Orthogonal Polynomial Approximation in Higher Dimensions: Applications in Astrodynamics

We propose novel methods to utilize orthogonal polynomial approximation in higher dimension spaces, which enable us to modify classical differential equation solvers to perform high precision, long-term orbit propagation. These methods have immediate application to efficient propagation of catalogs of Resident Space Objects (RSOs) and improved accounting for the uncertainty in the ephemeris of these objects. More fundamentally, the methodology promises to be of broad utility in solving initial and two point boundary value problems from a wide class of mathematical representations of problems arising in engineering, optimal control, physical sciences and applied mathematics. We unify and extend classical results from function approximation theory and consider their utility in astrodynamics. Least square approximation, using the classical Chebyshev polynomials as basis functions, is reviewed for discrete samples of the to-be-approximated function. We extend the orthogonal approximation ideas to n-dimensions in a novel way, through the use of array algebra and Kronecker operations. Approximation of test functions illustrates the resulting algorithms and provides insight into the errors of approximation, as well as the associated errors arising when the approximations are differentiated or integrated. Two sets of applications are considered that are challenges in astrodynamics. The first application addresses local approximation of high degree and order geopotential models, replacing the global spherical harmonic series by a family of locally precise orthogonal polynomial approximations for efficient computation. A method is introduced which adapts the approximation degree radially, compatible with the truth that the highest degree approximations (to ensure maximum acceleration error < 10^−9ms^−2, globally) are required near the Earths surface, whereas lower degree approximations are required as radius increases. We show that a four order of magnitude speedup is feasible, with both speed and storage efficiency op- timized using radial adaptation. The second class of problems addressed includes orbit propagation and solution of associated boundary value problems. The successive Chebyshev-Picard path approximation method is shown well-suited to solving these problems with over an order of magnitude speedup relative to known methods. Furthermore, the approach is parallel-structured so that it is suited for parallel implementation and further speedups. Used in conjunction with orthogonal Finite Element Model (FEM) gravity approximations, the Chebyshev-Picard path approximation enables truly revolutionary speedups in orbit propagation without accuracy loss

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&lt;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&lt;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

Investigation of the flowfield surrounding small photodriven flapping wings

The flowfield surrounding wings with a pure flapping motion was studied in quiescent air at a Reynolds number of approximately 200 using particle image velocimetry (PIV) in unusually thin illuminated planes (̃0.3 mm). Typical wing semi-spans were on the order of a few millimeters. The polymer cantilever wings consisting of monodomain liquid crystal polymers made from azobenzene (azo-LCN) were flapped at 30 Hz at a large amplitude (\u3e170⁰). Chordwise and spanwise planar slices of the flow across the wings were obtained and used to estimate the unsteady aerodynamic forces generated by the flapping wings. This study focuses on the flapping flight of small-scale wings in order to visualize the flowfield characteristics. The small-scale wings were, indeed, able to induce the surrounding flowfield and generate aerodynamic contribution, which was clearly observed in spanwise plane. Images at various spanwise and chordwise locations were acquired and processed. In terms of results, the spanwise flow was the dominant. The chordwise results were not conclusive useful due to the poor light filtering. The PIV displacement and velocity uncertainties were small quantitatives compared to the vorticity and circulation uncertaintie

Global variation in postoperative mortality and complications after cancer surgery: a multicentre, prospective cohort study in 82 countries

Background: 80% of individuals with cancer will require a surgical procedure, yet little comparative data exist on early outcomes in low-income and middle-income countries (LMICs). We compared postoperative outcomes in breast, colorectal, and gastric cancer surgery in hospitals worldwide, focusing on the effect of disease stage and complications on postoperative mortality. Methods: This was a multicentre, international prospective cohort study of consecutive adult patients undergoing surgery for primary breast, colorectal, or gastric cancer requiring a skin incision done under general or neuraxial anaesthesia. The primary outcome was death or major complication within 30 days of surgery. Multilevel logistic regression determined relationships within three-level nested models of patients within hospitals and countries. Hospital-level infrastructure effects were explored with three-way mediation analyses. This study was registered with ClinicalTrials.gov, NCT03471494. Findings: Between April 1, 2018, and Jan 31, 2019, we enrolled 15 958 patients from 428 hospitals in 82 countries (high income 9106 patients, 31 countries; upper-middle income 2721 patients, 23 countries; or lower-middle income 4131 patients, 28 countries). Patients in LMICs presented with more advanced disease compared with patients in high-income countries. 30-day mortality was higher for gastric cancer in low-income or lower-middle-income countries (adjusted odds ratio 3·72, 95% CI 1·70–8·16) and for colorectal cancer in low-income or lower-middle-income countries (4·59, 2·39–8·80) and upper-middle-income countries (2·06, 1·11–3·83). No difference in 30-day mortality was seen in breast cancer. The proportion of patients who died after a major complication was greatest in low-income or lower-middle-income countries (6·15, 3·26–11·59) and upper-middle-income countries (3·89, 2·08–7·29). Postoperative death after complications was partly explained by patient factors (60%) and partly by hospital or country (40%). The absence of consistently available postoperative care facilities was associated with seven to 10 more deaths per 100 major complications in LMICs. Cancer stage alone explained little of the early variation in mortality or postoperative complications. Interpretation: Higher levels of mortality after cancer surgery in LMICs was not fully explained by later presentation of disease. The capacity to rescue patients from surgical complications is a tangible opportunity for meaningful intervention. Early death after cancer surgery might be reduced by policies focusing on strengthening perioperative care systems to detect and intervene in common complications. Funding: National Institute for Health Research Global Health Research Unit

Global variation in postoperative mortality and complications after cancer surgery: a multicentre, prospective cohort study in 82 countries

© 2021 The Author(s). Published by Elsevier Ltd. This is an Open Access article under the CC BY-NC-ND 4.0 licenseBackground: 80% of individuals with cancer will require a surgical procedure, yet little comparative data exist on early outcomes in low-income and middle-income countries (LMICs). We compared postoperative outcomes in breast, colorectal, and gastric cancer surgery in hospitals worldwide, focusing on the effect of disease stage and complications on postoperative mortality. Methods: This was a multicentre, international prospective cohort study of consecutive adult patients undergoing surgery for primary breast, colorectal, or gastric cancer requiring a skin incision done under general or neuraxial anaesthesia. The primary outcome was death or major complication within 30 days of surgery. Multilevel logistic regression determined relationships within three-level nested models of patients within hospitals and countries. Hospital-level infrastructure effects were explored with three-way mediation analyses. This study was registered with ClinicalTrials.gov, NCT03471494. Findings: Between April 1, 2018, and Jan 31, 2019, we enrolled 15 958 patients from 428 hospitals in 82 countries (high income 9106 patients, 31 countries; upper-middle income 2721 patients, 23 countries; or lower-middle income 4131 patients, 28 countries). Patients in LMICs presented with more advanced disease compared with patients in high-income countries. 30-day mortality was higher for gastric cancer in low-income or lower-middle-income countries (adjusted odds ratio 3·72, 95% CI 1·70–8·16) and for colorectal cancer in low-income or lower-middle-income countries (4·59, 2·39–8·80) and upper-middle-income countries (2·06, 1·11–3·83). No difference in 30-day mortality was seen in breast cancer. The proportion of patients who died after a major complication was greatest in low-income or lower-middle-income countries (6·15, 3·26–11·59) and upper-middle-income countries (3·89, 2·08–7·29). Postoperative death after complications was partly explained by patient factors (60%) and partly by hospital or country (40%). The absence of consistently available postoperative care facilities was associated with seven to 10 more deaths per 100 major complications in LMICs. Cancer stage alone explained little of the early variation in mortality or postoperative complications. Interpretation: Higher levels of mortality after cancer surgery in LMICs was not fully explained by later presentation of disease. The capacity to rescue patients from surgical complications is a tangible opportunity for meaningful intervention. Early death after cancer surgery might be reduced by policies focusing on strengthening perioperative care systems to detect and intervene in common complications. Funding: National Institute for Health Research Global Health Research Unit

Effects of hospital facilities on patient outcomes after cancer surgery: an international, prospective, observational study

© 2022 The Author(s). Published by Elsevier Ltd. This is an Open Access article under the CC BY 4.0 licenseBackground: 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. Funding: National Institute for Health and Care Research

The value of open-source clinical science in pandemic response: lessons from ISARIC

International audienc