Uniform bounds on the 1-norm of the inverse of lower triangular Toeplitz matrices

A uniform bound on the 1-norm is given for the inverse of a lower triangular Toeplitz matrix with non-negative monotonically decreasing entries whose limit is zero. The new bound is sharp under certain specified constraints. This result is then employed to throw light upon a long standing open problem posed by Brunner concerning the convergence of the one-point collocationmethod for the Abel equation. In addition, the recent conjecture of Gauthier et al. is proved

Dispersion measure variability for 36 millisecond pulsars at 150MHz with LOFAR

Context. Radio pulses from pulsars are affected by plasma dispersion, which results in a frequency-dependent propagation delay. Variations in the magnitude of this effect lead to an additional source of red noise in pulsar timing experiments, including pulsar timing arrays (PTAs) that aim to detect nanohertz gravitational waves. Aims. We aim to quantify the time-variable dispersion with much improved precision and characterise the spectrum of these variations. Methods. We use the pulsar timing technique to obtain highly precise dispersion measure (DM) time series. Our dataset consists of observations of 36 millisecond pulsars, which were observed for up to 7.1 yr with the LOw Frequency ARray (LOFAR) telescope at a centre frequency of ~150 MHz. Seventeen of these sources were observed with a weekly cadence, while the rest were observed at monthly cadence. Results. We achieve a median DM precision of the order of 10−5 cm−3 pc for a significant fraction of our sources. We detect significant variations of the DM in all pulsars with a median DM uncertainty of less than 2 × 10−4 cm−3 pc. The noise contribution to pulsar timing experiments at higher frequencies is calculated to be at a level of 0.1–10 μs at 1.4 GHz over a timespan of a few years, which is in many cases larger than the typical timing precision of 1 μs or better that PTAs aim for. We found no evidence for a dependence of DM on radio frequency for any of the sources in our sample. Conclusions. The DM time series we obtained using LOFAR could in principle be used to correct higher-frequency data for the variations of the dispersive delay. However, there is currently the practical restriction that pulsars tend to provide either highly precise times of arrival (ToAs) at 1.4 GHz or a high DM precision at low frequencies, but not both, due to spectral properties. Combining the higher-frequency ToAs with those from LOFAR to measure the infinite-frequency ToA and DM would improve the result

COVID-19: Rapid antigen detection for SARS-CoV-2 by lateral flow assay: A national systematic evaluation of sensitivity and specificity for mass-testing

Background Lateral flow device (LFD) viral antigen immunoassays have been developed around the world as diagnostic tests for SARS-CoV-2 infection. They have been proposed to deliver an infrastructure-light, cost-economical solution giving results within half an hour. Methods LFDs were initially reviewed by a Department of Health and Social Care team, part of the UK government, from which 64 were selected for further evaluation from 1st August to 15th December 2020. Standardised laboratory evaluations, and for those that met the published criteria, field testing in the Falcon-C19 research study and UK pilots were performed (UK COVID-19 testing centres, hospital, schools, armed forces). Findings 4/64 LFDs so far have desirable performance characteristics (orient Gene, Deepblue, Abbott and Innova SARS-CoV-2 Antigen Rapid Qualitative Test). All these LFDs have a viral antigen detection of >90% at 100,000 RNA copies/ml. 8951 Innova LFD tests were performed with a kit failure rate of 5.6% (502/8951, 95% CI: 5.1–6.1), false positive rate of 0.32% (22/6954, 95% CI: 0.20–0.48). Viral antigen detection/sensitivity across the sampling cohort when performed by laboratory scientists was 78.8% (156/198, 95% CI 72.4–84.3). Interpretation Our results suggest LFDs have promising performance characteristics for mass population testing and can be used to identify infectious positive individuals. The Innova LFD shows good viral antigen detection/sensitivity with excellent specificity, although kit failure rates and the impact of training are potential issues. These results support the expanded evaluation of LFDs, and assessment of greater access to testing on COVID-19 transmission. Funding Department of Health and Social Care. University of Oxford. Public Health England Porton Down, Manchester University NHS Foundation Trust, National Institute of Health Research

Dust in Supernovae and Supernova Remnants II: Processing and survival

Observations have recently shown that supernovae are efficient dust factories, as predicted for a long time by theoretical models. The rapid evolution of their stellar progenitors combined with their efficiency in precipitating refractory elements from the gas phase into dust grains make supernovae the major potential suppliers of dust in the early Universe, where more conventional sources like Asymptotic Giant Branch (AGB) stars did not have time to evolve. However, dust yields inferred from observations of young supernovae or derived from models do not reflect the net amount of supernova-condensed dust able to be expelled from the remnants and reach the interstellar medium. The cavity where the dust is formed and initially resides is crossed by the high velocity reverse shock which is generated by the pressure of the circumstellar material shocked by the expanding supernova blast wave. Depending on grain composition and initial size, processing by the reverse shock may lead to substantial dust erosion and even complete destruction. The goal of this review is to present the state of the art about processing and survival of dust inside supernova remnants, in terms of theoretical modelling and comparison to observations

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

Lack of telopeptides in fibrillar collagen I promotes the invasion of a metastatic breast tumor cell line.

Defective fibrillar collagen polymerization in primary tumors has been correlated with increased metastasis. However, it is unclear how collagen organization influences tumor invasion. In this study, we show that collagen I polymerized without telopeptides (the flanking regions of collagen molecules) can differentially affect the three-dimensional migration of mammary carcinoma cells. MDA-MB-231 cells capable of proteolytic degradation and mesenchymal motion, invaded telopeptide-intact and telopeptide-free collagen gels to the same extent. In contrast, MDA-MB-435S cells, with typical features of amoeboid cells (poor collagenolytic activity, rounded cell morphology), were 5-fold more invasive in telopeptide-free than telopeptide-intact collagen. A fraction of the MDA-MB-435S cells that invaded telopeptide-intact or telopeptide-free collagen had a rounded morphology; however, in telopeptide-free collagen, a significant fraction of the cells switched from a rounded to elongated morphology (protrusion formation). The dynamic changes in cellular shape facilitated MDA-MB-435S locomotion through the narrow interfiber gaps, which were smaller than cell diameters. Based on the spherical morphology of MDA-MB-435S cells, we tested if the changes in cell shape and invasion were related to RhoA-ROCK activity; GTP-bound RhoA was measured in pull-down assays. RhoA activity was 1.8-fold higher for MDA-MB-435S cells seeded on telopeptide-free than telopeptide-intact collagen. Y27632 inhibition of ROCK, a Rho effector, significantly reduced the changes in cellular morphodynamics and the invasion of MDA-MB-435S cells but did not alter the invasion of MDA-MB-231 cells. Thus, the higher RhoA activity of MDA-MB-435S cells in telopeptide-free collagen enhances the changes in cellular morphodynamics associated with motility and invasion