The Expanding Zoo of Calabi-Yau Threefolds

This is a short review of recent constructions of new Calabi-Yau threefolds with small Hodge numbers and/or non-trivial fundamental group, which are of particular interest for model-building in the context of heterotic string theory. The two main tools are topological transitions and taking quotients by actions of discrete groups. Both of these techniques can produce new manifolds from existing ones, and they have been used to bring many new specimens to the previously sparse corner of the Calabi-Yau zoo where both Hodge numbers are small. Two new manifolds are also obtained here from hyperconifold transitions, including the first example with fundamental group S3, the smallest non-Abelian group.Comment: 24 pages, PDFLaTeX. To be published in the special issue "Computational Algebraic Geometry in String and Gauge Theory" of Advances in High Energy Physics. v2: Added reference, and data for four new manifolds constructed therei

Hyperconifold Transitions, Mirror Symmetry, and String Theory

Multiply-connected Calabi-Yau threefolds are of particular interest for both string theorists and mathematicians. Recently it was pointed out that one of the generic degenerations of these spaces (occurring at codimension one in moduli space) is an isolated singularity which is a finite cyclic quotient of the conifold; these were called hyperconifolds. It was also shown that if the order of the quotient group is even, such singular varieties have projective crepant resolutions, which are therefore smooth Calabi-Yau manifolds. The resulting topological transitions were called hyperconifold transitions, and change the fundamental group as well as the Hodge numbers. Here Batyrev's construction of Calabi-Yau hypersurfaces in toric fourfolds is used to demonstrate that certain compact examples containing the remaining hyperconifolds - the Z_3 and Z_5 cases - also have Calabi-Yau resolutions. The mirrors of the resulting transitions are studied and it is found, surprisingly, that they are ordinary conifold transitions. These are the first examples of conifold transitions with mirrors which are more exotic extremal transitions. The new hyperconifold transitions are also used to construct a small number of new Calabi-Yau manifolds, with small Hodge numbers and fundamental group Z_3 or Z_5. Finally, it is demonstrated that a hyperconifold is a physically sensible background in Type IIB string theory. In analogy to the conifold case, non-perturbative dynamics smooth the physical moduli space, such that hyperconifold transitions correspond to non-singular processes in the full theory.Comment: 23 pages, PDFLaTeX. v2: Abstract and introduction slightly expanded, and examples of new manifolds added. Also added references and hyperref. v3: Minor corrections, including to relations on pg.

New Calabi-Yau Manifolds with Small Hodge Numbers

It is known that many Calabi-Yau manifolds form a connected web. The question of whether all Calabi-Yau manifolds form a single web depends on the degree of singularity that is permitted for the varieties that connect the distinct families of smooth manifolds. If only conifolds are allowed then, since shrinking two-spheres and three-spheres to points cannot affect the fundamental group, manifolds with different fundamental groups will form disconnected webs. We examine these webs for the tip of the distribution of Calabi-Yau manifolds where the Hodge numbers (h^{11}, h^{21}) are both small. In the tip of the distribution the quotient manifolds play an important role. We generate via conifold transitions from these quotients a number of new manifolds. These include a manifold with \chi =-6 and manifolds with an attractive structure that may prove of interest for string phenomenology. We also examine the relation of some of these manifolds to the remarkable Gross-Popescu manifolds that have Euler number zero.Comment: 105 pages, pdflatex with about 70 pdf and jpeg figures. References corrected. Minor revisions to Fig1, and Table 9 extended to the range h^{11} + h^21 \leq 2

Quantum black holes in Type-IIA String Theory

We study black hole solutions of Type-IIA Calabi-Yau compactifications in the presence of perturbative quantum corrections. We define a class of black holes that only exist in the presence of quantum corrections and that, consequently, can be considered as purely quantum black holes. The regularity conditions of the solutions impose the topological constraint h^{1,1}>h^{2,1} on the Calabi-Yau manifold, defining a class of admissible compactifications, which we prove to be non-empty for h^{1,1}=3 by explicitly constructing the corresponding Calabi-Yau manifolds, new in the literature.Comment: 17 pages. References added. Explanation of the truncation improve

Dietary glycaemic carbohydrate, physical activity and cardiometabolic health in postpubertal adolescents

A thesis submitted to the University of Bedfordshire, in partial fulfilment of the requirements for the degree of Doctor of PhilosophyThe principle aims of this work were two fold; firstly to identify the current dietary intakes (specifically dietary glycaemic carbohydrate (CHO)) and physical activity (PA) and cardiorespiratory fitness (CRF) levels of a UK, postpubertal, adolescent population (n = 105) and assess the relationship between these factors, adiposity and cardiometabolic health. Diet and health relationships were assessed whilst accounting for energy misreporting and controlling for levels of PA and CRF. The effect of excluding dietary misreporters on the associations between glycaemic CHO and health was assessed whilst comparing an established technique (the Goldberg equation) to a novel approach (the ratio of energy intake (EI) to energy expenditure (EE)), which utilised RT3 accelerometry data (EI:EE(RT3)). Associations of PA and metabolic risk factors were also assessed whilst comparing two child specific PA thresholds for the assessment of PA subcomponents. Secondly, the impact of a flexible, ad libitum, low GI dietary intervention on cardiometabolic health was examined in an „at risk‟, overweight, postpubertal, adolescent population. Glycaemic index (GI) but not glycaemic load (GL) was shown to be associated significantly with anthropometric measures (body mass index (BMI), waist circumference (WC)) and adiposity (body fat percentage (BF%)) in this general group of post-pubertal adolescents from Bedfordshire. When adjusting for dietary intake, CRF was also associated with adiposity but PA was not. The prevalence of misreporting varied depending on the method used to assess the validity of dietary intakes; between 23% and 31% increasing to 62.1% (in overweight) of adolescents under reported energy intakes and up to 11.1% over reported. The novel application of a triaxial accelerometer to measure EE resulted in more under and over reporters being identified than when compared to the widely used Goldberg equation. Increased dietary GI was associated with increased odds of having a high WC; however, associations between GL and other risk factors were less clear; no associations with risk were observed. Excluding dietary misreporters from analysis had important implications for these associations. Only after removal of misreporters by EI:EE(RT3) was a borderline significant positive association between GL and blood glucose (BG) revealed using multiple analysis of covariance (MANCOVA), that was not present in prior analyses. Increased GI (moderate vs low GI intake) was significantly associated with reduced high density lipoprotein cholesterol (HDL) and increased triglyceride (TG) levels (borderline significant) after removal of misreporters. In addition, using different PA thresholds to assess PA intensity resulted in different relationships between PA subcomponents and metabolic risk factors. Regardless of the threshold used, evidence suggested that limiting sedentary (SED) behaviour and engaging in moderate to vigorous PA (MVPA) is beneficial for blood pressure (BP) in this adolescent population. Additionally, irrespective of the threshold utilised, higher levels of vigorous PA (VPA) were associated with reduced odds of having a high clustered risk score and the associations observed between CRF and risk factors were stronger than those observed with PA. Despite a lack of significant improvement in individual metabolic risk factors as a result of the low GI (LGI) dietary intervention, there was a significant reduction in clustered risk score for the LGI group at week 12. A borderline significant improvement in glycated haemoglobin (HbA1c) was also observed as a result of the LGI intervention compared to those in the control group. Conversely, there appeared to be an unfavourable effect of the LGI diet on fasting insulin levels and thus the diet‟s impact on health overall is unclear. The small sample size of this randomised controlled trial (RCT) means that caution is required when interpreting the results. These data suggest that future research in this age group should target improvements in CRF and a lower dietary GI to reduce adiposity. Controlling for dietary misreporting appears to have a significant impact on associations of glycaemic CHO and cardiometabolic health and should be an important consideration of future research. The low GI intervention may be an effective approach for reducing glycaemic CHO, whilst maintaining a healthy macronutrient intake, in comparison to more restricted dietary regimens published in the literature. However, the impact of this regime needs to be confirmed utilising a larger sample of adolescents. This may provide a useful approach for future research aiming to assess the impact of reduced GI and GL

Marriage and the politics of friendship: the family of Charles II of Anjou, King of Naples (1285-1309)

This thesis aims to reassert the importance of the supranational dynasties of Europe in medieval history by considering the so-called Angevins of Naples, and specifically Charles II (1285-1309), whose matrimonial policies led to the end of the first phase of the Sicilian War and to the peace of Caltabellotta (1302). In particular, the study emphasizes the fact that the Angevins were part of the Capetian French royal house and thus refocusses the role of the Capetians within Christendom at that time, as their previous historiography has concentrated on their role within France. It investigates the the part that the various marriage combinations played in the Sicilian peace process and how they connected with Charles II's internal family strategies, demonstrating how his plans to keep most of the patrimony for his primogenitus was compromised by deals that meant that large parts of the inheritance had to be passed to daughters instead. The following chapter shows how Charles was prepared to relegate other dynastic interests to achieve these deals and how his unbalanced provision for his sons led to conflict within the dynasty. Moving on to a discussion of the legal side of marriage, the thesis discusses how Charles II was able to work within the canon law on consent, consanguinity and divorce to achieve his aims and how far the aristocratic ideas of the Duby model still conflicted with the Church. Taking the discussion of political marriage beyond the marriage treaties themselves, using the extensive correspondence between the Angevins and the royal house of Aragon, it is argued that the importance of dynastic marriage lay as much in the bonds of friendship forged between houses that were the basis of reciprocal duties and favours that were the warp and weft of medieval political life

The validity of two compartment model methods of body composition as compared to magnetic resonance imaging in Asian Indian versus Caucasian males

Background: The two-compartment (2C) model is a relatively accessible, inexpensive and time efficient method for body composition measurement. There is very little validated research on the 2C model in Asian Indians: a high risk population in terms of obesity and related disorders. This highlights the need for valid estimates of body composition from the 2C model. Purpose: The goal was to compare 2C model (predictor) estimates of body composition to those from magnetic resonance imaging (MRI) (criterion), an established gold standard measure of total adiposity in order to determine the validity of the 2C model in the Asian Indian population. From this data it is hoped that a correction equation may be determined for more accurate prediction of Asian Indian body composition using 2C model methods. Methods: 21 males (10 Asian Indian and 11 Caucasian, aged 18-55 yrs) had estimates of percent body fat from 2C methods (sum of four skinfolds and anthropometry, bioelectrical impedance analysis [Bodystat 1500 and Tanita segmental impedance analyser], air displacement plethysmography [Bod Pod] and hydrostatic weighing) compared to MRI measured body composition values. Agreement was assessed using multiple linear regression analysis and Bland-Altman plots. Differences were assessed using repeated measures analysis of variance. Results: Regression analysis showed air displacement plethysmography predicts MRI body composition in Caucasian males (adjusted r2 = 0.74; SEE =3.27 ). In Asian Indians, tricep skinfold thickness and hydrostatic weighing predicted MRI body composition with a low prediction error (adjusted r2 = 0.90; SEE =1.75). Despite strong correlations and no significant difference between mean differences of the 2C methods, used in the prediction model, and MRI, BlandAltman plots revealed no acceptable limits of agreement between the methods. Asian Indian body composition was underestimated by all two compartment devices compared to MRI. Conclusion: There appears to be potential for the use of tricep skinfold thickness and hydrostatic weighing to predict an established reference measure (MRI) in the high risk Asian Indian population. The 2C model underestimated Asian Indian body composition, this suggests that un-validated, the 2C model may misidentify obesity and in turn health risk. However the small sample tested, has implications for the interpretation of the findings. Further investigation is required with a greater sample size to validate the 2C model against an established reference measure such as MRI as there is currently little published validation data in this ethnic group