Interior Point Methods and Preconditioning for PDE-Constrained Optimization Problems Involving Sparsity Terms

PDE-constrained optimization problems with control or state constraints are challenging from an analytical as well as numerical perspective. The combination of these constraints with a sparsity-promoting $\rm L^1$ term within the objective function requires sophisticated optimization methods. We propose the use of an Interior Point scheme applied to a smoothed reformulation of the discretized problem, and illustrate that such a scheme exhibits robust performance with respect to parameter changes. To increase the potency of this method we introduce fast and efficient preconditioners which enable us to solve problems from a number of PDE applications in low iteration numbers and CPU times, even when the parameters involved are altered dramatically

Fast interior point solution of quadratic programming problems arising from PDE-constrained optimization

Interior point methods provide an attractive class of approaches for solving linear, quadratic and nonlinear programming problems, due to their excellent efficiency and wide applicability. In this paper, we consider PDE-constrained optimization problems with bound constraints on the state and control variables, and their representation on the discrete level as quadratic programming problems. To tackle complex problems and achieve high accuracy in the solution, one is required to solve matrix systems of huge scale resulting from Newton iteration, and hence fast and robust methods for these systems are required. We present preconditioned iterative techniques for solving a number of these problems using Krylov subspace methods, considering in what circumstances one may predict rapid convergence of the solvers in theory, as well as the solutions observed from practical computations

Refined saddle-point preconditioners for discretized Stokes problems

This paper is concerned with the implementation of efficient solution algorithms for elliptic problems with constraints. We establish theory which shows that including a simple scaling within well-established block diagonal preconditioners for Stokes problems can result in significantly faster convergence when applying the preconditioned MINRES method. The codes used in the numerical studies are available online

Tracheal adenoid cystic carcinoma masquerading asthma: A case report

BACKGROUND: Tracheal tumors are often misdiagnosed as asthma and are treated with inhaled steroids and bronchodilators without resolution. CASE PRESENTATION: Here, a patient with tracheal adenoid cystic carcinoma who had been previously diagnosed with difficult asthma was reported. The possibility of the presence of localized airway obstruction was raised when the flow-volume curve suggesting fixed airway obstruction, was obtained. CONCLUSION: The presenting case report emphasizes the fact that not all wheezes are asthma. It is critical to bear in mind that if a patient does not respond to appropriate anti-asthma therapy, localized obstructions should be ruled out before establishing the diagnosis of asthma

Matching Schur complement approximations for certain saddle-point systems

The solution of many practical problems described by mathematical models requires approximation methods that give rise to linear(ized) systems of equations, solving which will determine the desired approximation. This short contribution describes a particularly effective solution approach for a certain class of so-called saddle-point linear systems which arises in different contexts

Characterizations of how species mediate ecosystem properties require more comprehensive functional effect descriptors

The importance of individual species in mediating ecosystem process and functioning is generally accepted, but categorical descriptors that summarize species-specific contributions to ecosystems tend to reference a limited number of biological traits and underestimate the importance of how organisms interact with their environment. Here, we show how three functionally contrasting sediment-dwelling marine invertebrates affect fluid and particle transport - important processes in mediating nutrient cycling - and use high-resolution reconstructions of burrow geometry to determine the extent and nature of biogenic modification. We find that individual functional effect descriptors fall short of being able to adequately characterize how species mediate the stocks and flows of important ecosystem properties and that, in contrary to common practice and understanding, they are not substitutable with one another because they emphasize different aspects of species activity and behavior. When information derived from these metrics is combined with knowledge of how species behave and modify their environment, however, detailed mechanistic information emerges that increases the likelihood that a species functional standing will be appropriately summarized. Our study provides evidence that more comprehensive functional effect descriptors are required if they are to be of value to those tasked with projecting how altered biodiversity will influence future ecosystems

Post tracheostomy and post intubation tracheal stenosis: Report of 31 cases and review of the literature

<p>Abstract</p> <p>Background</p> <p>Severe post tracheostomy (PT) and post intubation (PI) tracheal stenosis is an uncommon clinical entity that often requires interventional bronchoscopy before surgery is considered. We present our experience with severe PI and PT stenosis in regards to patient characteristics, possible risk factors, and therapy.</p> <p>Methods</p> <p>We conducted a retrospective chart review of 31 patients with PI and PT stenosis treated at Lahey Clinic over the past 8 years. Demographic characteristics, body mass index, co-morbidities, stenosis type and site, procedures performed and local treatments applied were recorded.</p> <p>Results</p> <p>The most common profile of a patient with tracheal stenosis in our series was a female (75%), obese (66%) patient with a history of diabetes mellitus (35.4%), hypertension (51.6%), and cardiovascular disease (45.1%), who was a current smoker (38.7%). Eleven patients (PI group) had only oro-tracheal intubation (5.2 days of intubation) and developed web-like stenosis at the cuff site. Twenty patients (PT group) had undergone tracheostomy (54.5 days of intubation) and in 17 (85%) of them the stenosis appeared around the tracheal stoma. There was an average of 2.4 procedures performed per patient. Rigid bronchoscopy with Nd:YAG laser and dilatation (mechanical or balloon) were the preferred methods used. Only 1(3.2%) patient was sent to surgery for re-stenosis after multiple interventional bronchoscopy treatments.</p> <p>Conclusion</p> <p>We have identified putative risk factors for the development of PI and PT stenosis. Differences in lesions characteristics and stenosis site were noted in our two patient groups. All patients underwent interventional bronchoscopy procedures as the first-line, and frequently the only treatment approach.</p

How do surgeons decide? Conduit choice in coronary artery bypass graft surgery in the UK

OBJECTIVES Conduits used in coronary artery bypass grafting may have significant impact on outcomes, but evidence is mixed and there is large variation in practice. This study provides insights into the opinions of the UK surgeons on conduit use and their decision-making processes. METHODS A questionnaire was created using the Ottawa Decision Support Framework to elicit the importance that surgeons placed on bilateral internal mammary artery grafting, skeletonization, total arterial revascularization and sequential anastomoses on a scale of 1–10. Scores ≥8 were deemed ‘important’ and ≤3 ‘not important’. Surgeons were asked to specify changes to practice in frail patients or emergencies. Additional questions included conduit type used, factors affecting decision-making and vein harvesting methods. Questionnaires were administered in person with data analysed centrally. RESULTS Ninety-seven consultant cardiac surgeons from 25 centres responded. Thirty-two percent surgeons routinely used radial arteries and 36% used right internal mammary artery. High-quality evidence contributed most to decision-making receiving a total of 328/960 points, with consultant experience being the second (255/960 points). There was a bimodal distribution of perceived importance of bilateral internal mammary artery use, with 29 (30%) ‘important’ and ‘not important’ scores each. 23% of surgeons found total arterial revascularization important. Most surgeons (64%) preferred pedicled mammary arteries. Twenty-six percent of surgeons considered sequential grafting to be important. CONCLUSIONS Low uptake of total arterial revascularization and bilateral internal mammary artery among the UK consultants may be due to the lack of high-quality evidence demonstrating a significant benefit. It is also possible that reluctance to use certain conduits may stem from low levels of exposure to conduits or inadequate training, particularly given the importance of consultant experience on decision-making

A Unifying Framework for Evaluating the Predictive Power of Genetic Variants Based on the Level of Heritability Explained

An increasing number of genetic variants have been identified for many complex diseases. However, it is controversial whether risk prediction based on genomic profiles will be useful clinically. Appropriate statistical measures to evaluate the performance of genetic risk prediction models are required. Previous studies have mainly focused on the use of the area under the receiver operating characteristic (ROC) curve, or AUC, to judge the predictive value of genetic tests. However, AUC has its limitations and should be complemented by other measures. In this study, we develop a novel unifying statistical framework that connects a large variety of predictive indices together. We showed that, given the overall disease probability and the level of variance in total liability (or heritability) explained by the genetic variants, we can estimate analytically a large variety of prediction metrics, for example the AUC, the mean risk difference between cases and non-cases, the net reclassification improvement (ability to reclassify people into high- and low-risk categories), the proportion of cases explained by a specific percentile of population at the highest risk, the variance of predicted risks, and the risk at any percentile. We also demonstrate how to construct graphs to visualize the performance of risk models, such as the ROC curve, the density of risks, and the predictiveness curve (disease risk plotted against risk percentile). The results from simulations match very well with our theoretical estimates. Finally we apply the methodology to nine complex diseases, evaluating the predictive power of genetic tests based on known susceptibility variants for each trait

The impact of smoking cessation on multiple sclerosis disease progression

The negative impact of smoking in MS is well established, however, there is much less evidence as to whether smoking cessation is beneficial to progression in MS. Adults with MS registered on the United Kingdom MS Register (2011-2020) formed this retrospective and prospective cohort study. Primary outcomes were changes in 3 patient reported outcomes (PROs): normalised MS Physical Impact Scale (MSIS-29-Phys), normalised MS Walking Scale (MSWS-12) and the Hospital Anxiety and Depression Scale (HADS-Anxiety and HADS-Depression). Time to event outcomes were clinically significant increases in the PROs. 7983 participants were included, 4130 (51.7%) of these had ever smoked; of whom 1315 (16.5%) were current smokers and 2815/4130 (68.2%) were former smokers. For all PROs, current smokers at the time of completing their first questionnaire had higher PRO scores indicating higher disability compared to those who had never smoked (∼10 points difference in MSIS-29-Phys and MSWS-12; 1.5-1.8 point for HADS-anxiety and HADS-depression). There was no improvement in PRO scores with increasing time since quitting in former smokers. 923 participants formed the prospective parallel group, which demonstrated that MSIS-29-phy 5.03, [3.71, 6.34], MSWS-12 5.28, [3.62, 6.94] and HADS-depression 0.71, [0.47, 0.96] worsened over a period of 4 years, whereas HADS-anxiety remained stable. Smoking status was significant at year 4; current smokers had higher MSIS-29-Phys and HADS-Anxiety scores (3.05 [0.22, 5.88], 1.14 [0.52,1.76]) while former smokers had a lower MSIS-29 score of -2.91[-5.03, -0.79]. 4642 participants comprised the time to event analysis. Still smoking was associated with a shorter time to worsening event in all PROs (MSIS-29-Phys: n = 4436, p = 0.0013; MSWS-12: n = 3902, p = 0.0061; HADS-anxiety: n = 4511, p = 0.0017; HADS-depression: n = 4511, p &amp;lt; 0.0001). Worsening in motor disability (MSIS-29-Phys and MSWS-12) was independent of baseline HADS-anxiety and HADS-depression scores. There was no statistically significant difference in the rate of worsening between never and former smokers. When smokers quit, there is a slowing in the rate of motor disability deterioration so that it matches the rate of motor decline in those who have never smoked. This suggests that smoking cessation is beneficial for people with MS