A restricted signature normal form for Hermitian matrices, quasi-spectral decompositions, and applications

In recent years, a number of results on the relationships between the inertias of Hermitian matrices and the inertias of their principal submatrices appeared in the literature. We study restricted congruence transformation of Hermitian matrices M which, at the same time, induce a congruence transformation of a given principal submatrix A of M. Such transformations lead to concept of the restricted signature normal form of M. In particular, by means of this normal form, we obtain short proofs of most of the known inertia theorems and also derive some new results of this type. For some applications, a special class of almost unitary restricted congruence transformations turns out to be useful. We show that, with such transformations, M can be reduced to a quasi-diagonal form which, in particular, displays the eigenvalues of A. Finally, applications of this quasi-spectral decomposition to generalize inverses and Hermitian matrix pencils are discussed

An extension problem for H-unitary matrices with applications to Hermitian Toeplitz matrices

AbstractGiven a Hermitian matrix H, a matrix U is said to be H-unitary if UHHU = H. We consider the following extension problem: If U0 is a rectangular matrix such that UH0HU0 = A, where A is a leading principal submatrix of H, can U0 be extended to an H-unitary matrix? After presenting necessary conditions for a more general situation, we state a necessary and sufficient criterion for this problem and give a description of all its solutions. Finally, these results are used to derive some properties of factorizations of Hermitian Toeplitz matrices

Multigrid methods for anisotropic BTTB systems

AbstractMultigrid methods are highly efficient solution techniques for large sparse multilevel Toeplitz systems which are positive definite and ill-conditioned. In this paper, we develop multigrid methods which are especially designed for anisotropic two-level Toeplitz (BTTB) matrices. First, a method is described for systems with anisotropy along coordinate axes as a suitable combination of semicoarsening and full coarsening steps. Although the basic idea is known from the solution of partial differential equations, we present it here in a more formal way using generating functions and their level curves. This enables us not only to prove the optimal convergence of the two-grid method, but also to carry over the results to systems with anisotropy in other directions. We introduce new coordinates in order to describe these more complicated systems in terms of generating functions. This enables us to solve them with the same efficiency. For the two-level method, we present a convergence proof in this more general case

A restricted signature normal form for Hermitian matrices, quasi-spectral decompositions, and applications

AbstractIn recent years, a number of results on the relationships between the inertias of Hermitian matrices and the inertias of their principal submatrices have appeared in the literature. In this paper, we study restricted congruence transformations of Hermitian matrices M that, at the same time, induce a congruence transformation of a given principal submatrix A of M. Such transformations lead to the concept of the restricted signature normal form of M. In particular, by means of this normal form, we obtain new and shorter proofs for several known inertia theorems and also derive some new results of this type. For some applications, a special class of “almost” unitary restricted congruence transformations turns out to be useful. We show that, with such transformations, M can be reduced to a quasi-diagonal form, which, in particular, displays the eigenvalues of A. Moreover, this quasi-spectral decomposition is used to derive a generalized signature formula and to study Hermitian matrix pencils

Final technical report : The International Alcohol Control (IAC) Study - Working Meeting, Torino, Italy, 7th and 8th June 2014

This is part of a funding proposal report. Funding received was used to support costs associated with the preparation, facilitation and hosting of the IAC study meeting in Torino, Italy. In addition the financial support enabled three low and middle income (LMIC) researchers and one member of the New Zealand IAC study team to attend the working meeting. IAC survey data was shared from participating countries; cross-country analyses were discussed and planned; and methodological issues encountered by the different research teams were discussed

Effective alcohol policies and lifetime abstinence An analysis of the International Alcohol Control policy index

Introduction Alcohol abstinence remains common among adults globally, although low and middle-income countries are experiencing declines in abstention. The effect of alcohol policies on lifetime abstinence is poorly understood. The International Alcohol Control (IAC) policy index was developed to benchmark and monitor the uptake of effective alcohol policies and has shown strong associations with alcohol per capita consumption and drinking patterns. Uniquely, the index incorporates both policy ‘stringency’ and ‘impact’, reflecting policy implementation and enforcement, across effective policies. Here we assessed the association of the IAC policy index with lifetime abstinence in a diverse sample of jurisdictions. Methods We conducted a cross-sectional analysis of the relationship between the IAC policy index score, and its components, and lifetime abstinence among adults (15+ years) in 13 high and middle-income jurisdictions. We examined the correlations for each component of the index and stringency and impact separately. Results Overall, the total IAC policy index scores were positively correlated with lifetime abstinence (r = 0.76), as were both the stringency (r = 0.62) and impact (r = 0.82) scores. Marketing restrictions showed higher correlations with lifetime abstinence than other policy domains (r = 0.80), including restrictions on physical availability, pricing policies and drink-driving prevention. Discussion and Conclusion Our findings suggest that restricting alcohol marketing could be an important policy for the protection of alcohol abstention. The IAC policy index may be a useful tool to benchmark the performance of alcohol policy in supporting alcohol abstention in high and middle-income countries

Benefits from using mixed precision computations in the ELPA-AEO and ESSEX-II eigensolver projects

We first briefly report on the status and recent achievements of the ELPA-AEO (Eigenvalue Solvers for Petaflop Applications - Algorithmic Extensions and Optimizations) and ESSEX II (Equipping Sparse Solvers for Exascale) projects. In both collaboratory efforts, scientists from the application areas, mathematicians, and computer scientists work together to develop and make available efficient highly parallel methods for the solution of eigenvalue problems. Then we focus on a topic addressed in both projects, the use of mixed precision computations to enhance efficiency. We give a more detailed description of our approaches for benefiting from either lower or higher precision in three selected contexts and of the results thus obtained

Effective alcohol policies and lifetime abstinence An analysis of the International Alcohol Control policy index

Introduction Alcohol abstinence remains common among adults globally, although low and middle-income countries are experiencing declines in abstention. The effect of alcohol policies on lifetime abstinence is poorly understood. The International Alcohol Control (IAC) policy index was developed to benchmark and monitor the uptake of effective alcohol policies and has shown strong associations with alcohol per capita consumption and drinking patterns. Uniquely, the index incorporates both policy ‘stringency’ and ‘impact’, reflecting policy implementation and enforcement, across effective policies. Here we assessed the association of the IAC policy index with lifetime abstinence in a diverse sample of jurisdictions. Methods We conducted a cross-sectional analysis of the relationship between the IAC policy index score, and its components, and lifetime abstinence among adults (15+ years) in 13 high and middle-income jurisdictions. We examined the correlations for each component of the index and stringency and impact separately. Results Overall, the total IAC policy index scores were positively correlated with lifetime abstinence (r = 0.76), as were both the stringency (r = 0.62) and impact (r = 0.82) scores. Marketing restrictions showed higher correlations with lifetime abstinence than other policy domains (r = 0.80), including restrictions on physical availability, pricing policies and drink-driving prevention. Discussion and Conclusion Our findings suggest that restricting alcohol marketing could be an important policy for the protection of alcohol abstention. The IAC policy index may be a useful tool to benchmark the performance of alcohol policy in supporting alcohol abstention in high and middle-income countries.Output Status: Forthcoming/Available Onlin

The Swift Ultra-Violet/Optical Telescope

The UV/Optical Telescope (UVOT) is one of three instruments flying aboard the Swift Gamma-ray Observatory. It is designed to capture the early (approximately 1 minute) UV and optical photons from the afterglow of gamma-ray bursts in the 170-600 nm band as well as long term observations of these afterglows. This is accomplished through the use of UV and optical broadband filters and grisms. The UVOT has a modified Ritchey-Chretien design with micro-channel plate intensified charged-coupled device detectors that record the arrival time of individual photons and provide sub-arcsecond positioning of sources. We discuss some of the science to be pursued by the UVOT and the overall design of the instrument.Comment: 55 Pages, 28 Figures, To be published in Space Science Review

Effect of Hydrocortisone on Mortality and Organ Support in Patients With Severe COVID-19: The REMAP-CAP COVID-19 Corticosteroid Domain Randomized Clinical Trial.

Importance: Evidence regarding corticosteroid use for severe coronavirus disease 2019 (COVID-19) is limited. Objective: To determine whether hydrocortisone improves outcome for patients with severe COVID-19. Design, Setting, and Participants: An ongoing adaptive platform trial testing multiple interventions within multiple therapeutic domains, for example, antiviral agents, corticosteroids, or immunoglobulin. Between March 9 and June 17, 2020, 614 adult patients with suspected or confirmed COVID-19 were enrolled and randomized within at least 1 domain following admission to an intensive care unit (ICU) for respiratory or cardiovascular organ support at 121 sites in 8 countries. Of these, 403 were randomized to open-label interventions within the corticosteroid domain. The domain was halted after results from another trial were released. Follow-up ended August 12, 2020. Interventions: The corticosteroid domain randomized participants to a fixed 7-day course of intravenous hydrocortisone (50 mg or 100 mg every 6 hours) (n = 143), a shock-dependent course (50 mg every 6 hours when shock was clinically evident) (n = 152), or no hydrocortisone (n = 108). Main Outcomes and Measures: The primary end point was organ support-free days (days alive and free of ICU-based respiratory or cardiovascular support) within 21 days, where patients who died were assigned -1 day. The primary analysis was a bayesian cumulative logistic model that included all patients enrolled with severe COVID-19, adjusting for age, sex, site, region, time, assignment to interventions within other domains, and domain and intervention eligibility. Superiority was defined as the posterior probability of an odds ratio greater than 1 (threshold for trial conclusion of superiority >99%). Results: After excluding 19 participants who withdrew consent, there were 384 patients (mean age, 60 years; 29% female) randomized to the fixed-dose (n = 137), shock-dependent (n = 146), and no (n = 101) hydrocortisone groups; 379 (99%) completed the study and were included in the analysis. The mean age for the 3 groups ranged between 59.5 and 60.4 years; most patients were male (range, 70.6%-71.5%); mean body mass index ranged between 29.7 and 30.9; and patients receiving mechanical ventilation ranged between 50.0% and 63.5%. For the fixed-dose, shock-dependent, and no hydrocortisone groups, respectively, the median organ support-free days were 0 (IQR, -1 to 15), 0 (IQR, -1 to 13), and 0 (-1 to 11) days (composed of 30%, 26%, and 33% mortality rates and 11.5, 9.5, and 6 median organ support-free days among survivors). The median adjusted odds ratio and bayesian probability of superiority were 1.43 (95% credible interval, 0.91-2.27) and 93% for fixed-dose hydrocortisone, respectively, and were 1.22 (95% credible interval, 0.76-1.94) and 80% for shock-dependent hydrocortisone compared with no hydrocortisone. Serious adverse events were reported in 4 (3%), 5 (3%), and 1 (1%) patients in the fixed-dose, shock-dependent, and no hydrocortisone groups, respectively. Conclusions and Relevance: Among patients with severe COVID-19, treatment with a 7-day fixed-dose course of hydrocortisone or shock-dependent dosing of hydrocortisone, compared with no hydrocortisone, resulted in 93% and 80% probabilities of superiority with regard to the odds of improvement in organ support-free days within 21 days. However, the trial was stopped early and no treatment strategy met prespecified criteria for statistical superiority, precluding definitive conclusions. Trial Registration: ClinicalTrials.gov Identifier: NCT02735707