Infinite motion and 2-distinguishability of graphs and groups

A group A acting faithfully on a set X is 2-distinguishable if there is a 2-coloring of X that is not preserved by any nonidentity element of A, equivalently, if there is a proper subset of X with trivial setwise stabilizer. The motion of an element a in A is the number of points of X that are moved by a, and the motion of the group A is the minimal motion of its nonidentity elements. When A is finite, the Motion Lemma says that if the motion of A is large enough (specifically at least 2 log_2 |A|), then the action is 2-distinguishable. For many situations where X has a combinatorial or algebraic structure, the Motion Lemma implies that the action of Aut(X) on X is 2-distinguishable in all but finitely many instances. We prove an infinitary version of the Motion Lemma for countably infinite permutation groups, which states that infinite motion is large enough to guarantee 2-distinguishability. From this we deduce a number of results, including the fact that every locally finite, connected graph whose automorphism group is countably infinite is 2-distinguishable. One cannot extend the Motion Lemma to uncountable permutation groups, but nonetheless we prove that (under the permutation topology) every closed permutation group with infinite motion has a dense subgroup which is 2-distinguishable. We conjecture an extension of the Motion Lemma which we expect holds for a restricted class of uncountable permutation groups, and we conclude with a list of open questions. The consequences of our results are drawn for orbit equivalence of infinite permutation groups

Global, regional, and national incidence, prevalence, and mortality of HIV, 1980–2017, and forecasts to 2030, for 195 countries and territories: a systematic analysis for the Global Burden of Diseases, Injuries, and Risk Factors Study 2017

Background Understanding the patterns of HIV/AIDS epidemics is crucial to tracking and monitoring the progress of prevention and control efforts in countries. We provide a comprehensive assessment of the levels and trends of HIV/AIDS incidence, prevalence, mortality, and coverage of antiretroviral therapy (ART) for 1980–2017 and forecast these estimates to 2030 for 195 countries and territories. Methods We determined a modelling strategy for each country on the basis of the availability and quality of data. For countries and territories with data from population-based seroprevalence surveys or antenatal care clinics, we estimated prevalence and incidence using an open-source version of the Estimation and Projection Package—a natural history model originally developed by the UNAIDS Reference Group on Estimates, Modelling, and Projections. For countries with cause-specific vital registration data, we corrected data for garbage coding (ie, deaths coded to an intermediate, immediate, or poorly defined cause) and HIV misclassification. We developed a process of cohort incidence bias adjustment to use information on survival and deaths recorded in vital registration to back-calculate HIV incidence. For countries without any representative data on HIV, we produced incidence estimates by pulling information from observed bias in the geographical region. We used a re-coded version of the Spectrum model (a cohort component model that uses rates of disease progression and HIV mortality on and off ART) to produce age-sex-specific incidence, prevalence, and mortality, and treatment coverage results for all countries, and forecast these measures to 2030 using Spectrum with inputs that were extended on the basis of past trends in treatment scale-up and new infections. Findings Global HIV mortality peaked in 2006 with 1·95 million deaths (95% uncertainty interval 1·87–2·04) and has since decreased to 0·95 million deaths (0·91–1·01) in 2017. New cases of HIV globally peaked in 1999 (3·16 million, 2·79–3·67) and since then have gradually decreased to 1·94 million (1·63–2·29) in 2017. These trends, along with ART scale-up, have globally resulted in increased prevalence, with 36·8 million (34·8–39·2) people living with HIV in 2017. Prevalence of HIV was highest in southern sub-Saharan Africa in 2017, and countries in the region had ART coverage ranging from 65·7% in Lesotho to 85·7% in eSwatini. Our forecasts showed that 54 countries will meet the UNAIDS target of 81% ART coverage by 2020 and 12 countries are on track to meet 90% ART coverage by 2030. Forecasted results estimate that few countries will meet the UNAIDS 2020 and 2030 mortality and incidence targets. Interpretation Despite progress in reducing HIV-related mortality over the past decade, slow decreases in incidence, combined with the current context of stagnated funding for related interventions, mean that many countries are not on track to reach the 2020 and 2030 global targets for reduction in incidence and mortality. With a growing population of people living with HIV, it will continue to be a major threat to public health for years to come. The pace of progress needs to be hastened by continuing to expand access to ART and increasing investments in proven HIV prevention initiatives that can be scaled up to have population-level impact

Between proper and strong edge-colorings of subcubic graphs

In a proper edge-coloring the edges of every color form a matching. A matching is induced if the end-vertices of its edges induce a matching. A strong edge-coloring is an edge-coloring in which the edges of every color form an induced matching. We consider intermediate types of edge-colorings, where edges of some colors are allowed to form matchings, and the remaining form induced matchings. Our research is motivated by the conjecture proposed in a recent paper of Gastineau and Togni on S-packing edge-colorings (On S-packing edge-colorings of cubic graphs, Discrete Appl. Math. 259 (2019), 63-75) asserting that by allowing three additional induced matchings, one is able to save one matching color. We prove that every graph with maximum degree 3 can be decomposed into one matching and at most 8 induced matchings, and two matchings and at most 5 induced matchings. We also show that if a graph is in class I, the number of induced matchings can be decreased by one, hence confirming the above-mentioned conjecture for class I graphs

Grammar-based distance in progressive multiple sequence alignment

Background: We propose a multiple sequence alignment (MSA) algorithm and compare the alignment-quality and execution-time of the proposed algorithm with that of existing algorithms. The proposed progressive alignment algorithm uses a grammar-based distance metric to determine the order in which biological sequences are to be pairwise aligned. The progressive alignment occurs via pairwise aligning new sequences with an ensemble of the sequences previously aligned. Results: The performance of the proposed algorithm is validated via comparison to popular progressive multiple alignment approaches, ClustalW and T-Coffee, and to the more recently developed algorithms MAFFT, MUSCLE, Kalign, and PSAlign using the BAliBASE 3.0 database of amino acid alignment files and a set of longer sequences generated by Rose software. The proposed algorithm has successfully built multiple alignments comparable to other programs with significant improvements in running time. The results are especially striking for large datasets. Conclusion: We introduce a computationally efficient progressive alignment algorithm using a grammar based sequence distance particularly useful in aligning large datasets

Nucleologenesis in the Caenorhabditis elegans Embryo

In the Caenorhabditis elegans nematode, the oocyte nucleolus disappears prior to fertilization. We have now investigated the re-formation of the nucleolus in the early embryo of this model organism by immunostaining for fibrillarin and DAO-5, a putative NOLC1/Nopp140 homolog involved in ribosome assembly. We find that labeled nucleoli first appear in somatic cells at around the 8-cell stage, at a time when transcription of the embryonic genome begins. Quantitative analysis of radial positioning showed the nucleolus to be localized at the nuclear periphery in a majority of early embryonic nuclei. At the ultrastructural level, the embryonic nucleolus appears to be composed of a relatively homogenous core surrounded by a crescent-shaped granular structure. Prior to embryonic genome activation, fibrillarin and DAO-5 staining is seen in numerous small nucleoplasmic foci. This staining pattern persists in the germline up to the ∼100-cell stage, until the P4 germ cell divides to give rise to the Z2/Z3 primordial germ cells and embryonic transcription is activated in this lineage. In the ncl-1 mutant, which is characterized by increased transcription of rDNA, DAO-5-labeled nucleoli are already present at the 2-cell stage. Our results suggest a link between the activation of transcription and the initial formation of nucleoli in the C. elegans embryo

Measuring universal health coverage based on an index of effective coverage of health services in 204 countries and territories, 1990–2019: a systematic analysis for the Global Burden of Disease Study 2019

Background Achieving universal health coverage (UHC) involves all people receiving the health services they need, of high quality, without experiencing financial hardship. Making progress towards UHC is a policy priority for both countries and global institutions, as highlighted by the agenda of the UN Sustainable Development Goals (SDGs) and WHO's Thirteenth General Programme of Work (GPW13). Measuring effective coverage at the health-system level is important for understanding whether health services are aligned with countries' health profiles and are of sufficient quality to produce health gains for populations of all ages. Methods Based on the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2019, we assessed UHC effective coverage for 204 countries and territories from 1990 to 2019. Drawing from a measurement framework developed through WHO's GPW13 consultation, we mapped 23 effective coverage indicators to a matrix representing health service types (eg, promotion, prevention, and treatment) and five population-age groups spanning from reproductive and newborn to older adults (≥65 years). Effective coverage indicators were based on intervention coverage or outcome-based measures such as mortality-to-incidence ratios to approximate access to quality care; outcome-based measures were transformed to values on a scale of 0–100 based on the 2·5th and 97·5th percentile of location-year values. We constructed the UHC effective coverage index by weighting each effective coverage indicator relative to its associated potential health gains, as measured by disability-adjusted life-years for each location-year and population-age group. For three tests of validity (content, known-groups, and convergent), UHC effective coverage index performance was generally better than that of other UHC service coverage indices from WHO (ie, the current metric for SDG indicator 3.8.1 on UHC service coverage), the World Bank, and GBD 2017. We quantified frontiers of UHC effective coverage performance on the basis of pooled health spending per capita, representing UHC effective coverage index levels achieved in 2019 relative to country-level government health spending, prepaid private expenditures, and development assistance for health. To assess current trajectories towards the GPW13 UHC billion target—1 billion more people benefiting from UHC by 2023—we estimated additional population equivalents with UHC effective coverage from 2018 to 2023. Findings Globally, performance on the UHC effective coverage index improved from 45·8 (95% uncertainty interval 44·2–47·5) in 1990 to 60·3 (58·7–61·9) in 2019, yet country-level UHC effective coverage in 2019 still spanned from 95 or higher in Japan and Iceland to lower than 25 in Somalia and the Central African Republic. Since 2010, sub-Saharan Africa showed accelerated gains on the UHC effective coverage index (at an average increase of 2·6% [1·9–3·3] per year up to 2019); by contrast, most other GBD super-regions had slowed rates of progress in 2010–2019 relative to 1990–2010. Many countries showed lagging performance on effective coverage indicators for non-communicable diseases relative to those for communicable diseases and maternal and child health, despite non-communicable diseases accounting for a greater proportion of potential health gains in 2019, suggesting that many health systems are not keeping pace with the rising non-communicable disease burden and associated population health needs. In 2019, the UHC effective coverage index was associated with pooled health spending per capita (r=0·79), although countries across the development spectrum had much lower UHC effective coverage than is potentially achievable relative to their health spending. Under maximum efficiency of translating health spending into UHC effective coverage performance, countries would need to reach $1398 pooled health spending per capita (US$ adjusted for purchasing power parity) in order to achieve 80 on the UHC effective coverage index. From 2018 to 2023, an estimated 388·9 million (358·6–421·3) more population equivalents would have UHC effective coverage, falling well short of the GPW13 target of 1 billion more people benefiting from UHC during this time. Current projections point to an estimated 3·1 billion (3·0–3·2) population equivalents still lacking UHC effective coverage in 2023, with nearly a third (968·1 million [903·5–1040·3]) residing in south Asia. Interpretation The present study demonstrates the utility of measuring effective coverage and its role in supporting improved health outcomes for all people—the ultimate goal of UHC and its achievement. Global ambitions to accelerate progress on UHC service coverage are increasingly unlikely unless concerted action on non-communicable diseases occurs and countries can better translate health spending into improved performance. Focusing on effective coverage and accounting for the world's evolving health needs lays the groundwork for better understanding how close—or how far—all populations are in benefiting from UHC. Funding Bill & Melinda Gates Foundation

Global, regional, and national burden of upper respiratory infections and otitis media, 1990-2021: a systematic analysis from the Global Burden of Disease Study 2021

Background Upper respiratory infections (URIs) are the leading cause of acute disease incidence worldwide and contribute to a substantial health-care burden. Although acute otitis media is a common complication of URIs, the combined global burden of URIs and otitis media has not been studied comprehensively. We used results from the Global Burden of Diseases, Injuries, and Risk Factors Study 2021 to explore the fatal and non-fatal burden of the two diseases across all age groups, including a granular analysis of children younger than 5 years, in 204 countries and territories from 1990 to 2021. Methods Mortality due to URIs and otitis media was estimated with use of vital registration and sample-based vital registration data, which are used as inputs to the Cause of Death Ensemble model to separately model URIs and otitis media mortality by age and sex. Morbidity was modelled with a Bayesian meta-regression tool using data from published studies identified via systematic reviews, population-based survey data, and cause-specific URI and otitis media mortality estimates. Additionally, we assessed and compared the burden of otitis media as it relates to URIs and examined the collective burden and contributing risk factors of both diseases. Findings The global number of new episodes of URIs was 12·8 billion (95% uncertainty interval 11·4 to 14·5) for all ages across males and females in 2021. The global all-age incidence rate of URIs decreased by 10·1% (–12·0 to –8·1) from 1990 to 2019. From 2019 to 2021, the global all-age incidence rate fell by 0·5% (–0·8 to –0·1). Globally, the incidence rate of URIs was 162 484·8 per 100 000 population (144 834·0 to 183 289·4) in 2021, a decrease of 10·5% (–12·4 to –8·4) from 1990, when the incidence rate was 181 552·5 per 100 000 population (160 827·4 to 206 214·7). The highest incidence rates of URIs were seen in children younger than 2 years in 2021, and the largest number of episodes was in children aged 5–9 years. The number of new episodes of otitis media globally for all ages was 391 million (292 to 525) in 2021. The global incidence rate of otitis media was 4958·9 per 100 000 (3705·4 to 6658·6) in 2021, a decrease of 16·3% (–18·1 to –14·0) from 1990, when the incidence rate was 5925·5 per 100 000 (4371·8 to 8097·9). The incidence rate of otitis media in 2021 was highest in children younger than 2 years, and the largest number of episodes was in children aged 2–4 years. The mortality rate of URIs in 2021 was 0·2 per 100 000 (0·1 to 0·5), a decrease of 64·2% (–84·6 to –43·4) from 1990, when the mortality rate was 0·7 per 100 000 (0·2 to 1·1). In both 1990 and 2021, the mortality rate of otitis media was less than 0·1 per 100 000. Together, the combined burden accounted for by URIs and otitis media in 2021 was 6·86 million (4·24 to 10·4) years lived with disability and 8·16 million (4·99 to 12·0) disability-adjusted life-years (DALYs) for all ages across males and females. Globally, the all-age DALY rate of URIs and otitis media combined in 2021 was 103 per 100 000 (63 to 152). Infants aged 1–5 months had the highest combined DALY rate in 2021 (647 per 100 000 [189 to 1412]), followed by early neonates (aged 0–6 days; 582 per 100 000 [176 to 1297]) and late neonates (aged 7–24 days; 482 per 100 000 [161 to 1052]). Interpretation The findings of this study highlight the widespread burden posed by URIs and otitis media across all age groups and both sexes. There is a continued need for surveillance, prevention, and management to better understand and reduce the burden associated with URIs and otitis media, and research is needed to assess their impacts on individuals, communities, economies, and health-care systems worldwide. Funding Bill & Melinda Gates Foundation