On classical and other methods of discriminant analysis and estimation of log-odds

For two multinormal populations with equal covariance matrices the likelihood ratio discriminant function, an alternative allocation rule to the sample linear discriminant function when n1 ≠ n2 ,is studied analytically. With the assumption of a known covariance matrix its distribution is derived and the expectation of its actual and apparent error rates evaluated and compared with those of the sample linear discriminant function. This comparison indicates that the likelihood ratio allocation rule is robust to unequal sample sizes. The quadratic discriminant function is studied, its distribution reviewed and evaluation of its probabilities of misclassification discussed. For known covariance matrices the distribution of the sample quadratic discriminant function is derived. When the known covariance matrices are proportional exact expressions for the expectation of its actual and apparent error rates are obtained and evaluated. The effectiveness of the sample linear discriminant function for this case is also considered. Estimation of true log-odds for two multinormal populations with equal or unequal covariance matrices is studied. The estimative, Bayesian predictive and a kernel method are compared by evaluating their biases and mean square errors. Some algebraic expressions for these quantities are derived. With equal covariance matrices the predictive method is preferable. Where it derives this superiority is investigated by considering its performance for various levels of fixed true log-odds. It is also shown that the predictive method is sensitive to n1 ≠ n2. For unequal but proportional covariance matrices the unbiased estimative method is preferred. Product Normal kernel density estimates are used to give a kernel estimator of true log-odds. The effect of correlation in the variables with product kernels is considered. With equal covariance matrices the kernel and parametric estimators are compared by simulation. For moderately correlated variables and large dimension sizes the product kernel method is a good estimator of true log-odds.

Characterisation of the microbiota of traditional fermented beverages and screening these and other populations for novel antimicrobial producers and gene clusters

To screen for novel ribosomally synthesised antimicrobials, in-silico genome mining was performed on all publically available fully sequenced bacterial genomes. 49 novel type 1 lantibiotic clusters were identified from a number of species, genera and phyla not usually associated with lantibiotic production, and indicates high prevalence. A crucial step towards the commercialisation of fermented beverages is the characterisation of the microbial content. To achieve this goal, we applied next-generation sequencing techniques to analyse the bacterial and yeast populations of the organic, symbiotically-fermented beverages kefir, water kefir and kombucha. A number of minor components were revealed, many of which had not previously been associated with these beverages. The dominant microorganism in each of the water kefir grains and fermentates was Zymomonas, an ethanol-producing bacterium that had not previously been detected on such a scale. These studies represent the most accurate description of these populations to date, and should aid in future starter design and in determining which species are responsible for specific attributes of the beverages. Finally, high-throughput robotics was applied to screen for the presence of antimicrobial producers associated with these beverages. This revealed a low frequency of bacteriocin production amongst the bacterial isolates, with only lactococcins A, B and LcnN of lactococcin M being identified. However, a proteinaceous antimicrobial produced by the yeast Dekkera bruxellensis, isolated from kombucha, was found to be active against Lactobacillus bulgaricus. This peptide was patially purified.

Reasoning with sorted-pareto dominance and other qualitative and partially ordered preferences in soft constraints

In decision making problems where we need to choose a particular decision or alternative from a set of possible choices, we often have some preferences which determine if we prefer one decision over another. When these preferences give us an ordering on the decisions that is complete, then it is easy to choose the best or one of the best decisions. However it often occurs that the preferences relation is partially ordered, and we have no best decision. In this thesis, we look at what happens when we have such a partial order over a set of decisions, in particular when we have multiple orderings on a set of decisions, and we present a framework for qualitative decision making. We look at the different natural notions of optimal decision that occur in this framework, which gives us different optimality classes, and we examine the relationships between these classes. We then look in particular at a qualitative preference relation called Sorted-Pareto Dominance, which is an extension of Pareto Dominance, and we give a semantics for this relation as one that is compatible with any order-preserving mapping of an ordinal preference scale to a numerical one. We apply Sorted-Pareto dominance to a Soft Constraints setting, where we solve problems in which the soft constraints associate qualitative preferences to decisions in a decision problem. We also examine the Sorted-Pareto dominance relation in the context of our qualitative decision making framework, looking at the relevant optimality classes for the Sorted-Pareto case, which gives us classes of decisions that are necessarily optimal, and optimal for some choice of mapping of an ordinal scale to a quantitative one. We provide some empirical analysis of Sorted-Pareto constraints problems and examine the optimality classes that result.

Religion, the study of religion and other products of transnational and colonial imaginings

The category of ‘religion’ as contemporary scholarship has demonstrated is a fairly recent innovation, dating back only a few hundred years in Western thought, and ‘world religions’ as we think of it and as we teach it is an even more recent category, emerging out of European colonialism. Thus the academic study of religion is both the product and, at times, the agent of colonial modes of knowledge. And yet, it is perhaps because ‘religion’ continues to be invented and reinvented through connections across cultures that investigating the work of religious ideas and practices offers such fruitful possibilities for understanding the work of culture and power. This article investigates religion and the study of religion as a mode of anti-colonial practice, seeking to understand how each have the potential to cross boundaries, build bridges and produce critical insights into assumptions and worldviews too often taken for granted.

Monstrative acts and becoming-monster: on identity, bodies, and the feminine other

Using two examples of literary monsters, the Creature in Mary Shelley’s Frankenstein (1818), and Grendel’s Mother in Beowulf, this thesis demonstrates the bearing fictional identities have on “real” bodies, through an examination of two further literary texts, David Henry Hwang’s play, M. Butterfly (1986) and J. M. Coetzee’s novel, Disgrace (1999). Western definitions of Being have historically divided body and mind, favouring the mind as formative of subjective experience and denigrating the body as secondary and impure. This thesis demonstrates that this mind/body binary is symptomatic of the masculine ontological imperative to disown the body and its effects on Being, simultaneously ridding itself of the feminine it believes is its irrational opposite. Using recent feminist reviews of the canon, which emphasise the body’s importance to ontology and demonstrate the conceptual association between the feminine and the corporeal, this thesis links performative identity practices to theories of monstrosity, explaining how fictional qualities adhere to monstrous bodies by proposing a new theoretical category, the “monstrative.” The monstrative is a performative force that makes the Other into a living sign of Otherness; however, unlike earlier theories of Othering, the monstrative accounts for the Other’s being other to herself. This thesis also attempts to read the misrepresented body of the Other as a possible site for more empowered identity performances, where the monstrous “I” is interpreted as a potentially positive model for identity practice, through the conceptualisation of identity as a process of Becoming rather than Being. The transferal from a noun to a verb not only emphasises the performativity of identity, but also suggests fluidity and multiplicity in identity practice, which always already indicates a monstrosity at work. Thus, while monstrative acts constitute bodies as monstrous, Becoming-monster is an empathetic response to the Other’s monstrosity.