Flattening Functions on Flowers

Let $T$ be an orientation-preserving Lipschitz expanding map of the circle \T. A pre-image selector is a map \tau:\T\to\T with finitely many discontinuities, each of which is a jump discontinuity, and such that $\tau(x)\in T^{-1}(x)$ for all x\in\T. The closure of the image of a pre-image selector is called a flower, and a flower with $p$ connected components is called a $p$-flower. We say that a real-valued Lipschitz function can be Lipschitz flattened on a flower whenever it is Lipschitz cohomologous to a constant on that flower. The space of Lipschitz functions which can be flattened on a given $p$-flower is shown to be of codimension $p$ in the space of all Lipschitz functions, and the linear constraints determining this subspace are derived explicitly. If a Lipschitz function $f$ has a maximizing measure $S$ which is Sturmian (i.e. is carried by a 1-flower), it is shown that $f$ can be Lipschitz flattened on some 1-flower carrying $S$.Comment: Accepted for publication and confirmed for december 200

Architecture Live Projects acquiring and applying missing practice-ready skills

This study concerns itself with examining the degree to which Live Projects can deliver learning experiences that enable architecture students to gain specific professional practice-ready skills and capabilities currently perceived to be lacking within the existing school curriculum - (1) collaborative interaction within and between inter-disciplinary teams, (2) participatory engagement with clients & civic concerns and the (3) capability to manage emergent ambiguities in risk exposure & decision-making –and as a consequence examine (4) how embryonic Live Project assessment rudiments might contribute to this acquisition? Architects are under increased pressure to demonstrate the value of their contribution within the process of building design and construction. They are tasked with working effectively in teams, collaborating effectively with clients and end users and to cope with growing levels of risk and liability, uncertainty and ambiguity, often requiring greater creative leadership and commercial risk-taking in order to succeed. The need for architects to acquire three skillsets to cope with these conditions imposes changing expectations around the architect's role in practice and places increased pressure upon schools of Architecture to ensure their students are equipped with gaining these skillsets. The question emerges as to whether a less-established teaching model – Live Projects - might be able to deliver skills that will not only respond to, but also endure the ongoing changes within professional practice? And if so, in relation to what skillsets? In contrast to other research enquiries concerning Live Projects and literature concerning architectural education in general, this thesis gathered evidence from a highly diverse range of sources – including data on emergent economic and industrial trends outside of the construction sector - as a means to define what the most valuable skillsets might be. For schools of architecture, the specific challenge is to not only to work out how to teach these skillsets but to design and then assess learning activities that facilitate and reward their acquisition. Subsequently, this thesis also examines whether tentative assessment rudiments can play an enabling role in this respect. Within a broader learning theory context, this enquiry supports a wider body of emergent evidence that Live Projects offer learning experiences consistent with much of the literature regarding effective pedagogy - one that involves authentic and active engagement with real situations being more effective at enabling learning more relevant to the nascent demands of wider industry. Subsequently, the main question being considered – as reflected in the title - is: To what extent do Live Projects enable the acquisition and application of three ‘practice-ready’ skillsets? This question is then operationalised by examining this efficacy in relation to four sub-questions. 1. To what extent can Live Projects enable students to acquire inter-disciplinary teamwork capabilities? 2. To what extent can Live Projects enable students to acquire client collaboration & civic engagement capabilities? 3. To what extent can Live Projects enable students to acquire ambiguity tolerance & risk management capabilities? 4. To what extent might Live Project assessment rudiments assist in the acquisition of the three skillsets? In order to answer these questions, the enquiry employed qualitative as well as quantitative data collection methods. The qualitative evidence largely utilised grounded theory methods and analysis as a means to examine the perceptions of educators, architects and students. This involved the discovery of theory through the analysis of data and real world research, which focuses upon problem solving with a view to creating meaningful change. The mixed methods approach relied upon triangulation as a means to cross-examine evidence from the different data sets and to strengthen validity. The themes relating to the missing skillsets were then inter-related to highlight any interdependencies and to ensure a rigorous level of analysis and abstraction. Findings in relation to each skillset were isolated within focused chapters. Mixed method or ‘multi-method’ analysis - involving a series of matrices - was used to compare both quantitative and (selected sections of) qualitative data. In line with practice-based research methodology, an extended and iterative period of data gathering and analysis allowed the researcher to consolidate observations regarding the acquisition of specific skills in both an academic as well as a practice context to consolidate into a concise set of learning concepts. The thesis subsequently used these learning concepts to define tentative assessment rudiments. The samples chosen for this study were situated in two distinctly different contexts; in practice and in education: encompassing architects, trainee architects, students and educators both with and without Live Project experience, to enable a clear set of variables for comparative analysis. The samples were also drawn from both the US and UK – a useful consequence of research funding in terms of providing quantitative data and comparable cohorts. These insights were then used to tentatively explore practical ways the acquisition of these skillsets could be assessed. The conclusions of this study identify that Live Projects can enable students to acquire the three skillsets due to their ability to offer experiences that more closely align with professional practice. However it also pinpoints specific contingencies such as ensuring Live Project success is measured in terms of processes and not just outcomes - and - that keeping Live Projects as non-compulsory, extra curricula options or adjuncts to more established teaching models allows them to retain their inherently flexible, adaptive and responsive nature. Whilst there is general view that a lack of formal acknowledgement of Live Projects within the curricula-validating infrastructure of RIBA & NAAB has contributed to a collective sense that Live Projects are undervalued, the evidence suggests that the opposite is true – that Live Projects do have the ability to meet the criteria for validation extensively and effectively and can make the validation criterion more accessible and meaningful to students – and -because Live Projects encompass a hugely diverse range of projects by their nature of being holistically responsive to a set of site and community specific circumstances – assessment rudiments (rather than a design brief) might be the only unifying criteria. Given the current crisis in underemployment and the rise of the unpaid internship, these capabilities are of increasing relevance and value. Furthermore, it is transposable skills – which all three of the skillsets are – as opposed to those that are exclusive and unique to architecture – that are most likely to best serve students in future, whether or not they choose to become professional architects. Traditional subject specific skills are undeniably important, but transposable skills deserve greater emphasis and investment given the economic reality of finite resources and demands for greater user participation. Finally, for architectural educators already engaged in or initiating Live Projects, this thesis provides theoretical as well as an applied-knowledge framework to draw from, encompassing a practical as well as passionate advocacy for their wider implementation

Non-response bias in estimates of HIV prevalence due to the mobility of absentees in national population-based surveys: a study of nine national surveys

OBJECTIVES: To measure the bias in national estimates of HIV prevalence in population-based surveys caused by mobility and refusal to test. METHODS: Data from nine demographic and health surveys and AIDS indicator surveys were used. Non-responders were divided into three groups: (i) "refusals" who were interviewed but not tested; (ii) "refusals" who were present in the household but not interviewed or tested; and (iii) "absentees" who were absent from the household. Correction for HIV status was made for the non-responders using multiple imputation methods with logistic regression models based on a common set of household-level and individual-level sociodemographic and behavioural factors for those tested and stratified by mobility status. RESULTS: The non-response groups were corrected to have higher risks of HIV than those who participated in the HIV tests, although these were only detected to be statistically significant in some of the countries. In Lesotho, the corrected prevalence for the absent household members was significantly higher than for those who were present in the household. However, the adjusted prevalences differed by less than a percentage point from the prevalences observed among those who were tested, so the overall effects of non-response on national estimates of HIV prevalence are minimal. CONCLUSIONS: The results indicate that the mobility of absentees does not substantially bias estimates of HIV prevalence from population-based surveys. None the less, if levels of non-response are high or if non-responders differ greatly from those who participate in HIV testing with respect to HIV status, non-response could still bias national estimates of HIV prevalence

Algebraic Number Starscapes

We study the geometry of algebraic numbers in the complex plane, and their Diophantine approximation, aided by extensive computer visualization. Motivated by these images, called algebraic starscapes, we describe the geometry of the map from the coefficient space of polynomials to the root space, focussing on the quadratic and cubic cases. The geometry describes and explains notable features of the illustrations, and motivates a geometric-minded recasting of fundamental results in the Diophantine approximation of the complex plane. The images provide a case-study in the symbiosis of illustration and research, and an entry-point to geometry and number theory for a wider audience. The paper is written to provide an accessible introduction to the study of homogeneous geometry and Diophantine approximation. We investigate the homogeneous geometry of root and coefficient spaces under the natural $\operatorname{PSL}(2;\mathbb{C})$ action, especially in degrees 2 and 3. We rediscover the quadratic and cubic root formulas as isometries, and determine when the map sending certain families of polynomials to their complex roots (our starscape images) are embeddings. We consider complex Diophantine approximation by quadratic irrationals, in terms of hyperbolic distance and the discriminant as a measure of arithmetic height. We recover the quadratic case of results of Bugeaud and Evertse, and give some geometric explanation for the dichotomy they discovered (Bugeaud, Y. and Evertse, J.-H., Approximation of complex algebraic numbers by algebraic numbers of bounded degree, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 8 (2009), no. 2, 333-368). Our statements go a little further in distinguishing approximability in terms of whether the target or approximations lie on rational geodesics. The paper comes with accompanying software, and finishes with a wide variety of open problems.Comment: 63 pages, 36 figures; this version includes a technical introduction for an expert audienc

The role of dietary supplements, including biotics, glutamine, polyunsaturated fatty acids and polyphenols, in reducing gastrointestinal side effects in patients undergoing pelvic radiotherapy : A systematic review and meta-analysis

Funding Information: This work was supported by Cancer Research UK Programme grant [C5255/A23755]. Chee Kin Then’s DPhil is funded by the Clarendon Fund, Balliol College and CRUK. The funding body had no role in the study design, collection, analysis, interpretation of data or in writing the manuscript.Peer reviewedPublisher PD

Evaluation of current clinical target volume definitions for glioblastoma using cell-based dosimetry stochastic methods

Determination of an optimal clinical target volume (CTV) is complex and remains uncertain. The aim of this study was to develop a glioblastoma multiforme (GBM) model to be used for evaluation of current CTV practices for external radiotherapy.The GBM model was structured as follows: (1) a Geant4 cellular model was developed to calculate the absorbed dose in individual cells represented by cubic voxels of 20 μm sides. The system was irradiated with opposing 6 MV X-ray beams. The beams encompassed planning target volumes corresponding to 2.0- and 2.5-cm CTV margins; (2) microscopic extension probability (MEP) models were developed using MATLAB(®) 2012a (MathWorks(®), Natick, MA), based on clinical studies reporting on GBM clonogenic spread; (3) the cellular dose distribution was convolved with the MEP models to evaluate cellular survival fractions (SFs) for both CTV margins.A CTV margin of 2.5 cm, compared to a 2.0-cm CTV margin, resulted in a reduced total SF from 12.9% ± 0.9% to 3.6% ± 0.2%, 5.5% ± 0.4% to 1.2% ± 0.1% and 11.1% ± 0.7% to 3.0% ± 0.2% for circular, elliptical and irregular MEP distributions, respectively.A Monte Carlo model was developed to quantitatively evaluate the impact of GBM CTV margins on total and penumbral SF. The results suggest that the reduction in total SF ranges from 3.5 to 5, when the CTV is extended by 0.5 cm.The model provides a quantitative tool for evaluation of different CTV margins in terms of cell kill efficacy. Cellular platform of the tool allows future incorporation of cellular properties of GBM.L. Moghaddasi, E. Bezak and W. Harriss-Phillip

First Multicharged Ion Irradiation Results from the CUEBIT Facility at Clemson University

A new electron beam ion trap (EBIT) based ion source and beamline were recently commissioned at Clemson University to produce decelerated beams of multi- to highly-charged ions for surface and materials physics research. This user facility is the first installation of a DREEBIT-designedsuperconducting trap and ion source (EBIS-SC) in the U.S. and includes custom-designed target preparation and irradiation setups. An overview of the source, beamline, and other facilities as well as results from first measurements on irradiated targets are discussed here. Results include extracted charge state distributions and first data on a series of irradiated metal-oxide-semiconductor (MOS) device targets. For the MOS devices, we show that voltage-dependent capacitance can serve as a record of theelectronic component of ion stopping power for an irradiated, encapsulated oxide target