Magnetic translation groups in an n-dimensional torus

A charged particle in a uniform magnetic field in a two-dimensional torus has a discrete noncommutative translation symmetry instead of a continuous commutative translation symmetry. We study topology and symmetry of a particle in a magnetic field in a torus of arbitrary dimensions. The magnetic translation group (MTG) is defined as a group of translations that leave the gauge field invariant. We show that the MTG on an n-dimensional torus is isomorphic to a central extension of a cyclic group Z_{nu_1} x ... x Z_{nu_{2l}} x T^m by U(1) with 2l+m=n. We construct and classify irreducible unitary representations of the MTG on a three-torus and apply the representation theory to three examples. We shortly describe a representation theory for a general n-torus. The MTG on an n-torus can be regarded as a generalization of the so-called noncommutative torus.Comment: 29 pages, LaTeX2e, title changed, re-organized, to be published in Journal of Mathematical Physic

Holocene volcanic soils in the Mt. Gambier region, South Australia

Volcanic soils derived from mid-Holocene basaltic tephra in the Mt. Gambier region of South Australia have developed in a xeric moisture regime. We studied two soils, one at Mt Gambier (MTG) and the other at nearby Mt Schank (MTS). Both volcanoes were active ca. 6000 cal. years ago. The MTG soil has a high content of CaCO₃ (incorporated during eruption through limestone) and other exotic materials intermixed with basaltic tephra containing low amounts of glass. The MTS soil is derived mainly from basaltic tephra with high glass content and much less CaCO₃ than at MTG. These parent mineralogies have led to markedly different clay compositions and chemical properties: the MTS soil contains abundant allophane (mainly) and ferrihydrite with few layer silicate clays, whereas the MTG soil is dominated by layer silicate clays and low allophane or ferrihydrite. Both soils are near neutral or alkaline. The MTS soil has a melanic horizon and andic properties and is classed as a Melanoxerand. The MTG soil has weak andic properties with insufficient glass to enable it to be classed in the Andisols, and is instead a Calcixeroll

A longitudinal, observational study examining the relationships of patient satisfaction with services and mental well-being to their clinical course in young people with Type 1 diabetes mellitus during transition from child to adult health services

AIM: We hypothesized that participant well-being and satisfaction with services would be positively associated with a satisfactory clinical course during transition from child to adult health care. METHODS: Some 150 young people with Type 1 diabetes mellitus from five diabetes units in England were recruited to a longitudinal study of transition. Each young person was visited at home four times by a research assistant; each visit was 1 year apart. Satisfaction with services (Mind the Gap; MTG) and mental well-being (Warwick-Edinburgh Mental Well-being Scale; WEMWBS) were captured. Change in HbA1c , episodes of ketoacidosis, clinic and retinal screening attendance were used to assess clinical course. In total, 108 of 150 (72%) young people had sufficient data for analysis at visit 4. RESULTS: Mean age at entry was 16 years. By visit 4, 81.5% had left paediatric healthcare services. Median HbA1c increased significantly (P = 0.01) from 69 mmol/mol (8.5%) at baseline to 75 mmol/mol (9.0%) at visit 4. WEMWBS scores were comparable with those in the general population at baseline and were stable over the study period. MTG scores were also stable. By visit 4, some 32 individuals had a 'satisfactory' and 76 a 'suboptimal' clinical course. There were no significant differences in average WEMWBS and MTG scores between the clinical course groups (P = 0.96, 0.52 respectively); nor was there a significant difference in transfer status between the clinical course groups. CONCLUSIONS: The well-being of young people with diabetes and their satisfaction with transition services are not closely related to their clinical course. Investigating whether innovative psycho-educational interventions can improve the clinical course is a research priority

Kaluza-Klein Towers in the Early Universe: Phase Transitions, Relic Abundances, and Applications to Axion Cosmology

We study the early-universe cosmology of a Kaluza-Klein (KK) tower of scalar fields in the presence of a mass-generating phase transition, focusing on the time-development of the total tower energy density (or relic abundance) as well as its distribution across the different KK modes. We find that both of these features are extremely sensitive to the details of the phase transition and can behave in a variety of ways significant for late-time cosmology. In particular, we find that the interplay between the temporal properties of the phase transition and the mixing it generates are responsible for both enhancements and suppressions in the late-time abundances, sometimes by many orders of magnitude. We map out the complete model parameter space and determine where traditional analytical approximations are valid and where they fail. In the latter cases we also provide new analytical approximations which successfully model our results. Finally, we apply this machinery to the example of an axion-like field in the bulk, mapping these phenomena over an enlarged axion parameter space that extends beyond those accessible to standard treatments. An important by-product of our analysis is the development of an alternate "UV-based" effective truncation of KK theories which has a number of interesting theoretical properties that distinguish it from the more traditional "IR-based" truncation typically used in the extra-dimension literature.Comment: 30 pages, LaTeX, 18 figures. Replaced to match published versio

AI Education Matters: Data Science and Machine Learning with Magic: The Gathering

In this column, we briefly describe a rich dataset with many opportunities for interesting data science and machine learning assignments and research projects, we take up a simple question, and we offer code illustrating use of the dataset in pursuit of answers to the question

Understanding Small Business Networking and ICTs: Exploring Face-to-Face and ICT-related opportunity creation mediated by Social Capital in East of England Micro-businesses

Small businesses that are sole traders or micro-businesses—with few, if any employees notoriously suffer from a ‘liability of smallness’ (Aldrich and Auster 1986), including poor access to various resources. However, many authors argue that the inherent problems of smallness can be overcome with networking and good network connections. Resources, the opportunities to access them and other benefits apparent from networks and networking are readily apparent in the literature. However, few articles, if any, have examined small business networking from the perspective of this study—using in-depth qualitative methods, the theoretical construct of social capital and exploring the increasing role of Information and Communication Technologies (ICTs) in networks and networking—as part of understanding a variety of entrepreneurial opportunities. This article provides much needed empirical insights on how and if ICTs support opportunity creation amongst small businesses within a spatial and social network perspective. Its ‘media ecology’ approach does not over-prioritise the role of ICTs, but instead examines their interrelationships with face-to-face contact—putting technology in its ‘place’. The article focuses on the notion of ‘opportunity creation’ from networks, since this is the outcome critical for the small businesses themselves in order to generate economic benefits for their business. It seeks to provide a higher level, outcomebased framework that helps specify the various sorts of opportunities created by networks for small businesses, based on original ethnographic material and findings from a case study of East of England micro-businesses

Magnetically induced termination of giant planet formation

Here a physical model for terminating giant planet formation is outlined and compared to other methods of late-stage giant planet formation. As has been pointed out before, gas accreting into a gap and onto the planet will encounter the planetary dynamo-generated magnetic field. The planetary magnetic field produces an effective cross section through which gas is accreted. Gas outside this cross section is recycled into the protoplanetary disk, hence only a fraction of mass that is accreted into the gap remains bound to the planet. This cross section inversely scales with the planetary mass, which naturally leads to stalled planetary growth late in the formation process. We show that this method naturally leads to Jupiter-mass planets and does not invoke any artificial truncation of gas accretion, as has been done in some previous population synthesis models. The mass accretion rate depends on the radius of the growing planet after the gap has opened, and we show that so-called hot-start planets tend to become more massive than cold-start planets. When this result is combined with population synthesis models, it might show observable signatures of cold-start versus hot-start planets in the exoplanet population.Comment: 8 pages, 3 figures, accepted for publication in Astronomy & Astrophysic