A literature survey of low-rank tensor approximation techniques

During the last years, low-rank tensor approximation has been established as a new tool in scientific computing to address large-scale linear and multilinear algebra problems, which would be intractable by classical techniques. This survey attempts to give a literature overview of current developments in this area, with an emphasis on function-related tensors

Preconditioned Low-Rank Methods for High-Dimensional Elliptic PDE Eigenvalue Problems

We consider elliptic PDE eigenvalue problems on a tensorized domain, discretized such that the resulting matrix eigenvalue problem Ax=λx exhibits Kronecker product structure. In particular, we are concerned with the case of high dimensions, where standard approaches to the solution of matrix eigenvalue problems fail due to the exponentially growing degrees of freedom. Recent work shows that this curse of dimensionality can in many cases be addressed by approximating the desired solution vector x in a low-rank tensor format. In this paper, we use the hierarchical Tucker decomposition to develop a low-rank variant of LOBPCG, a classical preconditioned eigenvalue solver. We also show how the ALS and MALS (DMRG) methods known from computational quantum physics can be adapted to the hierarchical Tucker decomposition. Finally, a combination of ALS and MALS with LOBPCG and with our low-rank variant is proposed. A number of numerical experiments indicate that such combinations represent the methods of choic

Non-invasive nuclear myocardial perfusion imaging improves the diagnostic yield of invasive coronary angiography

Aims Several studies reported on the moderate diagnostic yield of elective invasive coronary angiography (ICA) regarding the presence of coronary artery disease (CAD), but limited data are available on how prior testing for ischaemia may contribute to improve the diagnostic yield in an every-day clinical setting. This study aimed to assess the value and use of cardiac myocardial perfusion single photon emission computed tomography (MPS) in patient selection prior to elective ICA. Methods and results The rate of MPS within 90 days prior to elective ICA was assessed and the non-invasive test results were correlated with the presence of obstructive CAD on ICA (defined as stenosis of ≥50% of a major epicardial coronary vessel). Multivariate logistic regression analysis was performed to identify predictors of obstructive CAD. A total of 7530 consecutive patients were included. At catheterization, 3819 (50.7%) were diagnosed as having obstructive CAD. Patients with a positive result on MPS (performed in 23.5% of patients) were significantly more likely to have obstructive CAD as assessed by ICA than those who did not undergo non-invasive testing (74.4 vs. 45.6%, P < 0.001). Furthermore, a pathological MPS result was a strong, independent predictor for CAD findings among traditional risk factors and symptoms. Conclusion In an every-day clinical setting, the use of MPS substantially increases the diagnostic yield of elective ICA and provides incremental value over clinical risk factors and symptoms in predicting obstructive CAD, thus emphasizing its importance in the decision-making process leading to the use of diagnostic catheterizatio

An Error Analysis Of Galerkin Projection Methods For Linear Systems With Tensor Product Structure

Recent results on the convergence of a Galerkin projection method for the Sylvester equation are extended to more general linear systems with tensor product structure. In the Hermitian positive definite case, explicit convergence bounds are derived for Galerkin projection based on tensor products of rational Krylov subspaces. The results can be used to optimize the choice of shifts for these methods. Numerical experiments demonstrate that the convergence rates predicted by our bounds appear to be sharp

Choir singing improves respiratory muscle strength and quality of life in patients with structural heart disease - HeartChoir: a randomised clinical trial

Most patients with reduced exercise capacity and acquired or congenital structural heart disease also have a reduced respiratory muscle strength. The aim of this pilot study was to investigate whether choir singing in combination with respiratory muscle training positively influences respiratory muscle strength, exercise capacity and quality of life in this population.; In this single-centre, randomised and open-label interventional study we compared respiratory muscle strength, exercise capacity and quality of life in patients with acquired or congenital structural heart disease who received either standard of care and a 12-week intervention (weekly choir rehearsal and daily breathing exercises) or standard of care alone. The primary endpoint was the difference in change in maximum inspiratory pressure (∆MIP%predicted). Secondary endpoints included the difference in change in maximum expiratory pressure (∆MEP%predicted), exercise capacity quantified as maximal oxygen uptake during exercise (∆MVO2%predicted) and quality of life quantified by the Minnesota living with heart failure questionnaire (∆MLHFQ score).; Overall 24 patients (mean age 65, standard deviation [SD] 19 years, 46% male) were randomised after exclusion. ∆MIP%predicted was significantly higher in the intervention group (∆MIP%predicted +14, SD 21% vs −14, SD 23%; p = 0.008) and quality of life improved significantly (∆MLHFQ score −5, SD 6 vs 3, SD 5; p = 0.006) after 12 weeks. ∆MEP%predicted and ∆MVO2%predicted did not differ between both groups (∆MEP%predicted −3, SD 26% vs −3, SD 16%; p = 1.0 and ∆MVO2%predicted 18, SD 12% vs 10, SD 15%; p = 0.2).; Choir singing in combination with respiratory muscle training improved respiratory muscle strength and quality of life in patients with structural heart disease and may therefore be valuable supplements in cardiac rehabilitation. (Clinical trial registration number: NCT03297918)

Risk stratification of adults with congenital heart disease during the COVID-19 pandemic: insights from a multinational survey among European experts

Coronavirus SARS-CoV-2; COVID-19; 2019-nCoV; Congènit; Defectes cardíacsCoronavirus SARS-CoV-2; COVID-19; 2019-nCoV; Congénito; Defectos cardiacosCoronavirus SARS-CoV-2; COVID-19; 2019-nCoV; Congenital; Heart defectsObjective Adults with congenital heart disease (ACHD) may be at a higher risk of a fatal outcome in case of COVID-19. Current risk stratification among these patients relies on personal experience and extrapolation from patients with acquired heart disease. We aimed to provide an expert view on risk stratification while awaiting results from observational studies. Methods This study was an initiative of the EPOCH (European Collaboration for Prospective Outcome Research in Congenital Heart disease). Among nine European countries (Austria, Belgium, Denmark, France, Germany, Italy, the Netherlands, Spain and Switzerland), 24 experts from 23 tertiary ACHD centres participated in the survey. ACHD experts were asked to identify ACHD-specific COVID-19 risk factors from a list of potential outcome predictors and to estimate the risk of adverse COVID-19 outcomes in seven commonly seen patient scenarios. Results 82% of participants did not consider all ACHD patients at risk of COVID-19 related complications. There was a consensus on pulmonary arterial hypertension, Fontan physiology and cyanotic heart disease as risk factors for adverse outcomes. Among different ACHD scenarios, a patient with Eisenmenger syndrome was considered to be at the highest risk. There was a marked variability in risk estimation among the other potential outcome predictors and ACHD scenarios. Conclusions Pulmonary arterial hypertension, Fontan palliation and cyanotic heart disease were widely considered as risk factors for poor outcome in COVID-19. However, there was a marked disparity in risk estimation for other clinical scenarios. We are in urgent need of outcome studies in ACHD suffering from COVID-19.EPOCH-ASO is funded by internal grants without support from the pharmaceutical industry

MATHICSE Technical Report : Low-rank tensor approximation for high-order correlation functions of Gaussian random fields

Gaussian random fields are widely used as building blocks for modeling stochastic processes. This paper is concerned with the efficient representation of d-point correlations for such fields, which in turn enables the representation of more general stochastic processes that can be expressed as a function of one (or several) Gaussian random fields. Our representation consists of two ingredients. In the first step, we replace the random field by a truncated Karhunen-Loève expansion and analyze the resulting error. The parameters describing the d-point correlation can be arranged in a tensor, but its storage grows exponentially in d. To avoid this, the second step consists of approximating the tensor in a low-rank tensor format, the so called Tensor Train decomposition. By exploiting the particular structure of the tensor, an approximation algorithm is derived that does not need to form this tensor explicitly and allows to process correlations of order as high as d = 20. The resulting representation is very compact and its use is illustrated for elliptic partial differential equations with random Gaussian forcing terms