On the Existence of Configurations of Subspaces in a Hilbert Space with Fixed Angles

For a class of $*$-algebras, where $*$-algebra $A_{\Gamma,\tau}$ is generated by projections associated with vertices of graph $\Gamma$ and depends on a parameter $\tau$ $(0 < \tau \leq 1)$, we study the sets $\Sigma_\Gamma$ of values of $\tau$ such that the algebras $A_{\Gamma,\tau}$ have nontrivial $*$-representations, by using the theory of spectra of graphs. In other words, we study such values of $\tau$ that the corresponding configurations of subspaces in a Hilbert space exist.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Functional Changes in the Snail Statocyst System Elicited by Microgravity

BACKGROUND: The mollusk statocyst is a mechanosensing organ detecting the animal's orientation with respect to gravity. This system has clear similarities to its vertebrate counterparts: a weight-lending mass, an epithelial layer containing small supporting cells and the large sensory hair cells, and an output eliciting compensatory body reflexes to perturbations. METHODOLOGY/PRINCIPAL FINDINGS: In terrestrial gastropod snail we studied the impact of 16- (Foton M-2) and 12-day (Foton M-3) exposure to microgravity in unmanned orbital missions on: (i) the whole animal behavior (Helix lucorum L.), (ii) the statoreceptor responses to tilt in an isolated neural preparation (Helix lucorum L.), and (iii) the differential expression of the Helix pedal peptide (HPep) and the tetrapeptide FMRFamide genes in neural structures (Helix aspersa L.). Experiments were performed 13-42 hours after return to Earth. Latency of body re-orientation to sudden 90° head-down pitch was significantly reduced in postflight snails indicating an enhanced negative gravitaxis response. Statoreceptor responses to tilt in postflight snails were independent of motion direction, in contrast to a directional preference observed in control animals. Positive relation between tilt velocity and firing rate was observed in both control and postflight snails, but the response magnitude was significantly larger in postflight snails indicating an enhanced sensitivity to acceleration. A significant increase in mRNA expression of the gene encoding HPep, a peptide linked to ciliary beating, in statoreceptors was observed in postflight snails; no differential expression of the gene encoding FMRFamide, a possible neurotransmission modulator, was observed. CONCLUSIONS/SIGNIFICANCE: Upregulation of statocyst function in snails following microgravity exposure parallels that observed in vertebrates suggesting fundamental principles underlie gravi-sensing and the organism's ability to adapt to gravity changes. This simple animal model offers the possibility to describe general subcellular mechanisms of nervous system's response to conditions on Earth and in space

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 age-sex-specific mortality and life expectancy, 1950-2017: a systematic analysis for the Global Burden of Disease Study 2017

Background: Assessments of age-specific mortality and life expectancy have been done by the UN Population Division, Department of Economics and Social Affairs (UNPOP), the United States Census Bureau, WHO, and as part of previous iterations of the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD). Previous iterations of the GBD used population estimates from UNPOP, which were not derived in a way that was internally consistent with the estimates of the numbers of deaths in the GBD. The present iteration of the GBD, GBD 2017, improves on previous assessments and provides timely estimates of the mortality experience of populations globally. Methods: The GBD uses all available data to produce estimates of mortality rates between 1950 and 2017 for 23 age groups, both sexes, and 918 locations, including 195 countries and territories and subnational locations for 16 countries. Data used include vital registration systems, sample registration systems, household surveys (complete birth histories, summary birth histories, sibling histories), censuses (summary birth histories, household deaths), and Demographic Surveillance Sites. In total, this analysis used 8259 data sources. Estimates of the probability of death between birth and the age of 5 years and between ages 15 and 60 years are generated and then input into a model life table system to produce complete life tables for all locations and years. Fatal discontinuities and mortality due to HIV/AIDS are analysed separately and then incorporated into the estimation. We analyse the relationship between age-specific mortality and development status using the Socio-demographic Index, a composite measure based on fertility under the age of 25 years, education, and income. There are four main methodological improvements in GBD 2017 compared with GBD 2016: 622 additional data sources have been incorporated; new estimates of population, generated by the GBD study, are used; statistical methods used in different components of the analysis have been further standardised and improved; and the analysis has been extended backwards in time by two decades to start in 1950. Findings: Globally, 18·7% (95% uncertainty interval 18·4–19·0) of deaths were registered in 1950 and that proportion has been steadily increasing since, with 58·8% (58·2–59·3) of all deaths being registered in 2015. At the global level, between 1950 and 2017, life expectancy increased from 48·1 years (46·5–49·6) to 70·5 years (70·1–70·8) for men and from 52·9 years (51·7–54·0) to 75·6 years (75·3–75·9) for women. Despite this overall progress, there remains substantial variation in life expectancy at birth in 2017, which ranges from 49·1 years (46·5–51·7) for men in the Central African Republic to 87·6 years (86·9–88·1) among women in Singapore. The greatest progress across age groups was for children younger than 5 years; under-5 mortality dropped from 216·0 deaths (196·3–238·1) per 1000 livebirths in 1950 to 38·9 deaths (35·6–42·83) per 1000 livebirths in 2017, with huge reductions across countries. Nevertheless, there were still 5·4 million (5·2–5·6) deaths among children younger than 5 years in the world in 2017. Progress has been less pronounced and more variable for adults, especially for adult males, who had stagnant or increasing mortality rates in several countries. The gap between male and female life expectancy between 1950 and 2017, while relatively stable at the global level, shows distinctive patterns across super-regions and has consistently been the largest in central Europe, eastern Europe, and central Asia, and smallest in south Asia. Performance was also variable across countries and time in observed mortality rates compared with those expected on the basis of development. Interpretation: This analysis of age-sex-specific mortality shows that there are remarkably complex patterns in population mortality across countries. The findings of this study highlight global successes, such as the large decline in under-5 mortality, which reflects significant local, national, and global commitment and investment over several decades. However, they also bring attention to mortality patterns that are a cause for concern, particularly among adult men and, to a lesser extent, women, whose mortality rates have stagnated in many countries over the time period of this study, and in some cases are increasing

The evolving SARS-CoV-2 epidemic in Africa: Insights from rapidly expanding genomic surveillance

INTRODUCTION Investment in Africa over the past year with regard to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) sequencing has led to a massive increase in the number of sequences, which, to date, exceeds 100,000 sequences generated to track the pandemic on the continent. These sequences have profoundly affected how public health officials in Africa have navigated the COVID-19 pandemic. RATIONALE We demonstrate how the first 100,000 SARS-CoV-2 sequences from Africa have helped monitor the epidemic on the continent, how genomic surveillance expanded over the course of the pandemic, and how we adapted our sequencing methods to deal with an evolving virus. Finally, we also examine how viral lineages have spread across the continent in a phylogeographic framework to gain insights into the underlying temporal and spatial transmission dynamics for several variants of concern (VOCs). RESULTS Our results indicate that the number of countries in Africa that can sequence the virus within their own borders is growing and that this is coupled with a shorter turnaround time from the time of sampling to sequence submission. Ongoing evolution necessitated the continual updating of primer sets, and, as a result, eight primer sets were designed in tandem with viral evolution and used to ensure effective sequencing of the virus. The pandemic unfolded through multiple waves of infection that were each driven by distinct genetic lineages, with B.1-like ancestral strains associated with the first pandemic wave of infections in 2020. Successive waves on the continent were fueled by different VOCs, with Alpha and Beta cocirculating in distinct spatial patterns during the second wave and Delta and Omicron affecting the whole continent during the third and fourth waves, respectively. Phylogeographic reconstruction points toward distinct differences in viral importation and exportation patterns associated with the Alpha, Beta, Delta, and Omicron variants and subvariants, when considering both Africa versus the rest of the world and viral dissemination within the continent. Our epidemiological and phylogenetic inferences therefore underscore the heterogeneous nature of the pandemic on the continent and highlight key insights and challenges, for instance, recognizing the limitations of low testing proportions. We also highlight the early warning capacity that genomic surveillance in Africa has had for the rest of the world with the detection of new lineages and variants, the most recent being the characterization of various Omicron subvariants. CONCLUSION Sustained investment for diagnostics and genomic surveillance in Africa is needed as the virus continues to evolve. This is important not only to help combat SARS-CoV-2 on the continent but also because it can be used as a platform to help address the many emerging and reemerging infectious disease threats in Africa. In particular, capacity building for local sequencing within countries or within the continent should be prioritized because this is generally associated with shorter turnaround times, providing the most benefit to local public health authorities tasked with pandemic response and mitigation and allowing for the fastest reaction to localized outbreaks. These investments are crucial for pandemic preparedness and response and will serve the health of the continent well into the 21st century

Years lived with disability (YLDs) for 1160 sequelae of 289 diseases and injuries 1990-2010:a systematic analysis for the Global Burden of Disease Study 2010

BACKGROUND: Non-fatal health outcomes from diseases and injuries are a crucial consideration in the promotion and monitoring of individual and population health. The Global Burden of Disease (GBD) studies done in 1990 and 2000 have been the only studies to quantify non-fatal health outcomes across an exhaustive set of disorders at the global and regional level. Neither effort quantified uncertainty in prevalence or years lived with disability (YLDs).METHODS: Of the 291 diseases and injuries in the GBD cause list, 289 cause disability. For 1160 sequelae of the 289 diseases and injuries, we undertook a systematic analysis of prevalence, incidence, remission, duration, and excess mortality. Sources included published studies, case notification, population-based cancer registries, other disease registries, antenatal clinic serosurveillance, hospital discharge data, ambulatory care data, household surveys, other surveys, and cohort studies. For most sequelae, we used a Bayesian meta-regression method, DisMod-MR, designed to address key limitations in descriptive epidemiological data, including missing data, inconsistency, and large methodological variation between data sources. For some disorders, we used natural history models, geospatial models, back-calculation models (models calculating incidence from population mortality rates and case fatality), or registration completeness models (models adjusting for incomplete registration with health-system access and other covariates). Disability weights for 220 unique health states were used to capture the severity of health loss. YLDs by cause at age, sex, country, and year levels were adjusted for comorbidity with simulation methods. We included uncertainty estimates at all stages of the analysis.FINDINGS: Global prevalence for all ages combined in 2010 across the 1160 sequelae ranged from fewer than one case per 1 million people to 350,000 cases per 1 million people. Prevalence and severity of health loss were weakly correlated (correlation coefficient -0·37). In 2010, there were 777 million YLDs from all causes, up from 583 million in 1990. The main contributors to global YLDs were mental and behavioural disorders, musculoskeletal disorders, and diabetes or endocrine diseases. The leading specific causes of YLDs were much the same in 2010 as they were in 1990: low back pain, major depressive disorder, iron-deficiency anaemia, neck pain, chronic obstructive pulmonary disease, anxiety disorders, migraine, diabetes, and falls. Age-specific prevalence of YLDs increased with age in all regions and has decreased slightly from 1990 to 2010. Regional patterns of the leading causes of YLDs were more similar compared with years of life lost due to premature mortality. Neglected tropical diseases, HIV/AIDS, tuberculosis, malaria, and anaemia were important causes of YLDs in sub-Saharan Africa.INTERPRETATION: Rates of YLDs per 100,000 people have remained largely constant over time but rise steadily with age. Population growth and ageing have increased YLD numbers and crude rates over the past two decades. Prevalences of the most common causes of YLDs, such as mental and behavioural disorders and musculoskeletal disorders, have not decreased. Health systems will need to address the needs of the rising numbers of individuals with a range of disorders that largely cause disability but not mortality. Quantification of the burden of non-fatal health outcomes will be crucial to understand how well health systems are responding to these challenges. Effective and affordable strategies to deal with this rising burden are an urgent priority for health systems in most parts of the world.FUNDING: Bill &amp; Melinda Gates Foundation.</p