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This study presented a novel analytical method to investigate the coupled dynamic behavior of a supercritical helicopter tail transmission system, taking into account the friction-induced self-excitation of the floating spline, the rubbing between the limiting ring device and the shaft, and the time-varying meshing excitation experienced by multiple spiral bevel gear pairs. The tail transmission shaft was first modeled using Timoshenko beam elements in local coordinates. Subsequently, the centralized parameter method was employed to build dynamic models of critical components such as the floating spline, limiting ring devices, and multiple spiral bevel gear pairs. Finally, the system's dynamic equations were derived utilizing the interface coordination principle and spatial coordinate transformation. Numerical analyses were conducted to examine the dynamic behavior of the system, including the coupled vibration properties and the impact laws of the limiting ring device and floating spline on the system's response. The findings indicated that the limiting ring device resulted in a cross-critical vibration reduction in the tail horizontal shaft, achieved through the mechanisms of dry friction and rubbing impact. However, as a consequence, the natural and rubbing frequencies of the other shafts were generated. The self-excited vibration of the system, brought about by the friction of the spline tooth surface, had a significant impact on the shaft that was directly connected. The emergence of the self-excited vibration occurred when the speed surpassed the first-order natural speed of the directly connected shaft, with the corresponding self-excited frequency being the first-order natural frequency of said shaft. With the increase in the tooth surface friction coefficient of the spline, it even caused continuous rubbing between the shaft and the limiting ring device under a supercritical condition. The proposed dynamic analysis approach holds promise in offering theoretical guidance for the reduction of vibration and noise generated in supercritical tail transmission systems. [ABSTRACT FROM AUTHOR]

In this paper we focus on the space of C 2 quartic splines on uniform criss-cross triangulations and we propose a method based on weighted essentially non-oscillatory techniques and obtained by modifying classical spline quasi-interpolants in order to approximate piecewise smooth functions avoiding Gibbs phenomenon near discontinuities and, at the same time, maintaining the high-order accuracy in smooth regions. We analyse the convergence properties of the proposed quasi-interpolants and we provide some numerical and graphical tests confirming the theoretical results. [ABSTRACT FROM AUTHOR]

We develop a practical and computationally efficient penalised estimation approach for partially linear additive models to zero-inflated binary outcome data. To facilitate estimation, B-splines are employed to approximate unknown nonparametric components. A two-stage iterative expectation-maximisation (EM) algorithm is proposed to calculate penalised spline estimates. The large-sample properties such as the uniform convergence and the optimal rate of convergence for functional estimators, and the asymptotic normality and efficiency for regression coefficient estimators are established. Further, two variance-covariance estimation approaches are proposed to provide reliable Wald-type inference for regression coefficients. We conducted an extensive Monte Carlo study to evaluate the numerical properties of the proposed penalised methodology and compare it to the competing spline method [Li and Lu. 'Semiparametric Zero-Inflated Bernoulli Regression with Applications', Journal of Applied Statistics, 49, 2845–2869]. The methodology is further illustrated by an egocentric network study. [ABSTRACT FROM AUTHOR]

We study space–time isogeometric discretizations of the linear acoustic wave equation that use splines of arbitrary degree p , both in space and time. We propose a space–time variational formulation that is obtained by adding a non-consistent penalty term of order 2 p + 2 to the bilinear form coming from integration by parts. This formulation, when discretized with tensor-product spline spaces with maximal regularity in time, is unconditionally stable: the mesh size in time is not constrained by the mesh size in space. We give extensive numerical evidence for the good stability, approximation, dissipation and dispersion properties of the stabilized isogeometric formulation, comparing against stabilized finite element schemes, for a range of wave propagation problems with constant and variable wave speed. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel model to analyze serially correlated two-dimensional functional data observed sparsely and irregularly on a domain which may not be a rectangle. Our approach employs a mixed effects model that specifies the principal component functions as bivariate splines on triangles and the principal component scores as random effects which follow an auto-regressive model. We apply the thin-plate penalty for regularizing the bivariate function estimation and develop an effective EM algorithm along with Kalman filter and smoother for calculating the penalized likelihood estimates of the parameters. Our approach was applied on simulated datasets and on Texas monthly average temperature data from January year 1915 to December year 2014. Supplementary materials accompanying this paper appear online. [ABSTRACT FROM AUTHOR]

This article compared two high-order numerical schemes for convection-diffusion delay differential equation via two fractional operators with singular kernels. The objective is to present two effective schemes that give (3 - α) and second order of accuracy in the time direction when α ∈ (0 , 1) using Caputo and Modified Atangana-Baleanu Caputo derivatives, respectively. We also implemented a trigonometric spline technique in the space direction, giving second order of accuracy. Moreover, meticulous analysis shows these numerical schemes to be unconditionally stable and convergent. The efficiency and reliability of these schemes are illustrated by numerical experiments. The tabulated results obtained from test examples have also shown the comparison of these operators. [ABSTRACT FROM AUTHOR]

Accumulating animal studies have demonstrated associations between ambient air pollution (AP) and metabolic dysfunction-associated fatty liver disease (MAFLD), but relevant epidemiological evidence is limited. We evaluated the association of long-term exposure to AP with the risk of incident MAFLD in Northwest China. The average AP concentration between baseline and follow-up was used to assess individual exposure levels. Cox proportional hazard models and restricted cubic spline functions (RCS) were used to estimate the association of PM2.5 and its constituents with the risk of MAFLD and the dose–response relationship. Quantile g-computation was used to assess the joint effects of mixed exposure to air pollutants on MAFLD and the weights of the various pollutants. We observed 1516 cases of new-onset MAFLD, with an incidence of 10.89%. Increased exposure to pollutants was significantly associated with increased odds of MAFLD, with hazard ratios (HRs) of 2.93 (95% CI: 1.22, 7.00), 2.86 (1.44, 5.66), 7.55 (3.39, 16.84), 4.83 (1.89, 12.38), 3.35 (1.35, 8.34), 1.89 (1.02, 1.62) for each interquartile range increase in PM2.5, SO42−, NO3−, NH4+, OM, and BC, respectively. Stratified analyses suggested that females, frequent exercisers and never-drinkers were more susceptible to MAFLD associated with ambient PM2.5 and its constituents. Mixed exposure to SO42−, NO3−, NH4+, OM and BC was associated with an increased risk of MAFLD, and the weight of BC had the strongest effect on MAFLD. Exposure to ambient PM2.5 and its constituents increased the risk of MAFLD. [ABSTRACT FROM AUTHOR]

A collocation method is developed for discrete fracture models in the context of the partition‐of‐unity method. Spline technologies used in isogeometric analysis (IGA) are exploited to provide a smooth inter‐element transition of gradients, thus allowing to get rid of extra flux terms at element boundaries which are generated by Lagrange polynomials. Bézier extraction is utilised to formulate IGA commensurate with a standard finite element data‐structure. The efficacy of the proposed approach is examined through different numerical examples and is compared with other discrete methods for fracture analysis. The proposed approach is competitive in terms of accuracy with the least computational cost, rendering it a suitable candidate for superseding available collocation approaches for fracture simulation. Moreover, the approach naturally assesses the possibility of physics informed neural networks for fracture simulation, to which collocation is central. [ABSTRACT FROM AUTHOR]

Analysis-suitable G 1 (AS- G 1) multi-patch spline surfaces [7] are particular G 1 -smooth multi-patch spline surfaces, which ensure the construction of C 1 -smooth multi-patch spline spaces with optimal polynomial reproduction properties [20]. We present a local approach for the design of AS- G 1 multi-patch spline surfaces, which is based on the use of Lagrange multipliers. The presented method is simple and generates an AS- G 1 multi-patch spline surface by approximating a given G 1 -smooth but non-AS- G 1 multi-patch surface. Several numerical examples demonstrate the potential of the proposed technique for the construction of AS- G 1 multi-patch spline surfaces and show that these surfaces are especially suited for applications in isogeometric analysis by solving the biharmonic problem, a particular fourth order partial differential equation, with optimal rates of convergence over them. [ABSTRACT FROM AUTHOR]

Background: The correlation between oxidative stress and female infertility pathogenesis was established, and the oxidative balance score (OBS) can serve as a measure of overall oxidative stress burden within an individual. Prior reports have not addressed the relationship between OBS and female infertility. This study endeavors to investigate the association between infertility risk in female and OBS. Methods: The analysis focused on data from the National Health and Nutrition Examination Survey 2013-2018. OBS was determined from 16 dietary components and 4 lifestyle components. Multivariate logistic regression was employed to investigate the relationship between OBS and female infertility. Further stratified analysis was conducted to examine the associations across various subgroups. To elucidate the dose-response relationship between infertility risk in female and OBS, a restricted cubic spline function was employed. Results: The study included a total of 1410 participants. Through weighted multivariable logistic regression analysis, we observed a consistent inverse correlation between OBS and the risk of female infertility [OR (95% CI) = 0.97 (0.95, 0.99), p = 0.047]. When participants were segregated into quartiles based on OBS, those in the highest quartile had a 61% [OR (95% CI) = 0.39 (0.2, 0.79), p = 0.01] reduced risk of infertility compared to those in the lowest quartile of OBS. A trend test assessing OBS by quartile also revealed the relationship between OBS and female infertility. This correlation remained constant across both dietary and lifestyle OBS. Additionally, lifestyle OBS and female infertility exhibited a nonlinear association. A sensitivity analysis verified the consistency of our findings. Conclusion: The study found that a higher OBS is associated with a lower prevalence of female infertility. These results emphasized the potential role of oxidative homeostasis in the pathogenesis of infertility and highlighted the importance of follow-up studies and prevention strategies. [ABSTRACT FROM AUTHOR]

AbstractModel degrees of freedom ( df ) is a fundamental concept in statistics because it quantifies the flexibility of a fitting procedure and is indispensable in model selection. To investigate the gap between df and the number of independent variables in the fitting procedure, Tibshirani (2015) introduced the search degrees of freedom ( sdf ) concept to account for the search cost during model selection. However, this definition has two limitations: it does not consider fitting procedures in augmented spaces and does not use the same fitting procedure for sdf and df . We propose a modified search degrees of freedom ( msdf ) to directly account for the cost of searching in either original or augmented spaces. We check this definition for various fitting procedures, including classical linear regressions, spline methods, adaptive regressions (the best subset and the lasso), regression trees, and multivariate adaptive regression splines (MARS). In many scenarios when sdf is applicable, msdf reduces to sdf . However, for certain procedures like the lasso, msdf offers a fresh perspective on search costs. For some complex procedures like MARS, the df has been pre-determined during model fitting, but the df of the final fitted procedure might differ from the pre-determined one. To investigate this discrepancy, we introduce the concepts of nominal df and actual df , and define the property of self-consistency, which occurs when there is no gap between these two df ’s. We propose a correction procedure for MARS to align these two df ’s, demonstrating improved fitting performance through extensive simulations and two real data applications. [ABSTRACT FROM AUTHOR]

In this study, we present a numerical method named the logarithmic non-polynomial spline method. This method combines conformable derivative, finite difference, and non-polynomial spline techniques to solve the nonlinear inhomogeneous time-fractional Burgers–Huxley equation. The developed numerical scheme is characterized by a sixth-order convergence and conditional stability. The accuracy of the method is demonstrated with 3D mesh plots, while the effects of time and fractional order are shown in 2D plots. Comparative evaluations with the cubic B-spline collocation method are provided. To illustrate the suitability and effectiveness of the proposed method, two examples are tested, with the results are evaluated using L 2 and L ∞ norms. [ABSTRACT FROM AUTHOR]

The smoothing of surface curves is an essential tool in mesh processing, important to applications that require segmenting and cutting surfaces such as surgical planning. Surface curves are typically designed by professionals to match certain surface features. For this reason, the smoothed curves should be close to the original and easily adjustable by the user in interactive tools. Previous methods achieve this desired behavior, e.g., by utilizing energy‐minimizing splines or generalizations of Bézier splines, which require a significant number of control points and may not provide interactive frame rates or numerical stability. This paper presents a new algorithm for robust smoothing of discrete surface curves on triangular surface meshes. By using a scalar penalty potential as the fourth coordinate, the given surface mesh is embedded into the 4D Euclidean space. Our method is based on finding geodesics in this lifted surface, which are then projected back onto the original 3D surface. The benefits of this approach include guaranteed convergence and good approximation of the initial curve. We propose a family of penalty potentials with one single parameter for adjusting the trade‐off between smoothness and similarity. The implementation of our method is straightforward as we rely on existing methods for computing geodesics and penalty fields. We evaluate our implementation and confirm its robustness and efficiency. [ABSTRACT FROM AUTHOR]

In this article, with the help of fractal quintic spline, numerical solutions of singularly perturbed boundary value problem of ordinary differential equations are obtained. To check the accuracy of the proposed method, convergence analysis is derived. The developed method has fourth order convergence. To check the correctness of the proposed method, numerical examples are provided. [ABSTRACT FROM AUTHOR]

Range-resolved CH4 concentration measurement is important prior data for atmospheric physical and chemical models. Ground-based differential absorption lidar (DIAL) can measure the vertical distribution of CH4 concentration in the atmosphere. The traditional method uses lidar observational data and the lidar equation to calculate profiles, but the inversion accuracy is greatly affected by noise. Although some denoising methods can improve accuracy at low altitudes, the low signal-to-noise ratio caused by the effect of aerosol Mie scattering and lower aerosol concentrations at high altitudes cannot be solved. Here, an improved cubic smoothing spline fitting CH4 concentration profile inversion method is proposed to address this challenge. By adding a penalty term of the second derivative of the conventional cubic spline function to the objective function, this penalty term acts to smooth the fitting, allowing the fitting function to avoid necessarily passing through those noisy sampling points. This avoids the large fluctuations caused by noisy sampling points, effectively suppresses noise, captures signals with lower noise levels, and thereby enhances the inversion accuracy of the profiles. Simulations and case studies demonstrated the superiority of the proposed method. Compared with the traditional method, cubic smoothing spline fitting can reduce the mean error of the whole CH4 profile by 85.54%. The standard deviation of CH4 concentration retrieved is 3.59 ppb–90.29 ppb and 0.01 ppb–6.75 ppb smaller than the traditional method and Chebyshev fitting, respectively. Three real cases also indicate that the CH4 concentration retrieved by cubic smoothing spline fitting is more consistent with in-situ measurements. In addition, long-term DIAL observations have also revealed notable diurnal and seasonal trends in CH4 concentration at observation sites. [ABSTRACT FROM AUTHOR]

Normalizing flows have emerged as a powerful brand of generative models, as they not only allow for efficient sampling of complicated target distributions but also deliver density estimation by construction. We propose here an in-depth comparison of coupling and autoregressive flows, both based on symmetric (affine) and non-symmetric (rational quadratic spline) bijectors, considering four different architectures: real-valued non-Volume preserving (RealNVP), masked autoregressive flow (MAF), coupling rational quadratic spline (C-RQS), and autoregressive rational quadratic spline (A-RQS). We focus on a set of multimodal target distributions of increasing dimensionality ranging from 4 to 400. The performances were compared by means of different test statistics for two-sample tests, built from known distance measures: the sliced Wasserstein distance, the dimension-averaged one-dimensional Kolmogorov–Smirnov test, and the Frobenius norm of the difference between correlation matrices. Furthermore, we included estimations of the variance of both the metrics and the trained models. Our results indicate that the A-RQS algorithm stands out both in terms of accuracy and training speed. Nonetheless, all the algorithms are generally able, without too much fine-tuning, to learn complicated distributions with limited training data and in a reasonable time of the order of hours on a Tesla A40 GPU. The only exception is the C-RQS, which takes significantly longer to train, does not always provide good accuracy, and becomes unstable for large dimensionalities. All algorithms were implemented using TensorFlow2 and TensorFlow Probability and have been made available on GitHub. [ABSTRACT FROM AUTHOR]

The accurate representation of real floor behavior is crucial for assessing human-induced vibration serviceability. Many researchers focus on developing computational models and field testing to reflect actual serviceability conditions. Although traditional boundary conditions are commonly used, limited attention has been given to optimizing these conditions. To begin with, this paper introduced semirigid boundary conditions into a finite-element model of the floor and optimized physical parameters and boundary constraint stiffness using the simulated annealing-particle swarm optimization (SA-PSO) method, resulting in a more realistic computational model. Subsequently, a random crowd load model was established by combining the social force model (SFM) and the pedestrian load model, and a random crowd-floor mutual coupling calculation model was established based on the improved pedestrian biomechanical model. In addition, the mode shape functions of the floor with semirigid boundary conditions were obtained by extracting the optimized mode shape vector of the floor and using cubic spline interpolation. The dynamic response of the floor was computed using the modal analysis method, and the accuracy of the suggested method and model was verified by experiment. Furthermore, the effect on the vibration serviceability of the floor was analyzed under crowd walks randomly on the floor with different boundary conditions both before and after optimization. This study revealed: (1) achieving a computational model consistent with real floors requires optimization of relevant parameters and boundary conditions, reducing the error in floor frequency from 39.48% to 5.44% compared to measured results. (2) The human-induced vibration serviceability for existing floors may be misjudged by using traditional boundary conditions. The mean value of peak acceleration of floor with semirigid boundary conditions increased by 35.92%, with a 42% increase in the probability of serviceability problems compared to the SSCC boundary. (3) High-frequency floors also experience human-induced vibration serviceability issues. For a floor with a fundamental frequency of 10.3540 Hz, simulation and experimental results during five-person random walks indicate that peak acceleration at the middle position of the floor exceeds serviceability limits. [ABSTRACT FROM AUTHOR]

Experimental tests of cross-laminated timber (CLT)-concrete composite floor panels were conducted. The tests consisted of linear-elastic tests of square CLT-concrete composite panels with a novel shear connector to determine elastic orthotropic plate properties. After the linear-elastic tests, the panels were subjected to a patch load at the center of the panel and tested to failure. To investigate load transfer across longitudinal joints between adjacent panels, nonuniform bending tests were conducted. Results from the experimentally measured orthotropic plate properties showed that the shear connector increased the bending stiffness in the weak direction of the panel compared to prior test results using conventional shear connectors. The tests to failure exhibited larger differences in behavior between the strong and weak orientations of the specimens, with both showing substantial inelastic behavior prior to failure. Numerical finite element models of the patch-load test showed good agreement with experimental results. Analytical formulas using the obtained orthotropic plate properties did not agree with experimental results for the patch-load at linear scales, suggesting the simplified method is currently not suited for CLT-concrete two-way bending. Load-transfer tests found that the reinforced concrete topping is capable of transferring load across the longitudinal joint of two parallel panels to enable two-way bending of composite timber–concrete floors and that the addition of a plywood spline with closely spaced screws enables a higher degree of force transfer. [ABSTRACT FROM AUTHOR]

Interaction analysis is a critical component of clinical and public health research and represents a key topic in precision health and medicine. In applied settings, however, interaction assessment is usually limited to the test of a product term in a regression model and to the presentation of results stratified by levels of additional covariates. Stratification of results often relies on categorizing or making linearity assumptions for continuous covariates, with substantial loss of precision and of relevant information. In time-to-event analysis, moreover, interaction assessment is often limited to the multiplicative hazard scale by inclusion of a product term in a Cox regression model, disregarding the clinically relevant information that is captured by the absolute risk scale. In this paper we present a user-friendly procedure, based on the prediction of individual absolute risks from the Cox model, for the estimation and presentation of interactive effects on both the multiplicative and additive scales in survival analysis. We describe how to flexibly incorporate interactions with continuous covariates, which potentially operate in a nonlinear fashion, provide software for replicating our procedure, and discuss different approaches to deriving CIs. The presented approach will allow clinical and public health researchers to assess complex relationships between multiple covariates as they relate to a clinical endpoint, and to provide a more intuitive and precise depiction of the results in applied research papers focusing on interaction and effect stratification. [ABSTRACT FROM AUTHOR]

Step selection functions (SSFs) are used to jointly describe animal movement patterns and habitat preferences. Recent work has extended this framework to model inter‐individual differences, account for unexplained structure in animals' space use and capture temporally varying patterns of movement and habitat selection.In this paper, we formulate SSFs with penalised smooths (similar to generalised additive models) to unify new and existing extensions, and conveniently implement the models in the popular, open‐source mgcv R package.We explore non‐linear patterns of movement and habitat selection, and use the equivalence between penalised smoothing splines and random effects to implement individual‐level and spatial random effects. This framework can also be used to fit varying‐coefficient models to account for temporally or spatially heterogeneous patterns of selection (e.g. resulting from behavioural variation), or any other non‐linear interactions between drivers of the animal's movement decisions.We provide the necessary technical details to understand several key special cases of smooths and their implementation in mgcv, showcase the ecological relevance using two illustrative examples and provide R code to facilitate the adoption of these methods. This paper offers a broad overview of how smooth effects can be applied to increase the flexibility and biological realism of SSFs. [ABSTRACT FROM AUTHOR]

Due to the non-local property of the fractional derivative, the analytic solutions of fractional differential equations are hardly available in most cases. Consequently, researches on the numerical solutions of fractional differential equations are of great importance. In this paper, we will propose a new numerical method to obtain the solutions of the Caputo-type fractional differential equations. The error analysis is given to prove the accuracy of our method when the order $ p $ of the fractional derivative satisfying $ p>1 $. The numerical experiments also show that both linear fractional equations and nonlinear fractional equations can be solved with this method. [ABSTRACT FROM AUTHOR]

In this paper, the three‐dimensional stress field in nonlinear laminated composite shells with piezoelectric patches subjected to displacement‐dependent loads is analyzed. To solve the problem, the geometrically exact (GeX) hybrid‐mixed four‐node solid‐shell element has been developed. The term GeX means that the middle surface is described by analytical functions, including spline functions, and, therefore, the coefficients of the first and second fundamental forms are taken exactly at the element nodes. The laminated solid‐shell element formulation is based on the choice of an arbitrary number of sampling surfaces (SaS) parallel to the middle surface and located at the Chebyshev polynomial nodes within the layers, in order to introduce the displacements and electric potentials of these surfaces as unknown functions. The outer surfaces and interfaces are also included into a set of SaS. Due to analytical integration utilized to evaluate the tangent stiffness matrix, the proposed GeX piezoelectric solid‐shell element under nonconservative loading exhibits superior performance in the case of coarse meshes and allows the use of only one load step in all considered benchmark problems. Therefore, it can be recommended for the large deformation analysis of doubly curved laminated composite shells with piezoelectric patches, since the SaS formulation allows one to find three‐dimensional solutions of electroelasticity with a prescribed accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we present a new numerical method for effectively solving general second-order ordinary differential equations with mixed boundary conditions. Our approach utilizes a quasi-variable mesh enabling us the flexibility to adapt the mesh density according to different boundary layer problems. By employing a discretization technique that incorporates the construction of exponential spline, we achieve third-order accuracy at internal grid points, while boundary points exhibit fourth-order accuracy. Since the method is based on off-step grid points, it eliminates the need to modify the method while employing it to singular problems. We provide computational results to various numerical problems which arise in different physical phenomena like Burger's equation and Sturm–Liouville equation. A comparison with recent findings underscores the superior performance of our method. [ABSTRACT FROM AUTHOR]

Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods to the so-represented data. The initial choice of a functional representation may have a significant impact on the second phase of the analysis, as shown in recent research, where data-driven spline bases outperformed the predefined rigid choice of functional representation. The method chooses an initial functional basis by an efficient placement of the knots using a simple machine-learning algorithm. The knot selection approach does not apply directly when the data are defined on domains of a higher dimension than one such as, for example, images. The reason is that in higher dimensions the convenient and numerically efficient spline spaces use tensor bases that require knots located on a lattice. This fundamentally limits flexible knot placement which is fundamental for the approach. The goal of this research is two-fold: first, to propose modified approaches that circumvent the issue by coding the irregular knot selection into the topology of the spaces of tensor-based splines; second, to apply the approach to a classification problem workflow for functional data that utilizes knot selection. The performance is preliminarily accessed on a benchmark dataset and shown to be comparable to or better than the previous methods. [ABSTRACT FROM AUTHOR]

This paper proposes a novel approach called Stack-GA2M to identify fraudulent reviewers in an inherently interpretable manner by fusing both target and non-target features. Specifically, for local interpretability, we adopt GA2M (Standard Generalized Additive Model plus interactions) as the basic classifier to produce three subordinate models trained by using the target features and the non-target features as review textual features and reviewer behavioral features. For global interpretability, we adopt LR (Logistic Regression) as the meta classifier to stack the outputs of three subordinate models to identify the fraudulent reviewers. The white-box model of LR enables us to understand the global interpretability of the target features and the non-target features in identifying fraudulent reviewers. With GA2M, the local interpretability of each subordinate model is derived by using feature importance, spline shape functions for individual features, and heatmaps for interaction terms. Extensive experiments on Yelp dataset demonstrate that the proposed Stack-GA2M approach is superior to state-of-the-art techniques in identifying fraudulent reviewers and exhibits favorable inherent interpretability. [ABSTRACT FROM AUTHOR]

Summary Often, causal mediation analysis is of interest when both the mediator and the final outcome are repeatedly measured, but limited work has been done for this situation (as opposed to where only the mediator is repeatedly measured). Available methods are primarily based on parametric models and tend to be sensitive to model assumptions. This article presents semiparametric, continuous‐time models to provide a flexible and robust approach to causal mediation analysis for longitudinal data, which allows these data to be unbalanced or irregular. Specifically, the method uses spline linear mixed‐effects models for the mediator and for the final outcome, with a two‐step approach to model‐fitting in which a predicted mediator is used as a covariate in the final outcome model. The models allow flexible functions for both the mean and individual response functions for each outcome. We derive estimated natural direct and indirect effects as a function of time using an extended mediation formula and sequential ignorability assumption. In simulation studies, we compare properties of estimated direct and indirect effects, and a delta method estimate of the standard error of the latter, under alternative approaches for predicting the mediator. The approach is illustrated using harmonised data from two cohort studies to examine attention as a mediator of the effect of prenatal tobacco exposure on externalising behaviour in children. [ABSTRACT FROM AUTHOR]

AbstractThis article discusses the estimating equation method for varying coefficient transformation models. The B spline technique is used to approximate the unknown functional coefficients, resulting in a parametric model. The approximated model is then given a set of estimation equations. Under some regular conditions, we demonstrate the large sample properties of the resulting estimates. Some simulation studies and a real data application are also employed to assess the performance of our proposed methodologies. [ABSTRACT FROM AUTHOR]

This paper demonstrates that the space of piecewise-smooth bivariate functions can be well-approximated by the space of the functions defined by a set of simple (non-linear) operations on smooth uniform tensor product splines. The examples include bivariate functions with jump discontinuities or normal discontinuities across curves, and even across more involved geometries such as a three-corner discontinuity. The provided data may be uniform or non-uniform, and noisy, and the approximation procedure involves non-linear least-squares minimization. Also included is a basic approximation theorem for functions with jump discontinuity across a smooth curve. [ABSTRACT FROM AUTHOR]

Objectives: Small-for-gestational-age (SGA) and large-for-gestational-age (LGA) births are major adverse birth outcomes related to newborn health. In contrast, the association between ambient air pollution levels and SGA or LGA births has not been investigated in Japan; hence, the purpose of our study is to investigate this association. Methods: We used birth data from Vital Statistics in Japan from 2017 to 2021 and municipality-level data on air pollutants, including nitrogen dioxide (NO2), sulfur dioxide (SO2), photochemical oxidants, and particulate matter 2.5 (PM2.5). Ambient air pollution levels throughout the first, second, and third trimesters, as well as the whole pregnancy, were calculated for each birth. The association between SGA/LGA and ambient levels of the air pollutants was investigated using crude and adjusted log-binomial regression models. In addition, a regression model with spline functions was also used to detect the non-linear association. Results: We analyzed data from 2,434,217 births. Adjusted regression analyses revealed statistically significant and positive associations between SGA birth and SO2 level, regardless of the exposure period. Specifically, the risk ratio for average SO2 values throughout the whole pregnancy was 1.014 (95% confidence interval [CI] 1.009, 1.019) per 1 ppb increase. In addition, regression analysis with spline functions indicated that an increase in risk ratio for SGA birth depending on SO2 level was linear. Furthermore, statistically significant and negative associations were observed between LGA birth and SO2 except for the third trimester. Conclusions: It was suggested that ambient level of SO2 during the pregnancy term is a risk factor for SGA birth in Japan. [ABSTRACT FROM AUTHOR]

Various studies have proved that PM2.5 pollution significantly impacts people's health and the environment. Reliable models on pollutant levels and trends are essential for policy-makers to decide on pollution reduction. Therefore, this research presents the sensitivity analysis of the Bicubic Spline Smoothing (BSS) and Inverse Distance Weighting (IDW) models built for the PM2.5 monthly series from MERRA-2 Reanalysis collected during January 2010–April 2017 in the region of the Persian Gulf, in the neighborhood of the United Arab Emirates Coast. The models' performances are assessed using the Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE). RMSE, Mean Bias Error (MBE), and Nash–Sutcliff Efficiency (NSE) were utilized to assess the models' sensitivity to various parameters. For the IDW, the Mean RMSE decreases as the power parameter increases from 1 to approximately 4 (the optimal beta value) and then stabilizes with a further increase. NSE values close to 1 indicate that the model's predictions are very efficient in capturing the variance of the observed data. NSE is almost constant as a function of the number of neighbors and the parameter when β > 4. In BSS, the RMSE and NBE plots suggest that incorporating more points into the mean calculation for buffer points leads to a general decrease in model accuracy. Moreover, the MBE plot shows that the mean bias error initially increases with the number of points but then starts to plateau. The increasing trend suggests that the model tends to systematically overestimate the PM2.5 values as more points are included. The leveling-off of the curve indicates that beyond a certain number of points, the bias introduced by including additional points does not significantly increase, suggesting a threshold beyond which further inclusion of points does not markedly change the mean bias. It was also proved that the methods' generalizability may depend on the dataset's specific spatial characteristics. [ABSTRACT FROM AUTHOR]

The goal of the paper is to establish quadrature formulas on combinatorial graphs. Three types of quadrature formulas are developed. Quadrature formulas of the first type are obtained through interpolation by variational splines. This set of formulas is exact on spaces of variational splines on graphs. Since bandlimited functions can be obtained as limits of variational splines we obtain quadrature formulas which are approximately exact on spaces of bandlimited functions. Accuracy of this type of quadrature formulas is given in terms of geometry of the set of nodes of splines and in terms of smoothness of functions which is measured by means of the combinatorial Laplace operator. Quadrature formulas of the second type are obtained through point-wise sampling for bandlimited functions and based on existence of certain frames in appropriate subspaces of bandlimited functions. The third type quadrature formulas are based on the average sampling over subgraphs. Our quadrature formulas which are based on sampling are exact on a relevant subspaces of bandlimited functions. The results of the paper have potential applications to problems that arise in data mining. [ABSTRACT FROM AUTHOR]

With rapid development of techniques to measure brain activity and structure, statistical methods for analyzing modern brain-imaging data play an important role in the advancement of science. Imaging data that measure brain function are usually multivariate high-density longitudinal data and are heterogeneous across both imaging sources and subjects, which lead to various statistical and computational challenges. In this article, we propose a group-based method to cluster a collection of multivariate high-density longitudinal data via a Bayesian mixture of smoothing splines. Our method assumes each multivariate high-density longitudinal trajectory is a mixture of multiple components with different mixing weights. Time-independent covariates are assumed to be associated with the mixture components and are incorporated via logistic weights of a mixture-of-experts model. We formulate this approach under a fully Bayesian framework using Gibbs sampling where the number of components is selected based on a deviance information criterion. The proposed method is compared to existing methods via simulation studies and is applied to a study on functional near-infrared spectroscopy, which aims to understand infant emotional reactivity and recovery from stress. The results reveal distinct patterns of brain activity, as well as associations between these patterns and selected covariates. [ABSTRACT FROM AUTHOR]

The structural compliance of annular ring gear can significantly influence the quasi-static and dynamic performance of an epicyclic gear set. As powertrain components are continually being optimized to their design limits, this influence becomes prominent and can no longer be ignored. The current paper will study the impact of ring gear compliance on the dynamic response of epicyclic gear sets in fixed ring kinematic configuration. To achieve this objective, the current study will incorporate a finite element-based ring gear formulation into the three-dimensional planetary load distribution model of Ryali and Talbot (2021, "A Dynamic Load Distribution Model of Planetary Gear Sets," Mech. Mach. Theory, 158, p. 104229). The proposed model employs a modified simplex algorithm to iteratively solve for the elastic gear mesh contacts in conjunction with a numerical integration scheme, which enables it to inherently capture the influence of several components and system-level design variations. The developed formulation is used to conduct parametric studies involving different planetary gear designs, ring gear fixtures (bolted vs. splined), and operating conditions (quasi-static, dynamic). In the case of a splined ring gear fixture, an external splined tooth contact model is developed, which will be used to validate the model against the quasi-static experiments of Kahraman et al. (2010, "Influence of Ring Gear Rim Thickness on Planetary Gear Set Behavior," ASME J. Mech. Des., 132(2), pp. 0210021-0210028). The discussed results demonstrate the fidelity of the developed model, thus making it an excellent tool for the design and analysis of planetary gears with thin annular ring gears. [ABSTRACT FROM AUTHOR]

We have developed in this paper a morphological disambiguation hybrid system for the Arabic language that identifies the stem, lemma and root of a given sentence words. Following an out-of-context analysis performed by the morphological analyser Alkhalil Morpho Sys, the system first identifies all the potential tags of each word of the sentence. Then, a disambiguation phase is carried out to choose for each word the right solution among those obtained during the first phase. This problem has been solved by equating the disambiguation issue with a surface optimization problem of spline functions. Tests have shown the interest of this approach and the superiority of its performances compared to those of the state of the art. [ABSTRACT FROM AUTHOR]

In the process of grey prediction modeling, the accumulation of original non-negative sequences can enhance the inherent regularity of data and the smoothness of sequences. The estimated method of background values and derivative values greatly affects the prediction accuracy and adaptability of the model. On the basis of the traditional GM(2,1) model, the GM(2,1) model with the fractional order accumulation is obtained by introducing a fractional order operator, which can be written as GMr(2,1) with r-AGO. In this work, we estimated the background values and derivative values based on a C¹ convexity-preserving rational quadratic interpolation spline, and thereby established a new GM²(2,1) model. Numerical examples showed that the new GM²(2,1) model had better prediction quality of data than the classical GM(2,1) and GM²(2,1) model and improved the precision of prediction in practice. [ABSTRACT FROM AUTHOR]

We use a Gaussian Process Regression (GPR) strategy to analyze different types of curves that are commonly encountered in parametric eigenvalue problems. We employ an offline-online decomposition method. In the offline phase, we generate the basis of the reduced space by applying the proper orthogonal decomposition (POD) method on a collection of pre-computed, full-order snapshots at a chosen set of parameters. Then we generate our GPR model using four different Matérn covariance functions. In the online phase, we use this model to predict both eigenvalues and eigenvectors at new parameters. We then illustrate how the choice of each covariance function influences the performance of GPR. Furthermore, we discuss the connection between Gaussian Process Regression and spline methods and compare the performance of the GPR method against linear and cubic spline methods. We show that GPR outperforms other methods for functions with a certain regularity. [ABSTRACT FROM AUTHOR]

We address the semiparametric challenge of identifying and estimating generalized additive partial linear models with nonignorable missingness in the response. Identifiability is ensured under instrumental variable assumption that there is an instrumental covariate related to the prospensity but unrelated to the response variable, or the assumption that the conditional score function is linear in the response variable. We propose a new estimating equation for the prospensity by taking expectation of the unobservable part on a linear combination of all covariates rather than the covariates themselves. This estimating equation does not suffer from the typical curse of dimensionality. Then the unknown nonparametric function is approximated by polynomial spline basis functions and we construct estimating equations for mean of response based on the inverse probability weighting. Under some regular conditions, we establish asymptotic normality of the proposed estimators for parametric components and consistency of the estimators of nonparametric functions. Simulation studies demonstrate that the proposed inference procedure performs well in many settings. The proposed method is applied to analyze the household income dataset from the Chinese Household Income Project Survey 2013. [ABSTRACT FROM AUTHOR]

This article presents a parameter uniform convergence numerical scheme for solving time fractional order singularly perturbed parabolic convectiondiffusion differential equations with a delay. We give a priori bounds on the exact solution and its derivatives obtained through the problem's asymptotic analysis. The Euler's method on a uniform mesh in the time direction and the extended cubic B-spline method with a fitted operator on a uniform mesh in the spatial direction is used to discretize the problem. The fitting factor is introduced for the term containing the singular perturbation parameter, and it is obtained from the zeroth-order asymptotic expansion of the exact solution. The ordinary B-splines are extended into the extended B-splines. Utilizing the optimization technique, the value of µ (free parameter, when the free parameter µ tends to zero the extended cubic B-spline reduced to convectional cubic B-spline functions) is determined. It is also demonstrated that this method is better than some existing methods in the literature. [ABSTRACT FROM AUTHOR]

In this paper, a singularly perturbed one-dimensional initial boundary value problem of a quasilinear Sobolev-type equation is presented. The nonlinear term of the problem is linearized by Newton's linearization method. Time derivatives are discretized by implicit Euler's method on nonuniform step size. A uniform trigonometric B-spline collocation method is used to treat the spatial variable. The convergence analysis of the scheme is proved, and the accuracy of the method is of order two in space and order one in time direction, respectively. To test the efficiency of the method, a model example is demonstrated. Results of the scheme are presented in tabular, and the figure indicates the scheme is uniformly convergent and has an initial layer at t = 0. [ABSTRACT FROM AUTHOR]

In the time-frequency analysis of the echoes from targets with composite micro-motions, there is a problem that the energy of time-frequency strip is difficult to focus, which affects the extraction and analysis of the target's micro-Doppler feature. To solve this problem, this paper proposes the concept of time-frequency harmonic stripes and corresponding time-frequency transformation methods. Based on the assumption that the composite micro-motions include central motion components and high-frequency motion components, firstly, spline function is used to fit the frequency curve of the central motion component, and therefore construct the time-frequency transform kernel is constructed. Then, parameterized time-frequency transform is used to convert the composite micro-Doppler signal in the time domain to harmonic stripes on the time-frequency plane. Compared with traditional methods such as short-time Fourier transform and pseudo Wigner-Ville distribution, the proposed method can significantly improve the energy aggregation and spur suppression of time-frequency transform of radar echoes from composite micro-motion targets. Simulation results verify the effectiveness of the proposed method and its adaptability to low signal-to-noise ratio (SNR) conditions. [ABSTRACT FROM AUTHOR]

In the automotive industry, ageing mechanisms and diagnosis of Li-ion batteries depending on charge rate are of tremendous importance. With this in mind, we have investigated the lifetime degradation of lithium-ion battery cells at three distinct charging rates using Electrochemical Impedance Spectroscopy (EIS). Impedance spectra of high-energy Panasonic NCR18650B batteries have been analysed in light of two distinct approaches, namely the time-dependent evaluation of the Constant Phase Element (CPE), and the single parameter investigation of resonance frequency of the circuit. SOH percentages were used to validate our approach. By monitoring the CPE-Q parameter at different charge rates of 0.5 C, 1 C, and 1.5 C, respectively, we applied a degradation speed analysis, allowing us to predict a quantitative value of the LIBs. The results are in complete agreement with the resonance frequency single parameter analysis, in which quite a similar trend was obtained after the spline fitting. [ABSTRACT FROM AUTHOR]

A hybrid method utilizing the collocation technique with B-splines and Lie-Trotter splitting algorithm applied for 3 model problems which include a single solitary wave, two solitary wave interaction, and a Maxwellian initial condition is designed for getting the approximate solutions for the generalized equal width (GEW) equation. Initially, the considered problem has been split into 2 sub-equations as linear Ut = Â(U) and nonlinear Ut = B(U) in the terms of time. After, numerical schemes have been constructed for these sub-equations utilizing the finite element method (FEM) together with quintic B-splines. Lie-Trotter splitting technique ÂoB has been used to generate approximate solutions of the main equation. The stability analysis of acquired numerical schemes has been examined by the Von Neumann method. Also, the error norms L2 and L∞ with mass, energy, and momentum conservation constants I1, I2, and I3, respectively are calculated to illustrate how perfect solutions this new algorithm applied to the problem generates and the ones produced are compared with those in the literature. These new results exhibit that the algorithm presented in this paper is more accurate and successful, and easily applicable to other non-linear partial differential equations (PDEs) as the present equation. [ABSTRACT FROM AUTHOR]