An efficient direct solver for a class of mixed finite element problems

In this paper we present an efficient, accurate and parallelizable direct method for the solution of the (indefinite) linear algebraic systems that arise in the solution of fourth-order partial differential equations (PDEs) using mixed finite element approximations. The method is intended particularly for use when multiple right-hand sides occur, and when high accuracy is required in these solutions. The algorithm is described in some detail and its performance is illustrated through the numerical solution of a biharmonic eigenvalue problem where the smallest eigenpair is approximated using inverse iteration after discretization via the Ciarlet–Raviart mixed finite element method

New, Highly Accurate Propagator for the Linear and Nonlinear Schr\"odinger Equation

A propagation method for the time dependent Schr\"odinger equation was studied leading to a general scheme of solving ode type equations. Standard space discretization of time-dependent pde's usually results in system of ode's of the form u_t -Gu = s where G is a operator (matrix) and u is a time-dependent solution vector. Highly accurate methods, based on polynomial approximation of a modified exponential evolution operator, had been developed already for this type of problems where G is a linear, time independent matrix and s is a constant vector. In this paper we will describe a new algorithm for the more general case where s is a time-dependent r.h.s vector. An iterative version of the new algorithm can be applied to the general case where G depends on t or u. Numerical results for Schr\"odinger equation with time-dependent potential and to non-linear Schr\"odinger equation will be presented.Comment: 14 page

Whole-genome sequencing reveals host factors underlying critical COVID-19

Critical COVID-19 is caused by immune-mediated inflammatory lung injury. Host genetic variation influences the development of illness requiring critical care1 or hospitalization2,3,4 after infection with SARS-CoV-2. The GenOMICC (Genetics of Mortality in Critical Care) study enables the comparison of genomes from individuals who are critically ill with those of population controls to find underlying disease mechanisms. Here we use whole-genome sequencing in 7,491 critically ill individuals compared with 48,400 controls to discover and replicate 23 independent variants that significantly predispose to critical COVID-19. We identify 16 new independent associations, including variants within genes that are involved in interferon signalling (IL10RB and PLSCR1), leucocyte differentiation (BCL11A) and blood-type antigen secretor status (FUT2). Using transcriptome-wide association and colocalization to infer the effect of gene expression on disease severity, we find evidence that implicates multiple genes—including reduced expression of a membrane flippase (ATP11A), and increased expression of a mucin (MUC1)—in critical disease. Mendelian randomization provides evidence in support of causal roles for myeloid cell adhesion molecules (SELE, ICAM5 and CD209) and the coagulation factor F8, all of which are potentially druggable targets. Our results are broadly consistent with a multi-component model of COVID-19 pathophysiology, in which at least two distinct mechanisms can predispose to life-threatening disease: failure to control viral replication; or an enhanced tendency towards pulmonary inflammation and intravascular coagulation. We show that comparison between cases of critical illness and population controls is highly efficient for the detection of therapeutically relevant mechanisms of disease

Mechanism of ethylene oxychlorination over ruthenium oxide

The oxychlorination of ethylene is an industrially relevant process within the manufacture of polyvinyl chloride (PVC). Although RuO2 is the best performing catalyst for the Deacon process (4HCl + O2? 2H2O + 2Cl2), experiments demonstrate a modest activity in the selective oxychlorination to vinyl chloride, favouring oxidation and polychlorinated saturated products. From the computational modelling three main contributions are found to control the performance: (i) coverage effects that alter the configuration of intermediates; (ii) the monodimensional arrangement of the active sites, in which the reaction of coadsorbed species works on a ‘‘first-come, first-served” basis; and (iii) the high reactivity of the oxygen species. Competition between oxidation and chlorination processes results in variable selectivity, depending on the reaction conditions (particularly temperature and reactant partial pressures), which influence the surface composition. From the analysis of the complex reaction network, the essential requirements for a good oxychlorination catalyst are formulated

Optimized Dense Matrix Multiplication on a Many-Core Architecture

Abstract. Traditional parallel programming methodologies for improv-ing performance assume cache-based parallel systems. However, new ar-chitectures, like the IBM Cyclops-64 (C64), belong to a new set of many-core-on-a-chip systems with a software managed memory hierarchy. New programming and compiling methodologies are required to fully exploit the potential of this new class of architectures. In this paper, we use dense matrix multiplication as a case of study to present a general methodology to map applications to these kinds of architectures. Our methodology exposes the following characteristics: (1) Balanced distribution of work among threads to fully exploit avail-able resources. (2) Optimal register tiling and sequence of traversing tiles, calculated analytically and parametrized according to the register file size of the processor used. This results in minimal memory transfers and optimal register usage. (3) Implementation of architecture specific optimizations to further increase performance. Our experimental evalu-ation on a real C64 chip shows a performance of 44.12 GFLOPS, which corresponds to 55.2 % of the peak performance of the chip. Additionally, measurements of power consumption prove that the C64 is very power efficient providing 530 MFLOPS/W for the problem under consideration.

Myocardial Infarction in Major Noncardiac Surgery: Epidemiology, Pathophysiology and Prevention

The number of subjects undergoing major noncardiac surgery who are at risk for perioperative myocardial infarction (MI) is growing worldwide. It has been estimated that 500,000 to 900,000 patients suffer major perioperative cardiovascular complications every year, with consequent heavy, long-term prognostic implications and costs. It is well known that perioperative MIs don’t share the same pathophysiology as nonsurgical MIs but the relative role of the different, potential triggers has not been completely clarified. Many aspects of the perioperative management, including risk-stratification and prophylactic or postoperative interventions have also not been completely defined. Throughout recent years many resources have been invested to clarify these aspects and experts have developed indices and algorithm-based strategies to better assess the cardiac risk and to guide the perioperative management. The scope of the present review is to discuss the main aspects of perioperative MI in noncardiac surgery, with particular regard to epidemiology, pathophysiology, preoperative risk stratification, prophylaxis and therapy