Quadratic Spline Research Articles

Age Dependence of the Risk of Intussusception Following Tetravalent Rhesus-Human Reassortant Rotavirus Tetravalent Vaccine: Is It Beyond Doubt?

The relation between the risk of intussusception and age at the time of receipt of the first dose of rhesus-human reassortant rotavirus tetravalent vaccine (RRV-TV) has been studied extensively on the basis of Centers for Disease Control and Prevention (CDC) matched case-control study data, using various statistical methods, including conditional logistic regression and quadratic smoothing splines. However, different conclusions have been reported in published analyses regarding the dependence of the risk of intussusception on age at first dose. The authors reanalyzed the CDC matched case-control data set using unrestricted and restricted quadratic smoothing spline methods for various exposure windows (i.e., intervals postvaccination). These analyses indicated that the use of different models may lead to different conclusions. The restricted quadratic smoothing spline with appropriately chosen knot locations showed a statistically significant increased risk of intussusception associated with RRV-TV for the exposure window 3-14 days after the first dose at an age as young as 49 days, the youngest age in the data set at which vaccine was administered; this implies an increased risk of intussusception associated with RRV-TV at all ages studied.

A two-dimensional minimum-derivative spline

We consider the construction of a C (1,1) interpolation parabolic spline function of two variables on a uniform rectangular grid, i.e., a function continuous in a given region together with its first partial derivatives which on every partial grid rectangle is a polynomial of second degree in x and second degree in y. The spline function is constructed as a minimum-derivative one-dimensional quadratic spline in one of the variables, and the spline coefficients themselves are minimum-derivative quadratic spline functions of the other variable.

A note on: Spline technique for modeling roadway profile to minimize earthwork cost

The gap constraint used in A. A. Moreb, Spline technique for modeling roadway profile to minimize earthwork cost, J. Ind. Man. & Opt., 5 (2) (2009), 275-283 introduces unnecessary errors, while the slope constraint may be violated for second- and higher-order splines. In this note we amend the gap constraint, while maintaining the linearity of the model. We also present an improved slope constraint for linear and quadratic splines, and show that it becomes nonlinear for cubic and higher order splines. The improvements also apply to A. Moreb, M. Aljohani, Quadratic representation for roadway profile that minimizes earthwork cost, J. Sys. Sci. & Sys. Eng., 13 (2) (2004), 245-252.

Comparison of parametric, orthogonal, and spline functions to model individual lactation curves for milk yield in Canadian Holsteins

Test day records for milk yield of 57,390 first lactation Canadian Holsteins were analyzed with a linear model that included the fixed effects of herd-test date and days in milk (DIM) interval nested within age and calving season. Residuals from this model were analyzed as a new variable and fitted with a five parameter model, fourth-order Legendre polynomials, with linear, quadratic and cubic spline models with three knots. The fit of the models was rather poor, with about 30%–40% of the curves showing an adjusted R-square lower than 0.20 across all models. Results underline a great difficulty in modelling individual deviations around the mean curve for milk yield. However, the Ali and Schaeffer (5 parameter) model and the fourth-order Legendre polynomials were able to detect two basic shapes of individual deviations among the mean curve. Quadratic and, especially, cubic spline functions had better fitting performances but a poor predictive ability due to their great flexibility that results in an abrupt change of the estimated curve when data are missing. Parametric and orthogonal polynomials seem to be robust and affordable under this standpoint.

電力系統の予防制御のための定態安定限界の高速探索 ―モード結合法の応用―

In this paper, high speed searching of stability limit output for preventive control of a power system is proposed. It is necessary to understand a range of stability limits of a generator in various possible operating conditions to execute preventive control. The possibility of an accident increases as a power system becomes large. Therefore, it takes a certain amount of time to conduct a stability analysis. Then, we propose three kinds of searching techniques (straight line method, quadratic curve method and spline curve method) to search for a stability limit in the power system at high speed, and the most effective method is identified through comparison of these methods. In this case, the mode coupling method (MC method) was used for the presumption of the eigenvalue that evaluated stability in the steady state stability analysis of the power system. Moreover, the MC method used this time selects major modes for that we pay attention and highly related modes. Next, these two or more selected modes are coupled and new eigenvalues of the coupled matrix are calculated. The size of the coupled matrix is very small. As a result, it found to be an effective method in which non-liner estimation of the eigenvalue is possible. Also, it became possible to search for the limit of the output in high accuracy by setting the estimated error as the situation demands.

Improved Multi-***scale Product Method for Glottal Opening Instants From Speech Signal

In this paper, we improve the glottal opening instant (GOI) detection from speech signal by a new approach based on Multi-***scale Product Method (MPM). We compute wavelet transform coefficients products at three scales using the quadratic spline wavelet. Glottal closure and opening instants appear respectively as strong maximum and weak minimum on the product signal. The GOI localisation is enhanced by refining the time interval containing this instant and based on the open quotient value. The proposed method is applied and evaluated on the Keele University database. Evaluation results show that the MPM detects GOIs with a performance rate equals to 96% for the entire database.

MPM Method and DYPSA Algorithm Evaluation for GCI Detection in a Noisy Speech Signal

This paper deals with the evaluation and the comparison of two methods for determining glottal closure instants (GCIs) from the speech signal. These methods are the Multi-scale Product Method (MPM) and the Dynamic Programming Phase Slope Algorithm (DYPSA). The MPM consists of determining abscissa of peaks appeared on the product of wavelet transform coefficients at three adjacent dyadic scales. The wavelet used to compute the product is the quadratic spline function. However, the DYPSA algorithm is based on the group delay function to generate the GCI candidates and the dynamic programming technique to select the true GCIs. The comparison of the two algorithms is operated without noise and with additive Gaussian noise at various SNR levels. The evaluation is operated on the Keele University database. Results show that the MPM is more robust to noise than the DYPSA with a good detection rate nearby 90% at an SNR level of 0 dB and a small false alarm rate. Besides, the DYPSA is more sensitive to noise with a good detection rate of 20% at 0 dB and a high false alarm rate surpassing 70%.

Quadratic Spline Collocation for the Smoothed Weakly Singular Fredholm Integral Equations

This article addresses a quadratic spline collocation method for the numerical solution of weakly singular Fredholm integral equations of the second kind. Using suitable smoothing techniques, optimal global convergence estimates are derived and a local superconvergence result is given.

Construction of spherical spline quasi-interpolants based on blossoming

A general theory of quasi-interpolants based on quadratic spherical Powell–Sabin splines on spherical triangulations of a sphere-like surface S is developed by using polar forms. As application, various families of discrete and differential quasi-interpolants reproducing quadratic spherical Bézier–Bernstein polynomials or the whole space of the spherical Powell–Sabin quadratic splines of class C 1 are presented.

Efficient Global Approximation of Generalized Nonlinear ℓ1-Regularized Solution Paths and Its Applications

We consider efficient construction of nonlinear solution paths for general ℓ1-regularization. Unlike the existing methods that incrementally build the solution path through a combination of local linear approximation and recalibration, we propose an efficient global approximation to the whole solution path. With the loss function approximated by a quadratic spline, we show that the solution path can be computed using a generalized Lars algorithm. The proposed methodology avoids high-dimensional numerical optimization and thus provides faster and more stable computation. The methodology also can be easily extended to more general regularization framework. We illustrate such flexibility with several examples, including a generalization of the elastic net and a new method that effectively exploits the so-called “support vectors” in kernel logistic regression.

Application of Kolmogorov–Johnson–Mehl–Avrami equations to non-isothermal conditions

Abstract A temperature domain form of the standard Kolmogorov–Johnson–Mehl–Avrami (KJMA) equation is presented which can be used simulate phenomena such as phase transformation and recrystallization kinetics under non-isothermal conditions. This form of the KJMA equation relies on a parameterized temperature–time history based on either a quadratic polynomial or shape preserving quadratic spline, and can be solved using a Gauss–Legendre quadrature scheme with low computational cost and algorithmic complexity. Sample calculations are included for the case of non-isothermal static recrystallization in a hot deformed C–Nb steel, and comparison is made with results obtained by conventional time domain schemes.

Rejoinder: Arsenic Exposure and Prevalence of Type 2 Diabetes

Rejoinder: Arsenic Exposure and Prevalence of Type 2 Diabetes

Gaussian‐Taylor signal‐to‐noise ratio estimation for scanning electron microscope images

A new and robust parameter estimation technique, named Gaussian-Taylor interpolation, is proposed to predict the signal-to-noise ratio (SNR) of scanning electron microscope images. The results of SNR and variance estimation values are tested and compared with piecewise cubic Hermite interpolation, quadratic spline interpolation, autoregressive moving average and moving average. Overall, the proposed estimations for noise-free peak and SNR are most consistent and accurate to within a certain acceptable degree compared with the others.

A Quadratic Spline based Interface (QUASI) reconstruction algorithm for accurate tracking of two-phase flows

A new Quadratic Spline based Interface (QUASI) reconstruction algorithm is presented which provides an accurate and continuous representation of the interface in a multiphase domain and facilitates the direct estimation of local interfacial curvature. The fluid interface in each of the mixed cells is represented by piecewise parabolic curves and an initial discontinuous PLIC approximation of the interface is progressively converted into a smooth quadratic spline made of these parabolic curves. The conversion is achieved by a sequence of predictor–corrector operations enforcing function ( C 0) and derivative ( C 1) continuity at the cell boundaries using simple analytical expressions for the continuity requirements. The efficacy and accuracy of the current algorithm has been demonstrated using standard test cases involving reconstruction of known static interface shapes and dynamically evolving interfaces in prescribed flow situations. These benchmark studies illustrate that the present algorithm performs excellently as compared to the other interface reconstruction methods available in literature. Quadratic rate of error reduction with respect to grid size has been observed in all the cases with curved interface shapes; only in situations where the interface geometry is primarily flat, the rate of convergence becomes linear with the mesh size. The flow algorithm implemented in the current work is designed to accurately balance the pressure gradients with the surface tension force at any location. As a consequence, it is able to minimize spurious flow currents arising from imperfect normal stress balance at the interface. This has been demonstrated through the standard test problem of an inviscid droplet placed in a quiescent medium. Finally, the direct curvature estimation ability of the current algorithm is illustrated through the coupled multiphase flow problem of a deformable air bubble rising through a column of water.

Numerical integration based on bivariate quadratic spline quasi-interpolants on bounded domains

In this paper we generate and study new cubature formulas based on spline quasi-interpolants defined as linear combinations of C1 bivariate quadratic B-splines on a rectangular domain Ω, endowed with a non-uniform criss-cross triangulation, with discrete linear functionals as coefficients. Such B-splines have their supports contained in Ω and there is no data point outside this domain. Numerical results illustrate the methods.

Quadratic spline collocation for one-dimensional linear parabolic partial differential equations

New methods for solving general linear parabolic partial differential equations (PDEs) in one space dimension are developed. The methods combine quadratic-spline collocation for the space discretization and classical finite differences, such as Crank-Nicolson, for the time discretization. The main computational requirements of the most efficient method are the solution of one tridiagonal linear system at each time step, while the resulting errors at the gridpoints and midpoints of the space partition are fourth order. The stability and convergence properties of some of the new methods are analyzed for a model problem. Numerical results demonstrate the stability and accuracy of the methods. Adaptive mesh techniques are introduced in the space dimension, and the resulting method is applied to the American put option pricing problem, giving very competitive results.

Linguistic color image segmentation using a hierarchical Bayesian approach

AbstractIn this work, we combine Bayesian techniques with a color categorization model, which leads to a method for the linguistic segmentation of color images. The categorization model considers the 11 universal color categories proposed by Berlin and Kay [Basic Color Terms: Their Universality and Evolution. Berkeley: University of California; 1969]. The likelihood for each category is represented by a linear combination of quadratic splines, and as a result, each voxel in the color space L*u*v* is described as a vector of probabilities, whose components express the degree to which the voxel belongs to a given color category. This gives rise to a probabilistic dictionary which is used for the segmentation, in which prior spatial granularity constraints are incorporated via an entropy‐controlled quadratic Markov measure field (ECQMMF) model, as proposed by Rivera et al. [IEEE Trans Image Process 2007;16:3047–3057]. We give a generalization of ECQMMF that allows one to consider the perceptual interactions between the basic colors that were experimentally established by Boynton and Olson [Color Res Appl 1987;12:94–105]. © 2009 Wiley Periodicals, Inc. Col Res Appl, 34, 299–309, 2009

Dynamics of functions with piecewise non-positive Schwarzian derivatives

This paper studies functions which are piecewise defined and have on each subinterval either a non-positive Schwarzian derivative or are constant. We show that this property is conserved under composition and that it allows to study the dynamics, fixed points and cycles, convergence and chaotic behavior of such functions. Many functions used for interpolation are in fact such functions. Noteworthy examples are piecewise affine functions, functions with (piecewise) negative Schwarzian derivatives, linear or quadratic splines and many fuzzy functions, which appear in recurrent fuzzy systems.

A multiresolution method for fitting scattered data on the sphere

In this work, we propose an efficient multiresolution method for fitting scattered data functions on a sphere S, using a tensor product method of periodic algebraic trigonometric splines of order 3 and quadratic polynomial splines defined on a rectangular map of S. We describe the decomposition and reconstruction algorithms corresponding to the polynomial and periodic algebraic trigonometric wavelets. As application of this method, we give an algorithm which allows to compress scattered data on spherelike surfaces. In order to illustrate our results, some numerical examples are presented.

FAILURE LIMIT INVESTIGATION FOR THE SPLINE AIDED SOLUTION TECHNIQUE

A formal investigation describing the failure limit of the spline aided solution technique has been carried out. The influence of spline width on trajectory assigning accuracy at different axial positions is discussed in detail. Additionally this influence has been investigated widely concerning the accuracy of aberration calculations for two different cases. In the first one, spline width was made variable for both trajectory and aberration calculations. The second one analyzed the case in which this width varies only for aberration determination. Results clearly show that spline width is the only parameter that affects calculations. Generally, the technique's accuracy is found to be proportional to the quadratic spline width and hence accurate results can be reached as long as the spline width is small.