A fast Metropolis-Hastings method for generating random correlation matrices

We propose a novel Metropolis-Hastings algorithm to sample uniformly from the space of correlation matrices. Existing methods in the literature are based on elaborated representations of a correlation matrix, or on complex parametrizations of it. By contrast, our method is intuitive and simple, based the classical Cholesky factorization of a positive definite matrix and Markov chain Monte Carlo theory. We perform a detailed convergence analysis of the resulting Markov chain, and show how it benefits from fast convergence, both theoretically and empirically. Furthermore, in numerical experiments our algorithm is shown to be significantly faster than the current alternative approaches, thanks to its simple yet principled approach.Comment: 8 pages, 3 figures, 2018 conferenc

A family of diameter-based eigenvalue bounds for quantum graphs

We establish a sharp lower bound on the first non-trivial eigenvalue of the Laplacian on a metric graph equipped with natural (i.e., continuity and Kirchhoff) vertex conditions in terms of the diameter and the total length of the graph. This extends a result of, and resolves an open problem from, [J. B. Kennedy, P. Kurasov, G. Malenov\'a and D. Mugnolo, Ann. Henri Poincar\'e 17 (2016), 2439--2473, Section 7.2], and also complements an analogous lower bound for the corresponding eigenvalue of the combinatorial Laplacian on a discrete graph. We also give a family of corresponding lower bounds for the higher eigenvalues under the assumption that the total length of the graph is sufficiently large compared with its diameter. These inequalities are sharp in the case of trees.Comment: Substantial revision of v1. The main result, originally for the first eigenvalue, has been generalised to the higher ones. The title has been changed and the proofs substantially reorganised to reflect the new result, and a section containing concluding remarks has been adde

Genetic testing of children for adult-onset conditions: opinions of the British adult population and implications for clinical practice

This study set out to explore the attitudes of a representative sample of the British public towards genetic testing in children to predict disease in the future. We sought opinions about genetic testing for adult-onset conditions for which no prevention/treatment is available during childhood, and about genetic 'carrier' status to assess future reproductive risks. The study also examined participants' level of agreement with the reasons professional organisations give in favour of deferring such testing. Participants (n=2998) completed a specially designed questionnaire, distributed by email. Nearly half of the sample (47%) agreed that parents should be able to test their child for adult-onset conditions, even if there is no treatment or prevention at time of testing. This runs contrary to professional guidance about genetic testing in children. Testing for carrier status was supported by a larger proportion (60%). A child's future ability to decide for her/himself if and when to be tested was the least supported argument in favour of deferring testing.European Journal of Human Genetics advance online publication, 5 November 2014; doi:10.1038/ejhg.2014.221

Quantum Tomography under Prior Information

We provide a detailed analysis of the question: how many measurement settings or outcomes are needed in order to identify a quantum system which is constrained by prior information? We show that if the prior information restricts the system to a set of lower dimensionality, then topological obstructions can increase the required number of outcomes by a factor of two over the number of real parameters needed to characterize the system. Conversely, we show that almost every measurement becomes informationally complete with respect to the constrained set if the number of outcomes exceeds twice the Minkowski dimension of the set. We apply the obtained results to determine the minimal number of outcomes of measurements which are informationally complete with respect to states with rank constraints. In particular, we show that 4d-4 measurement outcomes (POVM elements) is enough in order to identify all pure states in a d-dimensional Hilbert space, and that the minimal number is at most 2 log_2(d) smaller than this upper bound.Comment: v3: There was a mistake in the derived finer upper bound in Theorem 3. The corrected upper bound is +1 to the earlier versio

Randomised controlled trial of thermostatic mixer valves in reducing bath hot tap water temperature in families with young children in social housing: A protocol

<p>Abstract</p> <p>Background</p> <p>Each year in the UK 2000 children attend emergency departments and 500 are admitted to hospital following a bath water scald. The long term effects can include disability, disfigurement or psychological harm and repeated skin grafts may be required as the child grows. The costs of treating a severe scald are estimated at 250,000 GBP. Children living in the most deprived wards are at greatest risk of thermal injuries; hospital admission rates are three times that for children living in the least deprived wards.</p> <p>Domestic hot water, which is usually stored at around 60 degrees Celsius, can result in a second-degree burn after 3 seconds and a third-degree burn after 5 seconds. Educational strategies to encourage testing of tap water temperature and reduction of hot water thermostat settings have largely proved unsuccessful. Legislation in the USA mandating pre-setting hot water heater thermostats at 49 degrees Celsius was effective in reducing scald injuries, suggesting passive measures may have a greater impact. Thermostatic mixer valves (TMVs), recently developed for the domestic market, fitted across the hot and cold water supply pipes of the bath, allow delivery of water set at a fixed temperature from the hot bath tap. These valves therefore offer the potential to reduce scald injuries.</p> <p>Design/Methods</p> <p>A pragmatic, randomised controlled trial to assess the effectiveness of TMVs in reducing bath hot tap water temperatures in the homes of families with young children in rented social housing. Two parallel arms include an intervention group and a control group where the intervention will be deferred.</p> <p>The intervention will consist of fitting a TMV (set at 44 degrees Celsius) by a qualified plumber and provision of educational materials. The control arm will not receive a TMV or the educational materials for the study duration but will be offered the intervention after collection of follow-up data 12 months post randomisation.</p> <p>The primary outcome measure will be the bath hot tap water temperature. Fifteen families per arm are required to detect a reduction in the mean bath hot tap water temperature from 60.4 degrees Celsius (SD 9.1) in the control group to 46 degrees Celsius in the intervention group, with 90% power and a 5% significance level (2 sided). Secondary outcome measures including acceptability will require a sample size of 120 participants.</p> <p>Discussion</p> <p>Whilst TMVs have the potential to reduce scald injuries, to date there have been no randomised controlled trials assessing their effectiveness, acceptability and cost effectiveness.</p> <p>Trial Registration</p> <p>ISRCTN21179067</p

Changing the Paradigm for Management of Pediatric Primary Spontaneous Pneumothorax: A Simple Aspiration Test Predicts Need for Operation

Purpose Chest tube (CT) management for pediatric primary spontaneous pneumothorax (PSP) is associated with long hospital stays and high recurrence rates. To streamline management, we explored simple aspiration as a test to predict need for surgery. Methods A multi-institution, prospective pilot study of patients with first presentation for PSP at 9 children’s hospitals was performed. Aspiration was performed through a pigtail catheter, followed by 6 h observation with CT clamped. If pneumothorax recurred during observation, the aspiration test failed and subsequent management was per surgeon discretion. Results Thirty-three patients were managed with simple aspiration. Aspiration was successful in 16 of 33 (48%), while 17 (52%) failed the aspiration test and required hospitalization. Twelve who failed aspiration underwent CT management, of which 10 (83%) failed CT management owing to either persistent air leak requiring VATS or subsequent PSP recurrence. Recurrence rate was significantly greater in the group that failed aspiration compared to the group that passed aspiration [10/12 (83%) vs 7/16 (44%), respectively, P = 0.028]. Conclusion Simple aspiration test upon presentation with PSP predicts chest tube failure with 83% positive predictive value. We recommend changing the PSP management algorithm to include an initial simple aspiration test, and if that fails, proceed directly to VATS