A Bramble-Pasciak conjugate gradient method for discrete Stokes equations with random viscosity

We study the iterative solution of linear systems of equations arising from stochastic Galerkin finite element discretizations of saddle point problems. We focus on the Stokes model with random data parametrized by uniformly distributed random variables and discuss well-posedness of the variational formulations. We introduce a Bramble-Pasciak conjugate gradient method as a linear solver. It builds on a non-standard inner product associated with a block triangular preconditioner. The block triangular structure enables more sophisticated preconditioners than the block diagonal structure usually applied in MINRES methods. We show how the existence requirements of a conjugate gradient method can be met in our setting. We analyze the performance of the solvers depending on relevant physical and numerical parameters by means of eigenvalue estimates. For this purpose, we derive bounds for the eigenvalues of the relevant preconditioned sub-matrices. We illustrate our findings using the flow in a driven cavity as a numerical test case, where the viscosity is given by a truncated Karhunen-Lo\`eve expansion of a random field. In this example, a Bramble-Pasciak conjugate gradient method with block triangular preconditioner outperforms a MINRES method with block diagonal preconditioner in terms of iteration numbers.Comment: 19 pages, 1 figure, submitted to SIAM JU

POD model order reduction with space-adapted snapshots for incompressible flows

We consider model order reduction based on proper orthogonal decomposition (POD) for unsteady incompressible Navier-Stokes problems, assuming that the snapshots are given by spatially adapted finite element solutions. We propose two approaches of deriving stable POD-Galerkin reduced-order models for this context. In the first approach, the pressure term and the continuity equation are eliminated by imposing a weak incompressibility constraint with respect to a pressure reference space. In the second approach, we derive an inf-sup stable velocity-pressure reduced-order model by enriching the velocity reduced space with supremizers computed on a velocity reference space. For problems with inhomogeneous Dirichlet conditions, we show how suitable lifting functions can be obtained from standard adaptive finite element computations. We provide a numerical comparison of the considered methods for a regularized lid-driven cavity problem

Application of Proper Orthogonal Decomposition Methods in Reactive Pore Diffusion Simulations

Reactive pore diffusion is an important process in automotive exhaust-gas aftertreatment modelling the overall conversion of pollutants. It features highly nonlinear source terms from chemical reactions coupled with transport processes. This work examines the application of model reduction by proper orthogonal decomposition. It is shown that this technique can be successfully applied to the system using separate bases for each species. Using a basis obtained for baseline conditions, predictions can be made for species profiles within a pore system for different conditions, potentially leading to significantly reduced computational requirements

Recovery index, attentiveness and state of memory after xenon or isoflurane anaesthesia: a randomized controlled trial

<p>Abstract</p> <p>Background</p> <p>Performance of patients immediately after anaesthesia is an area of special interest and so a clinical trial was conducted to compare Xenon with Isoflurane anaesthesia. In order to assess the early cognitive recovery the syndrome short test (SST) according to Erzigkeit (Geromed GmbH) was applied.</p> <p>Methods</p> <p>ASA I and II patients undergoing long and short surgical interventions were randomised to receive either general anaesthesia with Xenon or Isoflurane. The primary endpoint was the validated SST which covering memory disturbances and attentiveness. The test was used on the day prior to intervention, one and three hours post extubation. The secondary endpoint was the recovery index (RI) measured after the end of the inhalation of Xenon or Isoflurane. In addition the Aldrete score was evaluated up to 180 min. On the first post-operative day the patients rated the quality of the anaesthetic using a scoring system from 1-6.</p> <p>Results</p> <p>The demographics of the groups were similar. The sum score of the SST delivered a clear trend one hour post extubation and a statistically significant superiority for Xenon three hours post extubation (p < 0.01). The RI likewise revealed a statistically significant superiority of Xenon 5 minutes post extubation (p < 0.01). The Aldrete score was significantly higher for 45 min. The scoring system results were also better after Xenon anaesthesia (p < 0.001).</p> <p>Conclusions</p> <p>The results show that recovery from anaesthesia and the early return of post-operative cognitive functions are significantly better after Xenon anaesthesia compared to Isoflurane. The results of the RI for Xenon are similar with the previously published results.</p> <p>Trial Registration</p> <p>The trial was registered with the number ISRCTN01110844 <url>http://www.controlled-trials.com/isrctn/pf/01110844</url>.</p

Effects of autologous bone marrow stem cell transplantation on beta-adrenoceptor density and electrical activation pattern in a rabbit model of non-ischemic heart failure

BACKGROUND: Since only little is known on stem cell therapy in non-ischemic heart failure we wanted to know whether a long-term improvement of cardiac function in non-ischemic heart failure can be achieved by stem cell transplantation. METHODS: White male New Zealand rabbits were treated with doxorubicine (3 mg/kg/week; 6 weeks) to induce dilative non-ischemic cardiomyopathy. Thereafter, we obtained autologous bone marrow stem cells (BMSC) and injected 1.5–2.0 Mio cells in 1 ml medium by infiltrating the myocardium via a left anterolateral thoracotomy in comparison to sham-operated rabbits. 4 weeks later intracardiac contractility was determined in-vivo using a Millar catheter. Thereafter, the heart was excised and processed for radioligand binding assays to detect β(1)- and β(2)-adrenoceptor density. In addition, catecholamine plasma levels were determined via HPLC. In a subgroup we investigated cardiac electrophysiology by use of 256 channel mapping. RESULTS: In doxorubicine-treated animals β-adrenoceptor density was significantly down-regulated in left ventricle and septum, but not in right ventricle, thereby indicating a typical left ventricular heart failure. Sham-operated rabbits exhibited the same down-regulation. In contrast, BMSC transplantation led to significantly less β-adrenoceptor down-regulation in septum and left ventricle. Cardiac contractility was significantly decreased in heart failure and sham-operated rabbits, but was significantly higher in BMSC-transplanted hearts. Norepinephrine and epinephrine plasma levels were enhanced in heart failure and sham-operated animals, while these were not different from normal in BMSC-transplanted animals. Electrophysiological mapping revealed unaltered electrophysiology and did not show signs of arrhythmogeneity. CONCLUSION: BMSC transplantation improves sympathoadrenal dysregualtion in non-ischemic heart failure

Evaluating expert-based habitat suitability information of terrestrial mammals with GPS-tracking data

Aim Macroecological studies that require habitat suitability data for many species often derive this information from expert opinion. However, expert-based information is inherently subjective and thus prone to errors. The increasing availability of GPS tracking data offers opportunities to evaluate and supplement expert-based information with detailed empirical evidence. Here, we compared expert-based habitat suitability information from the International Union for Conservation of Nature (IUCN) with habitat suitability information derived from GPS-tracking data of 1,498 individuals from 49 mammal species. Location Worldwide. Time period 1998-2021. Major taxa studied Forty-nine terrestrial mammal species. Methods Using GPS data, we estimated two measures of habitat suitability for each individual animal: proportional habitat use (proportion of GPS locations within a habitat type), and selection ratio (habitat use relative to its availability). For each individual we then evaluated whether the GPS-based habitat suitability measures were in agreement with the IUCN data. To that end, we calculated the probability that the ranking of empirical habitat suitability measures was in agreement with IUCN's classification into suitable, marginal and unsuitable habitat types. Results IUCN habitat suitability data were in accordance with the GPS data (> 95% probability of agreement) for 33 out of 49 species based on proportional habitat use estimates and for 25 out of 49 species based on selection ratios. In addition, 37 and 34 species had a > 50% probability of agreement based on proportional habitat use and selection ratios, respectively. Main conclusions We show how GPS-tracking data can be used to evaluate IUCN habitat suitability data. Our findings indicate that for the majority of species included in this study, it is appropriate to use IUCN habitat suitability data in macroecological studies. Furthermore, we show that GPS-tracking data can be used to identify and prioritize species and habitat types for re-evaluation of IUCN habitat suitability data

Effect of angiotensin-converting enzyme inhibitor and angiotensin receptor blocker initiation on organ support-free days in patients hospitalized with COVID-19

IMPORTANCE Overactivation of the renin-angiotensin system (RAS) may contribute to poor clinical outcomes in patients with COVID-19. Objective To determine whether angiotensin-converting enzyme (ACE) inhibitor or angiotensin receptor blocker (ARB) initiation improves outcomes in patients hospitalized for COVID-19. DESIGN, SETTING, AND PARTICIPANTS In an ongoing, adaptive platform randomized clinical trial, 721 critically ill and 58 non–critically ill hospitalized adults were randomized to receive an RAS inhibitor or control between March 16, 2021, and February 25, 2022, at 69 sites in 7 countries (final follow-up on June 1, 2022). INTERVENTIONS Patients were randomized to receive open-label initiation of an ACE inhibitor (n = 257), ARB (n = 248), ARB in combination with DMX-200 (a chemokine receptor-2 inhibitor; n = 10), or no RAS inhibitor (control; n = 264) for up to 10 days. MAIN OUTCOMES AND MEASURES The primary outcome was organ support–free days, a composite of hospital survival and days alive without cardiovascular or respiratory organ support through 21 days. The primary analysis was a bayesian cumulative logistic model. Odds ratios (ORs) greater than 1 represent improved outcomes. RESULTS On February 25, 2022, enrollment was discontinued due to safety concerns. Among 679 critically ill patients with available primary outcome data, the median age was 56 years and 239 participants (35.2%) were women. Median (IQR) organ support–free days among critically ill patients was 10 (–1 to 16) in the ACE inhibitor group (n = 231), 8 (–1 to 17) in the ARB group (n = 217), and 12 (0 to 17) in the control group (n = 231) (median adjusted odds ratios of 0.77 [95% bayesian credible interval, 0.58-1.06] for improvement for ACE inhibitor and 0.76 [95% credible interval, 0.56-1.05] for ARB compared with control). The posterior probabilities that ACE inhibitors and ARBs worsened organ support–free days compared with control were 94.9% and 95.4%, respectively. Hospital survival occurred in 166 of 231 critically ill participants (71.9%) in the ACE inhibitor group, 152 of 217 (70.0%) in the ARB group, and 182 of 231 (78.8%) in the control group (posterior probabilities that ACE inhibitor and ARB worsened hospital survival compared with control were 95.3% and 98.1%, respectively). CONCLUSIONS AND RELEVANCE In this trial, among critically ill adults with COVID-19, initiation of an ACE inhibitor or ARB did not improve, and likely worsened, clinical outcomes. TRIAL REGISTRATION ClinicalTrials.gov Identifier: NCT0273570

Stochastic Galerkin reduced basis methods for parametrized linear elliptic PDEs

We consider the estimation of parameter-dependent statistics of functional outputs of elliptic boundary value problems with parametrized random and deterministic inputs. For a given value of the deterministic parameter, a stochastic Galerkin finite element (SGFE) method can estimate the corresponding expectation and variance of a linear output at the cost of a single solution of a large block-structured linear algebraic system of equations. We propose a stochastic Galerkin reduced basis (SGRB) method as a means to lower the computational burden when statistical outputs are required for a large number of deterministic parameter queries. To derive an SGRB model, we project the spatial-stochastic weak solution of a parameter-dependent SGFE model onto a POD reduced basis generated from snapshots of the SGFE solution at representative values of the parameter. We propose residual-corrected estimates of the parameter-dependent expectation and variance of linear functional outputs and provide respective computable error bounds. We test the SGRB method numerically for a convection-diffusion-reaction problem, choosing the convective velocity as a deterministic parameter and the parametrized reactivity field as a random input. Compared to a standard reduced basis model embedded in a Monte Carlo sampling procedure, the SGRB model requires a similar number of reduced basis functions to meet a given tolerance requirement. However, only a single run of the SGRB model suffices to estimate a statistical output for a new deterministic parameter value, while the standard reduced basis model must be solved for each Monte Carlo sample