On a Family of Sequences Related to Chebyshev Polynomials

We consider the appearance of primes in a family of linear recurrence sequences labelled by a positive integer n. The terms of each sequence correspond to a particular class of Lehmer numbers, or (viewing them as polynomials in n) dilated versions of the so-called Chebyshev polynomials of the fourth kind, also known as airfoil polynomials. We prove that when the value of n is given by a dilated Chebyshev polynomial of the first kind evaluated at a suitable integer, either the sequence contains a single prime, or no term is prime. For all other values of n, we conjecture that the sequence contains infinitely many primes, whose distribution has analogous properties to the distribution of Mersenne primes among the Mersenne numbers. Similar results are obtained for the sequences associated with negative integers n, which correspond to Chebyshev polynomials of the third kind, and to another family of Lehmer numbers

BoBBLE: ocean-atmosphere interaction and its impact on the South Asian monsoon

The Bay of Bengal (BoB) plays a fundamental role in controlling the weather systems that make up the South Asian summer monsoon system. In particular,the southern BoB has cooler sea surface temperature (SST) that influence ocean-atmosphere interaction and impact on the monsoon. Compared to the southeast, the southwestern BoB is cooler, more saline, receives much less rain, and is influenced by the Summer Monsoon Current(SMC). To examine the impact of these features on the monsoon, the BoB Boundary Layer Experiment (BoBBLE) was jointly undertaken by India and the UK during June–July 2016. Physical and bio-geochemical observations were made using a CTD, five ocean gliders, a uCTD, a VMP, two ADCPs, Argo floats, drifting buoys, meteorological sensors and upper air radiosonde balloons. The observations were made along a zonal section at 8◦N between 85.3◦E and 89◦E with a 10-day time series at 89◦E, 8◦N. This paper presents the new observed features of the southern BoB from the BoBBLE field program, supported by satellite data. Key results from the BoBBLE field campaign show the Sri Lanka Dome and the SMC in different stages of their seasonal evolution and two freshening events during which salinity decreased in the upper layer leading to the formation of thick barrier layers. BoBBLE observations were taken during a suppressed phase of the intraseasonal oscillation; they captured in detail the warming of the ocean mixed layer and preconditioning of the atmosphere to convection

Heliophysics and Amateur Radio:Citizen Science Collaborations for Atmospheric, Ionospheric, and Space Physics Research and Operations

The amateur radio community is a global, highly engaged, and technical community with an intense interest in space weather, its underlying physics, and how it impacts radio communications. The large-scale observational capabilities of distributed instrumentation fielded by amateur radio operators and radio science enthusiasts offers a tremendous opportunity to advance the fields of heliophysics, radio science, and space weather. Well-established amateur radio networks like the RBN, WSPRNet, and PSKReporter already provide rich, ever-growing, long-term data of bottomside ionospheric observations. Up-and-coming purpose-built citizen science networks, and their associated novel instruments, offer opportunities for citizen scientists, professional researchers, and industry to field networks for specific science questions and operational needs. Here, we discuss the scientific and technical capabilities of the global amateur radio community, review methods of collaboration between the amateur radio and professional scientific community, and review recent peer-reviewed studies that have made use of amateur radio data and methods. Finally, we present recommendations submitted to the U.S. National Academy of Science Decadal Survey for Solar and Space Physics (Heliophysics) 2024–2033 for using amateur radio to further advance heliophysics and for fostering deeper collaborations between the professional science and amateur radio communities. Technical recommendations include increasing support for distributed instrumentation fielded by amateur radio operators and citizen scientists, developing novel transmissions of RF signals that can be used in citizen science experiments, developing new amateur radio modes that simultaneously allow for communications and ionospheric sounding, and formally incorporating the amateur radio community and its observational assets into the Space Weather R2O2R framework. Collaborative recommendations include allocating resources for amateur radio citizen science research projects and activities, developing amateur radio research and educational activities in collaboration with leading organizations within the amateur radio community, facilitating communication and collegiality between professional researchers and amateurs, ensuring that proposed projects are of a mutual benefit to both the professional research and amateur radio communities, and working towards diverse, equitable, and inclusive communities

Latitude dictates plant diversity effects on instream decomposition

Running waters contribute substantially to global carbon fluxes through decomposition of terrestrial plant litter by aquatic microorganisms and detritivores. Diversity of this litter may influence instream decomposition globally in ways that are not yet understood. We investigated latitudinal differences in decomposition of litter mixtures of low and high functional diversity in 40 streams on 6 continents and spanning 113 degrees of latitude. Despite important variability in our dataset, we found latitudinal differences in the effect of litter functional diversity on decomposition, which we explained as evolutionary adaptations of litter-consuming detritivores to resource availability. Specifically, a balanced diet effect appears to operate at lower latitudes versus a resource concentration effect at higher latitudes. The latitudinal pattern indicates that loss of plant functional diversity will have different consequences on carbon fluxes across the globe, with greater repercussions likely at low latitudes

Photography-based taxonomy is inadequate, unnecessary, and potentially harmful for biological sciences

The question whether taxonomic descriptions naming new animal species without type specimen(s) deposited in collections should be accepted for publication by scientific journals and allowed by the Code has already been discussed in Zootaxa (Dubois & Nemésio 2007; Donegan 2008, 2009; Nemésio 2009a–b; Dubois 2009; Gentile & Snell 2009; Minelli 2009; Cianferoni & Bartolozzi 2016; Amorim et al. 2016). This question was again raised in a letter supported by 35 signatories published in the journal Nature (Pape et al. 2016) on 15 September 2016. On 25 September 2016, the following rebuttal (strictly limited to 300 words as per the editorial rules of Nature) was submitted to Nature, which on 18 October 2016 refused to publish it. As we think this problem is a very important one for zoological taxonomy, this text is published here exactly as submitted to Nature, followed by the list of the 493 taxonomists and collection-based researchers who signed it in the short time span from 20 September to 6 October 2016

Global, regional, and national incidence and mortality for HIV, tuberculosis, and malaria during 1990–2013: a systematic analysis for the Global Burden of Disease Study 2013

BACKGROUND: The Millennium Declaration in 2000 brought special global attention to HIV, tuberculosis, and malaria through the formulation of Millennium Development Goal (MDG) 6. The Global Burden of Disease 2013 study provides a consistent and comprehensive approach to disease estimation for between 1990 and 2013, and an opportunity to assess whether accelerated progress has occured since the Millennium Declaration. METHODS: To estimate incidence and mortality for HIV, we used the UNAIDS Spectrum model appropriately modified based on a systematic review of available studies of mortality with and without antiretroviral therapy (ART). For concentrated epidemics, we calibrated Spectrum models to fit vital registration data corrected for misclassification of HIV deaths. In generalised epidemics, we minimised a loss function to select epidemic curves most consistent with prevalence data and demographic data for all-cause mortality. We analysed counterfactual scenarios for HIV to assess years of life saved through prevention of mother-to-child transmission (PMTCT) and ART. For tuberculosis, we analysed vital registration and verbal autopsy data to estimate mortality using cause of death ensemble modelling. We analysed data for corrected case-notifications, expert opinions on the case-detection rate, prevalence surveys, and estimated cause-specific mortality using Bayesian meta-regression to generate consistent trends in all parameters. We analysed malaria mortality and incidence using an updated cause of death database, a systematic analysis of verbal autopsy validation studies for malaria, and recent studies (2010-13) of incidence, drug resistance, and coverage of insecticide-treated bednets. FINDINGS: Globally in 2013, there were 1·8 million new HIV infections (95% uncertainty interval 1·7 million to 2·1 million), 29·2 million prevalent HIV cases (28·1 to 31·7), and 1·3 million HIV deaths (1·3 to 1·5). At the peak of the epidemic in 2005, HIV caused 1·7 million deaths (1·6 million to 1·9 million). Concentrated epidemics in Latin America and eastern Europe are substantially smaller than previously estimated. Through interventions including PMTCT and ART, 19·1 million life-years (16·6 million to 21·5 million) have been saved, 70·3% (65·4 to 76·1) in developing countries. From 2000 to 2011, the ratio of development assistance for health for HIV to years of life saved through intervention was US$4498 in developing countries. Including in HIV-positive individuals, all-form tuberculosis incidence was 7·5 million (7·4 million to 7·7 million), prevalence was 11·9 million (11·6 million to 12·2 million), and number of deaths was 1·4 million (1·3 million to 1·5 million) in 2013. In the same year and in only individuals who were HIV-negative, all-form tuberculosis incidence was 7·1 million (6·9 million to 7·3 million), prevalence was 11·2 million (10·8 million to 11·6 million), and number of deaths was 1·3 million (1·2 million to 1·4 million). Annualised rates of change (ARC) for incidence, prevalence, and death became negative after 2000. Tuberculosis in HIV-negative individuals disproportionately occurs in men and boys (versus women and girls); 64·0% of cases (63·6 to 64·3) and 64·7% of deaths (60·8 to 70·3). Globally, malaria cases and deaths grew rapidly from 1990 reaching a peak of 232 million cases (143 million to 387 million) in 2003 and 1·2 million deaths (1·1 million to 1·4 million) in 2004. Since 2004, child deaths from malaria in sub-Saharan Africa have decreased by 31·5% (15·7 to 44·1). Outside of Africa, malaria mortality has been steadily decreasing since 1990. INTERPRETATION: Our estimates of the number of people living with HIV are 18·7% smaller than UNAIDS's estimates in 2012. The number of people living with malaria is larger than estimated by WHO. The number of people living with HIV, tuberculosis, or malaria have all decreased since 2000. At the global level, upward trends for malaria and HIV deaths have been reversed and declines in tuberculosis deaths have accelerated. 101 countries (74 of which are developing) still have increasing HIV incidence. Substantial progress since the Millennium Declaration is an encouraging sign of the effect of global action. FUNDING: Bill & Melinda Gates Foundation

Global, regional, and national under-5 mortality, adult mortality, age-specific mortality, and life expectancy, 1970–2016: a systematic analysis for the Global Burden of Disease Study 2016

BACKGROUND: Detailed assessments of mortality patterns, particularly age-specific mortality, represent a crucial input that enables health systems to target interventions to specific populations. Understanding how all-cause mortality has changed with respect to development status can identify exemplars for best practice. To accomplish this, the Global Burden of Diseases, Injuries, and Risk Factors Study 2016 (GBD 2016) estimated age-specific and sex-specific all-cause mortality between 1970 and 2016 for 195 countries and territories and at the subnational level for the five countries with a population greater than 200 million in 2016. METHODS: We have evaluated how well civil registration systems captured deaths using a set of demographic methods called death distribution methods for adults and from consideration of survey and census data for children younger than 5 years. We generated an overall assessment of completeness of registration of deaths by dividing registered deaths in each location-year by our estimate of all-age deaths generated from our overall estimation process. For 163 locations, including subnational units in countries with a population greater than 200 million with complete vital registration (VR) systems, our estimates were largely driven by the observed data, with corrections for small fluctuations in numbers and estimation for recent years where there were lags in data reporting (lags were variable by location, generally between 1 year and 6 years). For other locations, we took advantage of different data sources available to measure under-5 mortality rates (U5MR) using complete birth histories, summary birth histories, and incomplete VR with adjustments; we measured adult mortality rate (the probability of death in individuals aged 15-60 years) using adjusted incomplete VR, sibling histories, and household death recall. We used the U5MR and adult mortality rate, together with crude death rate due to HIV in the GBD model life table system, to estimate age-specific and sex-specific death rates for each location-year. Using various international databases, we identified fatal discontinuities, which we defined as increases in the death rate of more than one death per million, resulting from conflict and terrorism, natural disasters, major transport or technological accidents, and a subset of epidemic infectious diseases; these were added to estimates in the relevant years. In 47 countries with an identified peak adult prevalence for HIV/AIDS of more than 0·5% and where VR systems were less than 65% complete, we informed our estimates of age-sex-specific mortality using the Estimation and Projection Package (EPP)-Spectrum model fitted to national HIV/AIDS prevalence surveys and antenatal clinic serosurveillance systems. We estimated stillbirths, early neonatal, late neonatal, and childhood mortality using both survey and VR data in spatiotemporal Gaussian process regression models. We estimated abridged life tables for all location-years using age-specific death rates. We grouped locations into development quintiles based on the Socio-demographic Index (SDI) and analysed mortality trends by quintile. Using spline regression, we estimated the expected mortality rate for each age-sex group as a function of SDI. We identified countries with higher life expectancy than expected by comparing observed life expectancy to anticipated life expectancy on the basis of development status alone. FINDINGS: Completeness in the registration of deaths increased from 28% in 1970 to a peak of 45% in 2013; completeness was lower after 2013 because of lags in reporting. Total deaths in children younger than 5 years decreased from 1970 to 2016, and slower decreases occurred at ages 5-24 years. By contrast, numbers of adult deaths increased in each 5-year age bracket above the age of 25 years. The distribution of annualised rates of change in age-specific mortality rate differed over the period 2000 to 2016 compared with earlier decades: increasing annualised rates of change were less frequent, although rising annualised rates of change still occurred in some locations, particularly for adolescent and younger adult age groups. Rates of stillbirths and under-5 mortality both decreased globally from 1970. Evidence for global convergence of death rates was mixed; although the absolute difference between age-standardised death rates narrowed between countries at the lowest and highest levels of SDI, the ratio of these death rates-a measure of relative inequality-increased slightly. There was a strong shift between 1970 and 2016 toward higher life expectancy, most noticeably at higher levels of SDI. Among countries with populations greater than 1 million in 2016, life expectancy at birth was highest for women in Japan, at 86·9 years (95% UI 86·7-87·2), and for men in Singapore, at 81·3 years (78·8-83·7) in 2016. Male life expectancy was generally lower than female life expectancy between 1970 and 2016, an

Measuring performance on the Healthcare Access and Quality Index for 195 countries and territories and selected subnational locations: A systematic analysis from the Global Burden of Disease Study 2016

Background: A key component of achieving universal health coverage is ensuring that all populations have access to quality health care. Examining where gains have occurred or progress has faltered across and within countries is crucial to guiding decisions and strategies for future improvement. We used the Global Burden of Diseases, Injuries, and Risk Factors Study 2016 (GBD 2016) to assess personal health-care access and quality with the Healthcare Access and Quality (HAQ) Index for 195 countries and territories, as well as subnational locations in seven countries, from 1990 to 2016. Methods Drawing from established methods and updated estimates from GBD 2016, we used 32 causes from which death should not occur in the presence of effective care to approximate personal health-care access and quality by location and over time. To better isolate potential effects of personal health-care access and quality from underlying risk factor patterns, we risk-standardised cause-specific deaths due to non-cancers by location-year, replacing the local joint exposure of environmental and behavioural risks with the global level of exposure. Supported by the expansion of cancer registry data in GBD 2016, we used mortality-to-incidence ratios for cancers instead of risk-standardised death rates to provide a stronger signal of the effects of personal health care and access on cancer survival. We transformed each cause to a scale of 0-100, with 0 as the first percentile (worst) observed between 1990 and 2016, and 100 as the 99th percentile (best); we set these thresholds at the country level, and then applied them to subnational locations. We applied a principal components analysis to construct the HAQ Index using all scaled cause values, providing an overall score of 0-100 of personal health-care access and quality by location over time. We then compared HAQ Index levels and trends by quintiles on the Socio-demographic Index (SDI), a summary measure of overall development. As derived from the broader GBD study and other data sources, we examined relationships between national HAQ Index scores and potential correlates of performance, such as total health spending per capita. Findings In 2016, HAQ Index performance spanned from a high of 97\ub71 (95% UI 95\ub78-98\ub71) in Iceland, followed by 96\ub76 (94\ub79-97\ub79) in Norway and 96\ub71 (94\ub75-97\ub73) in the Netherlands, to values as low as 18\ub76 (13\ub71-24\ub74) in the Central African Republic, 19\ub70 (14\ub73-23\ub77) in Somalia, and 23\ub74 (20\ub72-26\ub78) in Guinea-Bissau. The pace of progress achieved between 1990 and 2016 varied, with markedly faster improvements occurring between 2000 and 2016 for many countries in sub-Saharan Africa and southeast Asia, whereas several countries in Latin America and elsewhere saw progress stagnate after experiencing considerable advances in the HAQ Index between 1990 and 2000. Striking subnational disparities emerged in personal health-care access and quality, with China and India having particularly large gaps between locations with the highest and lowest scores in 2016. In China, performance ranged from 91\ub75 (89\ub71-93\ub76) in Beijing to 48\ub70 (43\ub74-53\ub72) in Tibet (a 43\ub75-point difference), while India saw a 30\ub78-point disparity, from 64\ub78 (59\ub76-68\ub78) in Goa to 34\ub70 (30\ub73-38\ub71) in Assam. Japan recorded the smallest range in subnational HAQ performance in 2016 (a 4\ub78-point difference), whereas differences between subnational locations with the highest and lowest HAQ Index values were more than two times as high for the USA and three times as high for England. State-level gaps in the HAQ Index in Mexico somewhat narrowed from 1990 to 2016 (from a 20\ub79-point to 17\ub70-point difference), whereas in Brazil, disparities slightly increased across states during this time (a 17\ub72-point to 20\ub74-point difference). Performance on the HAQ Index showed strong linkages to overall development, with high and high-middle SDI countries generally having higher scores and faster gains for non-communicable diseases. Nonetheless, countries across the development spectrum saw substantial gains in some key health service areas from 2000 to 2016, most notably vaccine-preventable diseases. Overall, national performance on the HAQ Index was positively associated with higher levels of total health spending per capita, as well as health systems inputs, but these relationships were quite heterogeneous, particularly among low-to-middle SDI countries. Interpretation GBD 2016 provides a more detailed understanding of past success and current challenges in improving personal health-care access and quality worldwide. Despite substantial gains since 2000, many low-SDI and middle- SDI countries face considerable challenges unless heightened policy action and investments focus on advancing access to and quality of health care across key health services, especially non-communicable diseases. Stagnating or minimal improvements experienced by several low-middle to high-middle SDI countries could reflect the complexities of re-orienting both primary and secondary health-care services beyond the more limited foci of the Millennium Development Goals. Alongside initiatives to strengthen public health programmes, the pursuit of universal health coverage hinges upon improving both access and quality worldwide, and thus requires adopting a more comprehensive view-and subsequent provision-of quality health care for all populations

Measuring progress and projecting attainment on the basis of past trends of the health-related Sustainable Development Goals in 188 countries: an analysis from the Global Burden of Disease Study 2016

The UN’s Sustainable Development Goals (SDGs) are grounded in the global ambition of “leaving no one behind”. Understanding today’s gains and gaps for the health-related SDGs is essential for decision makers as they aim to improve the health of populations. As part of the Global Burden of Diseases, Injuries, and Risk Factors Study 2016 (GBD 2016), we measured 37 of the 50 health-related SDG indicators over the period 1990–2016 for 188 countries, and then on the basis of these past trends, we projected indicators to 2030