Universality of a double scaling limit near singular edge points in random matrix models

We consider unitary random matrix ensembles Z_{n,s,t}^{-1}e^{-n tr V_{s,t}(M)}dM on the space of Hermitian n x n matrices M, where the confining potential V_{s,t} is such that the limiting mean density of eigenvalues (as n\to\infty and s,t\to 0) vanishes like a power 5/2 at a (singular) endpoint of its support. The main purpose of this paper is to prove universality of the eigenvalue correlation kernel in a double scaling limit. The limiting kernel is built out of functions associated with a special solution of the P_I^2 equation, which is a fourth order analogue of the Painleve I equation. In order to prove our result, we use the well-known connection between the eigenvalue correlation kernel and the Riemann-Hilbert (RH) problem for orthogonal polynomials, together with the Deift/Zhou steepest descent method to analyze the RH problem asymptotically. The key step in the asymptotic analysis will be the construction of a parametrix near the singular endpoint, for which we use the model RH problem for the special solution of the P_I^2 equation. In addition, the RH method allows us to determine the asymptotics (in a double scaling limit) of the recurrence coefficients of the orthogonal polynomials with respect to the varying weights e^{-nV_{s,t}} on \mathbb{R}. The special solution of the P_I^2 equation pops up in the n^{-2/7}-term of the asymptotics.Comment: 32 pages, 3 figure

Universality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach

We obtain an asymptotic expansion for the solution of the Cauchy problem for the Korteweg-de Vries (KdV) equation in the small dispersion limit near the point of gradient catastrophe (x_c,t_c) for the solution of the dispersionless equation. The sub-leading term in this expansion is described by the smooth solution of a fourth order ODE, which is a higher order analogue to the Painleve I equation. This is in accordance with a conjecture of Dubrovin, suggesting that this is a universal phenomenon for any Hamiltonian perturbation of a hyperbolic equation. Using the Deift/Zhou steepest descent method applied on the Riemann-Hilbert problem for the KdV equation, we are able to prove the asymptotic expansion rigorously in a double scaling limit.Comment: 30 page

Diabetic patients with acute coronary syndromes in contemporary European registries: characteristics and outcomes

In acute coronary syndromes (ACS), those with diabetes mellitus (DM) are at high risk of recurrent cardiovascular events and premature death. We described patient characteristics, ACS management, and outcomes up to 1 year after hospital admission for an ACS/index-ACS event, in patients with DM in 10 contemporary European registries. In the 10 registries there were 28,899 with and 97,505 without without DM. In the DM population, the proportion of patients with ST-Segment Elevation Myocardial Infarction (STEMI) ranged from 22.1% to 100.0% (other patients had non-ST-Segment Elevation Myocardial Infarction (NSTEMI-ACS) or unstable angina). All-cause mortality in the registries ranged from 1.4% to 9.4% in-hospital; 2.8% to 7.9% at 30 days post-discharge; 5.1% to 10.7% at 180 days post-discharge; and 3.3% to 10.5% at 1 year post-discharge. Major bleeding events were reported in up to 3.8% of patients while in hospital (8 registries); up to 1.3% at 30 days (data from two registries only), and 2.0% at 1 year (one registry only). Registries differed substantially in terms of study setting, site, patient selection, definition and schedule of endpoints, and use of various P2Y12 inhibitors. Pooled risk ratios comparing cohorts with DM vs. no DM were in-hospital significantly higher in DM for all-cause death (1.66; 95% CI 1.42-1.94), for cardiovascular death (2.33; 1.78 - 3.03), and for major bleeding (1.35; 1.21-1.52)

Coronavirus disease 2019 (COVID-19) research agenda for healthcare epidemiology

This SHEA white paper identifies knowledge gaps and challenges in healthcare epidemiology research related to coronavirus disease 2019 (COVID-19) with a focus on core principles of healthcare epidemiology. These gaps, revealed during the worst phases of the COVID-19 pandemic, are described in 10 sections: epidemiology, outbreak investigation, surveillance, isolation precaution practices, personal protective equipment (PPE), environmental contamination and disinfection, drug and supply shortages, antimicrobial stewardship, healthcare personnel (HCP) occupational safety, and return to work policies. Each section highlights three critical healthcare epidemiology research questions with detailed description provided in supplementary materials. This research agenda calls for translational studies from laboratory-based basic science research to well-designed, large-scale studies and health outcomes research. Research gaps and challenges related to nursing homes and social disparities are included. Collaborations across various disciplines, expertise and across diverse geographic locations will be critical

Comparison of P2Y12 receptor inhibitors in patients with ST-elevation myocardial infarction in clinical practice: a propensity score analysis of five contemporary European registries

INTRODUCTION Among acute coronary syndromes (ACS), ST-segment elevation myocardial infarction (STEMI) has the most severe early clinical course. Recent randomized clinical trials have demonstrated that novel antithrombotic therapies improve in-hospital outcomes in STEMI patients. We aimed to describe the effectiveness and safety of P2Y12 receptor inhibitors in clinical practice in patients with STEMI based on data from contemporary European ACS registries. METHODS AND RESULTS Five registries from the PIRAEUS initiative (AAPCI/ADPAT, ALKK-PIC, AMIS Plus, Belgium STEMI, EYESHOT) provided data for the assessment of P2Y12 receptor inhibitor-based dual antiplatelet therapy. Registries were heterogeneous in terms of setting, patient characteristics and treatment selection. Matched pair analysis and propensity score matching were used to assess all-cause in-hospital death rates based on data from 25'250 patients (8'577 patients on prasugrel, 5'995 on ticagrelor, and 10'678 on clopidogrel). The odds ratio for death of any cause when compared to clopidogrel were 0.72 (CI 0.62 - 0.84, p < 0.001) in favor of the new P2Y12 receptor inhibitors (prasugrel and ticagrelor combined). In the comparison between prasugrel and ticagrelor, there were no relevant differences (OR 0.97; CI 0.77 -1.23, p = 0.81). Event rates of cardiovascular death and stroke were also substantially lower for the new P2Y12 receptor inhibitors. The differences between clopidogrel and prasugrel or ticagrelor on major bleeding were numerically in the same order as for death of any cause, but were not statistically significant. No differences in ischemic and bleeding outcomes were observed between prasugrel and ticagrelor. CONCLUSION This analysis suggests that the prasugrel or ticagrelor compared to clopidogrel have favorable outcomes in clinical practice while not being inferior in terms of safety

Unexplored Antarctic meteorite collection sites revealed through machine learning

Meteorites provide a unique view into the origin and evolution of the Solar System. Antarctica is the most productive region for recovering meteorites, where these extraterrestrial rocks concentrate at meteorite stranding zones. To date, meteorite-bearing blue ice areas are mostly identified by serendipity and through costly reconnaissance missions. Here, we identify meteorite-rich areas by combining state-of-the-art datasets in a machine learning algorithm and provide continent-wide estimates of the probability to find meteorites at any given location. The resulting set of ca. 600 meteorite stranding zones, with an estimated accuracy of over 80%, reveals the existence of unexplored zones, some of which are located close to research stations. Our analyses suggest that less than 15% of all meteorites at the surface of the Antarctic ice sheet have been recovered to date. The data-driven approach will greatly facilitate the quest to collect the remaining meteorites in a coordinated and cost-effective manner.info:eu-repo/semantics/publishe

Whitham Modulation Equations and Application to Small Dispersion Asymptotics and Long Time Asymptotics of Nonlinear Dispersive Equations

In this chapter we review the theory of modulation equations orWhitham equations for the travelling wave solution of KdV. We then apply the Whitham modulation equations to describe the long-time asymptotics and small dispersion asymptotics of the KdV solution

A data-driven approach to quantifying Antarctic blue ice areas and the presence of meteorites

info:eu-repo/semantics/publishe