Convex regions in the plane and their domes

We make a detailed study of the relation of a euclidean convex region $\Omega \subset \mathbb C$ to $\mathrm{Dome} (\Omega)$. The dome is the relative boundary, in the upper halfspace model of hyperbolic space, of the hyperbolic convex hull of the complement of $\Omega$. The first result is to prove that the nearest point retraction $r: \Omega \to \mathrm{Dome} (\Omega)$ is 2-quasiconformal. The second is to establish precise estimates of the distortion of $r$ near $\partial \Omega$

Acute lung injury in paediatric intensive care: course and outcome

Introduction: Acute lung injury (ALI) and acute respiratory distress syndrome (ARDS) carry a high morbidity and mortality (10-90%). ALI is characterised by non-cardiogenic pulmonary oedema and refractory hypoxaemia of multifactorial aetiology [1]. There is limited data about outcome particularly in children. Methods This retrospective cohort study of 85 randomly selected patients with respiratory failure recruited from a prospectively collected database represents 7.1% of 1187 admissions. They include those treated with High Frequency Oscillation Ventilation (HFOV). The patients were admitted between 1 November 1998 and 31 October 2000. Results: Of the 85, 49 developed acute lung injury and 47 had ARDS. There were 26 males and 23 females with a median age and weight of 7.7 months (range 1 day-12.8 years) and 8 kg (range 0.8-40 kg). There were 7 deaths giving a crude mortality of 14.3%, all of which fulfilled the Consensus I [1] criteria for ARDS. Pulmonary occlusion pressures were not routinely measured. The A-a gradient and PaO2/FiO2 ratio (median + [95% CI]) were 37.46 [31.82-43.1] kPa and 19.12 [15.26-22.98] kPa respectively. The non-survivors had a significantly lower PaO2/FiO2 ratio (13 [6.07-19.93] kPa) compared to survivors (23.85 [19.57-28.13] kPa) (P = 0.03) and had a higher A-a gradient (51.05 [35.68-66.42] kPa) compared to survivors (36.07 [30.2-41.94]) kPa though not significant (P = 0.06). Twenty-nine patients (59.2%) were oscillated (Sensormedics 3100A) including all 7 non-survivors. There was no difference in ventilation requirements for CMV prior to oscillation. Seventeen of the 49 (34.7%) were treated with Nitric Oxide including 5 out of 7 non-survivors (71.4%). The median (95% CI) number of failed organs was 3 (1.96-4.04) for non-survivors compared to 1 (0.62-1.62) for survivors (P = 0.03). There were 27 patients with isolated respiratory failure all of whom survived. Six (85.7%) of the non-survivors also required cardiovascular support.Conclusion: A crude mortality of 14.3% compares favourably to published data. The A-a gradient and PaO2/FiO2 ratio may be of help in morbidity scoring in paediatric ARDS. Use of Nitric Oxide and HFOV is associated with increased mortality, which probably relates to the severity of disease. Multiple organ failure particularly respiratory and cardiac disease is associated with increased mortality. ARDS with isolated respiratory failure carries a good prognosis in children

Effectors of hemoglobin. Separation of allosteric and affinity factors

The relative contributions of the allosteric and affinity factors toward the change in p50 have been calculated for a series of effectors of hemoglobin (Hb). Shifts in the ligand affinity of deoxy Hb and the values for 50% ligand saturation (p50) were obtained from oxygen equilibrium data. Because the high-affinity parameters (liganded conformation) are poorly determined from the equilibrium curves, they were determined from kinetic measurements of the association and dissociation rates with CO as ligand. The CO on-rates were obtained by flash photolysis measurements. The off-rates were determined from the rate of oxidation of HbCO by ferricyanide, or by replacement of CO with NO. The partition function of fully liganded hemoglobin for oxygen and CO is only slightly changed by the effectors. Measurements were made in the presence of the effectors 2,3-diphosphoglycerate (DPG), inositol hexakisphosphate (IHP), bezafibrate (Bzf), and two recently synthesized derivatives of Bzf (LR16 and L35). Values of p50 change by over a factor of 60; the on-rates decrease by nearly a factor of 8, with little change in the off-rates for the liganded conformation. The data indicate that both allosteric and affinity parameters are changed by the effectors; the changes in ligand affinity represent the larger contribution toward shifts in p50

Fingering a Murderer: A Successful Anthropological and Radiological Collaboration

We illustrate an interdisciplinary approach to identify a victim in a case with complex taphonomic and procedural issues. Burning, fragmentation, species commingling, and examination by multiple experts required anthropological preparation and analysis combined with radio- graphic adaptations to image and match trabecular patterns in unusually small, burned specimens. A missing person was last seen in the company of a reclusive female on a remote rural property. A warranted search found several burn sites containing human and animal bones. Fragment prepara- tion, analysis, and development of a biological profile by anthropologists enabled examination by the odontologist, molecular biologist, and radiolo- gist, and justified use of antemortem radiographs from one potential victim. Visual and radiological comparison resulted in a positive (later confirmed) identification of the victim by radiological matches of three carpal phalanges. Although some dimensional changes are expected with burning, morphological details were preserved, aided by selection of relatively intact, small bones for comparison

Modelling of root reinforcement and erosion control by ‘Veronese’ poplar on pastoral hill country in New Zealand

Background The control of erosion processes is an important issue worldwide. In New Zealand, previous studies have shown the benefits of reforestation or bioengineering measures to control erosion. The impetus for this work focuses on linking recent research to the needs of practitioners by formulating quantitative guidelines for planning and evaluation of ground bioengineering stabilisation measures. Methods Two root distribution datasets of ‘Veronese’ poplar (Populus deltoides x nigra) were used to calibrate a root distribution model for application on single root systems and to interacting root systems at the hillslope scale. The root distribution model results were then used for slope stability calculations in order to quantitatively evaluate the mechanical stabilisation effects of spaced trees on pastoral hillslopes. Results This study shows that root distribution data are important inputs for quantifying root reinforcement at the hillslope scale, and that root distribution strongly depends on local environmental conditions and on the tree planting density. The results also show that the combination of soil mechanical properties (soil angle of internal friction and cohesion) and topographic conditions (slope inclination) are the major parameters to define how much root reinforcement is needed to stabilise a specific slope, and thus the spacing of the trees to achieve this. Conclusions For the worst scenarios, effective root reinforcement (>2 kPa) is reached for tree spacing ranging from 2500 stems per hectare (sph) for 0.1 m stem diameter at breast height (DBH) to 300 sph for 0.3 m stem DBH. In ideal growing conditions, tree spacing less than 100 sph is sufficient for stem DBH greater than 0.15 m. New quantitative information gained from this study can provide a basis for evaluating planting strategies using poplar trees for erosion control on pastoral hill country in New Zealand

Evaluation of Year 1 of the Academic Mentoring Programme: Impact Evaluation for Year 11. Evaluation Report: An exploration of impact in Year 11

The National Tutoring Programme (NTP) Academic Mentoring (AM) programme (2020/21) was designed to help disadvantaged pupils ‘catch up’ on missed learning by providing trained academic mentors to deliver one to one and small group tutoring in schools. This evaluation covers year 1 of the AM programme as delivered by Teach First from November 2020 to July 2021 (delivery was in three waves starting 26th October 2020, 15th January 2021 and 22nd February 2021). AM was one arm of the NTP. The NTP aimed to support teachers and schools in providing a sustained response to the Covid-19 pandemic and to provide a longer -term contribution to closing the attainment gap between disadvantaged pupils and their peers. The NTP was part of a wider government response to the pandemic, funded by the Department for Education (DfE) and was originally developed by the Education Endowment Foundation (EEF), Nesta, Impetus, The Sutton Trust, Teach First, and with the support of the KPMG Foundation. The DfE appointed Teach First to manage the provision of mentors (referred to as ‘academic mentors’) to schools; recruiting, training and placing them in schools. The mentor worked in the school setting as an employee of the school. It was expected that each academic mentor would work with at least 50 pupils between the date they started in school and the end of the academic year. Mentoring was provided online and/or face-to-face; and was one to one, or in groups of 2-4 pupils; and available in English/literacy, maths, science, humanities, and modern foreign languages. Mentoring was expected to be delivered in schools during normal teaching time, as well as before or after school. In certain circumstances, mentoring could be delivered online with pupil(s) at home. The AM programme was targeted at state-maintained primary and secondary schools serving disadvantaged populations. 89% of the schools met Teach First’s priority criteria, which is based on the proportion of children living in income deprived families (IDACI) and whether the school is in an area of chronic and persistent underperformance (AEA). The remaining 11% of schools had an above average proportion of pupils eligible for Pupil Premium (Teach First, 2021). Participating schools could decide which pupils received support from academic mentors. However, the programme encouraged them to select pupils from disadvantaged households or those whose education had been disproportionately impacted by Covid-19. Pupils in Years 1–11 were eligible (5–16 years old). The programme aimed to reach a minimum of 900 schools and 50,000 children, with 1,000 academic mentors. By the end of February 2021, it had surpassed targets having trained and placed 1,124 academic mentors in 946 schools and delivered mentoring sessions to 103,862 pupils, 49% of whom were identified by mentors as being eligible for Pupil Premium of Free School Meals (FSM), and 23% of whom were identified as having a special educational need or disability. The AM programme was initiated and delivered at a time of great pressure for schools when the education system had been disrupted by a series of school closures to most pupils and was contending with ongoing widespread pupil and staff absences. Covid-19 related issues disrupted the anticipated operation of academic mentoring during the year. The AM programme involved initial training and ongoing support from Teach First as intended but there was greater variation in schools’ deployment of mentors during the latter stages of the Autumn Term 2020/21, and during the January to March 2021 period of school closures to most pupils. This evaluation report presents the analysis of the impact of the AM programme on maths and English attainment outcomes for Year 11 pupils only—who represent a very small proportion of individuals targeted by the AM programme. Originally, it was planned to evaluate impact across all year groups (Years 1 – 11) at primary and secondary level using schools’ standardised assessment data from Renaissance Learning (RL) assessments and, in addition, to evaluate the impact for Year 6 pupils using Key Stage (KS) 2 data. However, these analyses could not go ahead as KS2 assessments were cancelled in summer 2021 (related to the ongoing Covid-19 pandemic) and because the number of schools providing agreement to use their RL data was insufficient to warrant impact analyses. Data was only available for pupils in Year 11. Since GCSEs could not go ahead as planned in 2021, the data was in the form of Teacher Assessed Grades (TAGs), which had not previously been used as an outcome measurement tool. Checks were therefore undertaken to explore if TAGs would be suitable as an outcome measure. The only analysis that could proceed was therefore exploratory. The evaluation uses a quasi-experimental design (QED), in which a group of secondary schools and Year 11 pupils who did not receive the AM programme were selected for comparison with schools and pupils who received the AM programme. Comparison schools were selected by matching schools that were similar in important, observable regards to the schools that participated in AM. The evaluation included analysis on the availability of AM for pupils who were eligible for Pupil Premium (a key focus of the overall NTP), and all pupils, as these groups could be identified for both the AM and non-AM schools. In addition, the evaluation aimed to analyse the impact on pupils who received AM by predicting their participation and identifying a comparison group of pupils with similar characteristics. Analysis was based on data about Year 11 pupils’ attainment and characteristics from the National Pupil Database (NPD) merged with data provided by Teach First about pupils’ participation in AM. In total, 159 AM schools (8,977 Year 11 pupils eligible for Pupil Premium) and an equal number of comparison schools (8,419 Year 11 pupils eligible for Pupil Premium) were included in the final analysis. The evaluation assessed impact in English and maths using Teacher Assessed Grades (TAGs) from 2021. Where appropriate, this impact evaluation refers to important implementation features from the implementation and process evaluation (IPE) conducted by Teach First themselves. However, there is no independent IPE data to draw on in the interpretation of the impact results. Of the Year 11 pupils selected for Academic Mentoring in this evaluation, 46% of them were eligible for Pupil Premium, however, despite this it is important to note that the number of Year 11 Pupil Premium-eligible pupils selected for AM in AM schools was small as a proportion of all Year 11 Pupil Premium-eligible pupils, and the number of these Year 11 Pupil Premium-eligible pupils receiving AM in maths and/or English (as opposed to other subjects), was smaller still. The same is the case when considering the whole year group of Year 11 pupils – the number receiving AM was small as a proportion of all Year 11 pupils. This means that in the analysis, the number of Year 11 pupils who actually received AM in maths and/or English was heavily ‘diluted’ by the number of pupils who did not. The primary impact findings must be therefore treated with a high degree of caution. The analysis was subject to very high dilution; a large proportion of the pupils eligible for Pupil Premium included in the analysis in AM schools were not selected for AM. This was due to limited programme reach and a tendency for teachers to allocate both non-Pupil Premium and Pupil Premium eligible pupils to the programme. This dilution means that, in order to detect an effect, either the effect would need to be very strong amongst the very small proportion of Year 11 pupils eligible for Pupil Premium who were selected for mentoring (and there was no indication that this was the case elsewhere in our analysis), and/or there would need to be strong spillover effects amongst the rest of the Year 11 pupils eligible for Pupil Premium. Although the programme Theory of Change includes such a mechanism, it is unlikely to be relevant at the dilution levels seen. With such high dilution, it is hard to detect whether AM had an effect on those who received mentoring in the analyses focusing on pupils eligible for Pupil Premium and on all pupils. It is not possible to conclude whether a lack of observed impact is due to the small proportion of disadvantaged pupils who received mentoring, or because AM did not work for those who received it. An additional challenge was that it was not possible to construct a comparison group of similar Year 11 pupils in nonAM to schools to those who received mentoring in AM schools, based on observable, pupil-level characteristics, and this impact analysis did not go ahead. Schools used information such as classroom assessments to select pupils into the programme that was not observable in the available datasets, suggesting that pupil-level selection was driven by unobserved dimensions. These constraints, both of very high dilution and not being able to identify a comparison group with similar pupil characteristics, mean that the evaluation is unable to conclude, with any certainty, whether or not AM had an impact on the English or mathematics attainment outcomes of those pupils who received it. The report must be considered in the light of these caveats. Year 11 pupils eligible for Pupil Premium in schools that received AM made, on average, similar progress in English compared to Year 11 pupils eligible for Pupil Premium in comparison schools (there was no evidence of an effect). In maths, Year 11 pupils eligible for Pupil Premium in schools that received AM made, on average, slightly more progress (equivalent to 1 months’ additional progress) compared to Year 11 pupils eligible for Pupil Premium in comparison schools. However, there is uncertainty around this result; it is also consistent with a null (0 months) effect or an effect of slightly larger than 1 month’s additional progress. A particular challenge in interpretation is that, on average, only 13% of Year 11 pupils eligible for Pupil Premium were selected for mentoring by schools, and only 4.2% of Year 11 pupils eligible for Pupil Premium were selected for mentoring in maths and 2.9% in English, meaning that the vast majority of pupils eligible for Pupil Premium included in the analysis did not receive mentoring. Therefore, this estimated impact of AM is severely diluted and it is unlikely any of these differences were due to AM. When looking at all Year 11 pupils, pupils in schools that received AM made, on average, similar progress in English and maths compared to all Year 11 pupils in comparison schools (there was no evidence of an effect). However, this finding was similarly subject to severe dilution: on average only 10% of Year 11 pupils in the analysed schools were selected for mentoring, with 3.4% in maths and 2.1% in English, and therefore it is hard to detect any effect that may (or may not) have been present. Within schools that offered AM to Year 11 pupils, there was no association between the number of completed mentoring sessions in maths and Year 11 outcomes in maths, or between the number of completed mentoring sessions in English and Year 11 outcomes in English. These results are associations and not necessarily causal

Chaotic maps and flows: Exact Riemann-Siegel lookalike for spectral fluctuations

To treat the spectral statistics of quantum maps and flows that are fully chaotic classically, we use the rigorous Riemann-Siegel lookalike available for the spectral determinant of unitary time evolution operators $F$. Concentrating on dynamics without time reversal invariance we get the exact two-point correlator of the spectral density for finite dimension $N$ of the matrix representative of $F$, as phenomenologically given by random matrix theory. In the limit $N\to\infty$ the correlator of the Gaussian unitary ensemble is recovered. Previously conjectured cancellations of contributions of pseudo-orbits with periods beyond half the Heisenberg time are shown to be implied by the Riemann-Siegel lookalike

Quantum Chaotic Dynamics and Random Polynomials

We investigate the distribution of roots of polynomials of high degree with random coefficients which, among others, appear naturally in the context of "quantum chaotic dynamics". It is shown that under quite general conditions their roots tend to concentrate near the unit circle in the complex plane. In order to further increase this tendency, we study in detail the particular case of self-inversive random polynomials and show that for them a finite portion of all roots lies exactly on the unit circle. Correlation functions of these roots are also computed analytically, and compared to the correlations of eigenvalues of random matrices. The problem of ergodicity of chaotic wave-functions is also considered. For that purpose we introduce a family of random polynomials whose roots spread uniformly over phase space. While these results are consistent with random matrix theory predictions, they provide a new and different insight into the problem of quantum ergodicity. Special attention is devoted all over the paper to the role of symmetries in the distribution of roots of random polynomials.Comment: 33 pages, Latex, 6 Figures not included (a copy of them can be requested at [email protected]); to appear in Journal of Statistical Physic

I2N: image to nutrients, a sensor guided semi-automated tool for annotation of images for nutrition analysis of eating episodes

INTRODUCTION: Dietary assessment is important for understanding nutritional status. Traditional methods of monitoring food intake through self-report such as diet diaries, 24-hour dietary recall, and food frequency questionnaires may be subject to errors and can be time-consuming for the user. METHODS: This paper presents a semi-automatic dietary assessment tool we developed - a desktop application called Image to Nutrients (I2N) - to process sensor-detected eating events and images captured during these eating events by a wearable sensor. I2N has the capacity to offer multiple food and nutrient databases (e.g., USDA-SR, FNDDS, USDA Global Branded Food Products Database) for annotating eating episodes and food items. I2N estimates energy intake, nutritional content, and the amount consumed. The components of I2N are three-fold: 1) sensor-guided image review, 2) annotation of food images for nutritional analysis, and 3) access to multiple food databases. Two studies were used to evaluate the feasibility and usefulness of I2N: 1) a US-based study with 30 participants and a total of 60 days of data and 2) a Ghana-based study with 41 participants and a total of 41 days of data). RESULTS: In both studies, a total of 314 eating episodes were annotated using at least three food databases. Using I2N's sensor-guided image review, the number of images that needed to be reviewed was reduced by 93% and 85% for the two studies, respectively, compared to reviewing all the images. DISCUSSION: I2N is a unique tool that allows for simultaneous viewing of food images, sensor-guided image review, and access to multiple databases in one tool, making nutritional analysis of food images efficient. The tool is flexible, allowing for nutritional analysis of images if sensor signals aren't available

Initiation of antidepressant medication and risk of incident stroke: using the Adult Changes in Thought cohort to address time-varying confounding

Purpose Depression strongly predicts stroke incidence, suggesting that treating depression may reduce stroke risk. Antidepressant medications, however, may increase stroke risk via direct pathways. Previous evidence on antidepressant medication and stroke incidence is mixed. We evaluated associations between antidepressant use and incident stroke. Methods For 2302 Adult Changes in Thought cohort participants with no stroke at study entry, we characterized antidepressant use from pharmacy records, biennial depressive symptoms with a 10-item Centers for Epidemiologic Study–Depression scale, and incident strokes from ICD codes. We used discrete-time survival models with inverse probability weighting to compare stroke risk associated with filling antidepressant prescriptions and by medication category: tricyclic antidepressants (TCAs), selective serotonin reuptake inhibitors, or other. Results Over an average 8.4-year follow-up, 441 incident strokes occurred. Filling antidepressant medications 3+ times versus 0–2 times predicted 35% increased odds of stroke (OR = 1.35; 95% CI: 0.98, 1.66). Use of TCAs was associated with stroke onset (OR per 10 fills = 1.28; CI: 1.04, 1.57), but use of selective serotonin reuptake inhibitors (OR = 0.98; CI: 0.80, 1.20) or other antidepressants (OR = 0.99; CI: 0.67, 1.45) was not. Conclusions Although patients who received antidepressant medication were at higher risk of stroke, this association appeared specific to TCA prescriptions