley scattering matrix elements are calculated from these modes of the disordered alloy. It is found that alloy disorder has only a small effect on the overall inelastic intervalley scattering rate at room temperature. Intravalley acoustic scattering rates are calculated within the deformation potential approximation. The acoustic deformation potentials are found directly and the range of validity of the deformation potential approximation verified in long-wavelength frozen phonon calculations. Details of the calculation of elastic alloy scattering rates presented in an earlier paper are also given. Elastic alloy disorder scattering is found to dominate over inelastic scattering, except for almost pure silicon (x approximate to 0) or almost pure germanium (x approximate to 1), where acoustic phonon scattering is predominant. The n-type carrier mobility, calculated from the total (elastic plus inelastic) scattering rate, using the Boltzmann transport equation in the relaxation time approximation, is in excellent agreement with experiments on bulk, unstrained alloys..

Hybrid density functional theory description of N- and C-doping of NiO

The large intrinsic bandgap of NiO hinders its potential application as a photocatalyst under visible-light irradiation. In this study, we have performed first-principles screened exchange hybrid density functional theory with the HSE06 functional calculations of N- and C-doped NiO to investigate the effect of doping on the electronic structure of NiO. C-doping at an oxygen site induces gap states due to the dopant, the positions of which suggest that the top of the valence band is made up primarily of C 2p-derived states with some Ni 3d contributions, and the lowest-energy empty state is in the middle of the gap. This leads to an effective bandgap of 1.7 eV, which is of potential interest for photocatalytic applications. N-doping induces comparatively little dopant-Ni 3d interactions, but results in similar positions of dopant-induced states, i.e., the top of the valence band is made up of dopant 2p states and the lowest unoccupied state is the empty gap state derived from the dopant, leading to bandgap narrowing. With the hybrid density functional theory (DFT) results available, we discuss issues with the DFT corrected for on-site Coulomb description of these systems.

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.

Atomic layer deposition of copper – study through density functional theory

The wonder of the last century has been the rapid development in technology. One of the sectors that it has touched immensely is the electronic industry. There has been exponential development in the field and scientists are pushing new horizons. There is an increased dependence in technology for every individual from different strata in the society. Atomic Layer Deposition (ALD) is a unique technique for growing thin films. It is widely used in the semiconductor industry. Films as thin as few nanometers can be deposited using this technique. Although this process has been explored for a variety of oxides, sulphides and nitrides, a proper method for deposition of many metals is missing. Metals are often used in the semiconductor industry and hence are of significant importance. A deficiency in understanding the basic chemistry at the nanoscale for possible reactions has delayed the improvement in metal ALD. In this thesis, we study the intrinsic chemistry involved for Cu ALD. This work reports computational study using Density Functional Theory as implemented in TURBOMOLE program. Both the gas phase and surface reactions are studied in most of the cases. The merits and demerits of a promising transmetallation reaction have been evaluated at the beginning of the study. Further improvements in the structure of precursors and coreagent have been proposed. This has led to the proposal of metallocenes as co-reagents and Cu(I) carbene compounds as new set of precursors. A three step process for Cu ALD that generates ligand free Cu layer after every ALD pulse has also been studied. Although the chemistry has been studied under the umbrella of Cu ALD the basic principles hold true for ALD of other metals (e.g. Co, Ni, Fe ) and also for other branches of science like thin film deposition other than ALD, electrochemical reactions, etc.

Functional application of lactic acid bacteria exopolysaccharide in complex food systems

Lactic acid bacteria expolysaccharides (LAB-EPS), in particular those formed from sucrose have the potential to improve food and beverage rheology and enhance their sensory properties potentially replacing or reducing expensive hydrocolloids currently used as improvers in food and beverage industries. Addition of sucrose not only enables EPS formation but also affects organic acid formation, thus influencing the sensory properties of the resulting food/beverage products. The first part of the study the organoleptic modulation of barley malt derived wort fermented using in situ produced bacterial polysaccharides has been investigated. Weisella cibaria MG1 was capable to produce exopolysaccharides during sucrosesupplemented barley malt derived wort fermentation. Even though the strain dominated the (sucrose-supplemented) wort fermentation, it was found to produce EPS (14.4 g l-1) with lower efficiency than in SucMRS (34.6 g l-1). Higher maltose concentration in wort led to the increased formation of oligosaccharide (OS) at the expense of EPS. Additionally, small amounts of organic acids were formed and ethanol remained below 0.5% (v/v). W. cibaria MG1 fermented worts supplemented with 5 or 10% sucrose displayed a shear-thinning behaviour indicating the formation of polymers. This report showed how novel and nutritious LAB fermented wort-base beverage with prospects for further advancements can be formulated using tailored microbial cultures. In the next step, the impact of exopolysaccharide-producing Weissella cibaria MG1 on the ability to improve rheological properties of fermented plant-based milk substitute plant based soy and quinoa grain was evaluated. W. cibaria MG1 grew well in soy milk, exceeding a cell count of log 8 cfu/g within 6 h of fermentation. The presence of W. cibaria MG1 led to a decrease in gelation and fermentation time. EPS isolated from soy yoghurts supplemented with sucrose were higher in molecular weight (1.1 x 108 g/mol vs 6.6 x 107 g/mol), and resulted in reduced gel stiffness (190 ± 2.89 Pa vs 244 ± 15.9 Pa). Soy yoghurts showed typical biopolymer gels structure and the network structure changed to larger pores and less cross-linking in the presence of sucrose and increasing molecular weight of the EPS. In situ investigation of Weissella cibaria MG1 producing EPS on quinoa-based milk was performed. The production of quinoa milk, starting from wholemeal quinoa flour, was optimised to maximise EPS production. On doing that, enzymatic destructuration of protein and carbohydrate components of quinoa milk was successfully achieved applying alpha-amylase and proteases treatments. Fermented wholemeal quinoa milk using Weissella cibaria MG1 showed high viable cell counts (>109 cfu/mL), a pH of 5.16, and significantly higher water holding capacity (WHC, 100 %), viscosity (> 0. 5 Pa s) and exopolysaccharide (EPS) amount (40 mg/L) than the chemically acidified control. High EPS (dextran) concentration in quinoa milk caused earlier aggregation because more EPS occupy more space, and the chenopodin were forced to interact with each other. Direct observation of microstructure in fermented quinoa milk indicated that the network structures of EPS-protein could improve the texture of fermented quinoa milk. Overall, Weissella cibaria MG1 showed favorable technology properties and great potential for further possible application in the development of high viscosity fermented quinoa milk. The last part of the study investigate the ex-situ LAB-EPS (dextran) application compared to other hydrocolloids as a novel food ingredient to compensate for low protein in biscuit and wholemeal wheat flour. Three hydrocolloids, xanthan gum, dextran and hydroxypropyl methylcellulose, were incorporated into bread recipes based on high-protein flours, low-protein flours and coarse wholemeal flour. Hydrocolloid levels of 0–5 % (flour basis) were used in bread recipes to test the water absorption. The quality parameters of dough (farinograph, extensograph, rheofermentometre) and bread (specific volume, crumb structure and staling profile) were determined. Results showed that xanthan had negative impact on the dough and bread quality characteristics. HPMC and dextran generally improved dough and bread quality and showed dosage dependence. Volume of low-protein flour breads were significantly improved by incorporation of 0.5 % of the latter two hydrocolloids. However, dextran outperformed HPMC regarding initial bread hardness and staling shelf life regardless the flour applied in the formulation.