Spectral arbitrariness for trees fails spectacularly

If $G$ is a graph and $\mathbf{m}$ is an ordered multiplicity list which is realizable by at least one symmetric matrix with graph $G$, what can we say about the eigenvalues of all such realizing matrices for $\mathbf{m}$? It has sometimes been tempting to expect, especially in the case that $G$ is a tree, that any spacing of the multiple eigenvalues should be realizable. In 2004, however, F. Barioli and S. Fallat produced the first counterexample: a tree on 16 vertices and an ordered multiplicity list for which every realizing set of eigenvalues obeys a nontrivial linear constraint. We extend this by giving an infinite family of trees and ordered multiplicity lists whose sets of realizing eigenvalues are very highly constrained, with at most 5 degrees of freedom, regardless of the size of the tree in this family. In particular, we give the first examples of multiplicity lists for a tree which impose nontrivial nonlinear eigenvalue constraints and produce an ordered multiplicity list which is achieved by a unique set of eigenvalues, up to shifting and scaling.Comment: 45 page

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

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

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

Infants with esophageal atresia and right aortic arch: Characteristics and outcomes from the Midwest Pediatric Surgery Consortium

Purpose Right sided aortic arch (RAA) is a rare anatomic finding in infants with esophageal atresia with or without tracheoesophageal fistula (EA/TEF). In the presence of RAA, significant controversy exists regarding optimal side for thoracotomy in repair of the EA/TEF. The purpose of this study was to characterize the incidence, demographics, surgical approach, and outcomes of patients with RAA and EA/TEF. Methods A multi-institutional, IRB approved, retrospective cohort study of infants with EA/TEF treated at 11 children's hospitals in the United States over a 5-year period (2009 to 2014) was performed. All patients had a minimum of one-year follow-up. Results In a cohort of 396 infants with esophageal atresia, 20 (5%) had RAA, with 18 having EA with a distal TEF and 2 with pure EA. Compared to infants with left sided arch (LAA), RAA infants had a lower median birth weight, (1.96 kg (IQR 1.54–2.65) vs. 2.57 kg (2.00–3.03), p = 0.01), earlier gestational age (34.5 weeks (IQR 32–37) vs. 37 weeks (35–39), p = 0.01), and a higher incidence of congenital heart disease (90% vs. 32%, p  0.29). Conclusion RAA in infants with EA/TEF is rare with an incidence of 5%. Compared to infants with EA/TEF and LAA, infants with EA/TEF and RAA are more severely ill with lower birth weight and higher rates of prematurity and complex congenital heart disease. In neonates with RAA, surgical repair of the EA/TEF is technically feasible via thoracotomy from either chest. A higher incidence of anastomotic strictures may occur with a right-sided approach

Understanding the Value of Tumor Markers in Pediatric Ovarian Neoplasms

Purpose The purpose of this study was to determine the diagnostic accuracy of tumor markers for malignancy in girls with ovarian neoplasms. Methods A retrospective review of girls 2–21 years who presented for surgical management of an ovarian neoplasm across 10 children's hospitals between 2010 and 2016 was performed. Patients who had at least one concerning feature on imaging and had tumor marker testing were included in the study. Sensitivity, specificity, and negative and positive predictive values (PPV) of tumor markers were calculated. Results Our cohort included 401 patients; 22.4% had a malignancy. Testing for tumor markers was inconsistent. AFP had high specificity (98%) and low sensitivity (42%) with a PPV of 86%. The sensitivity, specificity, and PPV of beta-hCG was 44%, 76%, and 32%, respectively. LDH had high sensitivity (95%) and Inhibin A and Inhibin B had high specificity (97% and 92%, respectively). Conclusions Tumor marker testing is helpful in preoperative risk stratification of ovarian neoplasms for malignancy. Given the variety of potential tumor types, no single marker provides enough reliability, and therefore a panel of tumor marker testing is recommended if there is concern for malignancy. Prospective studies may help further elucidate the predictive value of tumor markers in a pediatric ovarian neoplasm population