Euclidean and hyperbolic lenghs of images of arcs

Let $f$ be a function that is analytic in the unit disc. We give new estimates, and new proofs of existing estimates, of the Euclidean length of the image under $f$ of a radial segment in the unit disc. Our methods are based on the hyperbolic geometry of plane domains, and we address some new questions that follow naturally from this approach.Comment: 26 page

The UK register of HIV seroconverters: Methods and analytical issues

A Register of HIV-infected persons who have had a negative antibody test within 3 years of their first antibody positive test (seroconverters) is being set up in the UK to monitor the distribution of times from HIV seroconversion to AIDS (the incubation period) and to death. It will also provide a national resource for use by those designing studies in this group of individuals. Clinicians caring for HIV-positive persons in Genito-Urinary Medicine, Infectious Disease and other departments throughout the UK were asked to participate by providing information on eligible subjects. Most laboratories undertaking HIV antibody testing were also contacted and asked to provide the name of the attending clinician for all seroconverters identified through the HIV laboratory reporting systems of the PHLS Communicable Disease Surveillance Centre (CDSC) and the Scottish Centre for Infection and Environmental Health (SCIEH) and for any other seroconverters known to them but not identified by CDSC or SCIEH. Data items sought for the Register include: sex, ethnic group, probable route of HIV transmission, annual CD4 counts, details of therapy and prophylaxis prescribed, AIDS-defining events and vital status. Follow up information is collected annually. Wherever possible, all seroconverters known to a clinic have been identified, whether currently alive or dead, either from clinic records or laboratory reporting or both. The objective is to establish and update a complete register of seroconverters on a long-term basis to provide reliable estimates of the incubation period on which future projections of AIDS cases in the UK can be made

The prevalence of vitamin B12 deficiency in a random sample from the Australian population

 Objective: Vitamin B12 deficiency is common in older adults, and may increase the risk of cognitive impairment. The distribution of vitamin B12 insufficiency in younger age groups is less studied. This study aims to assess the prevalence of vitamin B12 deficiency (<156ρmol/L) and subclinical low-normal levels (156-250ρmol/L) in a large, random sample of the Australian population across the adult life span. Methods: We examined serum vitamin B12 levels in a random sample of 1,085 men and 1,125 women aged 20-97 years between 1994 and 2006; in the Barwon Statistical Division, a regional area in south eastern Australia that is representative of the socioeconomic status of the Australian population. Results: The age-standardised prevalence of vitamin B12 deficiency in this cohort of men and women was 3.6%. Subclinical low-normal vitamin B12 levels (156-250ρmol/L) were found in 26%. Serum vitamin B12 levels declined with age among men (p-value <0.001) and were lower in men than women (p-value <0.001). Vitamin B12 levels were higher among supplement users (8.0% of the cohort). Conclusions: Vitamin B12 levels decline with age, and have been associated with neurodegenerative diseases and cognitive decline. Early intervention by diet education or supplement use to address this age-associated decline in vitamin levels may be an effective strategy to prevent decline in a significant segment of the population. Such intervention may need to start in mid-life (from 50-years of age) before the onset age-related decline in vitamin B12 levels

Unbounded violation of tripartite Bell inequalities

We prove that there are tripartite quantum states (constructed from random unitaries) that can lead to arbitrarily large violations of Bell inequalities for dichotomic observables. As a consequence these states can withstand an arbitrary amount of white noise before they admit a description within a local hidden variable model. This is in sharp contrast with the bipartite case, where all violations are bounded by Grothendieck's constant. We will discuss the possibility of determining the Hilbert space dimension from the obtained violation and comment on implications for communication complexity theory. Moreover, we show that the violation obtained from generalized GHZ states is always bounded so that, in contrast to many other contexts, GHZ states do in this case not lead to extremal quantum correlations. The results are based on tools from the theories of operator spaces and tensor norms which we exploit to prove the existence of bounded but not completely bounded trilinear forms from commutative C*-algebras.Comment: Substantial changes in the presentation to make the paper more accessible for a non-specialized reade

INNOVATE: A prospective cohort study combining serum and urinary biomarkers with novel diffusion-weighted magnetic resonance imaging for the prediction and characterization of prostate cancer

BACKGROUND: Whilst multi-parametric magnetic resonance imaging (mp-MRI) has been a significant advance in the diagnosis of prostate cancer, scanning all patients with elevated prostate specific antigen (PSA) levels is considered too costly for widespread National Health Service (NHS) use, as the predictive value of PSA levels for significant disease is poor. Despite the fact that novel blood and urine tests are available which may predict aggressive disease better than PSA, they are not routinely employed due to a lack of clinical validity studies. Furthermore approximately 40% of mp-MRI studies are reported as indeterminate, which can lead to repeat examinations or unnecessary biopsy with associated patient anxiety, discomfort, risk and additional costs. METHODS AND ANALYSIS: We aim to clinically validate a panel of minimally invasive promising blood and urine biomarkers, to better select patients that will benefit from a multiparametric prostate MRI. We will then test whether the performance of the mp-MRI can be improved by the addition of an advanced diffusion-weighted MRI technique, which uses a biophysical model to characterise tissue microstructure called VERDICT; Vascular and Extracellular Restricted Diffusion for Cytometry in Tumours. INNOVATE is a prospective single centre cohort study in 365 patients. mpMRI will act as the reference standard for the biomarker panel. A clinical outcome based reference standard based on biopsy, mp-MRI and follow-up will be used for VERDICT MRI. We expect the combined effect of biomarkers and VERDICT MRI will improve care by better detecting aggressive prostate cancer early and make mp-MRI before biopsy economically viable for universal NHS adoption. ETHICS AND DISSEMINATION: INNOVATE received UK Research Ethics Committee approval on 23rd December 2015 by the NRES Committee London—Surrey Borders with REC reference 15/LO/0692. REGISTRATION DETAILS: INNOVATE is registered on ClinicalTrials.gov, with reference NCT0268927