On the Prime Number Lemma of Selberg

The key result needed in almost all elementary proofs of the Prime Number Theorem is a prime number lemma proved by Atle Selberg in 1948.Without restricting ourselves to purely elementary techniques we show how the error term in Selberg’s fundamental lemma relates to the error term in the Prime Number Theorem. In spite of all the interest in this topic over the last sixty years this particular question seems to have been overlooked in the past

Bounds for Recurrences on Ranked Posets

This note considers an extension of the concept of linear recurrence to recurrences on ranked posets. Some results on growth rates in the linear case are then extended to this generalized scenario. The work is motivated by recent results on multi-dimensional recurrences which have had applications for obtaining bounds for complex multidimensional generating functions. Some further connections to Möbius functions for binary relations and inverses of {0, 1} triangular matrices are also discussed

Does a Family Meetings Intervention Prevent Depression and Anxiety in Family Caregivers of Dementia Patients? A Randomized Trial

Family caregivers of dementia patients are at increased risk of developing depression or anxiety. A multi-component program designed to mobilize support of family networks demonstrated effectiveness in decreasing depressive symptoms in caregivers. However, the impact of an intervention consisting solely of family meetings on depression and anxiety has not yet been evaluated. This study examines the preventive effects of family meetings for primary caregivers of community-dwelling dementia patients.A randomized multicenter trial was conducted among 192 primary caregivers of community dwelling dementia patients. Caregivers did not meet the diagnostic criteria for depressive or anxiety disorder at baseline. Participants were randomized to the family meetings intervention (n = 96) or usual care (n = 96) condition. The intervention consisted of two individual sessions and four family meetings which occurred once every 2 to 3 months for a year. Outcome measures after 12 months were the incidence of a clinical depressive or anxiety disorder and change in depressive and anxiety symptoms (primary outcomes), caregiver burden and quality of life (secondary outcomes). Intention-to-treat as well as per protocol analyses were performed.A substantial number of caregivers (72/192) developed a depressive or anxiety disorder within 12 months. The intervention was not superior to usual care either in reducing the risk of disorder onset (adjusted IRR 0.98; 95% CI 0.69 to 1.38) or in reducing depressive (randomization-by-time interaction coefficient = -1.40; 95% CI -3.91 to 1.10) or anxiety symptoms (randomization-by-time interaction coefficient = -0.55; 95% CI -1.59 to 0.49). The intervention did not reduce caregiver burden or their health related quality of life.This study did not demonstrate preventive effects of family meetings on the mental health of family caregivers. Further research should determine whether this intervention might be more beneficial if provided in a more concentrated dose, when applied for therapeutic purposes or targeted towards subgroups of caregivers.Controlled-Trials.com ISRCTN90163486

Disrupting the rhythm of depression using Mobile Cognitive Therapy for recurrent depression: randomized controlled trial design and protocol

Background: Major depressive disorder (MDD) is projected to rank second on a list of 15 major diseases in terms of burden in 2030. The major contribution of MDD to disability and health care costs is largely due to its highly recurrent nature. Accordingly, efforts to reduce the disabling effects of this chronic condition should shift to preventing recurrence, especially in patients at high risk of recurrence. Given its high prevalence and the fact that interventions are necessary during the remitted phase, new approaches are needed to prevent relapse in depression. Methods/design: The best established effective and available psychological intervention is cognitive therapy. However, it is costly and not available for most patients. Therefore, we will compare the effectiveness and cost-effectiveness of self-management supported by online CT accompanied by SMS based tele-monitoring of depressive symptomatology, i.e. Mobile Cognitive Therapy (M-CT) versus treatment as us usual (TAU). Remitted patients (n = 268) with at least two previous depressive episodes will be recruited and randomized over (1) M-CT in addition to TAU versus (2) TAU alone, with follow-ups at 3, 12, and 24 months. Randomization will be stratified for number of previous episodes and type of treatment as usual. Primary outcome is time until relapse/recurrence over 24 months using DSM-IV-TR criteria as assessed by the Structured Clinical Interview for DSM-IV Axis I Disorders (SCID). For the economic evaluation the balance between costs and health outcomes will be compared across strategies using a societal perspective. Discussion: Internet-based interventions might be helpful in empowering patients to become their own disease managers in this lifelong recurrent disorder. This is, as far as we are aware of, the first study that examines the (cost) effectiveness of an E-mental health program using SMS monitoring of symptoms with therapist support to prevent relapse in remitted recurrently depressed patient

Sensitivity of Calcification to Thermal Stress Varies among Genera of Massive Reef-Building Corals

Reductions in calcification in reef-building corals occur when thermal conditions are suboptimal, but it is unclear how they vary between genera in response to the same thermal stress event. Using densitometry techniques, we investigate reductions in the calcification rate of massive Porites spp. from the Great Barrier Reef (GBR), and P. astreoides, Montastraea faveolata, and M. franksi from the Mesoamerican Barrier Reef (MBR), and correlate them to thermal stress associated with ocean warming. Results show that Porites spp. are more sensitive to increasing temperature than Montastraea, with calcification rates decreasing by 0.40 g cm−2 year−1 in Porites spp. and 0.12 g cm−2 year−1 in Montastraea spp. for each 1°C increase. Under similar warming trends, the predicted calcification rates at 2100 are close to zero in Porites spp. and reduced by 40% in Montastraea spp. However, these predictions do not account for ocean acidification. Although yearly mean aragonite saturation (Ωar) at MBR sites has recently decreased, only P. astreoides at Chinchorro showed a reduction in calcification. In corals at the other sites calcification did not change, indicating there was no widespread effect of Ωar changes on coral calcification rate in the MBR. Even in the absence of ocean acidification, differential reductions in calcification between Porites spp. and Montastraea spp. associated with warming might be expected to have significant ecological repercussions. For instance, Porites spp. invest increased calcification in extension, and under warming scenarios it may reduce their ability to compete for space. As a consequence, shifts in taxonomic composition would be expected in Indo-Pacific reefs with uncertain repercussions for biodiversity. By contrast, Montastraea spp. use their increased calcification resources to construct denser skeletons. Reductions in calcification would therefore make them more susceptible to both physical and biological breakdown, seriously affecting ecosystem function in Atlantic reefs

Global, regional, and national burden of low back pain, 1990–2020, its attributable risk factors, and projections to 2050: a systematic analysis of the Global Burden of Disease Study 2021

Background: Low back pain is highly prevalent and the main cause of years lived with disability (YLDs). We present the most up-to-date global, regional, and national data on prevalence and YLDs for low back pain from the Global Burden of Diseases, Injuries, and Risk Factors Study 2021. Methods: Population-based studies from 1980 to 2019 identified in a systematic review, international surveys, US medical claims data, and dataset contributions by collaborators were used to estimate the prevalence and YLDs for low back pain from 1990 to 2020, for 204 countries and territories. Low back pain was defined as pain between the 12th ribs and the gluteal folds that lasted a day or more; input data using alternative definitions were adjusted in a network meta-regression analysis. Nested Bayesian meta-regression models were used to estimate prevalence and YLDs by age, sex, year, and location. Prevalence was projected to 2050 by running a regression on prevalence rates using Socio-demographic Index as a predictor, then multiplying them by projected population estimates. Findings: In 2020, low back pain affected 619 million (95% uncertainty interval 554–694) people globally, with a projection of 843 million (759–933) prevalent cases by 2050. In 2020, the global age-standardised rate of YLDs was 832 per 100 000 (578–1070). Between 1990 and 2020, age-standardised rates of prevalence and YLDs decreased by 10·4% (10·9–10·0) and 10·5% (11·1–10·0), respectively. A total of 38·8% (28·7–47·0) of YLDs were attributed to occupational factors, smoking, and high BMI. Interpretation: Low back pain remains the leading cause of YLDs globally, and in 2020, there were more than half a billion prevalent cases of low back pain worldwide. While age-standardised rates have decreased modestly over the past three decades, it is projected that globally in 2050, more than 800 million people will have low back pain. Challenges persist in obtaining primary country-level data on low back pain, and there is an urgent need for more high-quality, primary, country-level data on both prevalence and severity distributions to improve accuracy and monitor change. Funding: Bill and Melinda Gates Foundation

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

Health in times of uncertainty in the eastern Mediterranean region, 1990–2013: a systematic analysis for the Global Burden of Disease Study 2013

Background: The eastern Mediterranean region is comprised of 22 countries: Afghanistan, Bahrain, Djibouti, Egypt, Iran, Iraq, Jordan, Kuwait, Lebanon, Libya, Morocco, Oman, Pakistan, Palestine, Qatar, Saudi Arabia, Somalia, Sudan, Syria, Tunisia, the United Arab Emirates, and Yemen. Since our Global Burden of Disease Study 2010 (GBD 2010), the region has faced unrest as a result of revolutions, wars, and the so-called Arab uprisings. The objective of this study was to present the burden of diseases, injuries, and risk factors in the eastern Mediterranean region as of 2013. Methods: GBD 2013 includes an annual assessment covering 188 countries from 1990 to 2013. The study covers 306 diseases and injuries, 1233 sequelae, and 79 risk factors. Our GBD 2013 analyses included the addition of new data through updated systematic reviews and through the contribution of unpublished data sources from collaborators, an updated version of modelling software, and several improvements in our methods. In this systematic analysis, we use data from GBD 2013 to analyse the burden of disease and injuries in the eastern Mediterranean region specifically. Findings: The leading cause of death in the region in 2013 was ischaemic heart disease (90·3 deaths per 100 000 people), which increased by 17·2% since 1990. However, diarrhoeal diseases were the leading cause of death in Somalia (186·7 deaths per 100 000 people) in 2013, which decreased by 26·9% since 1990. The leading cause of disability-adjusted life-years (DALYs) was ischaemic heart disease for males and lower respiratory infection for females. High blood pressure was the leading risk factor for DALYs in 2013, with an increase of 83·3% since 1990. Risk factors for DALYs varied by country. In low-income countries, childhood wasting was the leading cause of DALYs in Afghanistan, Somalia, and Yemen, whereas unsafe sex was the leading cause in Djibouti. Non-communicable risk factors were the leading cause of DALYs in high-income and middle-income countries in the region. DALY risk factors varied by age, with child and maternal malnutrition affecting the younger age groups (aged 28 days to 4 years), whereas high bodyweight and systolic blood pressure affected older people (aged 60–80 years). The proportion of DALYs attributed to high body-mass index increased from 3·7% to 7·5% between 1990 and 2013. Burden of mental health problems and drug use increased. Most increases in DALYs, especially from non-communicable diseases, were due to population growth. The crises in Egypt, Yemen, Libya, and Syria have resulted in a reduction in life expectancy; life expectancy in Syria would have been 5 years higher than that recorded for females and 6 years higher for males had the crisis not occurred. Interpretation: Our study shows that the eastern Mediterranean region is going through a crucial health phase. The Arab uprisings and the wars that followed, coupled with ageing and population growth, will have a major impact on the region's health and resources. The region has historically seen improvements in life expectancy and other health indicators, even under stress. However, the current situation will cause deteriorating health conditions for many countries and for many years and will have an impact on the region and the rest of the world. Based on our findings, we call for increased investment in health in the region in addition to reducing the conflicts

Global mortality from dementia : Application of a new method and results from the Global Burden of Disease Study 2019

Introduction Dementia is currently one of the leading causes of mortality globally, and mortality due to dementia will likely increase in the future along with corresponding increases in population growth and population aging. However, large inconsistencies in coding practices in vital registration systems over time and between countries complicate the estimation of global dementia mortality. Methods We meta-analyzed the excess risk of death in those with dementia and multiplied these estimates by the proportion of dementia deaths occurring in those with severe, end-stage disease to calculate the total number of deaths that could be attributed to dementia. Results We estimated that there were 1.62 million (95% uncertainty interval [UI]: 0.41-4.21) deaths globally due to dementia in 2019. More dementia deaths occurred in women (1.06 million [0.27-2.71]) than men (0.56 million [0.14-1.51]), largely but not entirely due to the higher life expectancy in women (age-standardized female-to-male ratio 1.19 [1.10-1.26]). Due to population aging, there was a large increase in all-age mortality rates from dementia between 1990 and 2019 (100.1% [89.1-117.5]). In 2019, deaths due to dementia ranked seventh globally in all ages and fourth among individuals 70 and older compared to deaths from other diseases estimated in the Global Burden of Disease (GBD) study. Discussion Mortality due to dementia represents a substantial global burden, and is expected to continue to grow into the future as an older, aging population expands globally.Peer reviewe

Use of multidimensional item response theory methods for dementia prevalence prediction: an example using the Health and Retirement Survey and the Aging, Demographics, and Memory Study.

BACKGROUND: Data sparsity is a major limitation to estimating national and global dementia burden. Surveys with full diagnostic evaluations of dementia prevalence are prohibitively resource-intensive in many settings. However, validation samples from nationally representative surveys allow for the development of algorithms for the prediction of dementia prevalence nationally. METHODS: Using cognitive testing data and data on functional limitations from Wave A (2001-2003) of the ADAMS study (n = 744) and the 2000 wave of the HRS study (n = 6358) we estimated a two-dimensional item response theory model to calculate cognition and function scores for all individuals over 70. Based on diagnostic information from the formal clinical adjudication in ADAMS, we fit a logistic regression model for the classification of dementia status using cognition and function scores and applied this algorithm to the full HRS sample to calculate dementia prevalence by age and sex. RESULTS: Our algorithm had a cross-validated predictive accuracy of 88% (86-90), and an area under the curve of 0.97 (0.97-0.98) in ADAMS. Prevalence was higher in females than males and increased over age, with a prevalence of 4% (3-4) in individuals 70-79, 11% (9-12) in individuals 80-89 years old, and 28% (22-35) in those 90 and older. CONCLUSIONS: Our model had similar or better accuracy as compared to previously reviewed algorithms for the prediction of dementia prevalence in HRS, while utilizing more flexible methods. These methods could be more easily generalized and utilized to estimate dementia prevalence in other national surveys