A second eigenvalue bound for the Dirichlet Schroedinger operator

Let $\lambda_i(\Omega,V)$ be the $i$th eigenvalue of the Schr\"odinger operator with Dirichlet boundary conditions on a bounded domain $\Omega \subset \R^n$ and with the positive potential $V$. Following the spirit of the Payne-P\'olya-Weinberger conjecture and under some convexity assumptions on the spherically rearranged potential $V_\star$, we prove that $\lambda_2(\Omega,V) \le \lambda_2(S_1,V_\star)$. Here $S_1$ denotes the ball, centered at the origin, that satisfies the condition $\lambda_1(\Omega,V) = \lambda_1(S_1,V_\star)$. Further we prove under the same convexity assumptions on a spherically symmetric potential $V$, that $\lambda_2(B_R, V) / \lambda_1(B_R, V)$ decreases when the radius $R$ of the ball $B_R$ increases. We conclude with several results about the first two eigenvalues of the Laplace operator with respect to a measure of Gaussian or inverted Gaussian density

Synchronous diversification of Sulawesi's iconic artiodactyls driven by recent geological events

The high degree of endemism on Sulawesi has previously been suggested to have vicariant origins, dating back to 40 Ma. Recent studies, however, suggest that much of Sulawesi’s fauna assembled over the last 15 Myr. Here, we test the hypothesis that more recent uplift of previously submerged portions of land on Sulawesi promoted diversification and that much of its faunal assemblage is much younger than the island itself. To do so, we combined palaeogeographical reconstructionswithgenetic andmorphometric datasets derived from Sulawesi’s three largest mammals: the babirusa, anoa and Sulawesi warty pig. Our results indicate that although these species most likely colonized the area that is now Sulawesi at different times (14 Ma to 2-3 Ma), they experienced an almost synchronous expansion from the central part of the island. Geological reconstructions indicate that this area was above sea level for most of the last 4 Myr, unlike most parts of the island. We conclude that emergence of land on Sulawesi (approx. 1-2 Myr) may have allowed species to expand synchronously. Altogether, our results indicate that the establishment of the highly endemic faunal assemblage on Sulawesiwas driven by geological events over the last few million years

Meta-analysis of genome-wide association studies identifies common susceptibility polymorphisms for colorectal and endometrial cancer near SH2B3 and TSHZ1

High-risk mutations in several genes predispose to both colorectal cancer (CRC) and endometrial cancer (EC). We therefore hypothesised that some lower-risk genetic variants might also predispose to both CRC and EC. Using CRC and EC genome-wide association series, totalling 13,265 cancer cases and 40,245 controls, we found that the protective allele [G] at one previously-identified CRC polymorphism, rs2736100 near TERT, was associated with EC risk (odds ratio (OR) = 1.08, P = 0.000167); this polymorphism influences the risk of several other cancers. A further CRC polymorphism near TERC also showed evidence of association with EC (OR = 0.92; P = 0.03). Overall, however, there was no good evidence that the set of CRC polymorphisms was associated with EC risk, and neither of two previously-reported EC polymorphisms was associated with CRC risk. A combined analysis revealed one genome-wide significant polymorphism, rs3184504, on chromosome 12q24 (OR = 1.10, P = 7.23 × 10−9) with shared effects on CRC and EC risk. This polymorphism, a missense variant in the gene SH2B3, is also associated with haematological and autoimmune disorders, suggesting that it influences cancer risk through the immune response. Another polymorphism, rs12970291 near gene TSHZ1, was associated with both CRC and EC (OR = 1.26, P = 4.82 × 10−8), with the alleles showing opposite effects on the risks of the two cancers

Cotton in the new millennium: advances, economics, perceptions and problems

Cotton is the most significant natural fibre and has been a preferred choice of the textile industry and consumers since the industrial revolution began. The share of man-made fibres, both regenerated and synthetic fibres, has grown considerably in recent times but cotton production has also been on the rise and accounts for about half of the fibres used for apparel and textile goods. To cotton’s advantage, the premium attached to the presence of cotton fibre and the general positive consumer perception is well established, however, compared to commodity man-made fibres and high performance fibres, cotton has limitations in terms of its mechanical properties but can help to overcome moisture management issues that arise with performance apparel during active wear. This issue of Textile Progress aims to: i. Report on advances in cotton cultivation and processing as well as improvements to conventional cotton cultivation and ginning. The processing of cotton in the textile industry from fibre to finished fabric, cotton and its blends, and their applications in technical textiles are also covered. ii. Explore the economic impact of cotton in different parts of the world including an overview of global cotton trade. iii. Examine the environmental perception of cotton fibre and efforts in organic and genetically-modified (GM) cotton production. The topic of naturally-coloured cotton, post-consumer waste is covered and the environmental impacts of cotton cultivation and processing are discussed. Hazardous effects of cultivation, such as the extensive use of pesticides, insecticides and irrigation with fresh water, and consequences of the use of GM cotton and cotton fibres in general on the climate are summarised and the effects of cotton processing on workers are addressed. The potential hazards during cotton cultivation, processing and use are also included. iv. Examine how the properties of cotton textiles can be enhanced, for example, by improving wrinkle recovery and reducing the flammability of cotton fibre

Large-scale external validation and comparison of prognostic models: an application to chronic obstructive pulmonary disease

Background: External validations and comparisons of prognostic models or scores are a prerequisite for their use in routine clinical care but are lacking in most medical fields including chronic obstructive pulmonary disease (COPD). Our aim was to externally validate and concurrently compare prognostic scores for 3-year all-cause mortality in mostly multimorbid patients with COPD. Methods: We relied on 24 cohort studies of the COPD Cohorts Collaborative International Assessment consortium, corresponding to primary, secondary, and tertiary care in Europe, the Americas, and Japan. These studies include globally 15,762 patients with COPD (1871 deaths and 42,203 person years of follow-up). We used network meta-analysis adapted to multiple score comparison (MSC), following a frequentist two-stage approach; thus, we were able to compare all scores in a single analytical framework accounting for correlations among scores within cohorts. We assessed transitivity, heterogeneity, and inconsistency and provided a performance ranking of the prognostic scores. Results: Depending on data availability, between two and nine prognostic scores could be calculated for each cohort. The BODE score (body mass index, airflow obstruction, dyspnea, and exercise capacity) had a median area under the curve (AUC) of 0.679 [1st quartile-3rd quartile = 0.655-0.733] across cohorts. The ADO score (age, dyspnea, and airflow obstruction) showed the best performance for predicting mortality (difference AUC(ADO) - AUC(BODE) = 0.015 [95% confidence interval (CI) = - 0.002 to 0.032]; p = 0.08) followed by the updated BODE (AUCBODE updated - AUCBODE = 0.008 [95% CI = -0.005 to +0.022]; p = 0.23). The assumption of transitivity was not violated. Heterogeneity across direct comparisons was small, and we did not identify any local or global inconsistency. Conclusions: Our analyses showed best discriminatory performance for the ADO and updated BODE scores in patients with COPD. A limitation to be addressed in future studies is the extension of MSC network meta-analysis to measures of calibration. MSC network meta-analysis can be applied to prognostic scores in any medical field to identify the best scores, possibly paving the way for stratified medicine, public health, and research

Mapping subnational HIV mortality in six Latin American countries with incomplete vital registration systems

BackgroundHuman immunodeficiency virus (HIV) remains a public health priority in Latin America. While the burden of HIV is historically concentrated in urban areas and high-risk groups, subnational estimates that cover multiple countries and years are missing. This paucity is partially due to incomplete vital registration (VR) systems and statistical challenges related to estimating mortality rates in areas with low numbers of HIV deaths. In this analysis, we address this gap and provide novel estimates of the HIV mortality rate and the number of HIV deaths by age group, sex, and municipality in Brazil, Colombia, Costa Rica, Ecuador, Guatemala, and Mexico.MethodsWe performed an ecological study using VR data ranging from 2000 to 2017, dependent on individual country data availability. We modeled HIV mortality using a Bayesian spatially explicit mixed-effects regression model that incorporates prior information on VR completeness. We calibrated our results to the Global Burden of Disease Study 2017.ResultsAll countries displayed over a 40-fold difference in HIV mortality between municipalities with the highest and lowest age-standardized HIV mortality rate in the last year of study for men, and over a 20-fold difference for women. Despite decreases in national HIV mortality in all countries-apart from Ecuador-across the period of study, we found broad variation in relative changes in HIV mortality at the municipality level and increasing relative inequality over time in all countries. In all six countries included in this analysis, 50% or more HIV deaths were concentrated in fewer than 10% of municipalities in the latest year of study. In addition, national age patterns reflected shifts in mortality to older age groups-the median age group among decedents ranged from 30 to 45years of age at the municipality level in Brazil, Colombia, and Mexico in 2017.ConclusionsOur subnational estimates of HIV mortality revealed significant spatial variation and diverging local trends in HIV mortality over time and by age. This analysis provides a framework for incorporating data and uncertainty from incomplete VR systems and can help guide more geographically precise public health intervention to support HIV-related care and reduce HIV-related deaths.Peer reviewe

Mapping geographical inequalities in childhood diarrhoeal morbidity and mortality in low-income and middle-income countries, 2000–17 : analysis for the Global Burden of Disease Study 2017

Background Across low-income and middle-income countries (LMICs), one in ten deaths in children younger than 5 years is attributable to diarrhoea. The substantial between-country variation in both diarrhoea incidence and mortality is attributable to interventions that protect children, prevent infection, and treat disease. Identifying subnational regions with the highest burden and mapping associated risk factors can aid in reducing preventable childhood diarrhoea. Methods We used Bayesian model-based geostatistics and a geolocated dataset comprising 15 072 746 children younger than 5 years from 466 surveys in 94 LMICs, in combination with findings of the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2017, to estimate posterior distributions of diarrhoea prevalence, incidence, and mortality from 2000 to 2017. From these data, we estimated the burden of diarrhoea at varying subnational levels (termed units) by spatially aggregating draws, and we investigated the drivers of subnational patterns by creating aggregated risk factor estimates. Findings The greatest declines in diarrhoeal mortality were seen in south and southeast Asia and South America, where 54·0% (95% uncertainty interval [UI] 38·1–65·8), 17·4% (7·7–28·4), and 59·5% (34·2–86·9) of units, respectively, recorded decreases in deaths from diarrhoea greater than 10%. Although children in much of Africa remain at high risk of death due to diarrhoea, regions with the most deaths were outside Africa, with the highest mortality units located in Pakistan. Indonesia showed the greatest within-country geographical inequality; some regions had mortality rates nearly four times the average country rate. Reductions in mortality were correlated to improvements in water, sanitation, and hygiene (WASH) or reductions in child growth failure (CGF). Similarly, most high-risk areas had poor WASH, high CGF, or low oral rehydration therapy coverage. Interpretation By co-analysing geospatial trends in diarrhoeal burden and its key risk factors, we could assess candidate drivers of subnational death reduction. Further, by doing a counterfactual analysis of the remaining disease burden using key risk factors, we identified potential intervention strategies for vulnerable populations. In view of the demands for limited resources in LMICs, accurately quantifying the burden of diarrhoea and its drivers is important for precision public health

Mapping subnational HIV mortality in six Latin American countries with incomplete vital registration systems

Background: Human immunodeficiency virus (HIV) remains a public health priority in Latin America. While the burden of HIV is historically concentrated in urban areas and high-risk groups, subnational estimates that cover multiple countries and years are missing. This paucity is partially due to incomplete vital registration (VR) systems and statistical challenges related to estimating mortality rates in areas with low numbers of HIV deaths. In this analysis, we address this gap and provide novel estimates of the HIV mortality rate and the number of HIV deaths by age group, sex, and municipality in Brazil, Colombia, Costa Rica, Ecuador, Guatemala, and Mexico. Methods: We performed an ecological study using VR data ranging from 2000 to 2017, dependent on individual country data availability. We modeled HIV mortality using a Bayesian spatially explicit mixed-effects regression model that incorporates prior information on VR completeness. We calibrated our results to the Global Burden of Disease Study 2017. Results: All countries displayed over a 40-fold difference in HIV mortality between municipalities with the highest and lowest age-standardized HIV mortality rate in the last year of study for men, and over a 20-fold difference for women. Despite decreases in national HIV mortality in all countries�apart from Ecuador�across the period of study, we found broad variation in relative changes in HIV mortality at the municipality level and increasing relative inequality over time in all countries. In all six countries included in this analysis, 50 or more HIV deaths were concentrated in fewer than 10 of municipalities in the latest year of study. In addition, national age patterns reflected shifts in mortality to older age groups�the median age group among decedents ranged from 30 to 45 years of age at the municipality level in Brazil, Colombia, and Mexico in 2017. Conclusions: Our subnational estimates of HIV mortality revealed significant spatial variation and diverging local trends in HIV mortality over time and by age. This analysis provides a framework for incorporating data and uncertainty from incomplete VR systems and can help guide more geographically precise public health intervention to support HIV-related care and reduce HIV-related deaths