MM Algorithms for Geometric and Signomial Programming

This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates.Comment: 16 pages, 1 figur

Theoretical size distribution of fossil taxa: analysis of a null model

BACKGROUND: This article deals with the theoretical size distribution (of number of sub-taxa) of a fossil taxon arising from a simple null model of macroevolution. MODEL: New species arise through speciations occurring independently and at random at a fixed probability rate, while extinctions either occur independently and at random (background extinctions) or cataclysmically. In addition new genera are assumed to arise through speciations of a very radical nature, again assumed to occur independently and at random at a fixed probability rate. CONCLUSION: The size distributions of the pioneering genus (following a cataclysm) and of derived genera are determined. Also the distribution of the number of genera is considered along with a comparison of the probability of a monospecific genus with that of a monogeneric family

The incidence of all stroke and stroke subtype in the United Kingdom, 1985 to 2008: a systematic review

<p>Abstract</p> <p>Background</p> <p>There is considerable geographic variation in stroke mortality around the United Kingdom (UK). Whether this is due to geographical differences in incidence or case-fatality is unclear. We conducted a systematic review of high-quality studies documenting the incidence of any stroke and stroke subtypes, between 1985 and 2008 in the UK. We aimed to study geographic and temporal trends in relation to equivalent mortality trends.</p> <p>Methods</p> <p>MEDLINE and EMBASE were searched, reference lists inspected and authors of included papers were contacted. All rates were standardised to the European Standard Population for those over 45, and between 45 and 74 years. Stroke mortality rates for the included areas were then calculated to produce rate ratios of stroke mortality to incidence for each location.</p> <p>Results</p> <p>Five papers were included in this review. Geographic variation was narrow but incidence appeared to largely mirror mortality rates for all stroke. For men over 45, incidence (and confidence intervals) per 100,000 ranged from 124 (109-141) in South London, to 185 (164-208) in Scotland. For men, premature (45-74 years) stroke incidence per 100,000 ranged from 79 (67-94) in the North West, to 112 (95-132) in Scotland. Stroke subtype data was more geographically restricted, but did suggest there is no sizeable variation in incidence by subtype around the country. Only one paper, based in South London, had data on temporal trends. This showed that there has been a decline in stroke incidence since the mid 1990 s. This could not be compared to any other locations in this review.</p> <p>Conclusions</p> <p>Geographic variations in stroke incidence appear to mirror variations in mortality rates. This suggests policies to reduce inequalities in stroke mortality should be directed at risk factor profiles rather than treatment after a first incident event. More high quality stroke incidence data from around the UK are needed before this can be confirmed.</p

The Persisting Burden of Intracerebral Haemorrhage: Can Effective Treatments Be Found?

Colin Josephson, Rustam Al-Shahi Salman, and colleagues discuss the effectiveness of treatments for intracerebral haemorrhage

European research priorities for intracerebral haemorrhage

Over 2 million people are affected by intracerebral haemorrhage (ICH) worldwide every year, one third of them dying within 1 month, and many survivors being left with permanent disability. Unlike most other stroke types, the incidence, morbidity and mortality of ICH have not declined over time. No standardised diagnostic workup for the detection of the various underlying causes of ICH currently exists, and the evidence for medical or surgical therapeutic interventions remains limited. A dedicated European research programme for ICH is needed to identify ways to reduce the burden of ICH-related death and disability. The European Research Network on Intracerebral Haemorrhage EURONICH is a multidisciplinary academic research collaboration that has been established to define current research priorities and to conduct large clinical studies on all aspects of ICH. Copyright (C) 2011 S. Karger AG, Base

Stable Isotope Biogeochemistry of Seabird Guano Fertilization: Results from Growth Chamber Studies with Maize (Zea Mays)

Stable isotope analysis is being utilized with increasing regularity to examine a wide range of issues (diet, habitat use, migration) in ecology, geology, archaeology, and related disciplines. A crucial component to these studies is a thorough understanding of the range and causes of baseline isotopic variation, which is relatively poorly understood for nitrogen (δ(15)N). Animal excrement is known to impact plant δ(15)N values, but the effects of seabird guano have not been systematically studied from an agricultural or horticultural standpoint.This paper presents isotopic (δ(13)C and δ(15)N) and vital data for maize (Zea mays) fertilized with Peruvian seabird guano under controlled conditions. The level of (15)N enrichment in fertilized plants is very large, with δ(15)N values ranging between 25.5 and 44.7‰ depending on the tissue and amount of fertilizer applied; comparatively, control plant δ(15)N values ranged between -0.3 and 5.7‰. Intraplant and temporal variability in δ(15)N values were large, particularly for the guano-fertilized plants, which can be attributed to changes in the availability of guano-derived N over time, and the reliance of stored vs. absorbed N. Plant δ(13)C values were not significantly impacted by guano fertilization. High concentrations of seabird guano inhibited maize germination and maize growth. Moreover, high levels of seabird guano greatly impacted the N metabolism of the plants, resulting in significantly higher tissue N content, particularly in the stalk.The results presented in this study demonstrate the very large impact of seabird guano on maize δ(15)N values. The use of seabird guano as a fertilizer can thus be traced using stable isotope analysis in food chemistry applications (certification of organic inputs). Furthermore, the fertilization of maize with seabird guano creates an isotopic signature very similar to a high-trophic level marine resource, which must be considered when interpreting isotopic data from archaeological material

Global, regional, and national burden of neurological disorders during 1990-2015: a systematic analysis for the Global Burden of Disease Study 2015

Background Comparable data on the global and country-specific burden of neurological disorders and their trends are crucial for health-care planning and resource allocation. The Global Burden of Diseases, Injuries, and Risk Factors (GBD) Study provides such information but does not routinely aggregate results that are of interest to clinicians specialising in neurological conditions. In this systematic analysis, we quantified the global disease burden due to neurological disorders in 2015 and its relationship with country development level. Methods We estimated global and country-specific prevalence, mortality, disability-adjusted life-years (DALYs), years of life lost (YLLs), and years lived with disability (YLDs) for various neurological disorders that in the GBD classification have been previously spread across multiple disease groupings. The more inclusive grouping of neurological disorders included stroke, meningitis, encephalitis, tetanus, Alzheimer's disease and other dementias, Parkinson's disease, epilepsy, multiple sclerosis, motor neuron disease, migraine, tension-type headache, medication overuse headache, brain and nervous system cancers, and a residual category of other neurological disorders. We also analysed results based on the Socio-demographic Index (SDI), a compound measure of income per capita, education, and fertility, to identify patterns associated with development and how countries fare against expected outcomes relative to their level of development. Findings Neurological disorders ranked as the leading cause group of DALYs in 2015 (250·7 [95% uncertainty interval (UI) 229·1 to 274·7] million, comprising 10·2% of global DALYs) and the second-leading cause group of deaths (9·4 [9·1 to 9·7] million], comprising 16·8% of global deaths). The most prevalent neurological disorders were tension-type headache (1505·9 [UI 1337·3 to 1681·6 million cases]), migraine (958·8 [872·1 to 1055·6] million), medication overuse headache (58·5 [50·8 to 67·4 million]), and Alzheimer's disease and other dementias (46·0 [40·2 to 52·7 million]). Between 1990 and 2015, the number of deaths from neurological disorders increased by 36·7%, and the number of DALYs by 7·4%. These increases occurred despite decreases in age-standardised rates of death and DALYs of 26·1% and 29·7%, respectively; stroke and communicable neurological disorders were responsible for most of these decreases. Communicable neurological disorders were the largest cause of DALYs in countries with low SDI. Stroke rates were highest at middle levels of SDI and lowest at the highest SDI. Most of the changes in DALY rates of neurological disorders with development were driven by changes in YLLs. Interpretation Neurological disorders are an important cause of disability and death worldwide. Globally, the burden of neurological disorders has increased substantially over the past 25 years because of expanding population numbers and ageing, despite substantial decreases in mortality rates from stroke and communicable neurological disorders. The number of patients who will need care by clinicians with expertise in neurological conditions will continue to grow in coming decades. Policy makers and health-care providers should be aware of these trends to provide adequate services

Global age-sex-specific fertility, mortality, healthy life expectancy (HALE), and population estimates in 204 countries and territories, 1950-2019 : a comprehensive demographic analysis for the Global Burden of Disease Study 2019

Background Accurate and up-to-date assessment of demographic metrics is crucial for understanding a wide range of social, economic, and public health issues that affect populations worldwide. The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2019 produced updated and comprehensive demographic assessments of the key indicators of fertility, mortality, migration, and population for 204 countries and territories and selected subnational locations from 1950 to 2019. Methods 8078 country-years of vital registration and sample registration data, 938 surveys, 349 censuses, and 238 other sources were identified and used to estimate age-specific fertility. Spatiotemporal Gaussian process regression (ST-GPR) was used to generate age-specific fertility rates for 5-year age groups between ages 15 and 49 years. With extensions to age groups 10-14 and 50-54 years, the total fertility rate (TFR) was then aggregated using the estimated age-specific fertility between ages 10 and 54 years. 7417 sources were used for under-5 mortality estimation and 7355 for adult mortality. ST-GPR was used to synthesise data sources after correction for known biases. Adult mortality was measured as the probability of death between ages 15 and 60 years based on vital registration, sample registration, and sibling histories, and was also estimated using ST-GPR. HIV-free life tables were then estimated using estimates of under-5 and adult mortality rates using a relational model life table system created for GBD, which closely tracks observed age-specific mortality rates from complete vital registration when available. Independent estimates of HIV-specific mortality generated by an epidemiological analysis of HIV prevalence surveys and antenatal clinic serosurveillance and other sources were incorporated into the estimates in countries with large epidemics. Annual and single-year age estimates of net migration and population for each country and territory were generated using a Bayesian hierarchical cohort component model that analysed estimated age-specific fertility and mortality rates along with 1250 censuses and 747 population registry years. We classified location-years into seven categories on the basis of the natural rate of increase in population (calculated by subtracting the crude death rate from the crude birth rate) and the net migration rate. We computed healthy life expectancy (HALE) using years lived with disability (YLDs) per capita, life tables, and standard demographic methods. Uncertainty was propagated throughout the demographic estimation process, including fertility, mortality, and population, with 1000 draw-level estimates produced for each metric. Findings The global TFR decreased from 2.72 (95% uncertainty interval [UI] 2.66-2.79) in 2000 to 2.31 (2.17-2.46) in 2019. Global annual livebirths increased from 134.5 million (131.5-137.8) in 2000 to a peak of 139.6 million (133.0-146.9) in 2016. Global livebirths then declined to 135.3 million (127.2-144.1) in 2019. Of the 204 countries and territories included in this study, in 2019, 102 had a TFR lower than 2.1, which is considered a good approximation of replacement-level fertility. All countries in sub-Saharan Africa had TFRs above replacement level in 2019 and accounted for 27.1% (95% UI 26.4-27.8) of global livebirths. Global life expectancy at birth increased from 67.2 years (95% UI 66.8-67.6) in 2000 to 73.5 years (72.8-74.3) in 2019. The total number of deaths increased from 50.7 million (49.5-51.9) in 2000 to 56.5 million (53.7-59.2) in 2019. Under-5 deaths declined from 9.6 million (9.1-10.3) in 2000 to 5.0 million (4.3-6.0) in 2019. Global population increased by 25.7%, from 6.2 billion (6.0-6.3) in 2000 to 7.7 billion (7.5-8.0) in 2019. In 2019, 34 countries had negative natural rates of increase; in 17 of these, the population declined because immigration was not sufficient to counteract the negative rate of decline. Globally, HALE increased from 58.6 years (56.1-60.8) in 2000 to 63.5 years (60.8-66.1) in 2019. HALE increased in 202 of 204 countries and territories between 2000 and 2019. Interpretation Over the past 20 years, fertility rates have been dropping steadily and life expectancy has been increasing, with few exceptions. Much of this change follows historical patterns linking social and economic determinants, such as those captured by the GBD Socio-demographic Index, with demographic outcomes. More recently, several countries have experienced a combination of low fertility and stagnating improvement in mortality rates, pushing more populations into the late stages of the demographic transition. Tracking demographic change and the emergence of new patterns will be essential for global health monitoring. Copyright (C) 2020 The Author(s). Published by Elsevier Ltd.Peer reviewe

Mapping geographical inequalities in access to drinking water and sanitation facilities in low-income and middle-income countries, 2000-17

Background Universal access to safe drinking water and sanitation facilities is an essential human right, recognised in the Sustainable Development Goals as crucial for preventing disease and improving human wellbeing. Comprehensive, high-resolution estimates are important to inform progress towards achieving this goal. We aimed to produce high-resolution geospatial estimates of access to drinking water and sanitation facilities. Methods We used a Bayesian geostatistical model and data from 600 sources across more than 88 low-income and middle-income countries (LMICs) to estimate access to drinking water and sanitation facilities on continuous continent-wide surfaces from 2000 to 2017, and aggregated results to policy-relevant administrative units. We estimated mutually exclusive and collectively exhaustive subcategories of facilities for drinking water (piped water on or off premises, other improved facilities, unimproved, and surface water) and sanitation facilities (septic or sewer sanitation, other improved, unimproved, and open defecation) with use of ordinal regression. We also estimated the number of diarrhoeal deaths in children younger than 5 years attributed to unsafe facilities and estimated deaths that were averted by increased access to safe facilities in 2017, and analysed geographical inequality in access within LMICs. Findings Across LMICs, access to both piped water and improved water overall increased between 2000 and 2017, with progress varying spatially. For piped water, the safest water facility type, access increased from 40.0% (95% uncertainty interval [UI] 39.4-40.7) to 50.3% (50.0-50.5), but was lowest in sub-Saharan Africa, where access to piped water was mostly concentrated in urban centres. Access to both sewer or septic sanitation and improved sanitation overall also increased across all LMICs during the study period. For sewer or septic sanitation, access was 46.3% (95% UI 46.1-46.5) in 2017, compared with 28.7% (28.5-29.0) in 2000. Although some units improved access to the safest drinking water or sanitation facilities since 2000, a large absolute number of people continued to not have access in several units with high access to such facilities (>80%) in 2017. More than 253 000 people did not have access to sewer or septic sanitation facilities in the city of Harare, Zimbabwe, despite 88.6% (95% UI 87.2-89.7) access overall. Many units were able to transition from the least safe facilities in 2000 to safe facilities by 2017; for units in which populations primarily practised open defecation in 2000, 686 (95% UI 664-711) of the 1830 (1797-1863) units transitioned to the use of improved sanitation. Geographical disparities in access to improved water across units decreased in 76.1% (95% UI 71.6-80.7) of countries from 2000 to 2017, and in 53.9% (50.6-59.6) of countries for access to improved sanitation, but remained evident subnationally in most countries in 2017. Interpretation Our estimates, combined with geospatial trends in diarrhoeal burden, identify where efforts to increase access to safe drinking water and sanitation facilities are most needed. By highlighting areas with successful approaches or in need of targeted interventions, our estimates can enable precision public health to effectively progress towards universal access to safe water and sanitation. Copyright (C) 2020 The Author(s). Published by Elsevier Ltd.Peer reviewe