Functional and isoperimetric inequalities for probability measures on H-type groups

We investigate isoperimetric and functional inequalities for probability measures in the sub-elliptic setting and more specifically, on groups of Heisenberg type. The approach we take is based on U-bounds as well as a Laplacian comparison theorem for H-type groups. We derive different forms of functional inequalities (of [Phi]-entropy and F-Sobolev type) and show that they can be equivalently stated as isoperimetric inequalities at the level of sets. Furthermore, we study transportation of measure via Talagrand-type inequalities. The methods used allow us to obtain gradient bounds for the heat semigroup. Finally, we examine some properties of more general operators given in Hormander’s sum of squares form and show that the associated semigroup converges to a probability measure as t → [infinity]

Regional contributions of six preventable risk factors to achieving the 25 × 25 non-communicable disease mortality reduction target: a modelling study

Background Countries have agreed to reduce premature mortality from the four main non-communicable diseases (NCDs) by 25% from 2010 levels by 2025 (referred to as the 25 × 25 target). Countries also agreed on a set of global voluntary targets for selected NCD risk factors. Previous analyses have shown that achieving the risk factor targets can contribute substantially towards meeting the 25 × 25 mortality target at the global level. We estimated the contribution of achieving six of the globally agreed risk factor targets towards meeting the 25 × 25 mortality target by region. Methods We estimated the eff ect of achieving the targets for six risk factors (tobacco and alcohol use, salt intake, obesity, and raised blood pressure and glucose) on NCD mortality between 2010 and 2025. Our methods accounted for multicausality of NCDs and for the fact that, when risk factor exposure increases or decreases, the harmful or benefi cial eff ects on NCDs accumulate gradually. We used data for risk factor and mortality trends from systematic analyses of available country data. Relative risks for the eff ects of individual and multiple risks, and for change in risk after decreases or increases in exposure, were from reanalyses and meta-analyses of epidemiological studies. Findings The probability of dying between the ages 30 years and 70 years from the four main NCDs in 2010 ranged from 19% in the region of the Americas to 29% in southeast Asia for men, and from 13% in Europe to 21% in southeast Asia for women. If current trends continue, the probability of dying prematurely from the four main NCDs is projected to increase in the African region but decrease in the other fi ve regions. If the risk factor targets are achieved, the 25 × 25 target will be surpassed in Europe in both men and women, and will be achieved in women (and almost achieved in men) in the western Pacifi c; the regions of the Americas, the eastern Mediterranean, and southeast Asia will approach the target; and the rising trend in Africa will be reversed. In most regions, a more ambitious approach to tobacco control (50% reduction relative to 2010 instead of the agreed 30%) will contribute the most to reducing premature NCD mortality among men, followed by addressing raised blood pressure and the agreed tobacco target. For women, the highest contributing risk factor towards the premature NCD mortality target will be raised blood pressure in every region except Europe and the Americas, where the ambitious (but not agreed) tobacco reduction would have the largest benefi t. Interpretation No WHO region will meet the 25 × 25 premature mortality target if current mortality trends continue. Achieving the agreed targets for the six risk factors will allow some regions to meet the 25 × 25 target and others to approach it. Meeting the 25 × 25 target in Africa needs other interventions, including those addressing infectionrelated cancers and cardiovascular disease

Lessons learned and lessons missed: impact of the coronavirus disease 2019 (COVID-19) pandemic on all-cause mortality in 40 industrialised countries and US states prior to mass vaccination.

BACKGROUND: Industrialised countries had varied responses to the COVID-19 pandemic, which may lead to different death tolls from COVID-19 and other diseases. METHODS: We applied an ensemble of 16 Bayesian probabilistic models to vital statistics data to estimate the number of weekly deaths if the pandemic had not occurred for 40 industrialised countries and US states from mid-February 2020 through mid-February 2021. We subtracted these estimates from the actual number of deaths to calculate the impacts of the pandemic on all-cause mortality. RESULTS: Over this year, there were 1,410,300 (95% credible interval 1,267,600-1,579,200) excess deaths in these countries, equivalent to a 15% (14-17) increase, and 141 (127-158) additional deaths per 100,000 people. In Iceland, Australia and New Zealand, mortality was lower than would be expected in the absence of the pandemic, while South Korea and Norway experienced no detectable change. The USA, Czechia, Slovakia and Poland experienced >20% higher mortality. Within the USA, Hawaii experienced no detectable change in mortality and Maine a 5% increase, contrasting with New Jersey, Arizona, Mississippi, Texas, California, Louisiana and New York which experienced >25% higher mortality. Mid-February to the end of May 2020 accounted for over half of excess deaths in Scotland, Spain, England and Wales, Canada, Sweden, Belgium, the Netherlands and Cyprus, whereas mid-September 2020 to mid-February 2021 accounted for >90% of excess deaths in Bulgaria, Croatia, Czechia, Hungary, Latvia, Montenegro, Poland, Slovakia and Slovenia. In USA, excess deaths in the northeast were driven mainly by the first wave, in southern and southwestern states by the summer wave, and in the northern plains by the post-September period. CONCLUSIONS: Prior to widespread vaccine-acquired immunity, minimising the overall death toll of the pandemic requires policies and non-pharmaceutical interventions that delay and reduce infections, effective treatments for infected patients, and mechanisms to continue routine health care

Functional and isoperimetric inequalities for probability measures on H-type groups

We investigate isoperimetric and functional inequalities for probability measures in the sub-elliptic setting and more specifically, on groups of Heisenberg type. The approach we take is based on U-bounds as well as a Laplacian comparison theorem for H-type groups. We derive different forms of functional inequalities (of [Phi]-entropy and F-Sobolev type) and show that they can be equivalently stated as isoperimetric inequalities at the level of sets. Furthermore, we study transportation of measure via Talagrand-type inequalities. The methods used allow us to obtain gradient bounds for the heat semigroup. Finally, we examine some properties of more general operators given in Hormander’s sum of squares form and show that the associated semigroup converges to a probability measure as t → [infinity].EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Ergodicity of Markov semigroups with Hörmander type generators in infinite dimensions

We develop an effective strategy for proving strong ergodicity of (nonsymmetric) Markov semigroups associated to Hörmander type generators when the underlying configuration space is infinite dimensional

The future of life expectancy and life expectancy inequalities in England and Wales:Bayesian spatiotemporal forecasting

Background - To plan for pensions and health and social services, future mortality and life expectancy need to be forecast. Consistent forecasts for all subnational units within a country are very rare. Our aim was to forecast mortality and life expectancy for England and Wales' districts. Methods - We developed Bayesian spatiotemporal models for forecasting of age-specific mortality and life expectancy at a local, small-area level. The models included components that accounted for mortality in relation to age, birth cohort, time, and space. We used geocoded mortality and population data between 1981 and 2012 from the Office for National Statistics together with the model with the smallest error to forecast age-specific death rates and life expectancy to 2030 for 375 of England and Wales' 376 districts. We measured model performance by withholding recent data and comparing forecasts with this withheld data. Findings - Life expectancy at birth in England and Wales was 79·5 years (95% credible interval 79·5–79·6) for men and 83·3 years (83·3–83·4) for women in 2012. District life expectancies ranged between 75·2 years (74·9–75·6) and 83·4 years (82·1–84·8) for men and between 80·2 years (79·8–80·5) and 87·3 years (86·0–88·8) for women. Between 1981 and 2012, life expectancy increased by 8·2 years for men and 6·0 years for women, closing the female–male gap from 6·0 to 3·8 years. National life expectancy in 2030 is expected to reach 85·7 (84·2–87·4) years for men and 87·6 (86·7–88·9) years for women, further reducing the female advantage to 1·9 years. Life expectancy will reach or surpass 81·4 years for men and reach or surpass 84·5 years for women in every district by 2030. Longevity inequality across districts, measured as the difference between the 1st and 99th percentiles of district life expectancies, has risen since 1981, and is forecast to rise steadily to 8·3 years (6·8–9·7) for men and 8·3 years (7·1–9·4) for women by 2030. Interpretation - Present forecasts underestimate the expected rise in life expectancy, especially for men, and hence the need to provide improved health and social services and pensions for elderly people in England and Wales. Health and social policies are needed to curb widening life expectancy inequalities, help deprived districts catch up in longevity gains, and avoid a so-called grand divergence in health and longevity

Short-term excess mortality following tropical cyclones in the United States.

Knowledge of excess deaths after tropical cyclones is critical to understanding their impacts, directly relevant to policies on preparedness and mitigation. We applied an ensemble of 16 Bayesian models to 40.7 million U.S. deaths and a comprehensive record of 179 tropical cyclones over 32 years (1988-2019) to estimate short-term all-cause excess deaths. The deadliest tropical cyclone was Hurricane Katrina in 2005, with 1491 [95% credible interval (CrI): 563, 3206] excess deaths (>99% posterior probability of excess deaths), including 719 [95% CrI: 685, 752] in Orleans Parish, LA (>99% probability). Where posterior probabilities of excess deaths were >95%, there were 3112 [95% CrI: 2451, 3699] total post-hurricane force excess deaths and 15,590 [95% CrI: 12,084, 18,835] post-gale to violent storm force deaths; 83.1% of post-hurricane force and 70.0% of post-gale to violent storm force excess deaths occurred more recently (2004-2019); and 6.2% were in least socially vulnerable counties