C∗^*-diagonals in AH-algebras arising from generalized diagonal connecting maps: spectrum and uniqueness

We associate a Bratteli-type diagram to AH-algebras arising from generalized diagonal connecting maps. We use this diagram to give an explicit description of the connected components of the spectrum of an associated canonical C$^*$-diagonal. We introduce a topological notion on these connected components, that of being spectrally incomplete, and use it as a tool to show how various classes of AI-algebras, including certain Goodearl algebras and AH-algebra models for dynamical systems $([0,1],\sigma)$, do not admit unique inductive limit Cartan subalgebras. We focus on a class of spectrally complete C$^*$-algebras, namely the AF-algebras, and prove that they admit unique inductive limit Cartan subalgebras. This is done via a method that generalizes Elliott's proof of classification of AF-algebras to include Cartan pairs.Comment: 18 page

Inductive Limits of Noncommutative Cartan Inclusions

We prove that an inductive limit of aperiodic noncommutative Cartan inclusions is a noncommutative Cartan inclusion whenever the connecting maps are injective, preserve normalisers and entwine conditional expectations. We show that under the additional assumption that the inductive limit Cartan subalgebra is either essentially separable, essentially simple or essentially of Type I we get an aperiodic inclusion in the limit. Consequently, we subsume the case where the building block Cartan subalgebras are commutative and provide a proof of a theorem of Xin Li without passing to twisted \'etale groupoids.Comment: Final version, some minor changes. To appear in Proc. Amer. Math. So

Constructing C*-diagonals in AH-algebras

We construct Cartan subalgebras and hence groupoid models for classes of AH-algebras. Our results cover all AH-algebras whose building blocks have base spaces of dimension at most one as well as Villadsen algebras, and thus go beyond classifiable simple C*-algebras

Constructing C*-diagonals in AH-algebras

We construct Cartan subalgebras and hence groupoid models for classes of AH-algebras. Our results cover all AH-algebras whose building blocks have base spaces of dimension at most one as well as Villadsen algebras, and thus go beyond classifiable simple C*-algebras

Age–sex differences in the global burden of lower respiratory infections and risk factors, 1990–2019: results from the Global Burden of Disease Study 2019

Summary Background The global burden of lower respiratory infections (LRIs) and corresponding risk factors in children older than 5 years and adults has not been studied as comprehensively as it has been in children younger than 5 years. We assessed the burden and trends of LRIs and risk factors across all age groups by sex, for 204 countries and territories. Methods In this analysis of data for the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2019, we used clinician-diagnosed pneumonia or bronchiolitis as our case definition for LRIs. We included International Classification of Diseases 9th edition codes 079.6, 466–469, 470.0, 480–482.8, 483.0–483.9, 484.1–484.2, 484.6–484.7, and 487–489 and International Classification of Diseases 10th edition codes A48.1, A70, B97.4–B97.6, J09–J15.8, J16–J16.9, J20–J21.9, J91.0, P23.0–P23.4, and U04–U04.9. We used the Cause of Death Ensemble modelling strategy to analyse 23 109 site-years of vital registration data, 825 site-years of sample vital registration data, 1766 site-years of verbal autopsy data, and 681 site-years of mortality surveillance data. We used DisMod-MR 2.1, a Bayesian meta-regression tool, to analyse age–sex-specific incidence and prevalence data identified via systematic reviews of the literature, population-based survey data, and claims and inpatient data. Additionally, we estimated age–sex-specific LRI mortality that is attributable to the independent effects of 14 risk factors. Findings Globally, in 2019, we estimated that there were 257 million (95% uncertainty interval [UI] 240–275) LRI incident episodes in males and 232 million (217–248) in females. In the same year, LRIs accounted for 1·30 million (95% UI 1·18–1·42) male deaths and 1·20 million (1·07–1·33) female deaths. Age-standardised incidence and mortality rates were 1·17 times (95% UI 1·16–1·18) and 1·31 times (95% UI 1·23–1·41) greater in males than in females in 2019. Between 1990 and 2019, LRI incidence and mortality rates declined at different rates across age groups and an increase in LRI episodes and deaths was estimated among all adult age groups, with males aged 70 years and older having the highest increase in LRI episodes (126·0% [95% UI 121·4–131·1]) and deaths (100·0% [83·4–115·9]). During the same period, LRI episodes and deaths in children younger than 15 years were estimated to have decreased, and the greatest decline was observed for LRI deaths in males younger than 5 years (–70·7% [–77·2 to –61·8]). The leading risk factors for LRI mortality varied across age groups and sex. More than half of global LRI deaths in children younger than 5 years were attributable to child wasting (population attributable fraction [PAF] 53·0% [95% UI 37·7–61·8] in males and 56·4% [40·7–65·1] in females), and more than a quarter of LRI deaths among those aged 5–14 years were attributable to household air pollution (PAF 26·0% [95% UI 16·6–35·5] for males and PAF 25·8% [16·3–35·4] for females). PAFs of male LRI deaths attributed to smoking were 20·4% (95% UI 15·4–25·2) in those aged 15–49 years, 30·5% (24·1–36·9) in those aged 50–69 years, and 21·9% (16·8–27·3) in those aged 70 years and older. PAFs of female LRI deaths attributed to household air pollution were 21·1% (95% UI 14·5–27·9) in those aged 15–49 years and 18·2% (12·5–24·5) in those aged 50–69 years. For females aged 70 years and older, the leading risk factor, ambient particulate matter, was responsible for 11·7% (95% UI 8·2–15·8) of LRI deaths. Interpretation The patterns and progress in reducing the burden of LRIs and key risk factors for mortality varied across age groups and sexes. The progress seen in children younger than 5 years was clearly a result of targeted interventions, such as vaccination and reduction of exposure to risk factors. Similar interventions for other age groups could contribute to the achievement of multiple Sustainable Development Goals targets, including promoting wellbeing at all ages and reducing health inequalities. Interventions, including addressing risk factors such as child wasting, smoking, ambient particulate matter pollution, and household air pollution, would prevent deaths and reduce health disparities