Quadratic Spline Research Articles

Nonlinear 2D C1 Quadratic Spline Quasi-Interpolants on Triangulations for the Approximation of Piecewise Smooth Functions

The aim of this paper is to present and study nonlinear bivariate C1 quadratic spline quasi-interpolants on uniform criss-cross triangulations for the approximation of piecewise smooth functions. Indeed, by using classical spline quasi-interpolants, the Gibbs phenomenon appears when approximating near discontinuities. Here, we use weighted essentially non-oscillatory techniques to modify classical quasi-interpolants in order to avoid oscillations near discontinuities and maintain high-order accuracy in smooth regions. We study the convergence properties of the proposed quasi-interpolants and we provide some numerical and graphical tests confirming the theoretical results.

Prediction of Soil Inorganic Carbon at Multiple Depths Using Quantile Regression Forest and Digital Soil Mapping Technique in the Thar Desert Regions of India

ABSTRACT Soil inorganic carbon (SIC) is important carbon reservoirs in desert ecosystems. However, little attention was paid to estimate carbon stock in these regions. In the present study, the distribution of SIC stock was investigated using digital soil mapping in Bikaner district, Rajasthan, India. A total of 187 soil profiles were used for SIC estimation by Quantile regression forest model. Landsat data, terrain attributes and bioclimatic variables were used as environmental variables. Ten-fold cross-validation was used to evaluate model. Equal-area quadratic splines were fitted to soil profile datasets to estimate SIC at six standard soil depths (0–5, 5–15, 15–30, 30–60, 60–100 and 100–200 cm). The SIC in the study area ranged from 0.27 to 27.85 g kg−1 in 0–5 cm and 0.31 to 27.84 g kg−1 in 5–15 cm, respectively. The model could capture reasonable variability (R2 = 11–21%) while predicting SIC for different depths. The Lin’s concordance correlation coefficient values ranged from 0.20 to 0.32, indicating poor relationship between the predicted and observed values. The values of prediction interval coverage probability (PICP) recorded 86.4–91.1% for SIC at different depths. Annual precipitation and precipitation seasonality were the most important covariates in soil below the 30 cm depth. The predicted SIC stocks were 10.3 ± 0.01, 81.6 ± 0.07 and 186.7 ± 0.13 Mg ha−1 at 0–15, 0–100 and 0–200 cm, depth, respectively. The uncertainty analysis suggests that there is room to improve the current spatial predictions of SIC. It is anticipated that this digital mapping of SIC will be useful for assessment of carbon cycle in arid regions.

Effect of semaglutide on major adverse cardiovascular events by baseline kidney parameters in participants with type 2 diabetes and at high risk of cardiovascular disease: SUSTAIN 6 and PIONEER 6 post hoc pooled analysis

BackgroundSemaglutide is a glucose-lowering treatment for type 2 diabetes (T2D) with demonstrated cardiovascular benefits; semaglutide may also have kidney-protective effects. This post hoc analysis investigated the association between major adverse cardiovascular events (MACE) and baseline kidney parameters and whether the effect of semaglutide on MACE risk was impacted by baseline kidney parameters in people with T2D at high cardiovascular risk.MethodsParticipants from the SUSTAIN 6 and PIONEER 6 trials, receiving semaglutide or placebo, were categorised according to baseline kidney function (estimated glomerular filtration rate [eGFR] < 45 and ≥ 45–<60 versus ≥ 60 mL/min/1.73 m2) or damage (urine albumin:creatinine ratio [UACR] ≥ 30–≤300 and > 300 versus < 30 mg/g). Relative risk of first MACE by baseline kidney parameters was evaluated using a Cox proportional hazards model. The same model, adjusted with inverse probability weighting, and a quadratic spline regression were applied to evaluate the effect of semaglutide on risk and event rate of first MACE across subgroups. The semaglutide effects on glycated haemoglobin (HbA1c), body weight (BW) and serious adverse events (SAEs) across subgroups were also evaluated.ResultsIndependently of treatment, participants with reduced kidney function (eGFR ≥ 45–<60 and < 45 mL/min/1.73 m2: hazard ratio [95% confidence interval]; 1.36 [1.04;1.76] and 1.52 [1.15;1.99]) and increased albuminuria (UACR ≥ 30–≤300 and > 300 mg/g: 1.53 [1.14;2.04] and 2.52 [1.84;3.42]) had an increased MACE risk versus those without. Semaglutide consistently reduced MACE risk versus placebo across all eGFR and UACR subgroups (interaction p value [pINT] > 0.05). Semaglutide reduced HbA1c regardless of baseline eGFR and UACR (pINT>0.05); reductions in BW were affected by baseline eGFR (pINT<0.001) but not UACR (pINT>0.05). More participants in the lower eGFR or higher UACR subgroups experienced SAEs versus participants in reference groups; the number of SAEs was similar between semaglutide and placebo arms in each subgroup.ConclusionsMACE risk was greater for participants with kidney impairment or damage than for those without. Semaglutide consistently reduced MACE risk across eGFR and UACR subgroups, indicating that semaglutide provides cardiovascular benefits in people with T2D and at high cardiovascular risk across a broad spectrum of kidney function and damage.Trial registrationsNCT01720446; NCT02692716.

Sleep-wake timing and chronotype in perinatal periods: longitudinal changes and associations with insomnia symptoms, sleep-related impairment, and mood from pregnancy to 2 years postpartum.

Across the perinatal transition, existing research focuses mainly on significant changes in sleep duration and quality, neglecting sleep timing. This study investigated change trajectories of sleep timing and chronotype from late pregnancy to 2 years postpartum and examined longitudinal associations of chronotype with symptoms of insomnia, daytime sleep-related impairment, and mood. Data were from a two-arm randomised controlled trial testing parent-focused wellbeing interventions. Participants were a community sample of nullipara without severe sleep/mental health conditions. Participants self-reported bedtime, rise-time, chronotype, insomnia symptoms, sleep-related impairment, depression, and anxiety at seven time points: gestation Weeks 30 and 35, and postpartum Months 1.5, 3, 6, 12 and 24. Trajectories were estimated using mixed-effects models with continuous time, quadratic splines, and a knot at childbirth, controlling for age and group allocation. A total of 163 participants (mean [SD] age 33.35 [3.42] years) took part. Bedtime and rise-times delayed during late pregnancy (~8 and ~20 min, respectively) but became progressively earlier (~20 and ~60 min, respectively) over the 2 postpartum years. Chronotype became more eveningness in late pregnancy, and more morningness after childbirth, however changes were small. Controlling for sleep duration and efficiency, greater morningness was associated with significantly less symptoms of insomnia and sleep-related impairment over time (all p < 0.001); longitudinal associations between chronotype and symptoms of depression and anxiety were non-significant (all p > 0.65). Sleep-wake timing and chronotype became progressively earlier from pregnancy to 2 years postpartum. Morningness chronotype may be sleep-protective during the transition from pregnancy to parenthood. Mechanisms underlying these associations require further research.

Quadratic Spline and Heligman-Pollard Methods in The Preparation of Life Tables in Gegelang Village West Lombok

Quadratic Spline and Heligman-Pollard Methods in The Preparation of Life Tables in Gegelang Village West Lombok

Estimation and variable selection of quantile partially linear additive models for correlated data

Longitudinal data arise frequently in many economic studies and epidemiological research. In this paper, we investigate the partially linear additive model for longitudinal data in the framework of quantile regression. To incorporate the within-subject correlation, we develop an estimation procedure using quadratic inference function (QIF) and polynomial spline approximation for unknown nonparametric functions. The theoretical properties of the resulting estimators are established, where the nonparametric functions achieve the optimal convergence rate and the parametric components are asymptotically normal even when the number of parameters in the linear part is diverging. We also propose a variable selection procedure based on penalization. Since the objective function is discontinuous, a practical estimation procedure is proposed using induced smoothing and we prove that the smoothed estimator is asymptotically equivalent to the original estimator. The proposed methods are evaluated via simulation studies and a real data application.

Population modeling and housing demand prediction for the Saudi 2030 Vision: a case study of Riyadh City

Purpose The Saudi 2030 Housing Program Vision aims to increase the population of Riyadh City, the capital of the Kingdom of Saudi Arabia, to between 15 and 20 million people. This paper aims to predict the demand for residential units in Riyadh City by 2030 in line with this vision. Design/methodology/approach This paper adopts a statistical modeling approach to estimate the residential demands for Riyadh City. Several population growth models, including the nonlinear quadratic polynomial spline regression model, the sigmoidal logistic power model and the exponential model, are tested and applied to Riyadh to estimate the expected population in 2030. The growth model closest to the Kingdom’s goal of reaching between 15 and 20 million people in 2030 is selected, and the paper predicts the required number of residential units for the population obtained from the selected model. Desktop database research is conducted to obtain the data required for the modeling and analytical stage. Findings The exponential model predicts a population of 16,476,470 in Riyadh City by 2030, and as a result, 2,636,235 household units are needed. This number of housing units required in Riyadh City exceeds the available residential units by almost 1,370,000, representing 108% of the available residential units in Riyadh in 2020. Originality/value This study provides valuable insights into the demand for residential units in Riyadh City by 2030 in line with the Saudi 2030 Housing Program Vision, filling the gap in prior research. The findings suggest that significant efforts are required to meet the housing demand in Riyadh City by 2030, and policymakers and stakeholders need to take appropriate measures to address this issue.

Biomechanical analysis of novel leaflet geometries for bioprosthetic valves

ObjectivesAlthough bioprosthetic valves have excellent hemodynamic properties and can eliminate the need for lifelong anticoagulation therapy, these devices are associated with high rates of reoperation and limited durability. Although there are many distinct bioprosthesis designs, all bioprosthetic valves have historically featured a trileaflet pattern. This in silico study examines the biomechanical effect of modulating the number of leaflets in a bioprosthetic valve. MethodsBioprosthetic valves with 2 to 6 leaflets were designed in Fusion 360 using quadratic spline geometry. Leaflets were modeled with standard mechanical parameters for fixed bovine pericardial tissue. A mesh of each design was structurally evaluated using finite element analysis software Abaqus CAE. Maximum von Mises stresses during valve closure were assessed for each leaflet geometry in both the aortic and mitral position. ResultsComputational analysis demonstrated that increasing the number of leaflets is associated with reduction in leaflet stresses. Compared with the standard trileaflet design, a quadrileaflet pattern reduces leaflet maximum von Mises stresses by 36% in the aortic position and 38% in the mitral position. Maximum stress was inversely proportional to the square of the leaflet quantity. Surface area increased linearly and central leakage increased quadratically with leaflet quantity. ConclusionsA quadrileaflet pattern was found to reduce leaflet stresses while limiting increases in central leakage and surface area. These findings suggest that modulating the number of leaflets can allow for optimization of the current bioprosthetic valve design, which may translate to more durable valve replacement bioprostheses.

Computing Invariant Densities of a Class of Piecewise Increasing Mappings

Let [Formula: see text] be a piecewise increasing mapping satisfying some generalized convexity condition, so that it possesses an invariant density that is a decreasing function. We show that this invariant density can be computed by a family of Markov finite approximations that preserve the monotonicity of integrable functions. We also construct a quadratic spline Markov method and demonstrate its merits numerically.

A new B-spline type approximation method for non-smooth functions

In this letter we present a non-linear modification of classical quadratic and cubic splines following the inspiration of the PPH (piecewise polynomial harmonic) interpolation method. The objective is to get rid of the oscillations that appear close to jump discontinuities in the function when we approximate using a classical spline.

Positivity and discretization of Fredholm integral operators

We provide sufficient conditions for vector-valued Fredholm integral operators and their commonly used spatial discretizations to be positive in terms of an order relation induced by a corresponding order cone. It turns out that reasonable Nyström methods preserve positivity. Among the projection methods, persistence is obtained for the simplest ones based on polynomial, piecewise linear or specific cubic interpolation (collocation), as well as for piecewise constant basis functions in a Bubnov-Galerkin approach. However, for semi-discretizations using quadratic splines or sinc-collocation we demonstrate that positivity is violated. Our results are illustrated in terms of eigenpairs for Krein-Rutman operators and form the basis of corresponding investigations for nonlinear integral operators.

Rational quadratic trigonometric spline fractal interpolation functions with variable scalings

Rational quadratic trigonometric spline fractal interpolation functions with variable scalings

Approximation Solution of Fuzzy Singular Volterra Integral Equation by Non-Polynomial Spline

A non-polynomial spline (NPS) is an approximation method that relies on the triangular and polynomial parts, so the method has infinite derivatives of the triangular part of the NPS to compensate for the loss of smoothness inherited by the polynomial. In this paper, we propose polynomial-free linear and quadratic spline types to solve fuzzy Volterra integral equations (FVIE) of the 2nd kind with the weakly singular kernel (FVIEWSK) and Abel's type kernel. The linear type algorithm gives four parameters to form a linear spline. In comparison, the quadratic type algorithm gives five parameters to create a quadratic spline, which is more of a credit for the exact solution. These algorithms process kernel singularities with a simple technique. Illustrative examples use MathCad software to deal with upper and lower-bound solutions to fuzzy problems. The method provides a reliable way to ensure that an exact solution is approximated. Also, figures and tables show the potential of the method.

Modeling Egg Curves In Partridges

In this study, a modeling study was carried out on the weekly average values of henna partridge egg production. For this purpose, weekly average of henna partridge egg yields of 148 days from the herd consisting of 320 breeders were taken and cubic spline, Gompertz, Logistic, Richard, Schunute, Quadratic Spline, McNally and Gamma equations were used in the modeling. In the comparison of the goodness of fit of the equations, Determination Coefficient〖(R〗^2), Mean Square Error (MSE), Durbin-Watson (DW) and Akaike Information Criteria (AIC) values were taken into account. As a result of the study, Logistic (MSE= 12.4, R^2= 0.994, AIC= 43.56, DW= 2.09), Cubic Spline (MSE= 10.56, R^2= 0.996, AIC= 46.55, DW= 1.95) and McNally (MSE= 11.02, R^2= 0.996, AIC= 48.67, DW= 2.11) models were found to have the best results with similar results. It was concluded that the Schnute (MSE= 11.24, R^2= 0.990, AIC= 136.51, DW= 0.49), Gamma (MSE= 24.67, R^2= 0.991, AIC= 69.89, DW= 2.95) and Quadratic Spline (MSE= 10.43, R^2= 0.946, AIC= 149.34, DW= 2.97) models had the worst results.

Solution of Integral Equations Using Local Splines of the Second Order

Splines are an important mathematical tool in Applied and Theoretical Mechanics. Several Problems in Mechanics are modeled with Differential Equations the solution of which demands Finite Elements and Splines. In this paper, we consider the construction of computational schemes for the numerical solution of integral equations of the second kind with a weak singularity. To construct the numerical schemes, local polynomial quadratic spline approximations and second-order nonpolynomial spline approximations are used. The results of the numerical experiments are given. This methodology has many applications in problems in Applied and Theoretical Mechanics

Ridge Regression for Functional Form Identification of Continuous Predictors of Clinical Outcomes in Glomerular Disease

Introduction: Penalized regression models can be used to identify and rank risk factors for poor quality of life or other outcomes. They often assume linear covariate associations, but the true associations may be nonlinear. There is no standard, automated method for determining optimal functional forms (shapes of relationships) between predictors and the outcome in high-dimensional data settings. Methods: We propose a novel algorithm, ridge regression for functional form identification of continuous predictors (RIPR) that models each continuous covariate with linear, quadratic, quartile, and cubic spline basis components in a ridge regression model to capture potential nonlinear relationships between continuous predictors and outcomes. We used a simulation study to test the performance of RIPR compared to standard and spline ridge regression models. Then, we applied RIPR to identify top predictors of Patient-Reported Outcomes Measurement Information System (PROMIS) adult global mental and physical health scores using demographic and clinical characteristics among N = 107 glomerular disease patients enrolled in the Nephrotic Syndrome Study Network (NEPTUNE). Results: RIPR resulted in better predictive accuracy than the standard and spline ridge regression methods in 56–80% of simulation repetitions under a variety of data characteristics. When applied to PROMIS scores in NEPTUNE, RIPR resulted in the lowest error for predicting physical scores, and the second-lowest error for mental scores. Further, RIPR identified hemoglobin quartiles as an important predictor of physical health that was missed by the other models. Conclusion: The RIPR algorithm can capture nonlinear functional forms of predictors that are missed by standard ridge regression models. The top predictors of PROMIS scores vary greatly across methods. RIPR should be considered alongside other machine learning models in the prediction of patient-reported outcomes and other continuous outcomes.

Investigation of the Utility of Multivariate Meta-Analysis Methods in Estimating the Summary Dose Response Curve.

Traditional meta-analyses often assess the effectiveness of different doses of the same intervention separately or examine the overall differences between intervention and placebo groups. The present study aimed to model the effect sizes obtained from different doses in multiple studies using a two-stage dose-response meta-analytic approach while taking dose variations into account. Different dose-response meta-analysis models using linear, quadratic, and restricted cubic spline (RCS) functions were fitted. A two-stage approach utilizing multivariate meta-analysis was performed and the obtained results were compared with those of the univariate meta-analysis. A random effect dose-response meta-analysis was performed using data from an existing systematic review on combination therapy with zonisamide and anti-Parkinson drugs for Parkinson's disease. The effective or optimum dose for producing maximum response was also investigated. Moreover, a sensitivity analysis was performed by changing the knots of the RCS model. Dose-response meta-analysis was performed using data from four double-blinded randomized controlled trials with 724 and 309 patients with Parkinson's disease in dose and placebo arms, respectively. The quadratic model yielded the smallest Akaike information criterion (AIC), compared to the linear and RCS models, indicating it to be the best fit for the data. Compared to the traditional approach, the two-stage approach could model the dose-dependent effect of zonisamide on the Unified Parkinson's Disease Rating Scale (UPRDS) part III score and predict the outcome for different doses through a single analysis.

Horizontal and vertical variation of soil clay content and its controlling factors in China

Detailed information on the variation of soil clay content at different soil depths are important for water repellency, management of soil fertility, and crop growth. However, studies on the variation of soil clay content at different depths at large scales are limited. In this study, 1446 soil profiles covering most areas of China were extracted from the World Soil Information Service (WoSIS) database and classified into 0–20, 20–60, and 60–100 cm depths using the equal-area quadratic splines. Random forest (RF) and Shapley additive explanations (SHAP) were used to investigate the relationship between soil clay content and environmental factors (climate, topography, land use, and soil types). The results showed that soil clay content and its variability increased with soil depth. The RF model predicted soil clay content at the three soil depths. The mean absolute error (MAE), root mean square error (RMSE), coefficient of determination (R2), and Lin's concordance correlation coefficient (CCC) ranged from 6.95 % to 8.74 %, 8.90 % to 11.30 %, 42 % to 46 %, and 56 % to 59 %, respectively. Mean annual temperature (MAT), mean annual precipitation (MAP), solar radiation (solarR), and elevation were the key factors that controlled the variation of soil clay content at depths of 0–20, 20–60, and 60–100 cm. In addition, the main effect values of SHAP can identify environmental thresholds consistent with significant areas by capturing the relationship between soil clay content and MAT, MAP, solarR, and elevation. Significant differences were found in soil clay content on both sides of the threshold at MAT of 15 °C, MAP of 800 mm, solarR of 15,000 Jm−2 yr−1, and elevation of 1200 m. The results provide clues to the management of national soil security under global and regional climate change.

Mechanical ventilation variables associated with high pulmonary artery pressures in ARDS patients: a post hoc analysis

BackgroundThe relationship between indices of mechanical ventilation and pulmonary artery pressures remains ill-defined in ARDS. As our understanding of mechanical ventilation has progressed, there is now a greater appreciation of the impact of high driving pressures and mechanical power in perpetuating lung injury. However, the relationship between the newer derived indices of mechanical ventilation and pulmonary artery pressure is unclear. We performed a post hoc analysis of the Fluid and Catheters Treatment Trial (FACTT) trial to investigate the associations between mechanical ventilation indices in ARDS patients and the prevalence of pulmonary hypertension. This may help elucidate future clinical targets for more, right ventricular protective, mechanical ventilation strategies.MethodsWe performed a post hoc analysis of the FACTT database to identify ARDS patients who had a pulmonary artery catheter (PAC) inserted and pulmonary artery pressure readings recorded. We excluded any patient with a PAC inserted who was spontaneously breathing, as driving pressure and mechanical power are not validated in this cohort. Three independent analyses were performed: a univariate analysis, to assess for associations between mPAP and mechanical ventilation parameters using Pearson correlation coefficients, a multivariate analysis, to assess for independent associations with mPAP using a multiple regression model according to Akaike’s information criteria and finally an analysis for nonlinearity, using the best-fitting model according to the Bayesian information criterion (BIC) from linear, quadratic, fractional polynomial and restricted cubic spline models.ResultsAll the ventilation parameters demonstrated a significant correlation with mPAP, except tidal volume (once adjusted for respiratory rate) in the univariate analysis. The multivariate analysis demonstrated that the blood pH level, P/F ratio, PaCO2 level, mean airway pressure and the mechanical power indexed to compliance were independently associated with mPAP. In the final nonlinear analysis, associations did not differ from linearity except for 4 variables for which the fractional polynomial was the best-fitting model. These were mechanical power (p = 0.01 compared to the linear model), respiratory rate (p = 0.04), peak pressure (p = 0.03) and mean airway pressure (p = 0.01). Two nonlinear variables associated with mPAP were assessed in more detail, respiratory rate and mechanical power. Inflexion points at a respiratory rate of 16.8 cycles per minute and a mechanical power of 8.8 J/min were demonstrated.ConclusionsThe associations identified between mPAP and mechanical ventilation variables in this analysis would suggest that classical ARDS lung protective strategies, including low tidal volume ventilation and permissive hypercapnia, may negatively impact the management of the subset of ARDS patients with associated right ventricular dysfunction or ACP. Additionally, respiratory rates above 17 cycles per minute show an incremental increase in mPAP. Therefore, increases in tidal volume (within the limitation of driving pressure < 18 cmH20) may represent a more right ventricular protective way to control CO2 and pH.

Numerical solution of two-dimensional Hammerstein integral equations via quadratic spline collocation

Numerical solution of two-dimensional Hammerstein integral equations via quadratic spline collocation