A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian) defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144

Virulence related sequences: insights provided by comparative genomics of Streptococcus uberis of differing virulence

Background: Streptococcus uberis, a Gram-positive, catalase-negative member of the family Streptococcaceae is an important environmental pathogen responsible for a significant proportion of subclinical and clinical bovine intramammary infections. Currently, the genome of only a single reference strain (0140J) has been described. Here we present a comparative analysis of complete draft genome sequences of an additional twelve S. uberis strains. Results: Pan and core genome analysis revealed the core genome common to all strains to be 1,550 genes in 1,509 orthologous clusters, complemented by 115-246 accessory genes present in one or more S. uberis strains but absent in the reference strain 0140J. Most of the previously predicted virulent genes were present in the core genome of all 13 strains but gene gain/loss was observed between the isolates in CDS associated with clustered regularly interspaced short palindromic repeats (CRISPRs), prophage and bacteriocin production. Experimental challenge experiments confirmed strain EF20 as non-virulent; only able to infect in a transient manner that did not result in clinical mastitis. Comparison of the genome sequence of EF20 with the validated virulent strain 0140J identified genes associated with virulence, however these did not relate clearly with clinical/non-clinical status of infection. Conclusion: The gain/loss of mobile genetic elements such as CRISPRs and prophage are a potential driving force for evolutionary change. This first “whole-genome” comparison of strains isolated from clinical vs non-clinical intramammary infections including the type virulent vs non-virulent strains did not identify simple gene gain/loss rules that readily explain, or be confidently associated with, differences in virulence. This suggests that a more complex dynamic determines infection potential and clinical outcome not simply gene content

Adaptive plasticity of killifish (Fundulus heteroclitus) embryos: dehydration-stimulated development and differential aquaporin-3 expression

13 pages, 7 figures, 3 tablesEmbryos of the marine killifish Fundulus heteroclitus are adapted to survive aerially. However, it is unknown if they are able to control development under dehydration conditions. Here, we show that air-exposed blastula embryos under saturated relative humidity were able to stimulate development, and hence the time of hatching was advanced with respect to embryos continuously immersed in seawater. Embryos exposed to air at later developmental stages did not hatch until water was added, while development was not arrested. Air-exposed embryos avoided dehydration probably because of their thickened egg envelope, although it suffered significant evaporative water loss. The potential role of aquaporins as part of the embryo response to dehydration was investigated by cloning the aquaporin-0 (FhAqp0), -1a (FhAqp1a), and -3 (FhAqp3) cDNAs. Functional expression in Xenopus laevis oocytes showed that FhaAqp1a was a water-selective channel, whereas FhAqp3 was permeable to water, glycerol, and urea. Expression of fhaqp0 and fhaqp1a was prominent during organogenesis, and their mRNA levels were similar between water- and air-incubated embryos. However, fhaqp3 transcripts were highly and transiently accumulated during gastrulation, and the protein product was localized in the basolateral membrane of the enveloping epithelial cell layer and in the membrane of ingressing and migrating blastomers. Interestingly, both fhaqp3 transcripts and FhAqp3 polypeptides were downregulated in air-exposed embryos. These data demonstrate that killifish embryos respond adaptively to environmental desiccation by accelerating development and that embryos are able to transduce dehydration conditions into molecular responses. The reduced synthesis of FhAqp3 may be one of these mechanisms to regulate water and/or solute transport in the embryo.This study was supported by the European Commission New and Emerging Science and Technologies (NEST) program (contract no. 012674-2 Sleeping Beauty) and by a grant from the Spanish Ministry of Education and Science (MEC; AGL2004-00316/ACU) to J. Cerda`. Participation of C. Zapater and F. Chauvigne´ was financed by a predoctoral fellowship from MEC (Spain) and by the European Commission [Marie Curie Research Training Network Aqua (glycero)porins, MRTN-CT-2006-035995], respectively.Peer reviewe

Burden of disease scenarios for 204 countries and territories, 2022–2050: a forecasting analysis for the Global Burden of Disease Study 2021

Background: Future trends in disease burden and drivers of health are of great interest to policy makers and the public at large. This information can be used for policy and long-term health investment, planning, and prioritisation. We have expanded and improved upon previous forecasts produced as part of the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) and provide a reference forecast (the most likely future), and alternative scenarios assessing disease burden trajectories if selected sets of risk factors were eliminated from current levels by 2050. Methods: Using forecasts of major drivers of health such as the Socio-demographic Index (SDI; a composite measure of lag-distributed income per capita, mean years of education, and total fertility under 25 years of age) and the full set of risk factor exposures captured by GBD, we provide cause-specific forecasts of mortality, years of life lost (YLLs), years lived with disability (YLDs), and disability-adjusted life-years (DALYs) by age and sex from 2022 to 2050 for 204 countries and territories, 21 GBD regions, seven super-regions, and the world. All analyses were done at the cause-specific level so that only risk factors deemed causal by the GBD comparative risk assessment influenced future trajectories of mortality for each disease. Cause-specific mortality was modelled using mixed-effects models with SDI and time as the main covariates, and the combined impact of causal risk factors as an offset in the model. At the all-cause mortality level, we captured unexplained variation by modelling residuals with an autoregressive integrated moving average model with drift attenuation. These all-cause forecasts constrained the cause-specific forecasts at successively deeper levels of the GBD cause hierarchy using cascading mortality models, thus ensuring a robust estimate of cause-specific mortality. For non-fatal measures (eg, low back pain), incidence and prevalence were forecasted from mixed-effects models with SDI as the main covariate, and YLDs were computed from the resulting prevalence forecasts and average disability weights from GBD. Alternative future scenarios were constructed by replacing appropriate reference trajectories for risk factors with hypothetical trajectories of gradual elimination of risk factor exposure from current levels to 2050. The scenarios were constructed from various sets of risk factors: environmental risks (Safer Environment scenario), risks associated with communicable, maternal, neonatal, and nutritional diseases (CMNNs; Improved Childhood Nutrition and Vaccination scenario), risks associated with major non-communicable diseases (NCDs; Improved Behavioural and Metabolic Risks scenario), and the combined effects of these three scenarios. Using the Shared Socioeconomic Pathways climate scenarios SSP2-4.5 as reference and SSP1-1.9 as an optimistic alternative in the Safer Environment scenario, we accounted for climate change impact on health by using the most recent Intergovernmental Panel on Climate Change temperature forecasts and published trajectories of ambient air pollution for the same two scenarios. Life expectancy and healthy life expectancy were computed using standard methods. The forecasting framework includes computing the age-sex-specific future population for each location and separately for each scenario. 95% uncertainty intervals (UIs) for each individual future estimate were derived from the 2·5th and 97·5th percentiles of distributions generated from propagating 500 draws through the multistage computational pipeline. Findings: In the reference scenario forecast, global and super-regional life expectancy increased from 2022 to 2050, but improvement was at a slower pace than in the three decades preceding the COVID-19 pandemic (beginning in 2020). Gains in future life expectancy were forecasted to be greatest in super-regions with comparatively low life expectancies (such as sub-Saharan Africa) compared with super-regions with higher life expectancies (such as the high-income super-region), leading to a trend towards convergence in life expectancy across locations between now and 2050. At the super-region level, forecasted healthy life expectancy patterns were similar to those of life expectancies. Forecasts for the reference scenario found that health will improve in the coming decades, with all-cause age-standardised DALY rates decreasing in every GBD super-region. The total DALY burden measured in counts, however, will increase in every super-region, largely a function of population ageing and growth. We also forecasted that both DALY counts and age-standardised DALY rates will continue to shift from CMNNs to NCDs, with the most pronounced shifts occurring in sub-Saharan Africa (60·1% [95% UI 56·8–63·1] of DALYs were from CMNNs in 2022 compared with 35·8% [31·0–45·0] in 2050) and south Asia (31·7% [29·2–34·1] to 15·5% [13·7–17·5]). This shift is reflected in the leading global causes of DALYs, with the top four causes in 2050 being ischaemic heart disease, stroke, diabetes, and chronic obstructive pulmonary disease, compared with 2022, with ischaemic heart disease, neonatal disorders, stroke, and lower respiratory infections at the top. The global proportion of DALYs due to YLDs likewise increased from 33·8% (27·4–40·3) to 41·1% (33·9–48·1) from 2022 to 2050, demonstrating an important shift in overall disease burden towards morbidity and away from premature death. The largest shift of this kind was forecasted for sub-Saharan Africa, from 20·1% (15·6–25·3) of DALYs due to YLDs in 2022 to 35·6% (26·5–43·0) in 2050. In the assessment of alternative future scenarios, the combined effects of the scenarios (Safer Environment, Improved Childhood Nutrition and Vaccination, and Improved Behavioural and Metabolic Risks scenarios) demonstrated an important decrease in the global burden of DALYs in 2050 of 15·4% (13·5–17·5) compared with the reference scenario, with decreases across super-regions ranging from 10·4% (9·7–11·3) in the high-income super-region to 23·9% (20·7–27·3) in north Africa and the Middle East. The Safer Environment scenario had its largest decrease in sub-Saharan Africa (5·2% [3·5–6·8]), the Improved Behavioural and Metabolic Risks scenario in north Africa and the Middle East (23·2% [20·2–26·5]), and the Improved Nutrition and Vaccination scenario in sub-Saharan Africa (2·0% [–0·6 to 3·6]). Interpretation: Globally, life expectancy and age-standardised disease burden were forecasted to improve between 2022 and 2050, with the majority of the burden continuing to shift from CMNNs to NCDs. That said, continued progress on reducing the CMNN disease burden will be dependent on maintaining investment in and policy emphasis on CMNN disease prevention and treatment. Mostly due to growth and ageing of populations, the number of deaths and DALYs due to all causes combined will generally increase. By constructing alternative future scenarios wherein certain risk exposures are eliminated by 2050, we have shown that opportunities exist to substantially improve health outcomes in the future through concerted efforts to prevent exposure to well established risk factors and to expand access to key health interventions

Causes of blindness and vision impairment in 2020 and trends over 30 years, and prevalence of avoidable blindness in relation to VISION 2020: the Right to Sight: an analysis for the Global Burden of Disease Study

Background: Many causes of vision impairment can be prevented or treated. With an ageing global population, the demands for eye health services are increasing. We estimated the prevalence and relative contribution of avoidable causes of blindness and vision impairment globally from 1990 to 2020. We aimed to compare the results with the World Health Assembly Global Action Plan (WHA GAP) target of a 25% global reduction from 2010 to 2019 in avoidable vision impairment, defined as cataract and undercorrected refractive error. Methods: We did a systematic review and meta-analysis of population-based surveys of eye disease from January, 1980, to October, 2018. We fitted hierarchical models to estimate prevalence (with 95% uncertainty intervals [UIs]) of moderate and severe vision impairment (MSVI; presenting visual acuity from <6/18 to 3/60) and blindness (<3/60 or less than 10° visual field around central fixation) by cause, age, region, and year. Because of data sparsity at younger ages, our analysis focused on adults aged 50 years and older. Findings: Global crude prevalence of avoidable vision impairment and blindness in adults aged 50 years and older did not change between 2010 and 2019 (percentage change −0·2% [95% UI −1·5 to 1·0]; 2019 prevalence 9·58 cases per 1000 people [95% IU 8·51 to 10·8], 2010 prevalence 96·0 cases per 1000 people [86·0 to 107·0]). Age-standardised prevalence of avoidable blindness decreased by −15·4% [–16·8 to −14·3], while avoidable MSVI showed no change (0·5% [–0·8 to 1·6]). However, the number of cases increased for both avoidable blindness (10·8% [8·9 to 12·4]) and MSVI (31·5% [30·0 to 33·1]). The leading global causes of blindness in those aged 50 years and older in 2020 were cataract (15·2 million cases [9% IU 12·7–18·0]), followed by glaucoma (3·6 million cases [2·8–4·4]), undercorrected refractive error (2·3 million cases [1·8–2·8]), age-related macular degeneration (1·8 million cases [1·3–2·4]), and diabetic retinopathy (0·86 million cases [0·59–1·23]). Leading causes of MSVI were undercorrected refractive error (86·1 million cases [74·2–101·0]) and cataract (78·8 million cases [67·2–91·4]). Interpretation: Results suggest eye care services contributed to the observed reduction of age-standardised rates of avoidable blindness but not of MSVI, and that the target in an ageing global population was not reached. Funding: Brien Holden Vision Institute, Fondation Théa, The Fred Hollows Foundation, Bill & Melinda Gates Foundation, Lions Clubs International Foundation, Sightsavers International, and University of Heidelberg