Towards a Classification of Charge-3 Monopoles with Symmetry

We classify all possible charge-3 monopole spectral curves with non-trivial automorphism group and within these identify those with elliptic quotients. By focussing on elliptic quotients the transcendental constraints for a monopole spectral curve become ones regarding periods of elliptic functions. We construct the Nahm data and new monopole spectral curves with $D_6$ and $V_4$ symmetry discovering a previously-unknown (to us) integrable complexification of Euler's equations. Extensions of our approach to higher charge and hyperbolic monopoles are discussed

Symmetries of Riemann surfaces and magnetic monopoles

This thesis studies, broadly, the role of symmetry in elucidating structure. In particular, I investigate the role that automorphisms of algebraic curves play in three specific contexts; determining the orbits of theta characteristics, influencing the geometry of the highly-symmetric Bring’s curve, and in constructing magnetic monopole solutions. On theta characteristics, I show how to turn questions on the existence of invariant characteristics into questions of group cohomology, compute comprehensive tables of orbit decompositions for curves of genus 9 or less, and prove results on the existence of infinite families of curves with invariant characteristics. On Bring’s curve, I identify key points with geometric significance on the curve, completely determine the structure of the quotients by subgroups of automorphisms, finding new elliptic curves in the process, and identify the unique invariant theta characteristic on the curve. With respect to monopoles, I elucidate the role that the Hitchin conditions play in determining monopole spectral curves, the relation between these conditions and the automorphism group of the curve, and I develop the theory of computing Nahm data of symmetric monopoles. As such I classify all 3-monopoles whose Nahm data may be solved for in terms of elliptic functions

Influence of obesity-related risk factors in the aetiology of glioma

BACKGROUND: Obesity and related factors have been implicated as possible aetiological factors for the development of glioma in epidemiological observation studies. We used genetic markers in a Mendelian randomisation framework to examine whether obesity-related traits influence glioma risk. This methodology reduces bias from confounding and is not affected by reverse causation. METHODS: Genetic instruments were identified for 10 key obesity-related risk factors, and their association with glioma risk was evaluated using data from a genome-wide association study of 12,488 glioma patients and 18,169 controls. The estimated odds ratio of glioma associated with each of the genetically defined obesity-related traits was used to infer evidence for a causal relationship. RESULTS: No convincing association with glioma risk was seen for genetic instruments for body mass index, waist-to-hip ratio, lipids, type-2 diabetes, hyperglycaemia or insulin resistance. Similarly, we found no evidence to support a relationship between obesity-related traits with subtypes of glioma-glioblastoma (GBM) or non-GBM tumours. CONCLUSIONS: This study provides no evidence to implicate obesity-related factors as causes of glioma

Mendelian randomization provides support for obesity as a risk factor for meningioma.

Little is known about the causes of meningioma. Obesity and obesity-related traits have been reported in several epidemiological observational studies to be risk factors for meningioma. We performed an analysis of genetic variants associated with obesity-related traits to assess the relationship with meningioma risk using Mendelian randomization (MR), an approach unaffected by biases from temporal variability and reverse causation that might have affected earlier investigations. We considered 11 obesity-related traits, identified genetic instruments for these factors, and assessed their association with meningioma risk using data from a genome-wide association study comprising 1,606 meningioma patients and 9,823 controls. To evaluate the causal relationship between the obesity-related traits and meningioma risk, we consider the estimated odds ratio (OR) of meningioma for each genetic instrument. We identified positive associations between body mass index (odds ratio [ORSD] = 1.27, 95% confidence interval [CI] = 1.03-1.56, P = 0.028) and body fat percentage (ORSD = 1.28, 95% CI = 1.01-1.63, P = 0.042) with meningioma risk, albeit non-significant after correction for multiple testing. Associations for basal metabolic rate, diastolic blood pressure, fasting glucose, high-density lipoprotein cholesterol, low-density lipoprotein cholesterol, systolic blood pressure, total cholesterol, triglycerides and waist circumference with risk of meningioma were non-significant. Our analysis provides additional support for obesity being associated with an increased risk of meningioma

Impact of atopy on risk of glioma : a Mendelian randomisation study

Background: An inverse relationship between allergies with glioma risk has been reported in several but not all epidemiological observational studies. We performed an analysis of genetic variants associated with atopy to assess the relationship with glioma risk using Mendelian randomisation (MR), an approach unaffected by biases from temporal variability and reverse causation that might have affected earlier investigations. Methods: Two-sample MR was undertaken using genome-wide association study data. We used single nucleotide polymorphisms (SNPs) associated with atopic dermatitis, asthma and hay fever, IgE levels, and self-reported allergy as instrumental variables. We calculated MR estimates for the odds ratio (OR) for each risk factor with glioma using SNP-glioma estimates from 12,488 cases and 18,169 controls, using inverse-variance weighting (IVW), maximum likelihood estimation (MLE), weighted median estimate (WME) and mode-based estimate (MBE) methods. Violation of MR assumptions due to directional pleiotropy were sought using MR-Egger regression and HEIDI-outlier analysis. Results: Under IVW, MLE, WME and MBE methods, associations between glioma risk with asthma and hay fever, self-reported allergy and IgE levels were non-significant. An inverse relationship between atopic dermatitis and glioma risk was found by IVW (OR 0.96, 95% confidence interval (CI) 0.93-1.00, P = 0.041) and MLE (OR 0.96, 95% CI 0.94-0.99, P = 0.003), but not by WME (OR 0.96, 95% CI 0.91-1.01, P = 0.114) or MBE (OR 0.97, 95% CI 0.92-1.02, P = 0.194). Conclusions: Our investigation does not provide strong evidence for relationship between atopy and the risk of developing glioma, but findings do not preclude a small effect in relation to atopic dermatitis. Our analysis also serves to illustrate the value of using several MR methods to derive robust conclusions

Additional file 6: of Impact of atopy on risk of glioma: a Mendelian randomisation study

Table S5. Simulation analyses. (XLSX 28 kb

Additional file 4: of Impact of atopy on risk of glioma: a Mendelian randomisation study

Table S3. Percentage of variance explained by the combined sets of single nucleotide polymorphisms used as instrumental variables. (XLSX 33 kb

Additional file 2: of Impact of atopy on risk of glioma: a Mendelian randomisation study

Table S1. Summary of the eight glioma genome-wide association studies. (XLSX 29 kb

Additional file 1: of Impact of atopy on risk of glioma: a Mendelian randomisation study

Figure S1. Forest plot of Wald odds ratios (ORs) and 95% confidence intervals generated from single nucleotide polymorphisms (SNPs) associated with atopic dermatitis, including rs909341. ORs for individual SNPs are listed according to magnitude of effect in the instrumental variable analysis and are presented with pooled effects using the inverse-variance weighting method. Squares represent the point estimate, and the bars are the 95% confidence intervals. (DOCX 89 kb