Combined homotopy and neighboring extremal optimal control

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High order structure preserving explicit methods for solving linear-quadratic optimal control problems

[EN] We consider the numerical integration of linear-quadratic optimal control problems. This problem requires the solution of a boundary value problem: a non-autonomous matrix Riccati differential equation (RDE) with final conditions coupled with the state vector equation with initial conditions. The RDE has positive definite matrix solution and to numerically preserve this qualitative property we propose first to integrate this equation backward in time with a sufficiently accurate scheme. Then, this problem turns into an initial value problem, and we analyse splitting and Magnus integrators for the forward time integration which preserve the positive definite matrix solutions for the RDE. Duplicating the time as two new coordinates and using appropriate splitting methods, high order methods preserving the desired property can be obtained. The schemes make sequential computations and do not require the storrage of intermediate results, so the storage requirements are minimal. The proposed methods are also adapted for solving linear-quadratic N-player differential games. The performance of the splitting methods can be considerably improved if the system is a perturbation of an exactly solvable problem and the system is properly split. Some numerical examples illustrate the performance of the proposed methods.The author wishes to thank the University of California San Diego for its hospitality where part of this work was done. He also acknowledges the support of the Ministerio de Ciencia e Innovacion (Spain) under the coordinated project MTM2010-18246-C03. The author also acknowledges the suggestions by the referees to improve the presentation of this work.Blanes Zamora, S. (2015). High order structure preserving explicit methods for solving linear-quadratic optimal control problems. 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Effects of hospital facilities on patient outcomes after cancer surgery: an international, prospective, observational study

Background Early death after cancer surgery is higher in low-income and middle-income countries (LMICs) compared with in high-income countries, yet the impact of facility characteristics on early postoperative outcomes is unknown. The aim of this study was to examine the association between hospital infrastructure, resource availability, and processes on early outcomes after cancer surgery worldwide.Methods A multimethods analysis was performed as part of the GlobalSurg 3 study-a multicentre, international, prospective cohort study of patients who had surgery for breast, colorectal, or gastric cancer. The primary outcomes were 30-day mortality and 30-day major complication rates. Potentially beneficial hospital facilities were identified by variable selection to select those associated with 30-day mortality. Adjusted outcomes were determined using generalised estimating equations to account for patient characteristics and country-income group, with population stratification by hospital.Findings Between April 1, 2018, and April 23, 2019, facility-level data were collected for 9685 patients across 238 hospitals in 66 countries (91 hospitals in 20 high-income countries; 57 hospitals in 19 upper-middle-income countries; and 90 hospitals in 27 low-income to lower-middle-income countries). The availability of five hospital facilities was inversely associated with mortality: ultrasound, CT scanner, critical care unit, opioid analgesia, and oncologist. After adjustment for case-mix and country income group, hospitals with three or fewer of these facilities (62 hospitals, 1294 patients) had higher mortality compared with those with four or five (adjusted odds ratio [OR] 3.85 [95% CI 2.58-5.75]; p<0.0001), with excess mortality predominantly explained by a limited capacity to rescue following the development of major complications (63.0% vs 82.7%; OR 0.35 [0.23-0.53]; p<0.0001). Across LMICs, improvements in hospital facilities would prevent one to three deaths for every 100 patients undergoing surgery for cancer.Interpretation Hospitals with higher levels of infrastructure and resources have better outcomes after cancer surgery, independent of country income. Without urgent strengthening of hospital infrastructure and resources, the reductions in cancer-associated mortality associated with improved access will not be realised

Does varicocele repair improve conventional semen parameters? A meta-analytic study of before-after data

Purpose The purpose of this meta-analysis is to study the impact of varicocele repair in the largest cohort of infertile males with clinical varicocele by including all available studies, with no language restrictions, comparing intra-person conventional semen parameters before and after the repair of varicoceles. Materials and Methods The meta-analysis was performed according to PRISMA-P and MOOSE guidelines. A systematic search was performed in Scopus, PubMed, Cochrane, and Embase databases. Eligible studies were selected according to the PICOS model (Population: infertile male patients with clinical varicocele; Intervention: varicocele repair; Comparison: intra-person before-after varicocele repair; Outcome: conventional semen parameters; Study type: randomized controlled trials [RCTs], observational and case-control studies). Results Out of 1,632 screened abstracts, 351 articles (23 RCTs, 292 observational, and 36 case-control studies) were included in the quantitative analysis. The before-and-after analysis showed significant improvements in all semen parameters after varicocele repair (except sperm vitality); semen volume: standardized mean difference (SMD) 0.203, 95% CI: 0.129–0.278; p<0.001; I2=83.62%, Egger’s p=0.3329; sperm concentration: SMD 1.590, 95% CI: 1.474–1.706; p<0.001; I2=97.86%, Egger’s p<0.0001; total sperm count: SMD 1.824, 95% CI: 1.526–2.121; p<0.001; I2=97.88%, Egger’s p=0.0063; total motile sperm count: SMD 1.643, 95% CI: 1.318–1.968; p<0.001; I2=98.65%, Egger’s p=0.0003; progressive sperm motility: SMD 1.845, 95% CI: 1.537%–2.153%; p<0.001; I2=98.97%, Egger’s p<0.0001; total sperm motility: SMD 1.613, 95% CI 1.467%–1.759%; p<0.001; l2=97.98%, Egger’s p<0.001; sperm morphology: SMD 1.066, 95% CI 0.992%–1.211%; p<0.001; I2=97.87%, Egger’s p=0.1864. Conclusions The current meta-analysis is the largest to date using paired analysis on varicocele patients. In the current meta-analysis, almost all conventional semen parameters improved significantly following varicocele repair in infertile patients with clinical varicocele. Keywords Controlled before-after studies; Infertility, male; Meta-analysis; Varicocel

Controversy and Consensus on Indications for Sperm DNA Fragmentation Testing in Male Infertility: A Global Survey, Current Guidelines, and Expert Recommendations

Purpose: Sperm DNA fragmentation (SDF) testing was recently added to the sixth edition of the World Health Organization laboratory manual for the examination and processing of human semen. Many conditions and risk factors have been associated with elevated SDF; therefore, it is important to identify the population of infertile men who might benefit from this test. The purpose of this study was to investigate global practices related to indications for SDF testing, compare the relevant professional society guideline recommendations, and provide expert recommendations. Materials and Methods: Clinicians managing male infertility were invited to take part in a global online survey on SDF clinical practices. This was conducted following the CHERRIES checklist criteria. The responses were compared to professional society guideline recommendations related to SDF and the appropriate available evidence. Expert recommendations on indications for SDF testing were then formulated, and the Delphi method was used to reach consensus. Results: The survey was completed by 436 experts from 55 countries. Almost 75% of respondents test for SDF in all or some men with unexplained or idiopathic infertility, 39% order it routinely in the work-up of recurrent pregnancy loss (RPL), and 62.2% investigate SDF in smokers. While 47% of reproductive urologists test SDF to support the decision for varicocele repair surgery when conventional semen parameters are normal, significantly fewer general urologists (23%; p=0.008) do the same. Nearly 70% would assess SDF before assisted reproductive technologies (ART), either always or for certain conditions. Recurrent ART failure is a common indication for SDF testing. Very few society recommendations were found regarding SDF testing. Conclusions: This article presents the largest global survey on the indications for SDF testing in infertile men, and demonstrates diverse practices. Furthermore, it highlights the paucity of professional society guideline recommendations. Expert recommendations are proposed to help guide clinicians

On global existence of solutions to coupled matrix Riccati equations in closed-loop Nash games

Abstract. We present comparison and global existence results for solutions of coupled matrix Riccati differential equations appearing in closed loop Nash games and in mixed H2/H∞-type problems. Convergence of solutions is established for the diagonal case. Solutions of the corresponding algebraic equations are discussed using numerical examples. I