Association Between Stress Hyperglycemia Ratio and In-hospital Outcomes in Elderly Patients With Acute Myocardial Infarction

Backgrounds: Emerging evidence suggests that stress hyperglycemia ratio (SHR), an index of relative stress hyperglycemia, is of great prognostic value in acute myocardial infarction (AMI), but current evidence is limited in elderly patients. In this study, we aimed to assess whether SHR is associated with in-hospital outcomes in elderly patients with AMI.Methods: In this retrospective study, patients who were aged over 75 years and diagnosed with AMI were consecutively enrolled from 2015, January 1st to 2019, December 31th. Admission blood glucose and glycosylated hemoglobin (HbA1C) during the index hospitalization were used to calculate SHR. Restricted quadratic splines, receiver-operating curves, and logistic regression were performed to evaluate the association between SHR and in-hospital outcomes, including in-hospital all-cause death and in-hospital major adverse cardiac and cerebrovascular events (MACCEs) defined as a composite of all-cause death, cardiogenic shock, reinfarction, mechanical complications of MI, stroke, and major bleeding.Results: A total of 341 subjects were included in this study. Higher SHR levels were observed in patients who had MACCEs (n = 69) or death (n = 44) during hospitalization. Compared with a SHR value below 1.25, a high SHR was independently associated with in-hospital MACCEs (odds ratio [OR]: 2.945, 95% confidence interval [CI]: 1.626–5.334, P < 0.001) and all-cause death (OR: 2.871 95% CI: 1.428–5.772, P = 0.003) in univariate and multivariate logisitic analysis. This relationship increased with SHR levels based on a non-linear dose-response curve. In contrast, admission glucose was only associated with clinical outcomes in univariate analysis. In subgroup analysis, high SHR was significantly predictive of worse in-hospital clinical outcomes in non-diabetic patients (MACCEs: 2.716 [1.281–5.762], P = 0.009; all-cause death: 2.394 [1.040–5.507], P = 0.040), but the association was not significant in diabetic patients.Conclusion: SHR might serve as a simple and independent indicator of adverse in-hospital outcomes in elderly patients with AMI, especially in non-diabetic population.

Excess Mortality in Italy During the COVID-19 Pandemic: Assessing the Differences Between the First and the Second Wave, Year 2020

COVID-19 dramatically influenced mortality worldwide, in Italy as well, the first European country to experience the Sars-Cov2 epidemic. Many countries reported a two-wave pattern of COVID-19 deaths; however, studies comparing the two waves are limited. The objective of the study was to compare all-cause excess mortality between the two waves that occurred during the year 2020 using nationwide data. All-cause excess mortalities were estimated using negative binomial models with time modeled by quadratic splines. The models were also applied to estimate all-cause excess deaths “not directly attributable to COVD-19”, i.e., without a previous COVID-19 diagnosis. During the first wave (25th February−31st May), we estimated 52,437 excess deaths (95% CI: 49,213–55,863) and 50,979 (95% CI: 50,333–51,425) during the second phase (10th October−31st December), corresponding to percentage 34.8% (95% CI: 33.8%–35.8%) in the second wave and 31.0% (95%CI: 27.2%–35.4%) in the first. During both waves, all-cause excess deaths percentages were higher in northern regions (59.1% during the first and 42.2% in the second wave), with a significant increase in the rest of Italy (from 6.7% to 27.1%) during the second wave. Males and those aged 80 or over were the most hit groups with an increase in both during the second wave. Excess deaths not directly attributable to COVID-19 decreased during the second phase with respect to the first phase, from 10.8% (95% CI: 9.5%–12.4%) to 7.7% (95% CI: 7.5%–7.9%), respectively. The percentage increase in excess deaths from all causes suggests in Italy a different impact of the SARS-CoV-2 virus during the second wave in 2020. The decrease in excess deaths not directly attributable to COVID-19 may indicate an improvement in the preparedness of the Italian health care services during this second wave, in the detection of COVID-19 diagnoses and/or clinical practice toward the other severe diseases.

Data Interpolation by Near-Optimal Splines with Free Knots Using Linear Programming

The problem of obtaining an optimal spline with free knots is tantamount to minimizing derivatives of a nonlinear differentiable function over a Banach space on a compact set. While the problem of data interpolation by quadratic splines has been accomplished, interpolation by splines of higher orders is far more challenging. In this paper, to overcome difficulties associated with the complexity of the interpolation problem, the interval over which data points are defined is discretized and continuous derivatives are replaced by their discrete counterparts. The l∞-norm used for maximum rth order curvature (a derivative of order r) is then linearized, and the problem to obtain a near-optimal spline becomes a linear programming (LP) problem, which is solved in polynomial time by using LP methods, e.g., by using the Simplex method implemented in modern software such as CPLEX. It is shown that, as the mesh of the discretization approaches zero, a resulting near-optimal spline approaches an optimal spline. Splines with the desired accuracy can be obtained by choosing an appropriately fine mesh of the discretization. By using cubic splines as an example, numerical results demonstrate that the linear programming (LP) formulation, resulting from the discretization of the interpolation problem, can be solved by linear solvers with high computational efficiency and the resulting spline provides a good approximation to the sought-for optimal spline.

Data Interpolation by Optimal Splines with Free Knots Using Linear Programming

Studies have shown that in many practical applications, data interpolation by splines leads to better approximation and higher computational efficiency as compared to data interpolation by a single polynomial. Data interpolation by splines can be significantly improved if knots are allowed to be free rather than at a priori fixed locations such as data points. In practical applications, the smallest possible curvature is often desired. Therefore, optimal splines are determined by minimizing a derivative of continuously differentiable functions comprising the spline of the required order. The problem of obtaining an optimal spline is tantamount to minimizing derivatives of a nonlinear differentiable function over a Banach space on a compact set. While the problem of data interpolation by quadratic splines has been accomplished analytically, interpolation by splines of higher orders or in higher dimensions is challenging. In this paper, to overcome difficulties associated with the complexity of the interpolation problem, the interval over which data points are defined, is discretized and continuous derivatives are substituted by their discrete counterparts. It is shown that as the mesh of the discretization approaches zero, a resulting near-optimal spline approaches an optimal spline. Splines with the desired accuracy can be obtained by choosing an appropriate mesh of the discretization. By using cubic splines as an example, numerical results demonstrate that the linear programming (LP) formulation, resulting from the discretization of the interpolation problem, can be solved by linear solvers with high computational efficiency and resulting splines provide a good approximation to the optimal splines.

Quadratic Approximation of Cubic Curves

We present a simple degree reduction technique for piecewise cubic polynomial splines, converting them into piecewise quadratic splines that maintain the parameterization and C1 continuity. Our method forms identical tangent directions at the interpolated data points of the piecewise cubic spline by replacing each cubic piece with a pair of quadratic pieces. The resulting representation can lead to substantial performance improvements for rendering geometrically complex spline models like hair and fiber-level cloth. Such models are typically represented using cubic splines that are C1-continuous, a property that is preserved with our degree reduction. Therefore, our method can also be considered a new quadratic curve construction approach for high-performance rendering. We prove that it is possible to construct a pair of quadratic curves with C1 continuity that passes through any desired point on the input cubic curve. Moreover, we prove that when the pair of quadratic pieces corresponding to a cubic piece have equal parametric lengths, they join exactly at the parametric center of the cubic piece, and the deviation in positions due to degree reduction is minimized.

Superconvergent Isogeometric Transient Analysis of Wave Equations

A superconvergent isogeometric formulation is presented for the transient analysis of wave equations with particular reference to quadratic splines. This formulation is developed in the context of Newmark time integration schemes and superconvergent quadrature rules for isogeometric mass and stiffness matrices. A detailed analysis is carried out for the full-discrete isogeometric formulation of wave equations and an error measure for the full-discrete algorithm is established. It is shown that a desirable superconvergence regarding the isogeometric transient analysis of wave equations can be achieved by two ingredients, namely, the design of a superconvergent quadrature rule and the criteria to properly define the step size for temporal integration. It turns out that the semi-discrete and full-discrete isogeometric formulations of wave equations with quadratic splines share an identical quadrature rule for a sixth-order accurate superconvergent analysis. Meanwhile, the relationships between the time step size and the element size are presented for various typical Newmark time integration schemes, in order to ensure the sixth-order accuracy in transient analysis. Numerical results of the transient analysis of wave equations consistently reveal that the proposed superconvergent isogeometric formulation is sixth-order accurate with respect to spatial discretizations, in contrast to the fourth-order accuracy produced by the standard isogeometric approach with quadratic splines.

Optimal program control in the class of quadratic splines for linear systems

This article describes an algorithm for solving the optimal control problem in the case when the considered process is described by a linear system of ordinary differential equations. The initial and final states of the system are fixed and straight two-sided constraints for the control functions are defined. The purpose of optimization is to minimize the quadratic functional of control variables. The control is selected in the class of quadratic splines. There is some evolution of the method when control is selected in the class of piecewise constant functions. Conveniently, due to the addition/removal of constraints in knots, the control function can be piecewise continuous, continuous, or continuously differentiable. The solution algorithm consists in reducing the control problem to a convex mixed-integer quadratically-constrained programming problem, which could be solved by using well-known optimization methods that utilize special software.