New lower bounds for ε-nets

Following groundbreaking work by Haussler and Welzl (1987), the use of small ε-nets has become a standard technique for solving algorithmic and extremal problems in geometry and learning theory. Two significant recent developments are: (i) an upper bound on the size of the smallest ε-nets for set systems, as a function of their so-called shallow-cell complexity (Chan, Grant, Könemann, and Sharpe); and (ii) the construction of a set system whose members can be obtained by intersecting a point set in double-struck R4 by a family of half-spaces such that the size of any ε-net for them is Ω(1/ε log 1/ε) (Pach and Tardos). The present paper completes both of these avenues of research. We (i) give a lower bound, matching the result of Chan et al., and (ii) generalize the construction of Pach and Tardos to half-spaces in double-struck Rd, for any d ≥ 4, to show that the general upper bound, O(d/ε log 1/ε), of Haussler and Welzl for the size of the smallest ε-nets is tight. © Andrey Kupavskii, Nabil H. Mustafa, and János Pach

Influence of Curing Temperature on Mechanical Properties of Woven Jute Reinforced Polyester Composite

The aim of this work is to evaluate the influence of curing temperature onto the mechanical properties of woven jute/polyester composite using warm compression moulding. 40 vol.% woven jute fibres were compressed moulded at a pressure of 2.0 MPa, holding time of 900s by varying the fabrication temperature in three levels which are 150°C, 170°C and 180 °C. The mechanical and thermal properties were characterized using flexural and impact testing, DSC and TGA.  Optimum mechanical properties are achieved at moulding temperature of 170°C. The flexural strength and flexural modulus at the optimised moulding temperature are 37.20 MPa and 0.84 GPa respectively, while their impact strength is 19.38 kJm-2. Morphological examination revealed that the composite failed in brittle manner and due to fibre pull-out indicating of weak interface

On the Discrete Unit Disk Cover Problem

Abstract. Given a set P of n points and a set D of m unit disks on a 2-dimensional plane, the discrete unit disk cover (DUDC) problem is (i) to check whether each point in P is covered by at least one disk in D or not and (ii) if so, then find a minimum cardinality subset D ∗ ⊆ D such that unit disks in D ∗ cover all the points in P. The discrete unit disk cover problem is a geometric version of the general set cover problem which is NP-hard [14]. The general set cover problem is not approx-imable within c log |P|, for some constant c, but the DUDC problem was shown to admit a constant factor approximation. In this paper, we pro-vide an algorithm with constant approximation factor 18. The running time of the proposed algorithm is O(n log n+m logm+mn). The previ-ous best known tractable solution for the same problem was a 22-factor approximation algorithm with running time O(m2n4).

Quantifying risks and interventions that have affected the burden of diarrhoea among children younger than 5 years : an analysis of the Global Burden of Disease Study 2017

Background Many countries have shown marked declines in diarrhoea! disease mortality among children younger than 5 years. With this analysis, we provide updated results on diarrhoeal disease mortality among children younger than 5 years from the Global Burden of Diseases, Injuries, and Risk Factors Study 2017 (GBD 2017) and use the study's comparative risk assessment to quantify trends and effects of risk factors, interventions, and broader sociodemographic development on mortality changes in 195 countries and territories from 1990 to 2017. Methods This analysis for GBD 2017 had three main components. Diarrhoea mortality was modelled using vital registration data, demographic surveillance data, and verbal autopsy data in a predictive, Bayesian, ensemble modelling tool; and the attribution of risk factors and interventions for diarrhoea were modelled in a counterfactual framework that combines modelled population-level prevalence of the exposure to each risk or intervention with the relative risk of diarrhoea given exposure to that factor. We assessed the relative and absolute change in diarrhoea mortality rate between 1990 and 2017, and used the change in risk factor exposure and sociodemographic status to explain differences in the trends of diarrhoea mortality among children younger than 5 years. Findings Diarrhoea was responsible for an estimated 533 768 deaths (95% uncertainty interval 477 162-593 145) among children younger than 5 years globally in 2017, a rate of 78.4 deaths (70.1-87.1) per 100 000 children. The diarrhoea mortality rate ranged between countries by over 685 deaths per 100 000 children. Diarrhoea mortality per 100 000 globally decreased by 69.6% (63.1-74.6) between 1990 and 2017. Among the risk factors considered in this study, those responsible for the largest declines in the diarrhoea mortality rate were reduction in exposure to unsafe sanitation (13.3% decrease, 11.2-15.5), childhood wasting (9.9% decrease, 9.6-10.2), and low use of oral rehydration solution (6.9% decrease, 4-8-8-4). Interpretation Diarrhoea mortality has declined substantially since 1990, although there are variations by country. Improvements in sociodemographic indicators might explain some of these trends, but changes in exposure to risk factors-particularly unsafe sanitation, childhood growth failure, and low use of oral rehydration solution-appear to be related to the relative and absolute rates of decline in diarrhoea mortality. Although the most effective interventions might vary by country or region, identifying and scaling up the interventions aimed at preventing and protecting against diarrhoea that have already reduced diarrhoea mortality could further avert many thousands of deaths due to this illness

Anemia prevalence in women of reproductive age in low- and middle-income countries between 2000 and 2018

Anemia is a globally widespread condition in women and is associated with reduced economic productivity and increased mortality worldwide. Here we map annual 2000–2018 geospatial estimates of anemia prevalence in women of reproductive age (15–49 years) across 82 low- and middle-income countries (LMICs), stratify anemia by severity and aggregate results to policy-relevant administrative and national levels. Additionally, we provide subnational disparity analyses to provide a comprehensive overview of anemia prevalence inequalities within these countries and predict progress toward the World Health Organization’s Global Nutrition Target (WHO GNT) to reduce anemia by half by 2030. Our results demonstrate widespread moderate improvements in overall anemia prevalence but identify only three LMICs with a high probability of achieving the WHO GNT by 2030 at a national scale, and no LMIC is expected to achieve the target in all their subnational administrative units. Our maps show where large within-country disparities occur, as well as areas likely to fall short of the WHO GNT, offering precision public health tools so that adequate resource allocation and subsequent interventions can be targeted to the most vulnerable populations.Peer reviewe

Mapping local patterns of childhood overweight and wasting in low- and middle-income countries between 2000 and 2017

A double burden of malnutrition occurs when individuals, household members or communities experience both undernutrition and overweight. Here, we show geospatial estimates of overweight and wasting prevalence among children under 5 years of age in 105 low- and middle-income countries (LMICs) from 2000 to 2017 and aggregate these to policy-relevant administrative units. Wasting decreased overall across LMICs between 2000 and 2017, from 8.4 (62.3 (55.1�70.8) million) to 6.4 (58.3 (47.6�70.7) million), but is predicted to remain above the World Health Organization�s Global Nutrition Target of <5 in over half of LMICs by 2025. Prevalence of overweight increased from 5.2 (30 (22.8�38.5) million) in 2000 to 6.0 (55.5 (44.8�67.9) million) children aged under 5 years in 2017. Areas most affected by double burden of malnutrition were located in Indonesia, Thailand, southeastern China, Botswana, Cameroon and central Nigeria. Our estimates provide a new perspective to researchers, policy makers and public health agencies in their efforts to address this global childhood syndemic. © 2020, The Author(s)

Global, regional, and national age-sex-specific mortality and life expectancy, 1950–2017: a systematic analysis for the Global Burden of Disease Study 2017

BACKGROUND: Assessments of age-specific mortality and life expectancy have been done by the UN Population Division, Department of Economics and Social Affairs (UNPOP), the United States Census Bureau, WHO, and as part of previous iterations of the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD). Previous iterations of the GBD used population estimates from UNPOP, which were not derived in a way that was internally consistent with the estimates of the numbers of deaths in the GBD. The present iteration of the GBD, GBD 2017, improves on previous assessments and provides timely estimates of the mortality experience of populations globally. METHODS: The GBD uses all available data to produce estimates of mortality rates between 1950 and 2017 for 23 age groups, both sexes, and 918 locations, including 195 countries and territories and subnational locations for 16 countries. Data used include vital registration systems, sample registration systems, household surveys (complete birth histories, summary birth histories, sibling histories), censuses (summary birth histories, household deaths), and Demographic Surveillance Sites. In total, this analysis used 8259 data sources. Estimates of the probability of death between birth and the age of 5 years and between ages 15 and 60 years are generated and then input into a model life table system to produce complete life tables for all locations and years. Fatal discontinuities and mortality due to HIV/AIDS are analysed separately and then incorporated into the estimation. We analyse the relationship between age-specific mortality and development status using the Socio-demographic Index, a composite measure based on fertility under the age of 25 years, education, and income. There are four main methodological improvements in GBD 2017 compared with GBD 2016: 622 additional data sources have been incorporated; new estimates of population, generated by the GBD study, are used; statistical methods used in different components of the analysis have been further standardised and improved; and the analysis has been extended backwards in time by two decades to start in 1950. FINDINGS: Globally, 18·7% (95% uncertainty interval 18·4–19·0) of deaths were registered in 1950 and that proportion has been steadily increasing since, with 58·8% (58·2–59·3) of all deaths being registered in 2015. At the global level, between 1950 and 2017, life expectancy increased from 48·1 years (46·5–49·6) to 70·5 years (70·1–70·8) for men and from 52·9 years (51·7–54·0) to 75·6 years (75·3–75·9) for women. Despite this overall progress, there remains substantial variation in life expectancy at birth in 2017, which ranges from 49·1 years (46·5–51·7) for men in the Central African Republic to 87·6 years (86·9–88·1) among women in Singapore. The greatest progress across age groups was for children younger than 5 years; under-5 mortality dropped from 216·0 deaths (196·3–238·1) per 1000 livebirths in 1950 to 38·9 deaths (35·6–42·83) per 1000 livebirths in 2017, with huge reductions across countries. Nevertheless, there were still 5·4 million (5·2–5·6) deaths among children younger than 5 years in the world in 2017. Progress has been less pronounced and more variable for adults, especially for adult males, who had stagnant or increasing mortality rates in several countries. The gap between male and female life expectancy between 1950 and 2017, while relatively stable at the global level, shows distinctive patterns across super-regions and has consistently been the largest in central Europe, eastern Europe, and central Asia, and smallest in south Asia. Performance was also variable across countries and time in observed mortality rates compared with those expected on the basis of development. INTERPRETATION: This analysis of age-sex-specific mortality shows that there are remarkably complex patterns in population mortality across countries. The findings of this study highlight global successes, such as the large decline in under-5 mortality, which reflects significant local, national, and global commitment and investment over several decades. However, they also bring attention to mortality patterns that are a cause for concern, particularly among adult men and, to a lesser extent, women, whose mortality rates have stagnated in many countries over the time period of this study, and in some cases are increasing

Global, regional, and national burden of suicide mortality 1990 to 2016: Systematic analysis for the Global Burden of Disease Study 2016

Objectives To use the estimates from the Global Burden of Disease Study 2016 to describe patterns of suicide mortality globally, regionally, and for 195 countries and territories by age, sex, and Socio-demographic index, and to describe temporal trends between 1990 and 2016. Design Systematic analysis. Main outcome measures Crude and age standardised rates from suicide mortality and years of life lost were compared across regions and countries, and by age, sex, and Socio-demographic index (a composite measure of fertility, income, and education). Results The total number of deaths from suicide increased by 6.7 (95 uncertainty interval 0.4 to 15.6) globally over the 27 year study period to 817 000 (762 000 to 884 000) deaths in 2016. However, the age standardised mortality rate for suicide decreased by 32.7 (27.2 to 36.6) worldwide between 1990 and 2016, similar to the decline in the global age standardised mortality rate of 30.6. Suicide was the leading cause of age standardised years of life lost in the Global Burden of Disease region of high income Asia Pacific and was among the top 10 leading causes in eastern Europe, central Europe, western Europe, central Asia, Australasia, southern Latin America, and high income North America. Rates for men were higher than for women across regions, countries, and age groups, except for the 15 to 19 age group. There was variation in the female to male ratio, with higher ratios at lower levels of Socio-demographic index. Women experienced greater decreases in mortality rates (49.0, 95 uncertainty interval 42.6 to 54.6) than men (23.8, 15.6 to 32.7). Conclusions Age standardised mortality rates for suicide have greatly reduced since 1990, but suicide remains an important contributor to mortality worldwide. Suicide mortality was variable across locations, between sexes, and between age groups. Suicide prevention strategies can be targeted towards vulnerable populations if they are informed by variations in mortality rates. © Published by the BMJ Publishing Group Limited

Author Correction: Mapping local patterns of childhood overweight and wasting in low- and middle-income countries between 2000 and 2017 (Nature Medicine, (2020), 26, 5, (750-759), 10.1038/s41591-020-0807-6)

An amendment to this paper has been published and can be accessed via a link at the top of the paper. © 2020, The Author(s)