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In this thesis we study some of the problems which occur when type inference is used in a type system with subtyping. An underlying poset of atomic types is used as a basis for our subtyping systems. We argue that the class of Helly posets is of significant interest, as it includes lattices and trees, and is closed under type formation not only with structural constructors such as function space and list, but also records, tagged variants, Abadi-Cardelli object constructors, top and bottom. We develop a general theory relating consistency, solvability, and solution of sets of constraints between regular types built over Helly posets with these constructors, and introduce semantic notions of simplification and entailment for sets of constraints over Helly posets of base types. We extend Helly posets with inequalities of the form a <= tau, where tau is not necessarily atomic, and show how this enables us to deal with bounded quantification. Using bounded quantification we define a subtyping system which combines structural subtype polymorphism and predicative parametric polymorphism, and use this to extend with subtyping the type system of Laufer and Odersky for ML with type annotations. We define a complete algorithm which infers minimal types for our extension, using factorisations, solutions of subtyping problems analogous to principal unifiers for unification problems. We give some examples of typings computed by a prototype implementation.

This thesis explores the modelling for Internal Rating Based (IRB) of Credit Risk for Small and Medium Enterprises (SMEs) as required for implementation of Basel II Accord. There has been limited previous research for this important sector of the economy. There are two major approaches: Accounting Based and Merton Type, and these are compared. To make the comparison initially a small sample is considered and simulation is used to explore the use of the two approaches. The study indicates some of the limitation of analysis for both Accounting Based and Merton Type approaches, for example the issue of colinearity for the Accounting Based approach and lack of trading of SMEs’ equity affecting the Merton Type approach. A large sample is then investigated using standard Credit Scoring approaches for the Accounting Based modelling. Different definitions of default and distress are considered to overcome the problem of low number of defaults. These approaches are found to be viable. Merton Type model is then compared to benchmark models from the Accounting Based approach. The predictions are compared over differing time horizons. It is found that Merton Type models perform well within a limited period compared to the Accounting Base approach. Overall, credit scoring models demonstrated better performance when the sample group included a considerable number of ‘Bad’ firms or cutoff point was selected so that an acceptance rate was relatively low, otherwise model’s predictive accuracy would decline. Merton model presented better predictive accuracy with higher acceptance rates. Credit scoring models was able to give early signs of default year. In addition, one may take into consideration that if the company is going to decline credit quality or raise default probability this year, Merton type models can be helpful in adjusting credit rating. When considering a loan to a company, a bank wants to know the likelihood default for duration of loan. In this sense Merton models is only useful for a relatively short loan terms.

Names and name-binding are useful concepts in the theory and practice of formal systems. In this thesis we study them in the context of dependent type theory. We propose a novel dependent type theory with primitives for the explicit handling of names. As the main application, we consider programming and reasoning with abstract syntax involving variable binders. Gabbay and Pitts have shown that Fraenkel Mostowski (FM) set theory models a notion of name using which informal work with names and binding can be made precise. They have given a number of useful constructions for working with names and binding, such as a syntax-independent notion of freshness that formalises when two objects do not share names, and a freshness quantifier that simplifies working with names and binding. Related to FM set theory, a number of systems for working with names have been given, among them are the first-order Nominal Logic, the higher-order logic FM-HOL, the Theory of Contexts as well as the programming language FreshML. In this thesis we study how dependent type theory can be extended with primitives for working with names and binding. Our choice of primitives is different from that in FM set theory. In FM set theory the fundamental primitive for working with names is swapping. All other concepts such as \alpha-equivalence classes and binding are constructed from it. For dependent type theory, however, this approach of constructing everything from swapping is not ideal, since it requires us to make strong assumptions on the type theory. For instance, the construction of \alpha-equivalence classes from swapping appears to require quotient types. Our approach is to treat constructions such as \alpha-equivalence classes and name-binding directly, turning them into primitives of the type theory. To do this, it is convenient to take freshness rather than swapping as the fundamental primitive. Based on the close correspondence between type theories and categories, we approach the design of the dependent type theory by studying the categorical structure underlying FM set theory. We start from a monoidal structure capturing freshness. By analogy with the definition of simple dependent sums \Sigma and products \Pi from the cartesian product, we define monoidal dependent sums \Sigma * and products \Pi * from the monoidal structure. For the type of names N, we have an isomorphism \Sigma *_N\iso\Pi *_N generalising the freshness quantifier. We show that this structure includes \alpha-equivalence classes, name binding, unique choice of fresh names as well as the freshness quantifier. In addition to the set theoretic model corresponding to FM set theory, we also give a realizability model of this structure. The semantic structure leads us to a bunched type theory having both a dependent additive context structure and a non-dependent multiplicative context structure. This type theory generalises the simply-typed \alpha\lambda-calculus of O'Hearn and Pym in the additive direction. It includes novel monoidal products \Pi * and sums \Sigma * as well as hidden-name types H for working with names and binding. We give examples for the use of the type theory for programming and reasoning with abstract syntax involving binders. We show that abstract syntax can be handled both in the style of FM set theory and in the style of Weak Higher Order Abstract Syntax. Moreover, these two styles of working with abstract syntax can be mixed, which has interesting applications such as the derivation of a term for the unique choice of new names.

This thesis begins with a background chapter which explores the current diabetes epidemic and examines the role of obesity and oxidative stress as causative factors. Current dietary recommendations for prevention of type 2 diabetes are critically evaluated. A systematic review and meta-analysis was conducted to determine the independent role of fruit and vegetables in preventing diabetes. Convincing benefit for greater consumption of green leafy vegetables was demonstrated. An insignificant trend towards benefit was observed for fruit and vegetables. The Fruit and Vegetable Intake and Glucose Control Study (FIVE) is a sub study of the Let’s Prevent Diabetes Study. FIVE includes cross sectional analysis of baseline plasma vitamin C, (a biomarker for fruit and vegetable intake) from 2101 participants. FIVE further includes 12 months analysis of individuals with impaired glucose regulation, randomised to receive group education or usual care. Results demonstrate 29% of the population consumed at least 5 portions of fruit and vegetables a day. Fewer South Asian individuals met the recommendation compared to White Europeans (21% vs. 30% p = 0.003). Each additional piece of fruit or vegetable consumed (21.8μmol/l plasma vitamin C) was associated with a reduction of 0.04% in HbA1c, 0.05mmol/l in fasting and 0.22mol/l in 2 hour blood glucose. Participants who consumed 5 portions a day compared to those who did not, had a 24% associated reduced risk of being diagnosed with impaired glucose regulation (OR = 0.76, 95% CI: 0.59 to 0.98). At 12 months follow up those receiving lifestyle education had greater levels of plasma vitamin C compared to those in the usual care arm (36.1μmol/l (SD 20.7) vs.29.9μmol/l (SD 20.3)). No statistical difference in mean change between intervention arms was seen. The thesis provides novel, robust nutritional biomarker data from a large at risk, multi ethnic population. Results support recommendations to promote fruit and vegetables in the diet to prevent diabetes. The potential for tailored advice on increasing green leafy vegetables among those at risk of diabetes should be investigated further.

The present investigation was concerned with the effectiveness of religion in personality development and the significance of church attendance in ethical and moral control. These concepts were related to specific diagnoses of psychiatric patients to ascertain the effect of religion upon those patients diagnosed as paranoid-type schizophrenics and as sociopaths. In addition, the effect of this variable on other variables related to the patient's past religious experience, such as church attendance, was examined. The religiousness of the patients was measured by a single religious intensity questionnaire.

"Mycobacterium tuberculosis causes tuberculosis, one of the most life-threatening diseases of all time. It infects the host macrophages and survives in its phagosome. The host phagosome is a very hostile environment where M. tuberculosis copes with high concentration of transition metals (Zn2+, Cu2+), low levels of others (Mn2+, Fe2+) and acidic pH. P-ATPases are membrane proteins that transport various ions against their electrochemical gradients utilizing the energy of ATP hydrolysis. Based on their primary sequences; seven of the twelve mycobacterial ATPases are classified as putative heavy metal transporters and a K+-ATPase, while the substrate of four (CtpE, CtpF, CtpH and CtpI) remains unknown. Consistent with their membrane topology and conserved amino acids, CtpE and CtpF are possibly P2 or P3-ATPases that transport alkali metals or protons. We examined the cellular roles of orthologous CtpE and CtpF in M. smegmatis, a non-pathogenic model organism. We hypothesized that these novel P- ATPases play an important role in transporting alkali metals and/or protons. We analyzed growth fitness of strains carrying mutations of the coding gens of these enzymes, in presence of various metals and different pHs, as well as the gene expression levels under different stress conditions. We observed that the M. smegmatis mutant strains, lacking of CtpF or CtpE, are sensitive to high concentrations (mM) of Mn2+. Furthermore, CtpE mutant is sensitive to alkali pH. Our results indicate that CtpE and CtpF might be an Mn2+ or H+-ATPase that are required for cell’s homeostasis sustainability."

We describe groups of positive type and prove that a group G is of positive type if and only if G admits a non-trivial partition. We completely classify groups of type 2, and present examples of other groups of positive type as well as groups of type zero.

This thesis presents an account of the cubical sets model of homotopy type theory using an internal type theory for elementary topoi. Homotopy type theory is a variant of Martin-Lof type theory where we think of types as spaces, with terms as points in the space and elements of the identity type as paths. We actualise this intuition by extending type theory with Voevodsky's univalence axiom which identifies equalities between types with homotopy equivalences between spaces. Voevodsky showed the univalence axiom to be consistent by giving a model of homotopy type theory in the category of Kan simplicial sets in a paper with Kapulkin and Lumsdaine. However, this construction makes fundamental use of classical logic in order to show certain results. Therefore this model cannot be used to explain the computational content of the univalence axiom, such as how to compute terms involving univalence. This problem was resolved by Cohen, Coquand, Huber and Mortberg, who presented a new model of type theory in Kan cubical sets which validated the univalence axiom using a constructive metatheory. This meant that the model provided an understanding of the computational content of univalence. In fact, the authors present a new type theory, cubical type theory, where univalence is provable using a new "glueing" type former. This type former comes with appropriate definitional equalities which explain how the univalence axiom should compute. In particular, Huber proved that any term of natural number type constructed in this new type theory must reduce to a numeral. This thesis explores models of type theory based on the cubical sets model of Cohen et al. It gives an account of this model using the internal language of toposes, where we present a series of axioms which are sufficient to construct a model of cubical type theory, and hence a model of homotopy type theory. This approach therefore generalises the original model and gives a new and useful method for analysing models of type theory. We also discuss an alternative derivation of the univalence axiom and show how this leads to a potentially simpler proof of univalence in any model satisfying the axioms mentioned above, such as cubical sets. Finally, we discuss some shortcomings of the internal language approach with respect to constructing univalent universes. We overcome these difficulties by extending the internal language with an appropriate modality in order to manipulate global elements of an object.

The type II secretion system (T2SS) is widespread in Gram-negative bacteria that cause disease in animals and plants. In human and animal pathogens toxins are secreted (e.g. cholera toxin) and in plant pathogens lytic enzymes that breakdown the plant cell wall are exported in to the extracellular milieu (e.g. pectate lyase). Structurally the T2SS comprises at least 11 core proteins that form three major subassemblies spanning the inner-membrane, periplasmic space and outer-membrane: (i) the inner-membrane platform and associated cytoplasmic ATPase (E); (ii) the pseudopilus, which consists of five pseudopilins, G to K; and (iii) a large, pore-forming outer-membrane complex secretin D. The inner-membrane platform comprises three single transmembrane helix proteins, and one three transmembrane helix protein, OutF. The evidence from cryo-electron microscopy on the related type IVa pilus machine (T4PS) places the protein corresponding to OutF at the centre of this platform. This platform is responsible for assembling the pilus and for communicating between the periplasm and the cytoplasmic ATPase. To date, no high-resolution structure of a full-length OutF/PilC family protein is available. A low-resolution electron microscopy reconstruction of isolated PilG (PilC ortholog from Neisseria meningitides T4PS) showed a tetrameric two lobed structure. Here I report the results of studying the structure of the inner-membrane protein OutF from Dickeya dadantii and the complete inner-membrane platform comprising 9 proteins: OutEFGHIJKLM. This work involved cloning the corresponding operon, purifying the proteins, and using crystallography and electron microscopy. Key results reported here are the crystal structure of the first cytoplasmic domain of Dickeya dadantii, OutF65-172 and a preliminary three-dimensional model of the Dickeya dadantii inner-membrane platform. This model, and higher-resolution models to come, will provide valuable information about the oligomeric state, and arrangement of the inner-membrane proteins. These studies will help us to understand how the type II secretion system works.