This thesis considers the problem of program correctness within a rich theory of dependent types, the Extended Calculus of Constructions (ECC). This system contains a powerful programming language of higher-order primitive recursion and higher-order intuitionistic logic. It is supported by Pollack's versatile LEGO implementation, which I use extensively to develop the mathematical constructions studied here. I systematically investigate Burstall's notion of deliverable, that is, a program paired with a proof of correctness. This approach separates the concerns of programming and logic, since I want a simple program extraction mechanism. The Sigma-types of the calculus enable us to achieve this. There are many similarities with the subset interpretation of Martin-Löf type theory. I show that deliverables have a rich categorical structure, so that correctness proofs may be decomposed in a principled way. The categorical combinators which I define in the system package up much logical book-keeping, allowing one to concentrate on the essential structure of algorithms. I demonstrate our methodology with a number of small examples, culminating in a machine-checked proof of the Chinese remainder theorem, showing the utility of the deliverables idea. Some drawbacks are also encountered. I consider also semantic aspects of deliverables, examining the definitions in an abstract setting, again firmly based on category theory. The aim is to overcome the clumsiness of the language of categorical combinators, using dependent type theories and their interpretation in fibrations. I elaborate a concrete instance based on the category of sets, which generalises to an arbitrary topos. In the process, I uncover a subsystem of ECC within which one may speak of deliverables defined over the topos. In the presence of enough extra structure, the interpretation extends to the whole of ECC. The wheel turns full circle.

Enterohaemorrhagic Escherichia coli (EHEC) strains are associated with gastrointestinal and severe systemic disease in humans. EHEC O157:H7 is the most common serotype causing human infections in North America and the UK. Human infections mainly originate from cattle, through either direct contact with infected animals or indirectly through contamination of food or water with animal faeces. From the sequencing of EHEC O157 strains, it is clear that the genomes contain multiple prophages, many of them cryptic, which define this E. coli pathotype. These regions include the locus of enterocyte effacement (LEE) which is a critical horizontally acquired pathogenicity island and encodes a type III secretion system (T3SS). The T3SS translocates effector proteins into epithelial cells that enable tight attachment to these host cells and also modify innate responses and other cellular functions to promote persistence in the animal host. The T3SS is essential for the colonisation of cattle by EHEC O157 where it is localised to the terminal rectum. The regulation of T3S is complex with many regulators and environmental factors already identified. Previous work has demonstrated marked variation in the levels of T3S among EHEC O157 strains. The aim of this research was to further investigate the regulation of T3S towards two objectives: (1) to understand the localisation of EHEC O157 at the terminal rectum of cattle; (2) to understand the strain variation in T3S. (1) In relation to rectal and mucosal colonisation, established aerobic/anaerobic regulators were investigated including arcA, fnr, narX, narQ. Briefly, arcA, fnr, narX, narQ were deleted in an E. coli O157 strain ZAP198 by lambda red recombination. Apart from the fnr mutant which showed lower levels of T3S, the remaining mutants displayed similar T3S protein levels compared to the wild type strain. In addition, no significant changes in adherence and A/E lesion formation capacity were measured for the mutants following interaction with bovine epithelial cells. (2) Strain secretion variation was approached in two ways; the first was to control expression from the LEE1 operon, required for T3S expression, in order to both induce expression and examine the importance of downstream regulation. The second was to investigate variation in T3S between different phages types of EHEC O157. While attempts to construct an inducible T3SS were not successful, intermediate strains made in the process have been useful to dissect how regulators being studied in the laboratory control T3S. The main novel insights from the research have come from examining T3S in different EHEC O157 phage types. We found that the average level of T3S in PT 21/28 strains was lower than in PT 32 strains. Interestingly, most (90%) of PT 21/28 strains contained both Stx2 and Stx2c phages. In contrast, only 28% of PT 32 strains had both phages. Taken together, this raised the possibility that Stx phage integration might have a repressive impact on T3SS regulation in E.coli O157:H7. This hypothesis was addressed using a number of different approaches. Deletions of Stx phages were constructed and these had increased levels of T3S when compared to the parental strains. This phage regulation of T3SS was confirmed in an E. coli K12 background by examining an induced LEE1 reporter in the presence and absence of a transduced Stx2 phage. In addition, it was shown that deletion of the CII phage regulator led to increased T3S and may contribute to the Stx phage repression reported above. This work demonstrates for the first time that Stx phage integration represses T3S expression. It is proposed that this control may limit immune exposure of this critical colonisation factor and that the repression actually allows activation by prophage encoded regulators, including PchA/B, that co-ordinate T3S and non LEE-encoded effector expression to promote epithelial cell colonisation.

Type 1 diabetes is a condition which affects the lives of thousands of young people throughout the UK. Existing research has recognised the difficulties that adolescents have in managing their diabetes, and a large amount of research has focused on glycaemic control, and influential factors. This project attempted to establish what is known about young people’s experiences of living with type 1 diabetes, and to further develop this knowledge pertaining particularly to the school environment through qualitative research. Method A systematic review of the literature in relation to young people’s views of their life with type 1 diabetes was conducted and a synthesising thematic analysis was carried out. A qualitative research study was then carried out involving 7 adolescents aged 13-16 years who had a diagnosis of type 1 diabetes. Semi-structured interviews were carried out with the focus being on the young people’s experiences of type 1 diabetes within the school environment. Interview sessions were transcribed and Interpretative Phenomenological Analysis (IPA) was used to analyse the data. Results Five themes emerged from the systematic review. Analysis of the studies led to the emerging themes of: Normal/Different, Control/Management, Relationships, Health– care and Educational experiences. The articles revealed that the experiences of adolescents varied, and were frequently dependent upon the actions of others. Four major themes emerged from the analysis of the research study: Support, Knowledge and Understanding, Standing out, and Adjusting and Accepting. Discussion Systematic review of the articles revealed that the experiences of adolescents varied, and were frequently dependent upon the actions of others. A sense of normalcy was important, and the strict routine and activities of diabetes management impacted upon their ability to achieve it. The support of friends and family was valued, but could at times become overwhelming and educational and health professionals made a difference to their ability to successfully fit diabetes into their lives. The suggestions made by individuals within the studies were generally consistent, and have implications for healthcare providers, friends and families, and schools in relation to facilitating successful diabetic management. Many of the young people taking part in the present research study had encountered negative experiences within the school environment in relation to both peers and staff. However, they described elements of helpful practice and made suggestions for improvements that could be made within school to facilitate a more positive experience.

This study seeks to determine whether grammatical and presentational features of authentic non-fiction French texts are in any way related to the level of difficulty of texts as perceived by students who have taken Advanced Subsidiary Level (AS). The notions of text and genre are examined, as are the processes of reading in the first language (L1) and in the foreign language (L2). The question of ‘readability, and that of ‘authenticity’ in L2 are also examined. In order to ascertain students’ reactions to different text-types, 150 texts from French sources were gathered and classified. 100-word samples of each text were analysed for various linguistic features. Statistical tests on these were carried out, as well as statistical tests on the visual elements and layout of the whole texts. Further linguistic analysis was carried out within the text-type groups in order to ascertain their grammatical features. 31 students from local tertiary institutions were interviewed, and their perceptions on a sample of the texts were sought. This included the grading of texts for difficulty on a 1-5 Likert scale. The results of the interviews were triangulated with the statistical and linguistic analyses. A relationship was found between text-type and level of perceived difficulty. In the light of these results, the distinction between genre and text-type was examined, and a way was found of linking these into a textual taxonomy, which has close relations with the grammatical and presentational features which characterise the various text-types. In the light of these results, the question of the ‘topic approach’ to the teaching of French is examined, and a way found by which text-types that are perceived to be simpler are studied before those which are perceived to be more difficult. This approach advocates a more logical continuum of grammatical presentation than has hitherto been witnessed in course books for French at this level, while retaining the semantic integrity inherent in the ‘topic approach’.

Background Carbohydrate counting is a method used to calculate insulin doses to meals, in the treatment of diabetes type 1. Few studies are available with a clear consensus on its efficacy and effect on anthropometrics in children and adolescents. Aim To evaluate if carbohydrate counting as treatment method in diabetes type 1 improved glycemic control and anthropometrics compared to conventional treatment, one and two years after onset in children and adolescents at Astrid Lindgren children’s hospital. A secondary aim was to explore patients and caregivers perception of insulin dosage to meals with focus on efficacy, time consumption and adherence. Method A clinical prospective study was performed on data collected from the Swedish pediatric quality registry (Swediabkids). Children with diabetes onset between 2010 and 2014 registered at Astrid Lindgren Children’s hospital (n=371) were included and divided into two groups, carbohydrate counters and non-carbohydrate counters. Normal distribution was assumed and parametric tests were performed. The registry data was complemented with a web-based questionnaire providing information on perception of carbohydrate counting, answered by 78 subjects. Results Carbohydrate counting reduced insulin requirements (p<0.001) and eliminated differences between pump- and pen users (p<0.001) as well as differences between boys and girls. Glycemic control was not improved by carbohydrate counting one and two years after diabetes onset (p=0.233, p=0.295). An adverse effect was increased body mass index standard deviation score (BMI-sds) (p=0.044), especially amongst girls (p=0.038). Conclusion Carbohydrate counting lowers insulin requirements with maintained glycemic control. Contradictory, greater weight gain was found in the carbohydrate counting group, especially among girls. A plausible explanation is that carbohydrates have taken focus off protein- and fat intake in combination with a more liberal approach to energy dense foods, causing excess energy intake. The strength of carbohydrate counting does not lie in its ability to lower HbA1c-values but as a helpful tool, which patients are happy to use. / Bakgrund Kolhydraträkning är en metod som används för att beräkna insulindoser till måltider, i behandlingen av diabetes typ 1. Få studier finns för att ge en samlad konsensus gällande dess effekt på glykemisk kontroll och tillväxt hos barn och ungdomar. Syfte Att utvärdera om införandet av kolhydraträkning som behandlingsmetod vid diabetes typ 1 påverkat metabol kontroll och tillväxt i jämförelse med konventionell metod, ett och två år efter diabetesdebut. Ett andra syfte var att utforska patienters och vårdnadshavares uppfattning om insulindosering till måltider med fokus på effektivitet, tidskonsumtion och följsamhet. Metod En klinisk prospektiv studie utfördes med data inhämtad från Nationellt kvalitetsregister för barn och ungdomar med diabetes (Swediabkids). Barn och ungdomar som debuterade med diabetes typ 1 på Astrid Lindgrens barnsjukhus mellan 2010 och 2014 (n=371) inkluderades i studien och delades in i två grupper baserat på debutdatum; kolhydraträknare och icke-kolhydraträknare. Materialet bedömdes som normalfördelat och parametriska test utfördes. En tvärsnittsenkät administrerades till studiedeltagarna för att införskaffa fördjupad information om patienters och vårdnadshavares uppfattning om insulindosering till måltider. Den webbaserade enkäten besvarades av 78 deltagare. Resultat Kolhydraträkning reducerade insulinbehovet (p<0.001) och jämställde insulinbehovet mellan pump- och pennanvändare (p<0.001) liksom skillnader mellan pojkar och flickor inom gruppen. Glykemisk kontroll förändrades inte av kolhydraträkning ett och två år efter debut (p=0.233, p=0.295). En oönskad effekt av kolhydraträkningen var en ökning i BMI-sds (p=0.044), speciellt hos flickor (p=0.038). Slutsats Kolhydraträkning från diabetesdebut sänker insulinbehov med bibehållen glykemisk kontroll. Motsägelsefullt, så fanns en viktökning i gruppen som använde kolhydraträkning, speciellt hos flickor. En möjlig förklaring är att kolhydrater har tagit fokus från protein- och fettintag tillsammans med en mer frikostig syn på energität mat, vilket har orsakat ökat energiintag. Styrkan i kolhydraträkning ligger inte i dess förmåga att förbättra glykemisk kontroll men som ett användarvänligt verktyg som patienterna är nöjda med.

Class of 2009 Abstract / OBJECTIVES: To evaluate an educational booklet written in Chinese designed for Chinese-Americans with Type 2 diabetes mellitus. METHODS: Healthcare professionals who work with Chinese-American patients with Type 2 diabetes mellitus and proficiency in writing Chinese developed an educational booklet on Type 2 diabetes. An expert panel of Chinese American pharmacists and dietitians evaluated the booklet by rating language appropriateness, ease of reading, ease of locating information, overall presentation of the booklet, and usefulness of the booklet in a practice setting. Topics of the booklet were assessed for accuracy, relevance, and irrelevance. RESULTS: Questionnaires were completed by 8 healthcare professionals. In the expert panel, there were five pharmacists and three dietitians. Of the three dietitians, two were certified diabetes educator. The panel rated the booklet very highly; the mean overall rating was 22.4(±1.2) with 25 being the highest possible score. Overall, 100% of the evaluators would recommend this booklet for patients in their setting. CONCLUSIONS: Healthcare professionals found the booklet to be accurate, culturally relevant, and useful for their Chinese- American patients with type 2 diabetes mellitus.

Research shows a large variability in the degree to which adolescents with diabetes adjust to their illness. Adjustment to diabetes is important because it affects the mental health of adolescents, and has been shown to predict both adherence to treatment, and glycaemic control. This thesis proposed that attachment security has the potential to explain some of the variability in adjustment to diabetes. A causal pathway was hypothesised whereby attachment security both directly predicts adjustment to diabetes, and indirectly via choice of coping strategies. In addition, it was hypothesised that attachment security would indirectly predict adherence behaviours and glycaemic control. The relative importance of attachment to parents and peers was compared. The research hypotheses were tested in a sample of 99 adolescents aged 13-18 years, who had been diagnosed with diabetes for at least a year. Measures of attachment security, adjustment to diabetes, coping strategies, treatment adherence and glycaemic control were taken at one time point. The data were analysed using structural equation modelling to test the hypothesised causal pathway. The results suggested that attachment security both directly predicts adjustment to diabetes, and indirectly predicts adjustment to diabetes via avoidance focused coping strategies. Attachment to parents, but not to peers was associated with adjustment to diabetes, and some gender differences were observed. The results also suggested that attachment security indirectly predicts glycaemic control via adjustment to diabetes. There were no significant associations between adherence to treatment and any other variables. Neither attachment security nor adjustment to diabetes were associated with approach focused coping. It is concluded that attachment security may play an important part in both psychological and physical outcomes for adolescents with diabetes, and this has implications for attachment based interventions. The findings are discussed in relation to other theoretical models, and indications for future research are suggested.

Introduction: Poor glycemic control has been shown to exert deleterious influences on multiple body systems. Additionally, residing in a rural area is associated with poorer diabetes care The rural adolescent patient described in this case study has a well-documented history of poor T1DM control. Her pediatric endocrinologist is located over 2 hours away from her home. Reported blood glucose levels average above 200 mg/dL, with a recent glycosylated hemoglobin (HbA1c) level of 10.3%. Previous blood glucose levels have reached an excess of 900 mg/dL. This study attempts to identify the beliefs of a rural T1DM adolescent patient, her mother, and her pediatric endocrinologist as they pertain to the patient's T1DM management. Methods: An embedded single case design with multiple embedded units of analysis was applied. Data was collected from the patient, mother, and pediatric endocrinologist between May and June of 2016. The design consisted of a mixed method approach that collected data using the Patient, Parent, and Provider Perception Questionnaire (P4Q). A triangulation of the responses from these subjects was used to elicit differences and similarities of disease management perceptions.Results: There is disconnect in diabetes care management noted in most aspects of the patient's treatment program. Interpretation: Disconnect can occur in the management of rural adolescent diabetes. Understanding theoretical propositions of the HPM may provide a pathway to limiting the shortfalls in patient care, which may lead to improvement in rural adolescent diabetes outcomes.

In this work I have examined the spatially resolved properties of the local early- type galaxy population. Using Hubble Space Telescope and ground based pho- tometry I constructed Jeans Anisotropic Multi Gaussian Expansion models of the SAURON sample of early-type galaxies, from which I determined the depth of the local gravitational potential well, quantified by the local escape velocity, Vesc. I found that Vesc correlated tightly with the three Lick indices: Mgb, Fe5015 and Hβ. The Mgb-Vesc relation within individual galaxies is identical to that between different galaxies; the relation is both local and global. The Mgb-Vesc relation is: log Mgb = (0.35 ± 0.01) log Vesc − (0.41 ± 0.03). While the metallicity, [Z/H] is cor- related with Vesc it does not show the same local and global behaviour. Age (t) and alpha enhancement ([α/Fe]) are only weakly correlated with Vesc. A combination of [Z/H] and t is tightly correlated with Vesc, with scatter comparable to the Mgb-Vesc relation, and does show the local and global behaviour. This combination is given by: log Vesc = 0.85[Z/H] + 0.43 log t. Using the volume limited ATLAS3D sample of 260 local ETGs I examined in detail the behaviour of the Mgb-Vesc relation and its dependence on other galaxy properties. I found that systematic deviations from the relation correlate with the local environmental density and molecular gas mass of a galaxy, and with the local [α/Fe] measurement. I found that there is a population of galaxies that do not follow the relation, found only at Vesc < 400 kms−1. These galaxies have negative gradients, high central Hβ indices and young (t < 3 Gyrs) ages. Using stellar population models I demonstrated that these negative gradient galaxies are perturbed from the relation by recent star formation and will return to the relation as they age. I also describe the observation, reduction and analysis of a new sample of ETGs in the core of the Coma cluster, the highest density environment in the local Universe, observed with the SWIFT Integral Field Spectrograph. I determined the fraction of slow rotators in the sample, comparing it to results from the ATLAS3D survey, and found an enhanced slow rotator fraction in the Coma cluster. I also determined the Fundamental Plane of Coma early-type galaxies, given by: log Re = (1.20 ± 0.22) log σe − (0.79 ± 0.09) log⟨Ie⟩.

The purpose of this study is to examine the relationships between length of punishment and the two common groupings of types of punishment. Further, the influence of length of punishment on guilt responsivity will be examined.