Hydrodynamical Neutron-star Kicks in Electron-capture Supernovae and Implications for the CRAB Supernova

Neutron stars (NSs) obtain kicks of typically several 100 km/s at birth. The gravitational tug-boat mechanism can explain these kicks as consequences of asymmetric mass ejection during the supernova (SN) explosion. Support for this hydrodynamic explanation is provided by observations of SN remnants with associated NSs, which confirm the prediction that the bulk of the explosion ejecta, in particular chemical elements between silicon and the iron group, are dominantly expelled in the hemisphere opposite to the direction of the NS kick. Here, we present a large set of two- and three-dimensional explosion simulations of electron-capture SNe, considering explosion energies between ~3x10^49 erg and ~1.6x10^50 erg. We find that the fast acceleration of the SN shock in the steep density gradient delimiting the O-Ne-Mg core of the progenitor enables such a rapid expansion of neutrino-heated matter that the growth of neutrino-driven convection freezes out quickly in a high-mode spherical harmonics pattern. Since the corresponding momentum asymmetry of the ejecta is very small and the gravitational acceleration by the fast-expanding ejecta abates rapidly, the NS kick velocities are at most a few km/s. The extremely low core compactness of O-Ne-Mg-core progenitors therefore favors hydrodynamic NS kicks much below the ~160 km/s measured for the Crab pulsar. This suggests either that the Crab Nebula is not the remnant of an electron-capture SN, but of a low-mass iron-core progenitor, or that the Crab pulsar was not accelerated by the gravitational tug-boat mechanism but received its kick by a non-hydrodynamic mechanism such as, e.g., anisotropic neutrino emission.Comment: 23 pages, 9 figures; revised version accounting for referee and reader comments; accepted by Ap

Integrals over Gaussians under Linear Domain Constraints

Integrals of linearly constrained multivariate Gaussian densities are a frequent problem in machine learning and statistics, arising in tasks like generalized linear models and Bayesian optimization. Yet they are notoriously hard to compute, and to further complicate matters, the numerical values of such integrals may be very small. We present an efficient black-box algorithm that exploits geometry for the estimation of integrals over a small, truncated Gaussian volume, and to simulate therefrom. Our algorithm uses the Holmes-Diaconis-Ross (HDR) method combined with an analytic version of elliptical slice sampling (ESS). Adapted to the linear setting, ESS allows for rejection-free sampling, because intersections of ellipses and domain boundaries have closed-form solutions. The key idea of HDR is to decompose the integral into easier-to-compute conditional probabilities by using a sequence of nested domains. Remarkably, it allows for direct computation of the logarithm of the integral value and thus enables the computation of extremely small probability masses. We demonstrate the effectiveness of our tailored combination of HDR and ESS on high-dimensional integrals and on entropy search for Bayesian optimization

Numerical Integration as and for Probabilistic Inference

Numerical integration or quadrature is one of the workhorses of modern scientific computing and a key operation to perform inference in intractable probabilistic models. The epistemic uncertainty about the true value of an analytically intractable integral identifies the integration task as an inference problem itself. Indeed, numerical integration can be cast as a probabilistic numerical method known as Bayesian quadrature (BQ). BQ leverages structural assumptions about the function to be integrated via properties encoded in the prior. A posterior belief over the unknown integral value emerges by conditioning the BQ model on an actively selected point set and corresponding function evaluations. Iterative updates to the Bayesian model turn BQ into an adaptive quadrature method that quantifies its uncertainty about the solution of the integral in a principled way. This thesis traces out the scope of probabilistic integration methods and highlights types of integration tasks that BQ excels at. These arise when sample efficiency is required and encodable prior knowledge about the integration problem of low to moderate dimensionality is at hand. The first contribution addresses transfer learning with BQ. It extends the notion of active learning schemes to cost-sensitive settings where cheap approximations to an expensive-to-evaluate integrand are available. The degeneracy of acquisition policies in simple BQ is lifted upon generalization to the multi-source, cost-sensitive setting. This motivates the formulation of a set of desirable properties for BQ acquisition functions. A second application considers integration tasks arising in statistical computations on Riemannian manifolds that have been learned from data. Unsupervised learning algorithms that respect the intrinsic geometry of the data rely on the repeated estimation of expensive and structured integrals. Our custom-made active BQ scheme outperforms conventional integration tools for Riemannian statistics. Despite their unarguable benefits, BQ schemes provide limited flexibility to construct suitable priors while keeping the inference step tractable. In a final contribution, we identify the ubiquitous integration problem of computing multivariate normal probabilities as a type of integration task that is structurally taxing for BQ. The instead proposed method is an elegant algorithm based on Markov chain Monte Carlo that permits both sampling from and estimating the normalization constant of linearly constrained Gaussians that contain an arbitrarily small probability mass. As a whole, this thesis contributes to the wider goal of advancing integration algorithms to satisfy the needs imposed by contemporary probabilistic machine learning applications

Global and national Burden of diseases and injuries among children and adolescents between 1990 and 2013

Importance The literature focuses on mortality among children younger than 5 years. Comparable information on nonfatal health outcomes among these children and the fatal and nonfatal burden of diseases and injuries among older children and adolescents is scarce. Objective To determine levels and trends in the fatal and nonfatal burden of diseases and injuries among younger children (aged <5 years), older children (aged 5-9 years), and adolescents (aged 10-19 years) between 1990 and 2013 in 188 countries from the Global Burden of Disease (GBD) 2013 study. Evidence Review Data from vital registration, verbal autopsy studies, maternal and child death surveillance, and other sources covering 14 244 site-years (ie, years of cause of death data by geography) from 1980 through 2013 were used to estimate cause-specific mortality. Data from 35 620 epidemiological sources were used to estimate the prevalence of the diseases and sequelae in the GBD 2013 study. Cause-specific mortality for most causes was estimated using the Cause of Death Ensemble Model strategy. For some infectious diseases (eg, HIV infection/AIDS, measles, hepatitis B) where the disease process is complex or the cause of death data were insufficient or unavailable, we used natural history models. For most nonfatal health outcomes, DisMod-MR 2.0, a Bayesian metaregression tool, was used to meta-analyze the epidemiological data to generate prevalence estimates. Findings Of the 7.7 (95% uncertainty interval [UI], 7.4-8.1) million deaths among children and adolescents globally in 2013, 6.28 million occurred among younger children, 0.48 million among older children, and 0.97 million among adolescents. In 2013, the leading causes of death were lower respiratory tract infections among younger children (905 059 deaths; 95% UI, 810 304-998 125), diarrheal diseases among older children (38 325 deaths; 95% UI, 30 365-47 678), and road injuries among adolescents (115 186 deaths; 95% UI, 105 185-124 870). Iron deficiency anemia was the leading cause of years lived with disability among children and adolescents, affecting 619 (95% UI, 618-621) million in 2013. Large between-country variations exist in mortality from leading causes among children and adolescents. Countries with rapid declines in all-cause mortality between 1990 and 2013 also experienced large declines in most leading causes of death, whereas countries with the slowest declines had stagnant or increasing trends in the leading causes of death. In 2013, Nigeria had a 12% global share of deaths from lower respiratory tract infections and a 38% global share of deaths from malaria. India had 33% of the world’s deaths from neonatal encephalopathy. Half of the world’s diarrheal deaths among children and adolescents occurred in just 5 countries: India, Democratic Republic of the Congo, Pakistan, Nigeria, and Ethiopia. Conclusions and Relevance Understanding the levels and trends of the leading causes of death and disability among children and adolescents is critical to guide investment and inform policies. Monitoring these trends over time is also key to understanding where interventions are having an impact. Proven interventions exist to prevent or treat the leading causes of unnecessary death and disability among children and adolescents. The findings presented here show that these are underused and give guidance to policy makers in countries where more attention is needed

Global, regional, and national incidence, prevalence, and years lived with disability for 354 diseases and injuries for 195 countries and territories, 1990–2017: A systematic analysis for the Global Burden of Disease Study 2017

Background: The Global Burden of Diseases, Injuries, and Risk Factors Study 2017 (GBD 2017) includes a comprehensive assessment of incidence, prevalence, and years lived with disability (YLDs) for 354 causes in 195 countries and territories from 1990 to 2017. Previous GBD studies have shown how the decline of mortality rates from 1990 to 2016 has led to an increase in life expectancy, an ageing global population, and an expansion of the non-fatal burden of disease and injury. These studies have also shown how a substantial portion of the world's population experiences non-fatal health loss with considerable heterogeneity among different causes, locations, ages, and sexes. Ongoing objectives of the GBD study include increasing the level of estimation detail, improving analytical strategies, and increasing the amount of high-quality data. Methods: We estimated incidence and prevalence for 354 diseases and injuries and 3484 sequelae. We used an updated and extensive body of literature studies, survey data, surveillance data, inpatient admission records, outpatient visit records, and health insurance claims, and additionally used results from cause of death models to inform estimates using a total of 68 781 data sources. Newly available clinical data from India, Iran, Japan, Jordan, Nepal, China, Brazil, Norway, and Italy were incorporated, as well as updated claims data from the USA and new claims data from Taiwan (province of China) and Singapore. We used DisMod-MR 2.1, a Bayesian meta-regression tool, as the main method of estimation, ensuring consistency between rates of incidence, prevalence, remission, and cause of death for each condition. YLDs were estimated as the product of a prevalence estimate and a disability weight for health states of each mutually exclusive sequela, adjusted for comorbidity. We updated the Socio-demographic Index (SDI), a summary development indicator of income per capita, years of schooling, and total fertility rate. Additionally, we calculated differences between male and female YLDs to identify divergent trends across sexes. GBD 2017 complies with the Guidelines for Accurate and Transparent Health Estimates Reporting. Findings: Globally, for females, the causes with the greatest age-standardised prevalence were oral disorders, headache disorders, and haemoglobinopathies and haemolytic anaemias in both 1990 and 2017. For males, the causes with the greatest age-standardised prevalence were oral disorders, headache disorders, and tuberculosis including latent tuberculosis infection in both 1990 and 2017. In terms of YLDs, low back pain, headache disorders, and dietary iron deficiency were the leading Level 3 causes of YLD counts in 1990, whereas low back pain, headache disorders, and depressive disorders were the leading causes in 2017 for both sexes combined. All-cause age-standardised YLD rates decreased by 3·9% (95% uncertainty interval [UI] 3·1-4·6) from 1990 to 2017; however, the all-age YLD rate increased by 7·2% (6·0-8·4) while the total sum of global YLDs increased from 562 million (421-723) to 853 million (642-1100). The increases for males and females were similar, with increases in all-age YLD rates of 7·9% (6·6-9·2) for males and 6·5% (5·4-7·7) for females. We found significant differences between males and females in terms of age-standardised prevalence estimates for multiple causes. The causes with the greatest relative differences between sexes in 2017 included substance use disorders (3018 cases [95% UI 2782-3252] per 100 000 in males vs 1400 [1279-1524] per 100 000 in females), transport injuries (3322 [3082-3583] vs 2336 [2154-2535]), and self-harm and interpersonal violence (3265 [2943-3630] vs 5643 [5057-6302]). Interpretation: Global all-cause age-standardised YLD rates have improved only slightly over a period spanning nearly three decades. However, the magnitude of the non-fatal disease burden has expanded globally, with increasing numbers of people who have a wide spectrum of conditions. A subset of conditions has remained globally pervasive since 1990, whereas other conditions have displayed more dynamic trends, with different ages, sexes, and geographies across the globe experiencing varying burdens and trends of health loss. This study emphasises how global improvements in premature mortality for select conditions have led to older populations with complex and potentially expensive diseases, yet also highlights global achievements in certain domains of disease and injury

Global, regional, and national comparative risk assessment of 79 behavioural, environmental and occupational, and metabolic risks or clusters of risks, 1990-2015: a systematic analysis for the Global Burden of Disease Study 2015

Forouzanfar MH, Afshin A, Alexander LT, et al. Global, regional, and national comparative risk assessment of 79 behavioural, environmental and occupational, and metabolic risks or clusters of risks, 1990-2015: a systematic analysis for the Global Burden of Disease Study 2015. LANCET. 2016;388(10053):1659-1724.Background The Global Burden of Diseases, Injuries, and Risk Factors Study 2015 provides an up-to-date synthesis of the evidence for risk factor exposure and the attributable burden of disease. By providing national and subnational assessments spanning the past 25 years, this study can inform debates on the importance of addressing risks in context. Methods We used the comparative risk assessment framework developed for previous iterations of the Global Burden of Disease Study to estimate attributable deaths, disability-adjusted life-years (DALYs), and trends in exposure by age group, sex, year, and geography for 79 behavioural, environmental and occupational, and metabolic risks or clusters of risks from 1990 to 2015. This study included 388 risk-outcome pairs that met World Cancer Research Fund-defined criteria for convincing or probable evidence. We extracted relative risk and exposure estimates from randomised controlled trials, cohorts, pooled cohorts, household surveys, census data, satellite data, and other sources. We used statistical models to pool data, adjust for bias, and incorporate covariates. We developed a metric that allows comparisons of exposure across risk factors-the summary exposure value. Using the counterfactual scenario of theoretical minimum risk level, we estimated the portion of deaths and DALYs that could be attributed to a given risk. We decomposed trends in attributable burden into contributions from population growth, population age structure, risk exposure, and risk-deleted cause-specific DALY rates. We characterised risk exposure in relation to a Socio-demographic Index (SDI). Findings Between 1990 and 2015, global exposure to unsafe sanitation, household air pollution, childhood underweight, childhood stunting, and smoking each decreased by more than 25%. Global exposure for several occupational risks, high body-mass index (BMI), and drug use increased by more than 25% over the same period. All risks jointly evaluated in 2015 accounted for 57.8% (95% CI 56.6-58.8) of global deaths and 41.2% (39.8-42.8) of DALYs. In 2015, the ten largest contributors to global DALYs among Level 3 risks were high systolic blood pressure (211.8 million [192.7 million to 231.1 million] global DALYs), smoking (148.6 million [134.2 million to 163.1 million]), high fasting plasma glucose (143.1 million [125.1 million to 163.5 million]), high BMI (120.1 million [83.8 million to 158.4 million]), childhood undernutrition (113.3 million [103.9 million to 123.4 million]), ambient particulate matter (103.1 million [90.8 million to 115.1 million]), high total cholesterol (88.7 million [74.6 million to 105.7 million]), household air pollution (85.6 million [66.7 million to 106.1 million]), alcohol use (85.0 million [77.2 million to 93.0 million]), and diets high in sodium (83.0 million [49.3 million to 127.5 million]). From 1990 to 2015, attributable DALYs declined for micronutrient deficiencies, childhood undernutrition, unsafe sanitation and water, and household air pollution; reductions in risk-deleted DALY rates rather than reductions in exposure drove these declines. Rising exposure contributed to notable increases in attributable DALYs from high BMI, high fasting plasma glucose, occupational carcinogens, and drug use. Environmental risks and childhood undernutrition declined steadily with SDI; low physical activity, high BMI, and high fasting plasma glucose increased with SDI. In 119 countries, metabolic risks, such as high BMI and fasting plasma glucose, contributed the most attributable DALYs in 2015. Regionally, smoking still ranked among the leading five risk factors for attributable DALYs in 109 countries; childhood underweight and unsafe sex remained primary drivers of early death and disability in much of sub-Saharan Africa. Interpretation Declines in some key environmental risks have contributed to declines in critical infectious diseases. Some risks appear to be invariant to SDI. Increasing risks, including high BMI, high fasting plasma glucose, drug use, and some occupational exposures, contribute to rising burden from some conditions, but also provide opportunities for intervention. Some highly preventable risks, such as smoking, remain major causes of attributable DALYs, even as exposure is declining. Public policy makers need to pay attention to the risks that are increasingly major contributors to global burden. Copyright (C) The Author(s). Published by Elsevier Ltd