Jacobi-Davidson methods for polynomial two-parameter eigenvalue problems

We propose Jacobi-Davidson type methods for polynomial two-parameter eigenvalue problems (PMEP). Such problems can be linearized as singular two-parameter eigenvalue problems, whose matrices are of dimension k(k+1)n/2, where k is the degree of the polynomial and n is the size of the matrix coefficients in the PMEP. When k^2n is relatively small, the problem can be solved numerically by computing the common regular part of the related pair of singular pencils. For large k^2n, computing all solutions is not feasible and iterative methods are required. When k is large, we propose to linearize the problem first and then apply Jacobi-Davidson to the obtained singular two-parameter eigenvalue problem. The resulting method may for instance be used for computing zeros of a system of scalar bivariate polynomials close to a given target. On the other hand, when k is small, we can apply a Jacobi-Davidson type approach directly to the original matrices. The original matrices are projected onto a low-dimensional subspace, and the projected polynomial two-parameter eigenvalue problems are solved by a linearization. Keywords: Polynomial two-parameter eigenvalue problem (PMEP), quadratic two-parameter eigenvalue problem (QMEP), Jacobi-Davidson, correction equation, singular generalized eigenvalue problem, bivariate polynomial equations, determinantal representation, delay differential equations (DDEs), critical delays

SeeBridge Next Generation Bridge Inspection: Overview, Information Delivery Manual and Model View Definition

Innovative solutions for rapid and intelligent survey and assessment methods are required in maintenance, repair, retrofit and rebuild of enormous numbers of bridges in service throughout the world. Motivated by this need, a next-generation integrated bridge inspection system, called SeeBridge, has been proposed. An Information Delivery Manual (IDM) was compiled to specify the technical components, activities and information exchanges in the SeeBridge process, and a Model View Definition (MVD) was prepared to specify the data exchange schema to serve the IDM. The MVD was bound to the IFC4 Add2 data schema standard. The IDM and MVD support research and development of the system by rigorously defining the information and data that structure bridge engineers' knowledge. The SeeBridge process is mapped, parts of the data repositories are presented, and the future use of the IDM is discussed. The development underlines the real potential for automated inspection of infrastructure at large, because it demonstrates that the hurdles in the way of automated acquisition of detailed and semantically rich models of existing infrastructure are computational in nature, not instrumental, and are surmountable with existing technologies

Mortality from gastrointestinal congenital anomalies at 264 hospitals in 74 low-income, middle-income, and high-income countries: a multicentre, international, prospective cohort study

Background: Congenital anomalies are the fifth leading cause of mortality in children younger than 5 years globally. Many gastrointestinal congenital anomalies are fatal without timely access to neonatal surgical care, but few studies have been done on these conditions in low-income and middle-income countries (LMICs). We compared outcomes of the seven most common gastrointestinal congenital anomalies in low-income, middle-income, and high-income countries globally, and identified factors associated with mortality. // Methods: We did a multicentre, international prospective cohort study of patients younger than 16 years, presenting to hospital for the first time with oesophageal atresia, congenital diaphragmatic hernia, intestinal atresia, gastroschisis, exomphalos, anorectal malformation, and Hirschsprung's disease. Recruitment was of consecutive patients for a minimum of 1 month between October, 2018, and April, 2019. We collected data on patient demographics, clinical status, interventions, and outcomes using the REDCap platform. Patients were followed up for 30 days after primary intervention, or 30 days after admission if they did not receive an intervention. The primary outcome was all-cause, in-hospital mortality for all conditions combined and each condition individually, stratified by country income status. We did a complete case analysis. // Findings: We included 3849 patients with 3975 study conditions (560 with oesophageal atresia, 448 with congenital diaphragmatic hernia, 681 with intestinal atresia, 453 with gastroschisis, 325 with exomphalos, 991 with anorectal malformation, and 517 with Hirschsprung's disease) from 264 hospitals (89 in high-income countries, 166 in middle-income countries, and nine in low-income countries) in 74 countries. Of the 3849 patients, 2231 (58·0%) were male. Median gestational age at birth was 38 weeks (IQR 36–39) and median bodyweight at presentation was 2·8 kg (2·3–3·3). Mortality among all patients was 37 (39·8%) of 93 in low-income countries, 583 (20·4%) of 2860 in middle-income countries, and 50 (5·6%) of 896 in high-income countries (p<0·0001 between all country income groups). Gastroschisis had the greatest difference in mortality between country income strata (nine [90·0%] of ten in low-income countries, 97 [31·9%] of 304 in middle-income countries, and two [1·4%] of 139 in high-income countries; p≤0·0001 between all country income groups). Factors significantly associated with higher mortality for all patients combined included country income status (low-income vs high-income countries, risk ratio 2·78 [95% CI 1·88–4·11], p<0·0001; middle-income vs high-income countries, 2·11 [1·59–2·79], p<0·0001), sepsis at presentation (1·20 [1·04–1·40], p=0·016), higher American Society of Anesthesiologists (ASA) score at primary intervention (ASA 4–5 vs ASA 1–2, 1·82 [1·40–2·35], p<0·0001; ASA 3 vs ASA 1–2, 1·58, [1·30–1·92], p<0·0001]), surgical safety checklist not used (1·39 [1·02–1·90], p=0·035), and ventilation or parenteral nutrition unavailable when needed (ventilation 1·96, [1·41–2·71], p=0·0001; parenteral nutrition 1·35, [1·05–1·74], p=0·018). Administration of parenteral nutrition (0·61, [0·47–0·79], p=0·0002) and use of a peripherally inserted central catheter (0·65 [0·50–0·86], p=0·0024) or percutaneous central line (0·69 [0·48–1·00], p=0·049) were associated with lower mortality. // Interpretation: Unacceptable differences in mortality exist for gastrointestinal congenital anomalies between low-income, middle-income, and high-income countries. Improving access to quality neonatal surgical care in LMICs will be vital to achieve Sustainable Development Goal 3.2 of ending preventable deaths in neonates and children younger than 5 years by 2030

Prolonged survival in patients with breast cancer and a history of brain metastases: results of a preplanned subgroup analysis from the randomized phase III BEACON trial

Purpose: Conventional chemotherapy has limited activity in patients with breast cancer and brain metastases (BCBM). Etirinotecan pegol (EP), a novel long-acting topoisomerase-1 inhibitor, was designed using advanced polymer technology to preferentially accumulate in tumor tissue including brain metastases, providing sustained cytotoxic SN38 levels. Methods: The phase 3 BEACON trial enrolled 852 women with heavily pretreated locally recurrent or metastatic breast cancer between 2011 and 2013. BEACON compared EP with treatment of physician’s choice (TPC; eribulin, vinorelbine, gemcitabine, nab-paclitaxel, paclitaxel, ixabepilone, or docetaxel) in patients previously treated with anthracycline, taxane, and capecitabine, including those with treated, stable brain metastases. The primary endpoint, overall survival (OS), was assessed in a pre-defined subgroup of BCBM patients; an exploratory post hoc analysis adjusting for the diagnosis-specific graded prognostic assessment (GPA) index was also conducted. Results: In the trial, 67 BCBM patients were randomized (EP, n = 36; TPC, n = 31). Treatment subgroups were balanced for baseline characteristics and GPA indices. EP was associated with a significant reduction in the risk of death (HR 0.51; P < 0.01) versus TPC; median OS was 10.0 and 4.8 months, respectively. Improvement in OS was observed in both poorer and better GPA prognostic groups. Survival rates at 12 months were 44.4% for EP versus 19.4% for TPC. Consistent with the overall BEACON population, fewer patients on EP experienced grade ≥3 toxicity (50 vs. 70%). Conclusions: The significant improvement in survival in BCBM patients provides encouraging data for EP in this difficult-to-treat subgroup of patients. A phase three trial of EP in BCBM patients is underway (ClinicalTrials.gov NCT02915744)

Mortality from gastrointestinal congenital anomalies at 264 hospitals in 74 low-income, middle-income, and high-income countries: a multicentre, international, prospective cohort study

Summary Background Congenital anomalies are the fifth leading cause of mortality in children younger than 5 years globally. Many gastrointestinal congenital anomalies are fatal without timely access to neonatal surgical care, but few studies have been done on these conditions in low-income and middle-income countries (LMICs). We compared outcomes of the seven most common gastrointestinal congenital anomalies in low-income, middle-income, and high-income countries globally, and identified factors associated with mortality. Methods We did a multicentre, international prospective cohort study of patients younger than 16 years, presenting to hospital for the first time with oesophageal atresia, congenital diaphragmatic hernia, intestinal atresia, gastroschisis, exomphalos, anorectal malformation, and Hirschsprung’s disease. Recruitment was of consecutive patients for a minimum of 1 month between October, 2018, and April, 2019. We collected data on patient demographics, clinical status, interventions, and outcomes using the REDCap platform. Patients were followed up for 30 days after primary intervention, or 30 days after admission if they did not receive an intervention. The primary outcome was all-cause, in-hospital mortality for all conditions combined and each condition individually, stratified by country income status. We did a complete case analysis. Findings We included 3849 patients with 3975 study conditions (560 with oesophageal atresia, 448 with congenital diaphragmatic hernia, 681 with intestinal atresia, 453 with gastroschisis, 325 with exomphalos, 991 with anorectal malformation, and 517 with Hirschsprung’s disease) from 264 hospitals (89 in high-income countries, 166 in middleincome countries, and nine in low-income countries) in 74 countries. Of the 3849 patients, 2231 (58·0%) were male. Median gestational age at birth was 38 weeks (IQR 36–39) and median bodyweight at presentation was 2·8 kg (2·3–3·3). Mortality among all patients was 37 (39·8%) of 93 in low-income countries, 583 (20·4%) of 2860 in middle-income countries, and 50 (5·6%) of 896 in high-income countries (p<0·0001 between all country income groups). Gastroschisis had the greatest difference in mortality between country income strata (nine [90·0%] of ten in lowincome countries, 97 [31·9%] of 304 in middle-income countries, and two [1·4%] of 139 in high-income countries; p≤0·0001 between all country income groups). Factors significantly associated with higher mortality for all patients combined included country income status (low-income vs high-income countries, risk ratio 2·78 [95% CI 1·88–4·11], p<0·0001; middle-income vs high-income countries, 2·11 [1·59–2·79], p<0·0001), sepsis at presentation (1·20 [1·04–1·40], p=0·016), higher American Society of Anesthesiologists (ASA) score at primary intervention (ASA 4–5 vs ASA 1–2, 1·82 [1·40–2·35], p<0·0001; ASA 3 vs ASA 1–2, 1·58, [1·30–1·92], p<0·0001]), surgical safety checklist not used (1·39 [1·02–1·90], p=0·035), and ventilation or parenteral nutrition unavailable when needed (ventilation 1·96, [1·41–2·71], p=0·0001; parenteral nutrition 1·35, [1·05–1·74], p=0·018). Administration of parenteral nutrition (0·61, [0·47–0·79], p=0·0002) and use of a peripherally inserted central catheter (0·65 [0·50–0·86], p=0·0024) or percutaneous central line (0·69 [0·48–1·00], p=0·049) were associated with lower mortality. Interpretation Unacceptable differences in mortality exist for gastrointestinal congenital anomalies between lowincome, middle-income, and high-income countries. Improving access to quality neonatal surgical care in LMICs will be vital to achieve Sustainable Development Goal 3.2 of ending preventable deaths in neonates and children younger than 5 years by 2030

Jacobi-Davidson methods for polynomial two-parameter eigenvalue problems

We propose Jacobi–Davidson type methods for polynomial two-parameter eigenvalue problems (PMEP). Such problems can be linearized as singular two-parameter eigenvalue problems, whose matrices are of dimension k(k+1)n/2k(k+1)n/2, where kk is the degree of the polynomial and nn is the size of the matrix coefficients in the PMEP. When k2nk2n is relatively small, the problem can be solved numerically by computing the common regular part of the related pair of singular pencils. For large k2nk2n, computing all solutions is not feasible and iterative methods are required. When kk is large, we propose to linearize the problem first and then apply Jacobi–Davidson to the obtained singular two-parameter eigenvalue problem. The resulting method may for instance be used for computing zeros of a system of scalar bivariate polynomials close to a given target. On the other hand, when kk is small, we can apply a Jacobi–Davidson type approach directly to the original matrices. The original matrices are projected onto a low-dimensional subspace, and the projected polynomial two-parameter eigenvalue problems are solved by a linearization. Keywords: Polynomial two-parameter eigenvalue problem (PMEP); Jacobi–Davidson; Singular generalized eigenvalue problem; Bivariate polynomial equations; Determinantal representation; Delay differential equations (DDEs

On linearizations of the quadratic two-parameter eigenvalue problems

We present several transformations that can be used to solve the quadratic two-parameter eigenvalue problem (QMEP), by formulating an associated linear multiparameter eigenvalue problem. Two of these transformations are generalizations of the well-known linearization of the quadratic eigenvalue problem and linearize the QMEP as a singular two-parameter eigenvalue problem. The third replaces all nonlinear terms by new variables and adds new equations for their relations. The QMEP is thus transformed into a nonsingular five-parameter eigenvalue problem. The advantage of these transformations is that they enable one to solve the QMEP using existing numerical methods for multiparameter eigenvalue problems. We also consider several special cases of the QMEP, where some matrix coefficients are zero