Accuracy and Stability of Computing High-Order Derivatives of Analytic Functions by Cauchy Integrals

High-order derivatives of analytic functions are expressible as Cauchy integrals over circular contours, which can very effectively be approximated, e.g., by trapezoidal sums. Whereas analytically each radius r up to the radius of convergence is equal, numerical stability strongly depends on r. We give a comprehensive study of this effect; in particular we show that there is a unique radius that minimizes the loss of accuracy caused by round-off errors. For large classes of functions, though not for all, this radius actually gives about full accuracy; a remarkable fact that we explain by the theory of Hardy spaces, by the Wiman-Valiron and Levin-Pfluger theory of entire functions, and by the saddle-point method of asymptotic analysis. Many examples and non-trivial applications are discussed in detail.Comment: Version 4 has some references and a discussion of other quadrature rules added; 57 pages, 7 figures, 6 tables; to appear in Found. Comput. Mat

Impact of weight management nutrition interventions on dietary outcomes in children and adolescents with overweight or obesity: A systematic review with meta-analysis

Background The impact of obesity interventions on dietary intake in children and adolescents with overweight or obesity is unclear. This systematic review aimed to investigate the impact of the dietary component of weight management interventions on the change in diet in children and adolescents with overweight or obesity. Methods Eligible RCTs published between 1975 and 2020 were identified by a systematic search following PRISMA guidelines. Meta-analyses of eligible study outcomes was performed using R statistical software. A multi-level random effects model was used with three significant random effects fitted using Restricted Maximum Likelihood estimation. Results This review identified 109 RCTs, including 95 that reported at least one statistically significant dietary outcome change, and 14 reporting no significant dietary change. Results from the meta-analyses (n= 29 studies) indicated that compared to control groups, intervention groups achieved significantly greater reductions in mean total energy intake at ≤6 months (-194kcal/day, 95%CI -275.80 to -112.90kcal/day, p<0.001) and up to 12 months (-112k cal/ day 95% CI -218.92 to -5.83kcal/ day)p=0.038), increases in fruit and/or vegetable intakes over 2-12 months (n=34, range +0.6 to +1.5 servings/day) and reductions in consumption of sugar-sweetened beverages (n=28, range -0.25 to -1.5 servings/day) at 4-24 months follow-up. Conclusions Obesity interventions with a dietary component have a modest, but sustained impact on reducing total energy intake and improving intakes of specific food groups in children and adolescents with overweight or obesity. High quality RCTs that are powered to detect change in diet as a primary outcome are warranted

Observing the First Stars and Black Holes

The high sensitivity of JWST will open a new window on the end of the cosmological dark ages. Small stellar clusters, with a stellar mass of several 10^6 M_sun, and low-mass black holes (BHs), with a mass of several 10^5 M_sun should be directly detectable out to redshift z=10, and individual supernovae (SNe) and gamma ray burst (GRB) afterglows are bright enough to be visible beyond this redshift. Dense primordial gas, in the process of collapsing from large scales to form protogalaxies, may also be possible to image through diffuse recombination line emission, possibly even before stars or BHs are formed. In this article, I discuss the key physical processes that are expected to have determined the sizes of the first star-clusters and black holes, and the prospect of studying these objects by direct detections with JWST and with other instruments. The direct light emitted by the very first stellar clusters and intermediate-mass black holes at z>10 will likely fall below JWST's detection threshold. However, JWST could reveal a decline at the faint-end of the high-redshift luminosity function, and thereby shed light on radiative and other feedback effects that operate at these early epochs. JWST will also have the sensitivity to detect individual SNe from beyond z=10. In a dedicated survey lasting for several weeks, thousands of SNe could be detected at z>6, with a redshift distribution extending to the formation of the very first stars at z>15. Using these SNe as tracers may be the only method to map out the earliest stages of the cosmic star-formation history. Finally, we point out that studying the earliest objects at high redshift will also offer a new window on the primordial power spectrum, on 100 times smaller scales than probed by current large-scale structure data.Comment: Invited contribution to "Astrophysics in the Next Decade: JWST and Concurrent Facilities", Astrophysics & Space Science Library, Eds. H. Thronson, A. Tielens, M. Stiavelli, Springer: Dordrecht (2008

Eating disorders in weight-related therapy (EDIT): Protocol for a systematic review with individual participant data meta-analysis of eating disorder risk in behavioural weight management

The Eating Disorders In weight-related Therapy (EDIT) Collaboration brings together data from randomised controlled trials of behavioural weight management interventions to identify individual participant risk factors and intervention strategies that contribute to eating disorder risk. We present a protocol for a systematic review and individual participant data (IPD) meta-analysis which aims to identify participants at risk of developing eating disorders, or related symptoms, during or after weight management interventions conducted in adolescents or adults with overweight or obesity. We systematically searched four databases up to March 2022 and clinical trials registries to May 2022 to identify randomised controlled trials of weight management interventions conducted in adolescents or adults with overweight or obesity that measured eating disorder risk at pre- and post-intervention or follow-up. Authors from eligible trials have been invited to share their deidentified IPD. Two IPD meta-analyses will be conducted. The first IPD meta-analysis aims to examine participant level factors associated with a change in eating disorder scores during and following a weight management intervention. To do this we will examine baseline variables that predict change in eating disorder risk within intervention arms. The second IPD meta-analysis aims to assess whether there are participant level factors that predict whether participation in an intervention is more or less likely than no intervention to lead to a change in eating disorder risk. To do this, we will examine if there are differences in predictors of eating disorder risk between intervention and no-treatment control arms. The primary outcome will be a standardised mean difference in global eating disorder score from baseline to immediately post-intervention and at 6- and 12- months follow-up. Identifying participant level risk factors predicting eating disorder risk will inform screening and monitoring protocols to allow early identification and intervention for those at risk

Tracking early lung cancer metastatic dissemination in TRACERx using ctDNA

Circulating tumour DNA (ctDNA) can be used to detect and profile residual tumour cells persisting after curative intent therapy1. The study of large patient cohorts incorporating longitudinal plasma sampling and extended follow-up is required to determine the role of ctDNA as a phylogenetic biomarker of relapse in early-stage non-small-cell lung cancer (NSCLC). Here we developed ctDNA methods tracking a median of 200 mutations identified in resected NSCLC tissue across 1,069 plasma samples collected from 197 patients enrolled in the TRACERx study2. A lack of preoperative ctDNA detection distinguished biologically indolent lung adenocarcinoma with good clinical outcome. Postoperative plasma analyses were interpreted within the context of standard-of-care radiological surveillance and administration of cytotoxic adjuvant therapy. Landmark analyses of plasma samples collected within 120 days after surgery revealed ctDNA detection in 25% of patients, including 49% of all patients who experienced clinical relapse; 3 to 6 monthly ctDNA surveillance identified impending disease relapse in an additional 20% of landmark-negative patients. We developed a bioinformatic tool (ECLIPSE) for non-invasive tracking of subclonal architecture at low ctDNA levels. ECLIPSE identified patients with polyclonal metastatic dissemination, which was associated with a poor clinical outcome. By measuring subclone cancer cell fractions in preoperative plasma, we found that subclones seeding future metastases were significantly more expanded compared with non-metastatic subclones. Our findings will support (neo)adjuvant trial advances and provide insights into the process of metastatic dissemination using low-ctDNA-level liquid biopsy

Repositioning of the global epicentre of non-optimal cholesterol

High blood cholesterol is typically considered a feature of wealthy western countries1,2. However, dietary and behavioural determinants of blood cholesterol are changing rapidly throughout the world3 and countries are using lipid-lowering medications at varying rates. These changes can have distinct effects on the levels of high-density lipoprotein (HDL) cholesterol and non-HDL cholesterol, which have different effects on human health4,5. However, the trends of HDL and non-HDL cholesterol levels over time have not been previously reported in a global analysis. Here we pooled 1,127 population-based studies that measured blood lipids in 102.6 million individuals aged 18 years and older to estimate trends from 1980 to 2018 in mean total, non-HDL and HDL cholesterol levels for 200 countries. Globally, there was little change in total or non-HDL cholesterol from 1980 to 2018. This was a net effect of increases in low- and middle-income countries, especially in east and southeast Asia, and decreases in high-income western countries, especially those in northwestern Europe, and in central and eastern Europe. As a result, countries with the highest level of non-HDL cholesterol—which is a marker of cardiovascular risk—changed from those in western Europe such as Belgium, Finland, Greenland, Iceland, Norway, Sweden, Switzerland and Malta in 1980 to those in Asia and the Pacific, such as Tokelau, Malaysia, The Philippines and Thailand. In 2017, high non-HDL cholesterol was responsible for an estimated 3.9 million (95% credible interval 3.7 million–4.2 million) worldwide deaths, half of which occurred in east, southeast and south Asia. The global repositioning of lipid-related risk, with non-optimal cholesterol shifting from a distinct feature of high-income countries in northwestern Europe, north America and Australasia to one that affects countries in east and southeast Asia and Oceania should motivate the use of population-based policies and personal interventions to improve nutrition and enhance access to treatment throughout the world.</p

Rising rural body-mass index is the main driver of the global obesity epidemic in adults

Body-mass index (BMI) has increased steadily in most countries in parallel with a rise in the proportion of the population who live in cities 1,2 . This has led to a widely reported view that urbanization is one of the most important drivers of the global rise in obesity 3�6 . Here we use 2,009 population-based studies, with measurements of height and weight in more than 112 million adults, to report national, regional and global trends in mean BMI segregated by place of residence (a rural or urban area) from 1985 to 2017. We show that, contrary to the dominant paradigm, more than 55 of the global rise in mean BMI from 1985 to 2017�and more than 80 in some low- and middle-income regions�was due to increases in BMI in rural areas. This large contribution stems from the fact that, with the exception of women in sub-Saharan Africa, BMI is increasing at the same rate or faster in rural areas than in cities in low- and middle-income regions. These trends have in turn resulted in a closing�and in some countries reversal�of the gap in BMI between urban and rural areas in low- and middle-income countries, especially for women. In high-income and industrialized countries, we noted a persistently higher rural BMI, especially for women. There is an urgent need for an integrated approach to rural nutrition that enhances financial and physical access to healthy foods, to avoid replacing the rural undernutrition disadvantage in poor countries with a more general malnutrition disadvantage that entails excessive consumption of low-quality calories. © 2019, The Author(s)