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1

Finite difference preconditioning cubic spline collocation method of elliptic equations  

Microsoft Academic Search

Summary.   We discuss a finite difference preconditioner for the interpolatory cubic spline collocation method for a uniformly elliptic operator defined by in (the unit square) with homogeneous Dirichlet boundary conditions. Using the generalized field of values arguments, we discuss\\u000a the eigenvalues of the preconditioned matrix where is the matrix of the collocation discretization operator corresponding to , and is the

Hong Oh Kim; Sang Dong Kim; Yong Hun Lee

1997-01-01

2

B-spline Collocation with Domain Decomposition Method  

NASA Astrophysics Data System (ADS)

A global B-spline collocation method has been previously developed and successfully implemented by the present authors for solving elliptic partial differential equations in arbitrary complex domains. However, the global B-spline approximation, which is simply reduced to Bezier approximation of any degree p with C0 continuity, has led to the use of B-spline basis of high order in order to achieve high accuracy. The need for B-spline bases of high order in the global method would be more prominent in domains of large dimension. For the increased collocation points, it may also lead to the ill-conditioning problem. In this study, overlapping domain decomposition of multiplicative Schwarz algorithm is combined with the global method. Our objective is two-fold that improving the accuracy with the combination technique, and also investigating influence of the combination technique to the employed B-spline basis orders with respect to the obtained accuracy. It was shown that the combination method produced higher accuracy with the B-spline basis of much lower order than that needed in implementation of the initial method. Hence, the approximation stability of the B-spline collocation method was also increased.

Hidayat, M. I. P.; Ariwahjoedi, B.; Parman, S.

2013-04-01

3

B-spline collocation method for the singular-perturbation problem using artificial viscosity  

Microsoft Academic Search

In this paper, we develop a B-spline collocation method using artificial viscosity for solving singularly-perturbed equations given by ?u?(x)+a(x)u?(x)+b(x)u(x)=f(x),a(x)?a?>0,b(x)?b?>0,(0.1)u(0)=?,u(1)=?. We use the artificial viscosity to capture the exponential features of the exact solution on a uniform mesh and use B-spline collocation method which leads to a tridiagonal linear system. The convergence analysis is given and the method is shown to

Mohan K. Kadalbajoo; Puneet Arora

2009-01-01

4

A novel numerical scheme of cubic hermite spline collocation method for solving Burgers' equation  

NASA Astrophysics Data System (ADS)

In this paper 1D Burgers' equation is solved numerically. The proposed method is based on the Hopf-Cole transformation, which transforms the original nonlinear Burgers' equation into a linear heat equation. The equation is then solved by cubic Hermite spline collocation method, which is unconditionally stable. The performance of the method is validated by two standard problems by taking Gauss-Legendre quadrature points of order 2 as the collocation points. Computed results are compared with exact and other numerical results in literature for different values of Reynolds' number.

Ganaie, Ishfaq Ahmad; Kukreja, V. K.

2013-10-01

5

Quintic B-spline collocation method for numerical solution of the Kuramoto-Sivashinsky equation  

NASA Astrophysics Data System (ADS)

In this paper, the quintic B-spline collocation scheme is implemented to find numerical solution of the Kuramoto-Sivashinsky equation. The scheme is based on the Crank-Nicolson formulation for time integration and quintic B-spline functions for space integration. The accuracy of the proposed method is demonstrated by four test problems. The numerical results are found to be in good agreement with the exact solutions. Results are also shown graphically and are compared with results given in the literature.

Mittal, R. C.; Arora, Geeta

2010-10-01

6

An alternating direction implicit method for orthogonal spline collocation linear systems  

Microsoft Academic Search

Summary An Alternating Direction Implicit method is analyzed for the solution of linear systems arising in high-order, tensor-product orthogonal spline collocation applied to some separable, second order, linear, elliptic partial differential equations in rectangles. On anNxN partition, with Jordan's selection of the acceleration parameters, the method requiresO(N2 ln2N) arithmetic operations to produce an approximation whose accuracy, in theH1-norm, is that

Bernard Bialecki

1991-01-01

7

Numerical solution of fractional differential equations using cubic B-spline wavelet collocation method  

NASA Astrophysics Data System (ADS)

Physical processes with memory and hereditary properties can be best described by fractional differential equations due to the memory effect of fractional derivatives. For that reason reliable and efficient techniques for the solution of fractional differential equations are needed. Our aim is to generalize the wavelet collocation method to fractional differential equations using cubic B-spline wavelet. Analytical expressions of fractional derivatives in Caputo sense for cubic B-spline functions are presented. The main characteristic of the approach is that it converts such problems into a system of algebraic equations which is suitable for computer programming. It not only simplifies the problem but also speeds up the computation. Numerical results demonstrate the validity and applicability of the method to solve fractional differential equation.

Li, Xinxiu

2012-10-01

8

An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems  

NASA Astrophysics Data System (ADS)

An alternating direction implicit (ADI) orthogonal spline collocation (OSC) method is described for the approximate solution of a class of nonlinear reaction-diffusion systems. Its efficacy is demonstrated on the solution of well-known examples of such systems, specifically the Brusselator, Gray-Scott, Gierer-Meinhardt and Schnakenberg models, and comparisons are made with other numerical techniques considered in the literature. The new ADI method is based on an extrapolated Crank-Nicolson OSC method and is algebraically linear. It is efficient, requiring at each time level only O(N) operations where N is the number of unknowns. Moreover, it is shown to produce approximations which are of optimal global accuracy in various norms, and to possess superconvergence properties.

Fernandes, Ryan I.; Fairweather, Graeme

2012-08-01

9

Higher Order B-Spline Collocation at the Greville Abscissae  

SciTech Connect

Collocation methods are investigated because of their simplicity and inherent efficiency for application to a model problem with similarities to the equations of fluid dynamics. The model problem is a steady, one-dimensional convection-diffusion equation with constant coefficients. The objective of the present research is to compare the efficiency and accuracy of several collocation schemes as applied to the model problem for values of 15 and 50 for the associated Peclet number. The application of standard nodal and orthogonal collocation is compared to the use of the Greville abscissae for the collocation points, in conjunction with cubic and quartic B-splines. The continuity of the B-spline curve solution is varied from C1 continuity for traditional orthogonal collocation of cubic and quartic splines to C2-C3 continuity for cubic and quartic splines employing nodal, orthogonal and Greville point collocation. The application of nodal, one-point orthogonal, and Greville collocation for smoothest quartic B-splines is found to be as accurate as for traditional two-point orthogonal collocation using cubics, while having comparable or better efficiency based on operation count. Greville collocation is more convenient than nodal or 1-point orthogonal collocation because exactly the correct number of collocation points is available.

Johnson, Richard Wayne

2005-01-01

10

Fast Fourier Transform Solvers and Preconditioners for Quadratic Spline Collocation  

Microsoft Academic Search

Quadratic Spline Collocation (QSC) methods of optimal order of convergence have been recently developed for the solution of elliptic Partial Differentia l Equations (PDEs). In this paper, linear solvers based on Fast Fourier Transforms (FFT) are developed for the solution of the QSC equations. The complexity of the FFT solvers is , where is the gridsize in one dimension. These

Christina C. Christara; Kit Sun Ng

2000-01-01

11

Spline collocation for convolutional parabolic boundary integral equations  

Microsoft Academic Search

  \\u000a \\u000a \\u000a Summary. We consider spline collocation methods for a class of parabolic pseudodifferential operators. We show optimal order convergence\\u000a results in a large scale of anisotropic Sobolev spaces. The results cover for example the case of the single layer heat operator\\u000a equation when the spatial domain is a disc.

M. Costabel; J. Saranen

2000-01-01

12

Spline Collocation Method for Integral Equations of the First Kind with Logarithmic Singularity,  

National Technical Information Service (NTIS)

Integral equations of the first kind with a logarithmic singularity are encountered when solving a wide class of two-dimensional elliptic boundary value problems. Generally, integral equations of the first kind may be solved by means of methods of regular...

E. A. Guseinov A. J. Hermans

1987-01-01

13

Progress on the Development of B-spline Collocation for the Solution of Differential Model Equations: A Novel Algorithm for Adaptive Knot Insertion  

SciTech Connect

The application of collocation methods using spline basis functions to solve differential model equations has been in use for a few decades. However, the application of spline collocation to the solution of the nonlinear, coupled, partial differential equations (in primitive variables) that define the motion of fluids has only recently received much attention. The issues that affect the effectiveness and accuracy of B-spline collocation for solving differential equations include which points to use for collocation, what degree B-spline to use and what level of continuity to maintain. Success using higher degree B-spline curves having higher continuity at the knots, as opposed to more traditional approaches using orthogonal collocation, have recently been investigated along with collocation at the Greville points for linear (1D) and rectangular (2D) geometries. The development of automatic knot insertion techniques to provide sufficient accuracy for B-spline collocation has been underway. The present article reviews recent progress for the application of B-spline collocation to fluid motion equations as well as new work in developing a novel adaptive knot insertion algorithm for a 1D convection-diffusion model equation.

Johnson, Richard Wayne

2003-05-01

14

A fourth order spline collocation approach for a business cycle model  

NASA Astrophysics Data System (ADS)

A collocation approach, based on a fourth order cubic B-splines is presented for the numerical solution of a Kaleckian business cycle model formulated by a nonlinear delay differential equation. The equation is approximated and the nonlinearity is handled by employing an iterative scheme arising from Newton's method. It is shown that the model exhibits a conditionally dynamical stable cycle. The fourth-order rate of convergence of the scheme is verified numerically for different special cases.

Sayfy, A.; Khoury, S.; Ibdah, H.

2013-10-01

15

Spline methods for conversation equations  

SciTech Connect

The consider the numerical solution of physical theories, in particular hydrodynamics, which can be formulated as systems of conservation laws. To this end we briefly describe the Basis Spline and collocation methods, paying particular attention to representation theory, which provides discrete analogues of the continuum conservation and dispersion relations, and hence a rigorous understanding of errors and instabilities. On this foundation we propose an algorithm for hydrodynamic problems in which most linear and nonlinear instabilities are brought under control. Numerical examples are presented from one-dimensional relativistic hydrodynamics. 9 refs., 10 figs.

Bottcher, C.; Strayer, M.R.

1991-01-01

16

B-Spline-Based Colocation Method to Approximate the Solutions to the Equations of Fluid Dynamics.  

National Technical Information Service (NTIS)

The potential of a B-spline collocation method for numerically solving the equations of fluid dynamics is discussed. It is known that B-splines can resolve complex curves with drastically fewer data than can their standard shape function counterparts. Thi...

M. D. Landon R. W. Johnson

1999-01-01

17

A B-Spline Method for Solving the Navier Stokes Equations  

SciTech Connect

Collocation methods using piece-wise polynomials, including B-splines, have been developed to find approximate solutions to both ordinary and partial differential equations. Such methods are elegant in their simplicity and efficient in their application. The spline collocation method is typically more efficient than traditional Galerkin finite element methods, which are used to solve the equations of fluid dynamics. The collocation method avoids integration. Exact formulae are available to find derivatives on spline curves and surfaces. The primary objective of the present work is to determine the requirements for the successful application of B-spline collocation to solve the coupled, steady, 2D, incompressible Navier–Stokes and continuity equations for laminar flow. The successful application of B-spline collocation included the development of ad hoc method dubbed the Boundary Residual method to deal with the presence of the pressure terms in the Navier–Stokes equations. Historically, other ad hoc methods have been developed to solve the incompressible Navier–Stokes equations, including the artificial compressibility, pressure correction and penalty methods. Convergence studies show that the ad hoc Boundary Residual method is convergent toward an exact (manufactured) solution for the 2D, steady, incompressible Navier–Stokes and continuity equations. C1 cubic and quartic B-spline schemes employing orthogonal collocation and C2 cubic and C3 quartic B-spline schemes with collocation at the Greville points are investigated. The C3 quartic Greville scheme is shown to be the most efficient scheme for a given accuracy, even though the C1 quartic orthogonal scheme is the most accurate for a given partition. Two solution approaches are employed, including a globally-convergent zero-finding Newton's method using an LU decomposition direct solver and the variable-metric minimization method using BFGS update.

Johnson, Richard Wayne

2005-01-01

18

ABCs and fourth-order spline collocation for the solution of two-point boundary value problems over an infinite domain  

NASA Astrophysics Data System (ADS)

A mixed approach, based on cubic B-spline collocation and asymptotic boundary conditions (ABCs), is presented for the numerical solution of an extended class of two-point linear boundary value problems (BVPs) over an infinite interval as well as a system of BVPs. The condition at infinity is reduced to an asymptotic boundary condition that approaches the required value at infinity over a large finite interval. The resulting problem is handled using an adaptive spline collocation approach constructed over uniform meshes. The rate of convergence is verified numerically to be of fourth-order. The efficiency and applicability of the method are demonstrated by applying the strategy to a number of examples. The numerical solutions are compared with existing analytical solutions.

Khoury, S.; Ibdah, H.; Sayfy, A.

2013-10-01

19

ADI spectral collocation methods for parabolic problems  

NASA Astrophysics Data System (ADS)

We discuss the Crank-Nicolson and Laplace modified alternating direction implicit Legendre and Chebyshev spectral collocation methods for a linear, variable coefficient, parabolic initial-boundary value problem on a rectangular domain with the solution subject to non-zero Dirichlet boundary conditions. The discretization of the problems by the above methods yields matrices which possess banded structures. This along with the use of fast Fourier transforms makes the cost of one step of each of the Chebyshev spectral collocation methods proportional, except for a logarithmic term, to the number of the unknowns. We present the convergence analysis for the Legendre spectral collocation methods in the special case of the heat equation. Using numerical tests, we demonstrate the second order accuracy in time of the Chebyshev spectral collocation methods for general linear variable coefficient parabolic problems.

Bialecki, B.; de Frutos, J.

2010-07-01

20

Optimization of dynamic systems using collocation methods  

NASA Astrophysics Data System (ADS)

The time-based simulation is an important tool for the engineer. Often a time-domain simulation is the most expedient to construct, the most capable of handling complex modeling issues, or the most understandable with an engineer's physical intuition. Aeroelastic systems, for example, are often most easily solved with a nonlinear time-based approach to allow the use of high fidelity models. Simulations of automatic flight control systems can also be easier to model in the time domain, especially when nonlinearities are present. Collocation is an optimization method for systems that incorporate a time-domain simulation. Instead of integrating the equations of motion for each design iteration, the optimizer iteratively solves the simulation as it finds the optimal design. This forms a smooth, well-posed, sparse optimization problem, transforming the numerical integration's sequential calculation into a set of constraints that can be evaluated in any order, or even in parallel. The collocation method used in this thesis has been improved from existing techniques in several ways, in particular with a very simple and computationally inexpensive method of applying dynamic constraints, such as damping, that are more traditionally calculated with linear models in the frequency domain. This thesis applies the collocation method to a range of aircraft design problems, from minimizing the weight of a wing with a flutter constraint, to gain-scheduling the stability augmentation system of a small-scale flight control testbed, to aeroservoelastic design of a large aircraft concept. Collocation methods have not been applied to aeroelastic simulations in the past, although the combination of nonlinear aerodynamic analyses with structural dynamics and stability constraints is well-suited to collocation. The results prove the collocation method's worth as a tool for aircraft design, particularly when applied to the multidisciplinary numerical models used today.

Holden, Michael Eric

21

A B-Spline-Based Colocation Method to Approximate the Solutions to the Equations of Fluid Dynamics  

SciTech Connect

The potential of a B-spline collocation method for numerically solving the equations of fluid dynamics is discussed. It is known that B-splines can resolve curves with drastically fewer data than can their standard shape function counterparts. This feature promises to allow much faster numerical simulations of fluid flow than standard finite volume/finite element methods without sacrificing accuracy. An example channel flow problem is solved using the method.

Johnson, Richard Wayne; Landon, Mark Dee

1999-07-01

22

A B-Spline-Based Colocation Method to Approximate the Solutions to the Equations of Fluid Dynamics  

SciTech Connect

The potential of a B-spline collocation method for numerically solving the equations of fluid dynamics is discussed. It is known that B-splines can resolve complex curves with drastically fewer data than can their standard shape function counterparts. This feature promises to allow much faster numerical simulations of fluid flow than standard finite volume/finite element methods without sacrificing accuracy. An example channel flow problem is solved using the method.

M. D. Landon; R. W. Johnson

1999-07-01

23

Collocation method using artificial viscosity for solving stiff singularly perturbed turning point problem having twin boundary layers  

Microsoft Academic Search

A numerical scheme is proposed to solve singularly perturbed two-point boundary value problems with a turning point exhibiting twin boundary layers. The scheme comprises a B-spline collocation method on a uniform mesh, which leads to a tridiagonal linear system. Asymptotic bounds are established for the derivative of the analytical solution of a turning point problem. The analysis is done on

Mohan K. Kadalbajoo; Puneet Arora; Vikas Gupta

2011-01-01

24

Systems and methods for identifying collocation errors in text  

US Patent & Trademark Office Database

Systems and methods for detecting collocation errors in a text sample using a reference database from a corpus are provided. Collocation candidates are identified within the text sample based upon syntactic patterns in the text sample. Whether a given collocation candidate contains a collocation error is detected, the detecting including: determining a first association measure using the reference database for the given collocation candidate; determining whether the first association measure satisfies a predetermined condition and identifying the given collocation candidate as proper if the first association measure satisfies the predetermined condition; determining an additional association measure for a variation of the given collocation candidate using the reference database; and determining whether or not the collocation candidate contains an error based upon the additional association measure of the variation.

2013-06-25

25

A tensor product B-spline method for numerical grid generation  

SciTech Connect

We present a tensor product B-spline method for fast elliptic grid generation. The Cartesian coordinate functions for a block are represented as a sum of tensor product B-spline basis functions defined on the computational domain for the block. The tensor product B-spline basis functions are constructed so that the basis functions and their first partials are continuous on the computational domain for the block. The coordinate functions inherit this smoothness: a grid computed by evaluating the coordinate function along constant parameter lines leads to smooth grid lines with smoothly varying tangents. The expansion coefficients for the coordinates functions are computed by solving the elliptic grid generation equations using collocation. This assures that the computer grid has the smoothness and resolution expected for an elliptic grid with appropriate control. The collocation equations are solved with an ADI solution algorithm analogous to the ADI solution algorithm for the finite difference method. The speed of the method derives from the smoothness of the B-spline basis functions; in effect, a fine grid in the physical domain is obtained by constructing a smooth expansion of the coordinate functions on a coarse grid of knots in the computational domain. Thus, the tensor product B-spline method will be faster than the finite difference method, if a sufficiently smooth fine grid in the physical domain can be obtained for an appropriately coarse grid of knots in the computational domain.

Manke, J.

1989-10-01

26

A quadrature-based approach to improving the collocation method  

Microsoft Academic Search

Summary The collocation method is a popular method for the approximate solution of boundary integral equations, but typically does not achieve the high order of convergence reached by the Galerkin method in appropriate negative norms. In this paper a quadrature-based method for improving upon the collocation method is proposed, and developed in detail for a particular case. That case involves

Ian H. Sloan

1988-01-01

27

a Tensor Product B-Spline Method for Numerical Grid Generation  

NASA Astrophysics Data System (ADS)

We present a tensor product B-spline method for fast elliptic grid generation. The Cartesian coordinate functions for a block are represented as a sum of tensor product B-spline basis functions defined on the computational domain for the block. The tensor product B-spline basis functions are constructed so that the basis functions and their first partials are continuous on the computational domain for the block. The coordinate functions inherit this smoothness: a grid computed by evaluating the coordinate functions along constant parameter lines leads to smooth grid lines with smoothly varying tangents. The expansion coefficients for the coordinate functions are computed by solving the elliptic grid generation equations using collocation. This assures that the computed grid has the smoothness and resolution expected for an elliptic grid with appropriate control. The collocation equations are solved with an ADI solution algorithm analogous to the ADI solution algorithm for the finite difference method. The speed of the method derives from the smoothness of the B-spline basis functions; in effect, a fine grid in the physical domain is obtained by constructing a smooth expansion of the coordinate functions on a coarse grid of knots in the computational domain. Thus the tensor product B-spline method will be faster than the finite difference method, if a sufficiently smooth fine grid in the physical domain can be obtained for an appropriately coarse grid of knots in the computational domain. We implemented the tensor product B-spline method in a multi-block grid code for testing and comparison to the finite difference method. For the grid generation problems studied the tensor product B-spline method was 2 to 13 times faster than the finite difference method. We also introduced and tested in a multi-block grid code two new techniques for automatic analysis and processing of block interfaces in arbitrary multi-block grids: a graphical method to analyze block interfaces and an interface block method with overlap conditions to process block interfaces.^1 ftn ^1This research was supported in part by Boeing Computer Services Co., Seattle, WA, by AFSOR -86-0154 and by DOE-627815.

Manke, Joseph Walter

28

Collocation method for fractional quantum mechanics  

SciTech Connect

We show that it is possible to obtain numerical solutions to quantum mechanical problems involving a fractional Laplacian, using a collocation approach based on little sinc functions, which discretizes the Schroedinger equation on a uniform grid. The different boundary conditions are naturally implemented using sets of functions with the appropriate behavior. Good convergence properties are observed. A comparison with results based on a Wentzel-Kramers-Brillouin analysis is performed.

Amore, Paolo; Hofmann, Christoph P.; Saenz, Ricardo A. [Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Diaz del Castillo 340, Colima, Colima (Mexico); Fernandez, Francisco M. [INIFTA (Conicet, UNLP), Division Quimica Teorica, Diagonal 113 y 64 S/N, Sucursal 4, Casilla de correo 16, 1900 La Plata (Argentina)

2010-12-15

29

Tensor product B-spline method for numerical grid generation.  

National Technical Information Service (NTIS)

We present a tensor product B-spline method for fast elliptic grid generation. The Cartesian coordinate functions for a block are represented as a sum of tensor product B-spline basis functions defined on the computational domain for the block. The tensor...

J. Manke

1989-01-01

30

Symplectic wavelet collocation method for Hamiltonian wave equations  

NASA Astrophysics Data System (ADS)

This paper introduces a novel symplectic wavelet collocation method for solving nonlinear Hamiltonian wave equations. Based on the autocorrelation functions of Daubechies compactly supported scaling functions, collocation method is conducted for the spatial discretization, which leads to a finite-dimensional Hamiltonian system. Then, appropriate symplectic scheme is employed for the integration of the Hamiltonian system. Under the hypothesis of periodicity, the properties of the resulted space differentiation matrix are analyzed in detail. Conservation of energy and momentum is also investigated. Various numerical experiments show the effectiveness of the proposed method.

Zhu, Huajun; Tang, Lingyan; Song, Songhe; Tang, Yifa; Wang, Desheng

2010-04-01

31

Collocation Method for Numerical Solution of Coupled Nonlinear Schroedinger Equation  

SciTech Connect

The coupled nonlinear Schroedinger equation models several interesting physical phenomena presents a model equation for optical fiber with linear birefringence. In this paper we use collocation method to solve this equation, we test this method for stability and accuracy. Numerical tests using single soliton and interaction of three solitons are used to test the resulting scheme.

Ismail, M. S. [Department of Mathematics, College of Science, P.O.Box 80203, King Abdulaziz University, Jeddah (Saudi Arabia)

2010-09-30

32

Stochastic analysis of unsaturated flow with probabilistic collocation method  

Microsoft Academic Search

In this study, we present an efficient approach, called the probabilistic collocation method (PCM), for uncertainty analysis of flow in unsaturated zones, in which the constitutive relationship between the pressure head and the unsaturated conductivity is assumed to follow the van Genuchten-Mualem model. Spatial variability of soil parameters leads to uncertainty in predicting flow behaviors. The aim is to quantify

Weixuan Li; Zhiming Lu; Dongxiao Zhang

2009-01-01

33

Probabilistic collocation method for flow in porous media: Comparisons with other stochastic methods  

Microsoft Academic Search

An efficient method for uncertainty analysis of flow in random porous media is explored in this study, on the basis of combination of Karhunen-Loeve expansion and probabilistic collocation method (PCM). The random log transformed hydraulic conductivity field is represented by the Karhunen-Loeve expansion and the hydraulic head is expressed by the polynomial chaos expansion. Probabilistic collocation method is used to

Heng Li; Dongxiao Zhang

2007-01-01

34

A regularized collocation boundary element method for linear poroelasticity  

Microsoft Academic Search

This article presents a collocation boundary element method for linear poroelasticity, based on the first boundary integral\\u000a equation with only weakly singular kernels. This is possible due to a regularization of the strongly singular double layer\\u000a operator, based on integration by parts, which has been applied to poroelastodynamics for the first time. For the time discretization\\u000a the convolution quadrature method

Michael Messner; Martin Schanz

2011-01-01

35

The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications  

Microsoft Academic Search

Stochastic spectral methods are numerical techniques for approximating solutions to partial differential equations with random parameters. In this work, we present and examine the multi-element probabilistic collocation method (ME-PCM), which is a generalized form of the probabilistic collocation method. In the ME-PCM, the parametric space is discretized and a collocation\\/cubature grid is prescribed on each element. Both full and sparse

Jasmine Foo; Xiaoliang Wan; George Em Karniadakis

2008-01-01

36

Implementation of the spline method for mobile robot path control  

Microsoft Academic Search

This paper presents an implementation of a Spline Curve Algorithm in a mobile robot path-planning domain. This method is based on a continuous path mapped between two points. The path can easily be updated and modified as the robot moves. This feature makes the algorithm to be suitable for dynamic control as in the case of multiple mobile robots operating

Halit Eren; Chun Che Fung; Jeromy Evans

1999-01-01

37

B-spline methods for radial Dirac equations  

NASA Astrophysics Data System (ADS)

Although B-spline techniques have been used to solve two-point boundary value problems with Dirac Hamiltonians for more than 20 years, the treatment of boundary conditions is still a matter of controversy. Spurious, non-physical, solutions are endemic when boundary conditions are not handled correctly. These pathological problems are absent when traditional finite difference methods are used as in computer packages such as GRASP. Accurate approximation using both finite differences and B-splines depends on controlling local approximation errors, and this common property suggests no a priori reason to suppose that B-spline algorithms should be more prone to generate spurious solutions. The relativistic Bloch operators of [24], when added to the Dirac differential operator, permit the construction of a self-adjoint differential operator for the two-point boundary value problem on a finite interval. Approximate solution of this problem exploiting the properties of B-splines in variational or Galerkin schemes is then straightforward. Although the analysis is presented primarily in terms of the Dirac R-matrix method for electron-atom scattering, it is also relevant to other applications such as relativistic atomic and molecular structure calculations, many-body perturbation calculations of structure and properties and relativistic dynamics.

Grant, I. P.

2009-03-01

38

Stochastic analysis of unsaturated flow with probabilistic collocation method  

NASA Astrophysics Data System (ADS)

In this study, we present an efficient approach, called the probabilistic collocation method (PCM), for uncertainty analysis of flow in unsaturated zones, in which the constitutive relationship between the pressure head and the unsaturated conductivity is assumed to follow the van Genuchten-Mualem model. Spatial variability of soil parameters leads to uncertainty in predicting flow behaviors. The aim is to quantify the uncertainty associated with flow quantities such as the pressure head and the effective saturation. In the proposed approach, input random fields, i.e., the soil parameters, are represented via the Karhunen-Loeve expansion, and the flow quantities are expressed by polynomial chaos expansions (PCEs). The coefficients in the PCEs are determined by solving the equations for a set of carefully selected collocation points in the probability space. To illustrate this approach, we use two-dimensional examples with different input variances and correlation scales and under steady state and transient conditions. We also demonstrate how to deal with multiple-input random parameters. To validate the PCM, we compare the resulting mean and variance of the flow quantities with those from Monte Carlo (MC) simulations. The comparison reveals that the PCM can accurately estimate the flow statistics with a much smaller computational effort than the MC.

Li, Weixuan; Lu, Zhiming; Zhang, Dongxiao

2009-08-01

39

Regularized collocation method for Fredholm integral equations of the first kind  

Microsoft Academic Search

In this paper we consider a collocation method for solving Fredholm integral equations of the first kind, which is known to be an ill-posed problem. An “unregularized” use of this method can give reliable results in the case when the rate at which smallest singular values of the collocation matrices decrease is known a priori. In this case the number

M. Thamban Nair; Sergei V. Pereverzev

2007-01-01

40

Meshfree explicit local radial basis function collocation method for diffusion problems  

Microsoft Academic Search

This paper formulates a simple explicit local version of the classical meshless radial basis function collocation (Kansa) method. The formulation copes with the diffusion equation, applicable in the solution of a broad spectrum of scientific and engineering problems. The method is structured on multiquadrics radial basis functions. Instead of global, the collocation is made locally over a set of overlapping

B. Sarler; R. Vertnik

2006-01-01

41

Bethe-logarithm calculation using the B-spline method  

NASA Astrophysics Data System (ADS)

A method based on the B-spline basis set is developed that significantly simplifies the Bethe-logarithm calculations for the atomic hydrogen. Without any auxiliary optimization and extrapolation, this method not only can calculate the Bethe logarithms of low-lying states to high precision using relatively small basis sets, but can also calculate high-lying Rydberg states efficiently. For the ground state, the Bethe logarithm is calculated to 24 significant figures using 450 B-spline functions. For high-lying Rydberg states, we can reproduce all the results of Jentschura and Mohr [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.72.012110 72, 012110 (2005)].

Tang, Yongbo; Zhong, Zhenxiang; Li, Chengbin; Qiao, Haoxue; Shi, Tingyun

2013-02-01

42

Transport survey calculations using the spectral collocation method  

SciTech Connect

A novel transport survey code has been developed and is being used to study the sensitivity of stellarator reactor performance to various transport assumptions. Instead of following one of the usual approaches, the steady-state transport equation are solved in integral form using the spectral collocation method. This approach effectively combine the computational efficiency of global models with the general nature of 1-D solutions. A compact torsatron reactor test case was used to study the convergence properties and flexibility of the new method. The heat transport model combined Shaing's model for ripple-induced neoclassical transport, the Chang-Hinton model for axisymmetric neoclassical transport, and neoalcator scaling for anomalous electron heat flux. Alpha particle heating, radiation losses, classical electron-ion heat flow, and external heating were included. For the test problem, the method exhibited some remarkable convergence properties. As the number of basis functions was increased, the maximum, pointwise error in the integrated power balance decayed exponentially until the numerical noise level as reached. Better than 10% accuracy in the globally-averaged quantities was achieved with only 5 basis functions; better than 1% accuracy was achieved with 10 basis functions. The numerical method was also found to be very general. Extreme temperature gradients at the plasma edge which sometimes arise from the neoclassical models and are difficult to resolve with finite-difference methods were easily resolved. 8 refs., 6 figs.

Painter, S.L.; Lyon, J.F.

1989-01-01

43

Evaluation of Two New Smoothing Methods in Equating: The Cubic B-Spline Presmoothing Method and the Direct Presmoothing Method  

ERIC Educational Resources Information Center

This article considers two new smoothing methods in equipercentile equating, the cubic B-spline presmoothing method and the direct presmoothing method. Using a simulation study, these two methods are compared with established methods, the beta-4 method, the polynomial loglinear method, and the cubic spline postsmoothing method, under three sample…

Cui, Zhongmin; Kolen, Michael J.

2009-01-01

44

Weighted extended B-spline method for the approximation of the stationary Stokes problem  

Microsoft Academic Search

A new stabilized, mesh-free method for the approximation of the Stokes problem, using weighted extended B-splines (WEB-splines) as shape functions has been proposed. The web-spline based bilinear velocity–constant pressure element satisfies the so called inf–sup condition or Ladyshenskaya–Babus?ka–Brezzi (LBB) condition. The main advantage of this method over standard finite element methods is that it uses regular grids instead of irregular

V. V. K. Srinivas Kumar; B. V. Rathish Kumar; P. C. Das

2006-01-01

45

Weighted extended B-spline method for the approximation of the stationary Stokes problem  

Microsoft Academic Search

A new stabilized, mesh-free method for the approximation of the Stokes problem, using weighted extended B-splines (WEB-splines) as shape functions has been proposed. The web-spline based bilinear velocity-constant pressure element satisfies the so called inf-sup condition or Ladyshenskaya-Babus[breve]ka-Brezzi (LBB) condition. The main advantage of this method over standard finite element methods is that it uses regular grids instead of irregular

V. V. K. Srinivas Kumar; B. V. Rathish Kumar; P. C. Das

2006-01-01

46

Legendre multiwavelet collocation method for solving the linear fractional time delay systems  

NASA Astrophysics Data System (ADS)

In this article the Legendre multiwavelet basis with aid of collocation method has been applied to give approximate solution for fractional delay systems. The properties of Legendre multiwavelet are presented. These properties together with the collocation method are then utilized to reduce the problem to the solution of algebraic system. Numerical results and comparison with exact solutions in the cases when we have exact solution are given in test examples in order to demonstrate the applicability and efficiency of the method.

Yousefi, Sohrab Ali; Lotfi, Ali

2013-10-01

47

A stochastic collocation method for elliptic partial difierential equations with random input data  

Microsoft Academic Search

Abstract In this paper we propose and analyze a Stochastic-Collocation method to solve elliptic Partial Difierential Equations with random,coe?cients and forcing terms (input data of the model). The input data are assumed to depend on a flnite number of random,variables. The method consists in a Galerkin approximation in space and a collocation in the zeros of suitable tensor product orthogonal

I. Babu Ska; F. Nobile; R. Tempone; Dipartimento Di Matematica

48

WEB-Spline–Based Multigrid Methods for the Stationary Stokes Problem  

Microsoft Academic Search

We discuss a multigrid technique in solving a large system of linear algebraic equations arising in the approximation of Stokes equations by a new strategy based on weighted extended B-spline (WEB-spline) methods. Three types of WEB-spline–based Stokes elements satisfying the inf-sup condition are considered. First for a linear-constant type of Stokes element, we give the detailed multigrid algorithm and its

V. V. K. Srinivas Kumar; B. V. Rathish Kumar; P. C. Das

2006-01-01

49

Multidomain Spectral Collocation Method for the Stokes Problem.  

National Technical Information Service (NTIS)

A multidomain spectral collocation scheme is proposed for the approximation of the two-dimensional Stokes problem. It is shown that the discrete velocity vector field is exactly divergence-free and we prove error estimates both for the velocity and the pr...

G. S. Landriani H. Vandeven

1989-01-01

50

THE LOSS OF ACCURACY OF STOCHASTIC COLLOCATION METHOD IN SOLVING NONLINEAR DIFFERENTIAL EQUATIONS WITH RANDOM INPUT DATA  

SciTech Connect

n this paper we show how stochastic collocation method (SCM) could fail to con- verge for nonlinear differential equations with random coefficients. First, we consider Navier-Stokes equation with uncertain viscosity and derive error estimates for stochastic collocation discretization. Our analysis gives some indicators on how the nonlinearity negatively affects the accuracy of the method. The stochastic collocation method is then applied to noisy Lorenz system. Simulation re- sults demonstrate that the solution of a nonlinear equation could be highly irregular on the random data and in such cases, stochastic collocation method cannot capture the correct solution.

Webster, Clayton G [ORNL; Tran, Hoang A [ORNL; Trenchea, Catalin S [ORNL

2013-01-01

51

Splines in Statistics  

Microsoft Academic Search

This is a survey article that attempts to synthesize a broad variety of work on splines in statistics. Splines are presented as a nonparametric function estimating technique. After a general introduction to the theory of interpolating and smoothing splines, splines are treated in the nonparametric regression setting. The method of cross-validation for choosing the smoothing parameter is discussed and the

Edward J. Wegman; Ian W. Wright

1983-01-01

52

A numerical approach based on the meshless collocation method in elastodynamics  

NASA Astrophysics Data System (ADS)

In this paper, a collocation technique with the modified equilibrium on line method (ELM) for imposition of Neumann (natural) boundary conditions is presented for solving the two-dimensional problems of linear elastic body vibrations. In the modified ELM, equilibrium over the lines on the natural boundary is satisfied as Neumann boundary condition equations. In other words, the natural boundary conditions are satisfied naturally by using the weak formulation. The performance of the modified version of the ELM is studied for collocation methods based on two different ways to construct meshless shape functions: moving least squares approximation and radial basis point interpolation. Numerical examples of two-dimensional free and forced vibration analyses show that by using the modified ELM, more stable and accurate results would be obtained in comparison with the direct collocation method.

Sadeghirad, Alireza; Mahmoudzadeh Kani, Iradj; Rahimian, Mohammad; Vaziri Astaneh, Ali

2009-12-01

53

Bicubic B-spline interpolation method for two-dimensional Laplace's equations  

NASA Astrophysics Data System (ADS)

Two-dimensional Laplace's equation is solved using bicubic B-spline interpolation method. An arbitrary surface with some unknown coefficients is generated using bicubic B-spline surface's formula. This surface is presumed to be the solution for the equation. The values of the coefficients are calculated by spline interpolation technique using the corresponding differential equations and boundary conditions. This method produces approximated analytical solution for the equation. A numerical example will be presented along with a comparison of the results with finite element and isogeometrical methods.

Abd Hamid, Nur Nadiah; Abd. Majid, Ahmad; Md. Ismail, Ahmad Izani

2013-04-01

54

The golden section search algorithm for finding a good shape parameter for meshless collocation methods  

Microsoft Academic Search

In this paper we propose to apply the golden section search algorithm to determining a good shape parameter of multiquadrics (MQ) for the solution of partial differential equations. We use two radial basis function based meshless collocation methods, the method of approximate particular solutions (MAPS) and Kansa's method, to solve partial differential equations. Due to the severely ill-conditioned matrix system

C. H. Tsai; Joseph Kolibal; Ming Li

2010-01-01

55

Fast Spectral Collocation Method for Surface Integral Equations of Potential Problems in a Spheroid  

PubMed Central

This paper proposes a new technique to speed up the computation of the matrix of spectral collocation discretizations of surface single and double layer operators over a spheroid. The layer densities are approximated by a spectral expansion of spherical harmonics and the spectral collocation method is then used to solve surface integral equations of potential problems in a spheroid. With the proposed technique, the computation cost of collocation matrix entries is reduced from 𝒪(M2N4) to 𝒪(MN4), where N2 is the number of spherical harmonics (i.e., size of the matrix) and M is the number of one-dimensional integration quadrature points. Numerical results demonstrate the spectral accuracy of the method.

Xu, Zhenli; Cai, Wei

2009-01-01

56

Uncertainty quantification for unsaturated flow in porous media: a stochastic collocation method  

NASA Astrophysics Data System (ADS)

We present a stochastic collocation (SC) method to quantify epistemic uncertainty in predictions of unsaturated flow in porous media. SC provides a non-intrusive framework for uncertainty propagation in models based on the non-linear Richards' equation with arbitrary constitutive laws describing soil properties (relative conductivity and retention curve). To illustrate the approach, we use the Richards' equation with the van Genutchen-Mualem model for water retention and relative conductivity to describe infiltration into an initially dry soil whose uncertain parameters are treated as random fields. These parameters are represented using a truncated Karhunen-Loève expansion; Smolyak algorithm is used to construct a structured set of collocation points from univariate Gauss quadrature rules. A resulting deterministic problem is solved for each collocation point, and together with the collocation weights, the statistics of hydraulic head and infiltration rate are computed. The results are in agreement with Monte Carlo simulations. We demonstrate that highly heterogeneous soils (large variances of hydraulic parameters) require cubature formulas of high degree of exactness, while their short correlation lengths increase the dimensionality of the problem. Both effects increase the number of collocation points and thus of deterministic problems to solve, affecting the overall computational cost of uncertainty quantification.

Barajas-Solano, D. A.; Tartakovsky, D. M.

2011-12-01

57

Analysis of Triple Collocation Method for validation of model predicted significant wave height data  

Microsoft Academic Search

The validation of the model (Wam, Swan and Nested-Swan) predicted significant wave height data using the new triple collocated statistical method suggests that the predicted values are sufficiently accurate when compared with the buoy measurements. The Wam and Nested-Swan significant wave height estimations give significant positive correlation with deep and shallow water buoy measurements respectively. The linear regression (LR) method

G. Muraleedharan; A. D. Rao; Mourani Sinha; D. K. Mahapatra

2006-01-01

58

RATIONAL CHEBYSHEV COLLOCATION METHOD FOR SOLVING NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS OF LANE-EMDEN TYPE  

Microsoft Academic Search

Lane-Emden equation is a nonlinear singular equation that plays an important role in the astrophysics. In this paper, we have applied the collocation method based on rational Chebyshev functions to solve Lane-Emden type equations. The method reduces solving the nonlinear ordinary difierential equation to solving a system of nonlinear algebraic equations. The comparison of the results with the other numerical

KOUROSH PARAND; MEHDI SHAHINI

2010-01-01

59

A wavelet collocation method for evolution equations with energy conservation property  

Microsoft Academic Search

We describe a wavelet collocation method of computing numerical solutions to evolution equations that inherit energy conservation law. This method is based on the wavelet sampling approximation with Coifman scaling systems combined with the generalized energy integrals. In this paper, we shall focus on the theoretical background of our approach.

Toshihide Ueno; Takanori Ide; Masami Okada

2003-01-01

60

Development of quadrilateral spline thin plate elements using the B-net method  

NASA Astrophysics Data System (ADS)

The quadrilateral discrete Kirchhoff thin plate bending element DKQ is based on the isoparametric element Q8, however, the accuracy of the isoparametric quadrilateral elements will drop significantly due to mesh distortions. In a previouswork, we constructed an 8-node quadrilateral spline element L8 using the triangular area coordinates and the B-net method, which can be insensitive to mesh distortions and possess the second order completeness in the Cartesian coordinates. In this paper, a thin plate spline element is developed based on the spline element L8 and the refined technique. Numerical examples show that the present element indeed possesses higher accuracy than the DKQ element for distorted meshes.

Chen, Juan; Li, Chong-Jun

2013-08-01

61

Spline finite difference methods for singular two point boundary value problems  

Microsoft Academic Search

Summary In this paper we discuss the construction of a spline function for a class of singular two-point boundary value problemx-a(xau')=f (x, u),u(0)=A,u(1)=B, 0u'(0)=0,u(1)=B. Three point finite difference methods, using the above splines, are obtained for the solution of the boundary value problem. These methods are of second order and are illustrated by four numerical examples.

S. R. K. Iyengar; Pragya Jain

1986-01-01

62

Method of 5-axis Spline Interpolation and Realization in CNC System  

Microsoft Academic Search

An interpolation method using non-uniform rational B-spline (NURBS) technology in the CAD field is proposed and realized in a 5-axis computer numerically controlled (CNC) system. In this method, the tool path is represented to two NURBS curves, tool-tip and tool-orientation spline curve, based on the same knot vector. CL data is firstly calculated and then transformed to five motion commands

Liangji Chen

2009-01-01

63

Spline Methods Using Integration Lattices and Digital Nets  

Microsoft Academic Search

Splines are minimum-norm approximations of functions that interpolate the given data (x\\u000a \\u000a l\\u000a ,f(x\\u000a \\u000a l\\u000a )),l=0,…,N?1. This paper considers spline approximations to functions in certain reproducing kernel Hilbert spaces, with special choices\\u000a of the designs {x\\u000a \\u000a l\\u000a ,l=0,…,N?1}. The designs considered here are node sets of integration lattices and digital nets, and the domain of the functions to\\u000a be approximated,

Xiaoyan Zeng; Peter Kritzer; Fred J. Hickernell

2009-01-01

64

A multiscale probabilistic collocation method for subsurface flow in heterogeneous media  

NASA Astrophysics Data System (ADS)

Owing to the spatial variability of the media properties, uncertainty quantification for subsurface flow and solute transport usually requires high-resolution simulations. In this work, a multiscale probabilistic collocation method (MSPCM) is developed for solving such problems in a computationally efficient manner. The subsurface flow problem is cast in a stochastic framework, and probabilistic collocation strategy is used to represent the original stochastic differential equation. The resulting equations are a set of decoupled deterministic equations with respect to collocation points. A multiscale finite element method is utilized to solve these deterministic problems on a coarse mesh. Coarse-scale basis functions are constructed on a field in which the conductivity varies spatially at each set of stochastic collocation points. The coarse-scale solution is then obtained by solving a modified coarse formulation that takes into account the fine-scale heterogeneity. The fine-scale solution is reconstructed after the coarse-scale solution is available. Since the PCM and multiscale finite element method are implemented at different levels, the MSPCM inherits their respective advantages, in which a stochastic problem is decomposed by fewer realizations and is solved on a coarser grid. The performance of the proposed method is demonstrated with numerical examples. The capability of MSPCM in reproducing the probability density functions (PDFs) of head and velocity is investigated. The numerical results show that the MSPCM with proper coarsening level is able to capture small-scale heterogeneity with a coarse mesh and to generate satisfactory probability density functions of head and velocity.

Shi, Liangsheng; Zhang, Dongxiao; Lin, Lin; Yang, Jinzhong

2010-11-01

65

Maximum principle and convergence analysis for the meshfree point collocation method  

Microsoft Academic Search

The discrete Laplacian operator is considered in the sense of the meshfree point collocation method which will be called the strong meshfree Laplacian operator. To define the strong meshfree Laplacian operator, we use the fast version of the generalized moving least square approximation, which can calculate the approximated derivatives of shape functions. Some types of the locally layered node distribution

Do Wan Kim

2006-01-01

66

The collocation method based on a generalized inverse multiquadric basis for bound-state problems  

Microsoft Academic Search

The generalized inverse multiquadric basis function (1 + c2|| x ||2) ??\\/2, where c > 0, ? > d, and x ? ?d, is introduced for numerically solving the bound-state Schrödinger equation. Combined with the collocation method, this basis function can yield accurate eigenvalues of highly excited vibrations, as demonstrated by using one- and two-dimensional potentials. In addition, the generalized

Xu-Guang Hu; Tak-San Ho; Herschel Rabitz

1998-01-01

67

Alternating Direction Implicit Orthogonal Spline Collocation Methods for Solving Initial/Boundary Value Problems.  

National Technical Information Service (NTIS)

The primary focus of this project was on the analysis and development of new parallel algorithms for the solution of linear and nonlinear initial/ boundary value problems (IBVPs) in two space variables. Parabolic, second order hyperbolic, biharmonic, and ...

B. Bialecki G. Fairweather

1998-01-01

68

The extended cubic B-spline algorithm for a modified regularized long wave equation  

NASA Astrophysics Data System (ADS)

A collocation method based on an extended cubic B-spline function is introduced for the numerical solution of the modified regularized long wave equation. The accuracy of the method is illustrated by studying the single solitary wave propagation and the interaction of two solitary waves of the modified regularized long wave equation.

Da?, ?.; Irk, D.; Sar?, M.

2013-04-01

69

Stochastic collocation method for higher dimensional NDE problems with tensor product grids  

NASA Astrophysics Data System (ADS)

The stochastic collocation method has been used to propagate uncertainties in input parameters through eddy current testing simulations with success, primarily for low dimensional problems. For higher dimensional problems, the number of collocation points at which the simulation must be run grows exponentially. Several methods have been developed and shown to reduce some of this computational burden, many of which rely on techniques for high dimensional integration such as sparse tensor product grids. In this paper, the principals of sparse grids in uncertainty quantification are applied to an eddy current problem in which the conductivity of the host material is an uncertain field. Furthermore, this technique is implemented with inputs that have arbitrary distributions. The method is shown to converge quicker than standard interpolation approach and the full tensor product approach by orders of magnitude. Comparisons to the Monte Carlo sampling method are discussed, as well as some limitations of the method.

Cherry, M. R.; Knopp, J. S.

2013-01-01

70

A regularized least-squares radial point collocation method (RLS-RPCM) for adaptive analysis  

Microsoft Academic Search

This paper presents a stabilized meshfree method formulated based on the strong formulation and local approximation using\\u000a radial basis functions (RBFs). The purpose of this paper is two folds. First, a regularization procedure is developed for\\u000a stabilizing the solution of the radial point collocation method (RPCM). Second, an adaptive scheme using the stabilized RPCM\\u000a and residual based error indicator is

Bernard B. T. Kee; G. R. Liu; C. Lu

2007-01-01

71

Rigorous analysis of focusing grating couplers using a time-domain spectral collocation method  

NASA Astrophysics Data System (ADS)

Diffractive optical elements comprising sub-wavelength aperiodic surface reliefs of finite length require the use of rigorous solvers for Maxwell's equations. We present a detailed analysis of Focusing Grating Couplers (FGC's) using a recently introduced 2D spectral collocation method. The method, solving Maxwell's equations in the time domain, is based on a high-order Chebyshev collocation scheme has the advantage over traditionally used Finite Difference methods that much fewer points per wavelength is needed to accurately resolve wave propagation in diffracting structures. At the same time, the new method exhibits no numerical dispersion in contrast to, e.g., the Finite Difference Time-Domain method. In this presentation we analyze a number of sub-wavelength FGC's with lengths of up to 1000 wavelengths. The FGC's use analog surface reliefs due to their superior diffraction properties. For structures yielding a perpendicular out- coupling, we find that typically 10 - 12 collocation points per wavelength is sufficient. We find that the focal length depends strongly upon the depth of the surface relief, e.g. that a significant shift of the focal plane from the value expected from geometrical optics is seen if deep surface reliefs are used.

Dinesen, Palle G.; Hesthaven, Jan S.; Lynov, Jens-Peter

2000-03-01

72

Least-squares spectral collocation with the overlapping Schwarz method for the incompressible Navier-Stokes equations  

Microsoft Academic Search

A least-squares spectral collocation scheme is combined with the overlapping Schwarz method. The methods are succesfully applied to the incompressible Navier–Stokes equations. The collocation conditions and the interface conditions lead to an overdetermined system which can be efficiently solved by least-squares. The solution technique will only involve symmetric positive definite linear systems. The overlapping Schwarz method is used for the

Wilhelm Heinrichs

2006-01-01

73

An Accurate Probabilistic Collocation Method for Uncertainty Propagation in Tracer Transport  

NASA Astrophysics Data System (ADS)

The Karhunen-Loève decomposition and the probabilistic collocation method (PCM) are elegant and efficient tools for uncertainty propagation in porous media. Several contributions (e.g., Li and Zhang, WRR, 2007) have successfully applied KL/PCM-based frameworks for the flow problem. Recently, Lin and Tartakovsky (AWR, 2009) have shown that the accurate solution of the transport problem with KL/PCM is more challenging. We propose a new framework that utilizes PCM for the flow problem only. Subsequently, a particle-based sampling technique is used for transport, where each particle is associated with an individual flow field realization. The corresponding realizations are calculated very efficiently based on the flow problem solutions at the collocation points. Compared to a conventional MC method that includes both flow and transport, the proposed KL/PCM approach saves on the computational cost of the flow problem. Mainly, this is because the number of collocation points is much lower than the number of samples usually needed in a MC method to reach statistical convergence. The proposed method is applied for transport simulations in multi-Gaussian conductivity fields that are unconditional and conditioned on conductivity measurements.

Müller, F.; Meyer, D. W.; Jenny, P.

2010-12-01

74

Analysis of cold rigid-plastic axisymmetric forging problem by radial basis function collocation method  

Microsoft Academic Search

In the present work, an axi-symmetric cold forging problem is analyzed using radial basis function collocation method. The\\u000a material is assumed to be rigid-plastic strain hardening. At each increment of the punch displacement, the problem is solved\\u000a using an Eulerian control volume approach. The mixed pressure-velocity formulation is adopted, in which the hydrostatic stress\\u000a and velocities are approximated by linear

P. Mahadevan; P. S. Robi

2007-01-01

75

A compressed primal-dual method for generating bivariate cubic L1 splines  

NASA Astrophysics Data System (ADS)

In this paper, we develop a compressed version of the primal-dual interior point method for generating bivariate cubic L1 splines. Discretization of the underlying optimization model, which is a nonsmooth convex programming problem, leads to an overdetermined linear system that can be handled by interior point methods. Taking advantage of the special matrix structure of the cubic L1 spline problem, we design a compressed primal-dual interior point algorithm. Computational experiments indicate that this compressed primal-dual method is robust and is much faster than the ordinary (uncompressed) primal-dual interior point algorithm.

Wang, Yong; Fang, Shu-Cherng; Lavery, John E.

2007-04-01

76

A composite collocation method for the nonlinear mixed Volterra-Fredholm-Hammerstein integral equations  

NASA Astrophysics Data System (ADS)

This paper presents a computational technique for the solution of the nonlinear mixed Volterra-Fredholm-Hammerstein integral equations. The method is based on the composite collocation method. The properties of hybrid of block-pulse functions and Lagrange polynomials are discussed and utilized to define the composite interpolation operator. The estimates for the errors are given. The composite interpolation operator together with the Gaussian integration formula are then used to transform the nonlinear mixed Volterra-Fredholm-Hammerstein integral equations into a system of nonlinear equations. The efficiency and accuracy of the proposed method is illustrated by four numerical examples.

Marzban, H. R.; Tabrizidooz, H. R.; Razzaghi, M.

2011-03-01

77

Voronoi splines  

Microsoft Academic Search

We introduce a framework for construction of non-separable multivariate splines that are geometrically tailored for general sampling lattices. Voronoi splines are B-spline-like elements that inherit the geometry of a sampling lattice from its Voronoi cell and generate a lattice-shift-invariant spline space for approximation in Rd. The spline spaces associated with Voronoi splines have guaranteed approximation order and degree of continuity.

Mahsa Mirzargar; Alireza Entezari

2010-01-01

78

The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications  

SciTech Connect

Stochastic spectral methods are numerical techniques for approximating solutions to partial differential equations with random parameters. In this work, we present and examine the multi-element probabilistic collocation method (ME-PCM), which is a generalized form of the probabilistic collocation method. In the ME-PCM, the parametric space is discretized and a collocation/cubature grid is prescribed on each element. Both full and sparse tensor product grids based on Gauss and Clenshaw-Curtis quadrature rules are considered. We prove analytically and observe in numerical tests that as the parameter space mesh is refined, the convergence rate of the solution depends on the quadrature rule of each element only through its degree of exactness. In addition, the L{sup 2} error of the tensor product interpolant is examined and an adaptivity algorithm is provided. Numerical examples demonstrating adaptive ME-PCM are shown, including low-regularity problems and long-time integration. We test the ME-PCM on two-dimensional Navier-Stokes examples and a stochastic diffusion problem with various random input distributions and up to 50 dimensions. While the convergence rate of ME-PCM deteriorates in 50 dimensions, the error in the mean and variance is two orders of magnitude lower than the error obtained with the Monte Carlo method using only a small number of samples (e.g., 100). The computational cost of ME-PCM is found to be favorable when compared to the cost of other methods including stochastic Galerkin, Monte Carlo and quasi-random sequence methods.

Foo, Jasmine; Wan Xiaoliang [Division of Applied Mathematics, Brown University, 182 George Street, Box F, Providence, RI 02912 (United States); Karniadakis, George Em [Division of Applied Mathematics, Brown University, 182 George Street, Box F, Providence, RI 02912 (United States)], E-mail: gk@dam.brown.edu

2008-11-20

79

The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications  

NASA Astrophysics Data System (ADS)

Stochastic spectral methods are numerical techniques for approximating solutions to partial differential equations with random parameters. In this work, we present and examine the multi-element probabilistic collocation method (ME-PCM), which is a generalized form of the probabilistic collocation method. In the ME-PCM, the parametric space is discretized and a collocation/cubature grid is prescribed on each element. Both full and sparse tensor product grids based on Gauss and Clenshaw-Curtis quadrature rules are considered. We prove analytically and observe in numerical tests that as the parameter space mesh is refined, the convergence rate of the solution depends on the quadrature rule of each element only through its degree of exactness. In addition, the L error of the tensor product interpolant is examined and an adaptivity algorithm is provided. Numerical examples demonstrating adaptive ME-PCM are shown, including low-regularity problems and long-time integration. We test the ME-PCM on two-dimensional Navier-Stokes examples and a stochastic diffusion problem with various random input distributions and up to 50 dimensions. While the convergence rate of ME-PCM deteriorates in 50 dimensions, the error in the mean and variance is two orders of magnitude lower than the error obtained with the Monte Carlo method using only a small number of samples (e.g., 100). The computational cost of ME-PCM is found to be favorable when compared to the cost of other methods including stochastic Galerkin, Monte Carlo and quasi-random sequence methods.

Foo, Jasmine; Wan, Xiaoliang; Karniadakis, George Em

2008-11-01

80

Collocations in Language Learning: Corpus-Based Automatic Compilation of Collocations and Bilingual Collocation Concordancer.  

ERIC Educational Resources Information Center

|Presents an efficient method for extracting collocations from corpora, which uses the cost criteria measure and a tree-based data structure. Proposes a bilingual collocation concordancer, a tool that provides language learners with collocation correspondences between a native and foreign language. (Eight references) (Author/CK)|

Kita, Kenji; Ogata, Hiroaki

1997-01-01

81

Meshless collocation methods for the numerical solution of elliptic boundary valued problems the rotational shallow water equations on the sphere  

NASA Astrophysics Data System (ADS)

This dissertation thesis has three main goals: (1) To explore the anatomy of meshless collocation approximation methods that have recently gained attention in the numerical analysis community; (2) Numerically demonstrate why the meshless collocation method should clearly become an attractive alternative to standard finite-element methods due to the simplicity of its implementation and its high-order convergence properties; (3) Propose a meshless collocation method for large scale computational geophysical fluid dynamics models. We provide numerical verification and validation of the meshless collocation scheme applied to the rotational shallow-water equations on the sphere and demonstrate computationally that the proposed model can compete with existing high performance methods for approximating the shallow-water equations such as the SEAM (spectral-element atmospheric model) developed at NCAR. A detailed analysis of the parallel implementation of the model, along with the introduction of parallel algorithmic routines for the high-performance simulation of the model will be given. We analyze the programming and computational aspects of the model using Fortran 90 and the message passing interface (mpi) library along with software and hardware specifications and performance tests. Details from many aspects of the implementation in regards to performance, optimization, and stabilization will be given. In order to verify the mathematical correctness of the algorithms presented and to validate the performance of the meshless collocation shallow-water model, we conclude the thesis with numerical experiments on some standardized test cases for the shallow-water equations on the sphere using the proposed method.

Blakely, Christopher D.

82

Orthogonal grid generation of an irregular region using a local polynomial collocation method  

NASA Astrophysics Data System (ADS)

In this study, a 2-D orthogonal grid generation model is developed by solving the governing equations of coordinate transformation with a local polynomial collocation method accompanied with the moving least squares (MLS) approach. This method was developed in a way that on the boundaries both the governing equation and boundary condition are satisfied, so it is more robust and accurate than conventional collocation methods. Though the method used to solve the coordinate transforming equations is meshless, it does not deteriorate the value of present work, because most numerical models in modern use are grid-dependent, and grid generation of service to these models is still strongly desired, particularly for finite difference models in irregular domains. Before applying to grid generation problems, the performance of present method is tested by a bench mark potential flow problem. Additional to two basic grid generation problems, a bottleneck problem of previous works, which contains zero-degree corners in the domain, is carried out. Finally, the model is applied to the orthogonal grid generation in a multi-connected domain. The correctness is testified by checking the orthogonality of the generated results.

Wu, Nan-Jing; Tsay, Ting-Kuei; Yang, Tun-Chi; Chang, Hung-Yuan

2013-06-01

83

Cubic spline interpolation-based time-domain equivalent source method for modeling transient acoustic radiation  

NASA Astrophysics Data System (ADS)

Transient acoustic radiation from an arbitrarily-shaped source is modeled using a cubic spline interpolation-based time-domain equivalent source method. In the method, the cubic spline interpolation function is introduced to approximate the equivalent source strengths in the time domain for establishing the relationships between the acoustic quantities in the field, the normal acceleration on the source surface and the equivalent sources, and the least-squares solution of the equivalent source strengths at each time step is determined by an iterative solving process with the singular value decomposition technique. The proposed method has the abilities of calculating the acoustic quantities directly in the time domain and applying to arbitrarily-shaped sources. Numerical examples of calculating the transient acoustic fields from a baffled planar piston and an impulsively accelerating sphere demonstrate that the proposed method can model the transient acoustic radiation very well. The experimental results also further verify the validity of the proposed method.

Bi, Chuan-Xing; Geng, Lin; Zhang, Xiao-Zheng

2013-10-01

84

Numerical solution of fractional differential equations by using fractional B-spline  

NASA Astrophysics Data System (ADS)

In this paper, we present fractional B-spline collocation method for the numerical solution of fractional differential equations. We consider this method for solving linear fractional differential equations which involve Caputo-type fractional derivatives. The numerical results demonstrate that the method is efficient and quite accurate and it requires relatively less computational work. For this reason one can conclude that this method has advantage on other methods and hence demonstrates the importance of this work.

Jafari, Hossein; Khalique, Chaudry M.; Ramezani, Mohammad; Tajadodi, Haleh

2013-05-01

85

Multi-symplectic wavelet collocation method for the nonlinear Schrödinger equation and the Camassa-Holm equation  

NASA Astrophysics Data System (ADS)

In this paper, we develop a novel multi-symplectic wavelet collocation method for solving multi-symplectic Hamiltonian system with periodic boundary conditions. Based on the autocorrelation function of Daubechies scaling functions, collocation method is conducted for the spatial discretization. The obtained semi-discrete system is proved to have semi-discrete multi-symplectic conservation laws and semi-discrete energy conservation laws. Then, appropriate symplectic scheme is applied for time integration, which leads to full-discrete multi-symplectic conservation laws. Numerical experiments for the nonlinear Schrödinger equation and Camassa-Holm equation show the high accuracy, effectiveness and good conservation properties of the proposed method.

Zhu, Huajun; Song, Songhe; Tang, Yifa

2011-03-01

86

The Hydrogen Molecular Ion in Strong Fields Using the B-Spline Method  

NASA Astrophysics Data System (ADS)

An accurate method combining the spheroidal coordinate and B-spline for H2+ is tested. The equilibrium distances and the total energies of the states with |m| <= 4 for the magnetic field strength ? = 1 are given and compared with those obtained using different methods. Taking the advantages of the spheroidal coordinate and B-spline, a 10-9-10-12 accuracy is obtained for the energies of the states with |m| <= 3, and a 10-5-10-7 accuracy for the equilibrium distances. There are seven significant digits for the energy of the state 1?g and four significant digits for 1?u, which are consistent with those obtained by the high-precision method. There are three significant digits for the equilibrium distances of the 1?g,u states, which are consistent.

Zhang, Yue-Xia; Liu, Qiang; Shi, Ting-Yun

2013-04-01

87

MULTILEVEL ACCELERATION OF STOCHASTIC COLLOCATION METHODS FOR PDE WITH RANDOM INPUT DATA  

SciTech Connect

Stochastic Collocation (SC) methods for stochastic partial differential equa- tions (SPDEs) suffer from the curse of dimensionality, whereby increases in the stochastic dimension cause an explosion of computational effort. To combat these challenges, multilevel approximation methods seek to decrease computational complexity by balancing spatial and stochastic discretization errors. As a form of variance reduction, multilevel techniques have been successfully applied to Monte Carlo (MC) methods, but may be extended to accelerate other methods for SPDEs in which the stochastic and spatial degrees of freedom are de- coupled. This article presents general convergence and computational complexity analysis of a multilevel method for SPDEs, demonstrating its advantages with regard to standard, single level approximation. The numerical results will highlight conditions under which multilevel sparse grid SC is preferable to the more traditional MC and SC approaches.

Webster, Clayton G [ORNL; Jantsch, Peter A [ORNL; Teckentrup, Aretha L [ORNL; Gunzburger, Max D [ORNL

2013-01-01

88

A finite volume method to solve the 3D Navier–Stokes equations on unstructured collocated meshes  

Microsoft Academic Search

A new method to solve the Navier–Stokes equations for incompressible viscous flows and the transport of a scalar quantity is proposed. This method is based upon a fractional time step scheme and the finite volume method on unstructured meshes. The governing equations are discretized using a collocated, cell-centered arrangement of velocity and pressure. The solution variables are stored at the

Sébastien Perron; Sylvain Boivin; Jean-Marc Hérard

2004-01-01

89

THE DYNAMICALLY ADAPTIVE WAVELET COLLOCATION METHOD TO BE APPLIED TO THE DIRECT NUMERICAL SIMULATION OF RAYLEIGH-TAYLOR INSTABILITY  

Microsoft Academic Search

The Dynamically Adaptive Wavelet Collocation (DAWC) method is a proven numerical method, which is able to eciently solve partial dier- ential equations. The DAWC method's applicability to the simulations of Rayleigh-Taylor instability is promising, due to the nature of the instabil- ity. Current eorts are not able to push many parameters to the limits that would be necessary to simulate

SCOTT RECKINGER

90

A collocated method for the incompressible Navier-Stokes equations inspired by the Box scheme  

NASA Astrophysics Data System (ADS)

We present a new finite-difference numerical method to solve the incompressible Navier-Stokes equations using a collocated discretization in space on a logically Cartesian grid. The method shares some common aspects with, and it was inspired by, the Box scheme. It uses centered second-order-accurate finite-difference approximations for the spatial derivatives combined with semi-implicit time integration. The proposed method is constructed to ensure discrete conservation of mass and momentum by discretizing the primitive velocity-pressure form of the equations. The continuity equation is enforced exactly (to machine accuracy) at the collocated locations, whereas the momentum equations are evaluated in a staggered manner. This formulation preempts the appearance of spurious pressure modes in the embedded elliptic problem associated with the pressure. The method shows uniform order of accuracy, both in space and time, for velocity and pressure. In addition, the skew-symmetric form of the non-linear advection term of the Navier-Stokes equations improves discrete conservation of kinetic energy in the inviscid limit, to within the order of the truncation error of the time integrator. The method has been formulated to accommodate different types of boundary conditions; fully periodic, periodic channel, inflow-outflow and lid-driven cavity; always ensuring global mass conservation. A novel aspect of this finite-difference formulation is the derivation of the discretization near boundaries using the weak form of the equations, as in the finite element method. The method of manufactured solutions is utilized to perform accuracy analysis and verification of the solver. To assess the applicability of the new method presented in this paper, four realistic flow problems have been simulated and results are compared with those in the literature. These cases include a lid-driven cavity, backward-facing step, Kovasznay flow, and fully developed turbulent channel.

Ranjan, R.; Pantano, C.

2013-01-01

91

APPLICATION OF THE FLUX SPLINE METHOD IN GENERAL CURVILINEAR COORDINATES TO SEPARATED TWO-PHASE FLOW  

Microsoft Academic Search

We present preliminary results of the application of the flux-spline method of finite volumes for the numerical study of separated two-phase flows inside a circular tube. The problem consists in solving the Poisson's problem in the two-phase domain and assuring the continuity of the velocity and stress fields everywhere. Annular and stratified flow patterns of two immiscible viscous fluids are

Antonio C. Bannwart; Valter Silva Jr

92

Collocation method for calculating vibrational bound states of molecular systems: with application to Ar--HCl  

SciTech Connect

The ability of the collocation method to calculate vibrational bound states of molecules is investigated. The technique is simpler to implement than conventional variational methods; no integration over the basis functions is involved. We apply the method to the weakly bound complex Ar--HCl, a real multidimensional system of considerable physical interest, and find the procedure to be of equivalent accuracy to the corresponding variational approach at all times. This confirms the conclusions of our previous studies on one-dimensional test problems (W. Yang and A. C. Peet, Chem. Phys. Lett. (in press)). Both low lying and highly excited states are examined and the conclusions hold even for levels very close to the dissociation limit. A test of the wave functions obtained also finds these to be of good accuracy and very similar to the ones given by the variational procedure.

Peet, A.C.; Yang, W.

1989-02-01

93

Consistent projection methods for variable density incompressible Navier–Stokes equations with continuous surface forces on a rectangular collocated mesh  

Microsoft Academic Search

Two consistent projection methods of second-order temporal and spatial accuracy have been developed on a rectangular collocated mesh for variable density Navier–Stokes equations with a continuous surface force. Instead of the original projection methods (denoted as algorithms I and II in this paper), in which the updated cell center velocity from the intermediate velocity and the pressure gradient is not

Ming-Jiu Ni

2009-01-01

94

A method for stochastic constrained optimization using derivative-free surrogate pattern search and collocation  

SciTech Connect

Recent advances in coupling novel optimization methods to large-scale computing problems have opened the door to tackling a diverse set of physically realistic engineering design problems. A large computational overhead is associated with computing the cost function for most practical problems involving complex physical phenomena. Such problems are also plagued with uncertainties in a diverse set of parameters. We present a novel stochastic derivative-free optimization approach for tackling such problems. Our method extends the previously developed surrogate management framework (SMF) to allow for uncertainties in both simulation parameters and design variables. The stochastic collocation scheme is employed for stochastic variables whereas Kriging based surrogate functions are employed for the cost function. This approach is tested on four numerical optimization problems and is shown to have significant improvement in efficiency over traditional Monte-Carlo schemes. Problems with multiple probabilistic constraints are also discussed.

Sankaran, Sethuraman [Department of Mechanical and Aerospace Engineering, EBU II 569, University of California San Diego, La Jolla, CA 92093-0411 (United States); Audet, Charles [GERAD and Departement de mathematiques et de genie industriel, Ecole Polytechnique de Montreal, C.P. 6079, Succ. Centre-ville, Montreal (Quebec), H3C 3A7 (Canada); Marsden, Alison L. [Department of Mechanical and Aerospace Engineering, EBU II 569, University of California San Diego, La Jolla, CA 92093-0411 (United States)], E-mail: amarsden@ucsd.edu

2010-06-20

95

A Chebyshev spectral collocation method for the solution of the Reynolds equation of lubrication  

SciTech Connect

A multi-domain, Chebyshev collocation method is presented for the solution of ultra-thin gas bearing problems. The behavior of the flow varies across the computational domain with very sharp gradients occurring in the side and trailing edge boundary layers. The decomposition of the computational domain allows independent control over the representation of the solution in each subdomain. A multi-parameter continuation scheme is used to facilitate the convergence as the Parameters of the problem are varied over a wide range. The method is shown to be well suited for the simulation of lubrication flow between textured surfaces even in the presence of very steep pressure boundary layers. 16 refs., 8 figs., 2 tabs.

Raad, P.E. (Southern Methodist Univ., Dallas, TX (United States)); Karageorghis, A. (Univ. of Cyprus, Nicosia (Cyprus))

1993-05-01

96

A collocated grid finite volume method for aeroacoustic computations of low-speed flows  

Microsoft Academic Search

A numerical algorithm for simulation of acoustic noise generation, based on collocated grids, is described. The approach, that was originally developed using a viscous\\/inviscid decomposition technique, involves two steps comprising a viscous incompressible flow part and an inviscid or viscous acoustic part. On collocated grids the inviscid solution is found to be mesh dependent due to unavoidable extrapolations of the

Wen Zhong Shen; Jess A. Michelsen; Jens Nørkær Sørensen

2004-01-01

97

B-spline soliton solution of the fifth order KdV type equations  

NASA Astrophysics Data System (ADS)

In this paper, we develop a numerical solution based on sextic B-spline collocation method for solving the generalized fifth-order nonlinear evolution equations. Applying Von-Neumann stability analysis, the proposed technique is shown to be unconditionally stable. The accuracy of the presented method is demonstrated by a test problem. The numerical results are found to be in good agreement with the exact solution.

Zahra, W. K.; Ouf, W. A.; El-Azab, M. S.

2013-10-01

98

B-splines with artificial viscosity for solving singularly perturbed boundary value problems  

Microsoft Academic Search

In this paper, we propose a method for the numerical solution of singularly perturbed two-point boundary-value problems (BVPs). The artificial viscosity has been introduced to capture the exponential features of the exact solution on a uniform mesh and then the B-spline collocation method leads to a tridiagonal linear system. The analysis is done on a uniform mesh, which permits its

Mohan K. Kadalbajoo; Puneet Arora

2010-01-01

99

Quartic B-spline and two-step hybrid method applied to boundary value problem  

NASA Astrophysics Data System (ADS)

Boundary value problem of second order ordinary differential equation (ODE) has been identified as a problem. However, this work will focus on solving a special case of second order ODE. Special case of second order ODE is a second order differential equation without first derivative term. Then, this problem will be solved numerically using quartic b-spline interpolation method and fifth order singly diagonally two-step hybrid method. In order to study the efficiency of these two methods, results obtained have been compared with exact solution of the problem. Finally, error and norm for each method have been calculated.

Mat Zin, Shazalina; Abd Majid, Ahmad; Md Ismail, Ahmad Izani

2013-04-01

100

Two methods with different objectives: Splines and kriging  

Microsoft Academic Search

When drawing a contour map from a set of irregularly spaced data points, two methods are often used: The first corresponds to a rather aesthetic criterion and consists of obtaining contour lines which will be as smoothas possible and will honor the data points. This generally is the objective of the draftsman, and it can be automatically performed by the

Olivier Dubrule

1983-01-01

101

Computing singular solutions of the Navier-Stokes equations with the Chebyshev-collocation method  

NASA Astrophysics Data System (ADS)

The solution of fluid flow problems exhibits a singular behaviour when the conditions imposed on the boundary display some discontinuities or change in type. A treatment of these singularities has to be considered in order to preserve the accuracy of high-order methods, such as spectral methods. The present work concerns the computation of a singular solution of the Navier-Stokes equations using the Chebyshev-collocation method. A singularity subtraction technique is employed, which amounts to computing a smooth solution thanks to the subtraction of the leading part of the singular solution. The latter is determined from an asymptotic expansion of the solution near the singular points. In the case of non-homogeneous boundary conditions, where the leading terms of the expansion are completely determined by the local analysis, the high accuracy of the method is assessed on both steady and unsteady lid-driven cavity flows. An extension of this technique suitable for homogenous boundary conditions is developed for the injection of fluid into a channel. The ability of the method to compute high-Reynolds number flows is demonstrated on a piston-driven two-dimensional flow. Copyright

Botella, O.; Peyret, R.

2001-05-01

102

Wide angle and bi-directional beam propagation using the collocation method for the non-paraxial wave equation  

NASA Astrophysics Data System (ADS)

A method, based on the collocation method, for wide angle and bi-directional propagation of non-paraxial waves is presented. The second-order wave equation is converted to a matrix ordinary differential equation, which is solved numerically requiring no correction for energy conservation or evanescent mode suppression. No approximation for the wave equation such as the Fresnel approximation, or for the square root of the propagation operator is used. Examples show the performance of the method.

Sharma, Anurag; Agrawal, Arti

2003-02-01

103

A nonlinear rigid-plastic analysis for metal forming problem using the rigid-plastic point collocation method  

Microsoft Academic Search

A rigid-plastic point collocation method is applied to the analysis of plane strain forging, which is a nonlinear rigid-plastic problem of bulk metal forming. In general, the bulk metal forming problems are nonlinear and large deformation problems, used to be analyzed with the conventional rigid-plastic finite element methods. While the conventional rigid-plastic finite element methods have some shortcomings such as

Yong-ming Guo; Kenji Nakanishi; Yasuto Yokouchi

2005-01-01

104

Least-squares spectral collocation with the overlapping Schwarz method for the incompressible Navier?Stokes equations  

NASA Astrophysics Data System (ADS)

A least-squares spectral collocation scheme is combined with the overlapping Schwarz method. The methods are succesfully applied to the incompressible Navier?Stokes equations. The collocation conditions and the interface conditions lead to an overdetermined system which can be efficiently solved by least-squares. The solution technique will only involve symmetric positive definite linear systems. The overlapping Schwarz method is used for the iterative solution. For parallel implementation the subproblems are solved in a checkerboard manner. Our approach is successfully applied to the lid-driven cavity flow problem. Only a few Schwarz iterations are necessary in each time step. Numerical simulations confirm the high accuracy of our spectral least-squares scheme.

Heinrichs, Wilhelm

2006-09-01

105

Temporal registration of 2D x-ray mammogram using triangular B-splines finite element method (TBFEM)  

NASA Astrophysics Data System (ADS)

In this paper we develop a novel image processing technique to register two dimensional temporal mammograms for effective diagnosis and therapy. Our registration framework is founded upon triangular B-spline finite element method (TBFEM). In contrast to tensor-product B-splines, which is widely used in medical imaging, triangular B-splines are much more powerful, associated with many desirable advantages for image registration, such as flexible triangular domain, local control, space-varying smoothness, and sharp feature modeling. Empowered by the rigorous theory of triangular B-splines, our method can explicitly model the transformation between temporal mammogram pairs over irregular region of interest(ROI), using a collection of triangular B-splines. In addition, it is also capable of describing C0 continuous deformation at the interfaces between different elastic tissues, while the overall displacement field is smooth. Our registration process consists of two steps: 1) The template image is first nonlinearly deformed using TBFEM model, subject to pre-segmented feature constraints; 2) The deformed template image is further perturbed by applying pseudo image forces, aiming to reducing intensity-based discrepancies. The proposed registration framework has been tested extensively on practical clinical data, and the experimental results demonstrates that the registration accuracy is improved comparing to using conventional FEMs. Besides, the modeling of local C0 continuities of the displacement field helps to further increase the registration quality considerably.

Wang, Kexiang; He, Ying; Qin, Hong; Fisher, Paul R.; Zhao, Wei

2006-03-01

106

Collocation and least squares methods as a tool for handling gravity field dependent data obtained through space research techniques  

Microsoft Academic Search

Least squares adjustment and collocation methods have in the last decade been the tool for extracting gravity field information\\u000a from data obtained through space research techniques (satellite orbit tracking, altimeter observations, doppler determined\\u000a positions), and when combining these data with data observed at the surface of the Earth.\\u000a \\u000a The mathematical framework for the two models is described and the models

C. C. Tscherning

1978-01-01

107

Probabilistic collocation method for NDE problems with uncertain parameters with arbitrary distributions  

NASA Astrophysics Data System (ADS)

In order to quantify the reliability of NDE systems, large numbers of experiments are performed to develop a probability of detection (POD) curve for the system. These POD studies require a substantial amount of experimentation which can sometimes be cost prohibitive. To expedite the process of developing these curves, highly precise numerical models are used in conjunction with NDE sensors to understand the uncertainties associated with the inspections. Numerical models are also used in stochastic inversion methods such as Bayesian inversion, which provide a means of characterizing system properties with uncertainties. A strong basis has been developed in the modeling and simulation community for deterministic forward models in NDE, but to fully incorporate these models in model-assisted probability of detection (MAPOD) studies or stochastic inversion schemes, the models must be treated in a stochastic sense. A method of taking random inputs to a "black box" forward model and developing the full probability distribution function (PDF) of the response has been proposed. This method, called the probabilistic collocation method (PCM), takes random inputs to a forward model and uses orthogonal polynomials to construct a surrogate model in the area of the expected values of the inputs which is solved much quicker than the original forward model. In the NDE community, this method has only been used with inputs of known, named distributions. In this work, inputs of arbitrary distribution were used and the orthogonal polynomials for these inputs were developed with a recursion relationship that has been shown to produce orthogonal polynomials with respect to a given, continuous function. A concise code was written to make testing the method and incorporating it into MAPOD studies and inversion schemes relatively easy. The routine was tested with academic problems as well as eddy current problems.

Cherry, M. R.; Knopp, J. S.; Blodgett, M. P.

2012-05-01

108

Convergence of boundary element collocation methods for dirichlet and neumann screen problems in R  

Microsoft Academic Search

We study the numerical approximation of two pseudodifferential equations on a plane rectangle defined by the single layer potential and by the normal derivative of the double layer potential of the three-dimensional Laplacian. The solutions are approximated by nodal collocation with piecewise bilinear, respectively by bicubic, trial functions on a rectangular grid. The result for the single layer potential was

M. Costabel; F. Penzel; R. Schneider

1993-01-01

109

Characteristics method with cubic-spline interpolation for open channel flow computation  

NASA Astrophysics Data System (ADS)

In the framework of the specified-time-interval scheme, the accuracy of the characteristic method is greatly related to the form of the interpolation. The linear interpolation was commonly used to couple the characteristics method (LI method) in open channel flow computation. The LI method is easy to implement, but it leads to an inevitable smoothing of the solution. The characteristics method with the Hermite cubic interpolation (HP method, originally developed by Holly and Preissmann, 1977) was then proposed to largely reduce the error induced by the LI method. In this paper, the cubic-spline interpolation on the space line or on the time line is employed to integrate with characteristics method (CS method) for unsteady flow computation in open channel. Two hypothetical examples, including gradually and rapidly varied flows, are used to examine the applicability of the CS method as compared with the LI method, the HP method, and the analytical solutions. The simulated results show that the CS method is comparable to the HP method and more accurate than the LI method. Without tackling the additional equations for spatial or temporal derivatives, the CS method is easier to implement and more efficient than the HP method.

Tsai, Tung-Lin; Chiang, Shih-Wei; Yang, Jinn-Chuang

2004-10-01

110

Coordinate transformation in 3D image matching by a physics based method-elastic body splines  

Microsoft Academic Search

Any image matching scheme that is based on landmarks requires a coordinate transformation that maps landmark locations in one image to corresponding locations in a second image. The development of an approach to this coordinate transformation, called the elastic body spline (EBS), is outlined. The spline is used to match 3D magnetic resonance images (MRIs) of the breast that are

Malcolm H. Davis; Alireza Khotanzad; Duane P. Flamig; Steven E. Harms

1995-01-01

111

Cardiac Position Sensitivity Study in the Electrocardiographic Forward Problem Using Stochastic Collocation and Boundary Element Methods  

PubMed Central

The electrocardiogram (ECG) is ubiquitously employed as a diagnostic and monitoring tool for patients experiencing cardiac distress and/or disease. It is widely known that changes in heart position resulting from, for example, posture of the patient (sitting, standing, lying) and respiration significantly affect the body-surface potentials; however, few studies have quantitatively and systematically evaluated the effects of heart displacement on the ECG. The goal of this study was to evaluate the impact of positional changes of the heart on the ECG in the specific clinical setting of myocardial ischemia. To carry out the necessary comprehensive sensitivity analysis, we applied a relatively novel and highly efficient statistical approach, the generalized polynomial chaos-stochastic collocation method, to a boundary element formulation of the electrocardiographic forward problem, and we drove these simulations with measured epicardial potentials from whole-heart experiments. Results of the analysis identified regions on the body-surface where the potentials were especially sensitive to realistic heart motion. The standard deviation (STD) of ST-segment voltage changes caused by the apex of a normal heart, swinging forward and backward or side-to-side was approximately 0.2 mV. Variations were even larger, 0.3 mV, for a heart exhibiting elevated ischemic potentials. These variations could be large enough to mask or to mimic signs of ischemia in the ECG. Our results suggest possible modifications to ECG protocols that could reduce the diagnostic error related to postural changes in patients possibly suffering from myocardial ischemia.

Swenson, Darrell J.; Geneser, Sarah E.; Stinstra, Jeroen G.; Kirby, Robert M.; MacLeod, Rob S.

2012-01-01

112

Adaptive Wavelet Collocation Methods for Initial Value Boundary Problems of Nonlinear PDE's.  

National Technical Information Service (NTIS)

We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is construc...

W. Cai J. Wang

1993-01-01

113

An unfitted hp-adaptive finite element method based on hierarchical B-splines for interface problems of complex geometry  

Microsoft Academic Search

Generating finite element discretizations with direct interface parameterizations constitutes a considerable computational expense in case of complex interface geometries. The paper at hand introduces a B-spline finite element method, which circumvents parameterization of interfaces and offers fast and easy meshing irrespective of the geometric complexity involved. Its core idea is the adaptive approximation of discontinuities by hierarchical grid refinement, which

Dominik Schillinger; Ernst Rank

2011-01-01

114

Application of semiorthogonal spline wavelets and the Galerkin method to the numerical simulation of thin wire antennas  

NASA Astrophysics Data System (ADS)

The Bubnov-Galerkin method based on spline wavelets is used to solve singular integral equations. For the resulting systems of linear algebraic equations, the properties of their coefficient matrices are examined. Sparse approximations of these matrices are constructed by applying a cutting barrier. The results are used to numerically analyze thin wire antennas. Numerical results are presented.

Blatov, I. A.; Rogova, N. V.

2013-05-01

115

The Sinc-Legendre collocation method for a class of fractional convection-diffusion equations with variable coefficients  

NASA Astrophysics Data System (ADS)

This paper deals with the numerical solution of classes of fractional convection-diffusion equations with variable coefficients. The fractional derivatives are described based on the Caputo sense. Our approach is based on the collocation techniques. The method consists of reducing the problem to the solution of linear algebraic equations by expanding the required approximate solution as the elements of shifted Legendre polynomials in time and the Sinc functions in space with unknown coefficients. The properties of Sinc functions and shifted Legendre polynomials are then utilized to evaluate the unknown coefficients. Several examples are given and the numerical results are shown to demonstrate the efficiency of the newly proposed method.

Saadatmandi, Abbas; Dehghan, Mehdi; Azizi, Mohammad-Reza

2012-11-01

116

Interpolating Spline Methods for Density Estimation I. Equi-Spaced Knots.  

National Technical Information Service (NTIS)

Statistical properties of the histospline density estimate of Boneva-Kendall-Stefanov-Schoenberg are found. This density estimate is the derivative of a cubic spline of interpolation to the sample cumulative distribution at equally spaced points. The spac...

G. Wahba

1973-01-01

117

A class of methods based on non-polynomial spline functions for the solution of a special fourth-order boundary-value problems with engineering applications  

Microsoft Academic Search

We use a quintic non-polynomial spline functions to develop a numerical method for computing approximations to the solution of a system of fourth-order boundary-value problems associated with plate deflection theory. We show that the present family of methods gives better approximations and generalize all the existing finite difference and spline functions based methods up to order six. Convergence of the

Siraj-ul-islam; Syed Ikram A. Tirmizi; Saadat Ashraf

2006-01-01

118

A collocated grid finite volume method for aeroacoustic computations of low-speed flows  

NASA Astrophysics Data System (ADS)

A numerical algorithm for simulation of acoustic noise generation, based on collocated grids, is described. The approach, that was originally developed using a viscous/inviscid decomposition technique, involves two steps comprising a viscous incompressible flow part and an inviscid or viscous acoustic part. On collocated grids the inviscid solution is found to be mesh dependent due to unavoidable extrapolations of the acoustic pressure and density at walls, differing from the case on staggered grids where no extrapolation is needed. The situation is most pronounced when a sharp body is considered. A viscous acoustic algorithm is proposed to overcome the difficulty. Numerical computations of flows past a circular cylinder and a NACA 0015 airfoil show that a viscous/viscous coupling is more natural and gives excellent results as compared to those obtained in previous computations based on viscous/inviscid coupling on staggered grids. The model is applied to the problem of an airfoil exposed to a gust and results are compared to the numerical results of Lockard and Morris [AIAA J. 36(6) (1998) 907].

Shen, Wen Zhong; Michelsen, Jess A.; Sørensen, Jens Nørkær

2004-05-01

119

Boundary element method using B-splines with applications to groundwater flow  

SciTech Connect

The Boundary Element Method (BEM) is now established as a suitable and efficient technique for the analysis of engineering problems. However, as in other discretization procedures, inaccuracies can be introduced as a result of the lack of derivative continuity between adjacent elements. A new element formulation has been developed for BEM analysis using uniform cubic B-splines. These functions can be employed to provide higher degrees of continuity along the geometric boundary of the region, and also as interpolation functions for the problem variables. The formulation was then extended to include multiple knots and non-uniform blending functions. In this way, it is possible to lower the degree of continuity of the main variable at points of geometric discontinuity. Initially, applications are presented related to potential problems governed by Laplace's equation but there are no restrictions in the formulation regarding its extension to other physical problems. Continuity of the derivatives of the main variable is important to obtain a good representation of moving boundaries with iterative or time-marching schemes. This formulation is applied to stead-state and transient unconfined flow in homogeneous and inhomogeneous porous media. Finally, the formulation is applied to saltwater intrusion problems in confined, leaky and unconfined aquifers.

Cabral, J.J.S.P.

1992-01-01

120

A two-parameter continuation algorithm using radial basis function collocation method for rotating Bose-Einstein condensates  

NASA Astrophysics Data System (ADS)

We present an efficient numerical algorithm to observe the dynamical formation of vortex lattice of a rotating trapped Bose-Einstein condensate (BEC) via solving a two-dimensional Gross-Pitaevskii equation (GPE). We use a radial basis function collocation method (RBFCM) to discretize a two-dimensional coupled nonlinear Schrödinger equation (CNLSE) derived from the GPE. A two-parameter continuation algorithm is implemented here to trace the solution curve of the CNLSE. The numerical experiments show promise of the proposed method to observe a variety of vortices of a rotating BEC in optical lattices, and depict the densities of superfluid and the solution curves as a function of chemical potential and the rotation frequency for various vortex structures. This algorithm provides an efficient method for observing complicated convex structures and dynamical phenomena of vortices in rotating BEC when comparing with those existing numerical methods in the literature.

Shih, Yin-Tzer; Tsai, Chih-Ching

2013-11-01

121

Ray-tracing method for creeping waves on arbitrarily shaped nonuniform rational B-splines surfaces.  

PubMed

An accurate creeping ray-tracing algorithm is presented in this paper to determine the tracks of creeping waves (or creeping rays) on arbitrarily shaped free-form parametric surfaces [nonuniform rational B-splines (NURBS) surfaces]. The main challenge in calculating the surface diffracted fields on NURBS surfaces is due to the difficulty in determining the geodesic paths along which the creeping rays propagate. On one single parametric surface patch, the geodesic paths need to be computed by solving the geodesic equations numerically. Furthermore, realistic objects are generally modeled as the union of several connected NURBS patches. Due to the discontinuity of the parameter between the patches, it is more complicated to compute geodesic paths on several connected patches than on one single patch. Thus, a creeping ray-tracing algorithm is presented in this paper to compute the geodesic paths of creeping rays on the complex objects that are modeled as the combination of several NURBS surface patches. In the algorithm, the creeping ray tracing on each surface patch is performed by solving the geodesic equations with a Runge-Kutta method. When the creeping ray propagates from one patch to another, a transition method is developed to handle the transition of the creeping ray tracing across the border between the patches. This creeping ray-tracing algorithm can meet practical requirements because it can be applied to the objects with complex shapes. The algorithm can also extend the applicability of NURBS for electromagnetic and optical applications. The validity and usefulness of the algorithm can be verified from the numerical results. PMID:23595326

Chen, Xi; He, Si-Yuan; Yu, Ding-Feng; Yin, Hong-Cheng; Hu, Wei-Dong; Zhu, Guo-Qiang

2013-04-01

122

Analysis of three-dimensional splines and their application to the initial graphics exchange specification  

SciTech Connect

This research develops the fundamental theories associated with three-dimensional splines and the philosophies underlying the Initial Graphics Exchange Specification (IGES). Splines have been classified into three main categories: polynomial splines, splines-in-tension, and blending splines. The importance of a three-dimensional spline standard is given. It is shown that no single spline routine can adequately define a curve for every possible application. A possible three-dimensional spline standard should therefore contain a spline routine from each of the three categories. The B-spline, Cline's spline-in-tension, and Circle Spline were the three spline routines selected. The properties and characteristics that these splines should possess are defined. Two methods for extending a two-dimensional spline into three dimensions are given. The B-spline is extended parametrically and the Spline-in-Tension is extended explicitly. It will be shown that the parametric form is the more powerful and computationally efficient method. An alternative method for representing splines in IGES is presented. This alternate method uses the IGES Copious Data Entity. It has a smaller file size than the traditionally used Parametric Spline Curve Entity. The use of this method is geared toward the application of splines in design and analysis work. The data stored within the file by each spline routine represents the minimum amount of information required to uniquely define the spline curve. The alternative method for storing and transferring spline data is structured in a manner that allows each spline routine to read and write files efficiently. Using this data file, a spline routine can generate a curve by reading the output of another spline routine. It will be demonstrated that spline transfer between both similar and dissimilar spline routines can be done accurately and efficiently. 72 refs., 16 figs.

Dolin, R.M.

1985-08-01

123

Schur-decomposition for 3D matrix equations and its application in solving radiative discrete ordinates equations discretized by Chebyshev collocation spectral method  

SciTech Connect

The Schur-decomposition for three-dimensional matrix equations is developed and used to directly solve the radiative discrete ordinates equations which are discretized by Chebyshev collocation spectral method. Three methods, say, the spectral methods based on 2D and 3D matrix equation solvers individually, and the standard discrete ordinates method, are presented. The numerical results show the good accuracy of spectral method based on direct solvers. The CPU time cost comparisons against the resolutions between these three methods are made using MATLAB and FORTRAN 95 computer languages separately. The results show that the CPU time cost of Chebyshev collocation spectral method with 3D Schur-decomposition solver is the least, and almost only one thirtieth to one fiftieth CPU time is needed when using the spectral method with 3D Schur-decomposition solver compared with the standard discrete ordinates method.

Li Benwen [Key Laboratory of Electromagnetic Processing of Materials (Ministry of Education), Northeastern University, P.O. Box 314, Shenyang, Liaoning 110004 (China)], E-mail: heatli@hotmail.com; Tian Shuai; Sun Yasong; Hu, Zhang-Mao [Key Laboratory of Electromagnetic Processing of Materials (Ministry of Education), Northeastern University, P.O. Box 314, Shenyang, Liaoning 110004 (China)

2010-02-20

124

Testing Multivariate Adaptive Regression Splines (MARS) as a Method of Land Cover Classification of TERRA-ASTER Satellite Images  

PubMed Central

This work proposes a new method to classify multi-spectral satellite images based on multivariate adaptive regression splines (MARS) and compares this classification system with the more common parallelepiped and maximum likelihood (ML) methods. We apply the classification methods to the land cover classification of a test zone located in southwestern Spain. The basis of the MARS method and its associated procedures are explained in detail, and the area under the ROC curve (AUC) is compared for the three methods. The results show that the MARS method provides better results than the parallelepiped method in all cases, and it provides better results than the maximum likelihood method in 13 cases out of 17. These results demonstrate that the MARS method can be used in isolation or in combination with other methods to improve the accuracy of soil cover classification. The improvement is statistically significant according to the Wilcoxon signed rank test.

Quiros, Elia; Felicisimo, Angel M.; Cuartero, Aurora

2009-01-01

125

Interchangeable spline reference guide  

SciTech Connect

The WX-Division Integrated Software Tools (WIST) Team evolved from two previous committees, First was the W78 Solid Modeling Pilot Project`s Spline Subcommittee, which later evolved into the Vv`X-Division Spline Committee. The mission of the WIST team is to investigate current CAE engineering processes relating to complex geometry and to develop methods for improving those processes. Specifically, the WIST team is developing technology that allows the Division to use multiple spline representations. We are also updating the contour system (CONSYS) data base to take full advantage of the Division`s expanding electronic engineering process. Both of these efforts involve developing interfaces to commercial CAE systems and writing new software. The WIST team is comprised of members from V;X-11, -12 and 13. This {open_quotes}cross-functional{close_quotes} approach to software development is somewhat new in the Division so an effort is being made to formalize our processes and assure quality at each phase of development. Chapter one represents a theory manual and is one phase of the formal process. The theory manual is followed by a software requirements document, specification document, software verification and validation documents. The purpose of this guide is to present the theory underlying the interchangeable spline technology and application. Verification and validation test results are also presented for proof of principal.

Dolin, R.M.

1994-05-01

126

A fourth-order adaptive collocation approach for the solution of generalized Emden-Fowler type equations  

NASA Astrophysics Data System (ADS)

A cubic B-spline collocation approach is employed for the numerical solution of a generalized form of the Emden-Fowler type equation. The rate of convergence is discussed theoretically and verified numerically to be of fourthorder by using the double-mesh principle. The efficiency of the scheme is tested on a number of examples which represent special cases of the problem under consideration. The results are compared with analytical and other numerical solutions that are available in the literature. The proposed method reveals that the outcomes are reliable and very accurate when contrasted with other existing methods.

Khoury, S.; Sayfy, Ali

2012-09-01

127

Consistent projection methods for variable density incompressible Navier-Stokes equations with continuous surface forces on a rectangular collocated mesh  

NASA Astrophysics Data System (ADS)

Two consistent projection methods of second-order temporal and spatial accuracy have been developed on a rectangular collocated mesh for variable density Navier-Stokes equations with a continuous surface force. Instead of the original projection methods (denoted as algorithms I and II in this paper), in which the updated cell center velocity from the intermediate velocity and the pressure gradient is not guaranteed solenoidal, the consistent projection methods (denoted as algorithms III and IV) obtain the cell center velocity based on an interpolation from a conservative fluxes with velocity unit on surrounding cell faces. Dependent on treatment of the continuous surface force, the pressure gradient in algorithm III or the sum of the pressure gradient and the surface force in algorithm IV at a cell center is then conducted from the difference between the updated velocity and the intermediate velocity in a consistent projection method. A non-viscous 3D static drop with serials of density ratios is numerically simulated. Using the consistent projection methods, the spurious currents can be greatly reduced and the pressure jump across the interface can be accurately captured without oscillations. The developed consistent projection method are also applied for simulation of interface evolution of an initial ellipse driven by the surface tension and of an initial sphere bubble driven by the buoyancy with good accuracy and good resolution.

Ni, Ming-Jiu

2009-10-01

128

Discretely conservative, non-dissipative, and stable collocated method for solving the incompressible Navier-Stokes equations  

NASA Astrophysics Data System (ADS)

We present a new method for solving the incompressible Navier-Stokes equations. The method utilizes a collocated arrangement of all variables in space. It uses centered second-order accurate finite-difference approximations for all spatial derivatives and a third-order IMEX approach for time integration. The proposed method ensures discrete conservation of mass and momentum by discretizing the conservative form of the equations from the outset and never relying on continuum relations afterward. This ensures uniform high order of accuracy in time for all fields, including pressure. The pressure-momentum coupled equations can be easily segregated and solved sequentially, as in the pressure projection method but without a splitting error. In this approach there are no spurious kernel modes, checkerboard, in the embedded elliptic pressure problem. The method has been applied to different canonical problems, including a fully periodic box, a periodic channel, an inflow-outflow channel and a lid-driven cavity flow. Near wall boundaries, spatial derivatives are obtained using the weak form of the conservation equations, similar to a finite element approach. The results from some of the sample cases will be presented to illustrate the features of the method.

Ranjan, Reetesh; Pantano, Carlos

2010-11-01

129

Split spline screw  

NASA Astrophysics Data System (ADS)

A split spline screw type payload fastener assembly, including three identical male and female type split spline sections, is discussed. The male spline sections are formed on the head of a male type spline driver. Each of the split male type spline sections has an outwardly projecting load baring segment including a convex upper surface which is adapted to engage a complementary concave surface of a female spline receptor in the form of a hollow bolt head. Additionally, the male spline section also includes a horizontal spline releasing segment and a spline tightening segment below each load bearing segment. The spline tightening segment consists of a vertical web of constant thickness. The web has at least one flat vertical wall surface which is designed to contact a generally flat vertically extending wall surface tab of the bolt head. Mutual interlocking and unlocking of the male and female splines results upon clockwise and counter clockwise turning of the driver element.

Vranish, John M.

1993-11-01

130

Time-domain simulation of acoustic wave propagation and interaction with flexible structures using Chebyshev collocation method  

NASA Astrophysics Data System (ADS)

A time-domain Chebyshev collocation (ChC) method is used to simulate acoustic wave propagation and its interaction with flexible structures in ducts. The numerical formulation is described using a two-dimensional duct noise control system, which consists of an expansion chamber and a tensioned membrane covering the side-branch cavity. Full coupling between the acoustic wave and the structural vibration of the tensioned membrane is considered in the modelling. A systematic method of solution is developed for the discretized differential equations over multiple physical domains. The time-domain ChC model is tested against analytical solutions under two conditions: one with an initial state of wave motion; the other with a time-dependent acoustic source. Comparisons with the finite-difference time-domain (FDTD) method are also made. Results show that the time-domain ChC method is highly accurate and computationally efficient for the time-dependent solution of duct acoustic problems. For illustrative purposes, the time-domain ChC method is applied to investigate the acoustic performance of three typical duct noise control devices: the expansion chamber, the quarter wavelength resonator and the drum silencer. The time-dependent simulation of the sound-structure interaction in the drum silencer reveals the delicate role of the membrane mass and tension in its sound reflection capability.

Wang, Chunqi; Huang, Lixi

2012-09-01

131

Geodesic Interpolating Splines  

Microsoft Academic Search

We propose a simple and efficient method to interpolate landmark matching by a non-ambiguous mapping (a diffeomorphism). This\\u000a method is based on spline interpolation, and on recent techniques developed for the estimation of flows of diffeomorphisms.\\u000a Experimental results show interpolations of remarkable quality. Moreover, the method provides a Riemannian distance on sets\\u000a of landmarks (with fixed cardinality), which can be

Vincent Camion; Laurent Younes

2001-01-01

132

High-accuracy versions of the collocations and least squares method for the numerical solution of the Navier-Stokes equations  

NASA Astrophysics Data System (ADS)

An approach for the creation of high-accuracy versions of the collocations and least squares method for the numerical solution of the Navier-Stokes equations is proposed. New versions of up to the eighth order of accuracy inclusive are implemented. For smooth solutions, numerical experiments on a sequence of grids show that the approximate solutions produced by these versions converge to the exact one with a high order of accuracy as h ? 0, where h is the maximal linear cell size of a grid. The numerical results obtained for the benchmark problem of the lid-driven cavity flow suggest that the collocations and least squares method is well suited for the numerical simulation of viscous flows.

Isaev, V. I.; Shapeev, V. P.

2010-10-01

133

Modeling diffusion in random heterogeneous media: Data-driven models, stochastic collocation and the variational multiscale method  

SciTech Connect

In recent years, there has been intense interest in understanding various physical phenomena in random heterogeneous media. Any accurate description/simulation of a process in such media has to satisfactorily account for the twin issues of randomness as well as the multilength scale variations in the material properties. An accurate model of the material property variation in the system is an important prerequisite towards complete characterization of the system response. We propose a general methodology to construct a data-driven, reduced-order model to describe property variations in realistic heterogeneous media. This reduced-order model then serves as the input to the stochastic partial differential equation describing thermal diffusion through random heterogeneous media. A decoupled scheme is used to tackle the problems of stochasticity and multilength scale variations in properties. A sparse-grid collocation strategy is utilized to reduce the solution of the stochastic partial differential equation to a set of deterministic problems. A variational multiscale method with explicit subgrid modeling is used to solve these deterministic problems. An illustrative example using experimental data is provided to showcase the effectiveness of the proposed methodology.

Ganapathysubramanian, Baskar [Materials Process Design and Control Laboratory, Sibley School of Mechanical and Aerospace Engineering, 188 Frank H.T., Rhodes Hall, Cornell University, Ithaca, NY 14853-3801 (United States); Zabaras, Nicholas [Materials Process Design and Control Laboratory, Sibley School of Mechanical and Aerospace Engineering, 188 Frank H.T., Rhodes Hall, Cornell University, Ithaca, NY 14853-3801 (United States)], E-mail: zabaras@cornell.edu

2007-09-10

134

High-accuracy versions of the collocations and least squares method for the numerical solution of the Navier-Stokes equations  

Microsoft Academic Search

An approach for the creation of high-accuracy versions of the collocations and least squares method for the numerical solution\\u000a of the Navier-Stokes equations is proposed. New versions of up to the eighth order of accuracy inclusive are implemented.\\u000a For smooth solutions, numerical experiments on a sequence of grids show that the approximate solutions produced by these versions\\u000a converge to the

V. I. Isaev; V. P. Shapeev

2010-01-01

135

The B-spline R-matrix method for atomic processes: application to atomic structure, electron collisions and photoionization  

NASA Astrophysics Data System (ADS)

The basic ideas of the B-spline R-matrix (BSR) approach are reviewed, and the use of the method is illustrated with a variety of applications to atomic structure, electron-atom collisions and photo-induced processes. Special emphasis is placed on complex, open-shell targets, for which the method has proven very successful in reproducing, for example, a wealth of near-threshold resonance structures. Recent extensions to a fully relativistic framework and intermediate energies have allowed for an accurate treatment of heavy targets as well as a fully nonperturbative scheme for electron-impact ionization. Finally, field-free BSR Hamiltonian and electric dipole matrices can be employed in the time-dependent treatment of intense short-pulse laser-atom interactions.

Zatsarinny, Oleg; Bartschat, Klaus

2013-06-01

136

Simulation of groundwater flow in unconfined aquifer using meshfree point collocation method  

Microsoft Academic Search

For appropriate management of available groundwater, the flow behavior in the porous media has to be analyzed. The complex problem of groundwater flow can be studied by solving the governing equations analytically or by using numerical methods. As the analytical solutions are available only for simple idealized cases, numerical methods such as finite difference method (FDM) and finite element method

Mategaonkar Meenal; T. I. Eldho

2011-01-01

137

Two dimensional contaminant transport modeling using meshfree point collocation method (PCM)  

Microsoft Academic Search

Groundwater contamination is a severe problem in many parts of the world including India. The complex problem of groundwater flow and contaminant transport is studied generally by solving the governing equations of flow and transport using numerical models such as finite difference method (FDM) or finite element method (FEM). Meshfree (MFree) method is an alternative numerical approach to solve these

Mategaonkar Meenal; T. I. Eldho

138

Error estimation in high dimensional space for stochastic collocation methods on arbitrary sparse samples  

NASA Astrophysics Data System (ADS)

We have develop a fast method that can give high order error estimates of piecewise smooth functions in high dimensions with high order and low computational cost. This method can be used polynomial annihilation to estimate the smoothness of local regions of arbitrary samples in annihilation stochastic simulations. We compare the error estimation of this method to gaussian process error estimation techniques.

Archibald, Rick

2013-10-01

139

An adaptive sparse-grid high-order stochastic collocation method for Bayesian inference in groundwater reactive transport modeling  

SciTech Connect

Although Bayesian analysis has become vital to the quantification of prediction uncertainty in groundwater modeling, its application has been hindered due to the computational cost associated with numerous model executions needed for exploring the posterior probability density function (PPDF) of model parameters. This is particularly the case when the PPDF is estimated using Markov Chain Monte Carlo (MCMC) sampling. In this study, we develop a new approach that improves computational efficiency of Bayesian inference by constructing a surrogate system based on an adaptive sparse-grid high-order stochastic collocation (aSG-hSC) method. Unlike previous works using first-order hierarchical basis, we utilize a compactly supported higher-order hierar- chical basis to construct the surrogate system, resulting in a significant reduction in the number of computational simulations required. In addition, we use hierarchical surplus as an error indi- cator to determine adaptive sparse grids. This allows local refinement in the uncertain domain and/or anisotropic detection with respect to the random model parameters, which further improves computational efficiency. Finally, we incorporate a global optimization technique and propose an iterative algorithm for building the surrogate system for the PPDF with multiple significant modes. Once the surrogate system is determined, the PPDF can be evaluated by sampling the surrogate system directly with very little computational cost. The developed method is evaluated first using a simple analytical density function with multiple modes and then using two synthetic groundwater reactive transport models. The groundwater models represent different levels of complexity; the first example involves coupled linear reactions and the second example simulates nonlinear ura- nium surface complexation. The results show that the aSG-hSC is an effective and efficient tool for Bayesian inference in groundwater modeling in comparison with conventional MCMC sim- ulations. The computational efficiency is expected to be more beneficial to more computational expensive groundwater problems.

Zhang, Guannan [ORNL; Webster, Clayton G [ORNL; Gunzburger, Max D [ORNL

2012-09-01

140

Computing singular solutions of the Navier-Stokes equations with the Chebyshev-collocation method  

Microsoft Academic Search

The solution of fluid flow problems exhibits a singular behaviour when the conditions imposed on the boundary display some discontinuities or change in type. A treatment of these singularities has to be considered in order to preserve the accuracy of high-order methods, such as spectral methods. The present work concerns the computation of a singular solution of the Navier-Stokes equations

O. Botella; R. Peyret

2001-01-01

141

An Adaptive Wavelet Collocation Method for Fluid-Structure Interaction at High Reynolds Numbers  

Microsoft Academic Search

Two mathematical approaches are combined to calculate high Reynolds number in- compressible fluid-structure interaction: a wavelet method to dynamically adapt the computational grid to flow intermittency and obstacle motion, and Brinkman penalization to enforce solid bound- aries of arbitrary complexity. We also implement a wavelet-based multilevel solver for the Poisson problem for the pressure at each time step. The method

Nicholas K.-R. Kevlahan; Oleg V. Vasilyev

2005-01-01

142

Extension of Brinkman Penalization for Ocean Circulation Modeling using Adaptive Wavelet Collocation Method  

Microsoft Academic Search

This work improves the representation of continental topology and bottom bathymetry for use in ocean circulation models through an extension of the Brinkman penalization method. Due to the complicated geometry inherent in ocean boundaries, the stair-step representation used in the majority of current global ocean circulation models causes large accuracy and stability problems. Brinkman penalization is a numerical technique used

Shanon Reckinger; Oleg V. Vasilyev

2009-01-01

143

An efficient Bayesian inference approach to inverse problems based on an adaptive sparse grid collocation method  

Microsoft Academic Search

A new approach to modeling inverse problems using a Bayesian inference method is introduced. The Bayesian approach considers the unknown parameters as random variables and seeks the probabilistic distribution of the unknowns. By introducing the concept of the stochastic prior state space to the Bayesian formulation, we reformulate the deterministic forward problem as a stochastic one. The adaptive hierarchical sparse

Xiang Ma; Nicholas Zabaras

2009-01-01

144

Fractional Splines and Wavelets  

Microsoft Academic Search

We extend Schoenberg's family of polynomial splines with uniform knots to all fractional degrees ?> ?1. These splines, which involve linear combinations of the one-sided power functions x? + =max(0 ,x ) ?, are ?-Holder continuous for ?> 0. We construct the cor- responding B-splines by taking fractional finite differences and provide an explicit char- acterization in both time and

Michael Unser; Thierry Blu

2000-01-01

145

Experiments on Candidate Data for Collocation Extraction  

Microsoft Academic Search

The paper describes ongoing work on the evaluation of methods for extracting collocation candidates from large text corpora. Our research is based on a German treebank corpus used as gold standard. Results are available for adjective+noun pairs, which proved to be a comparatively easy extraction task. We plan to extend the evaluation to other types of collocations (e.g., PP+verb pairs).

Stefan Evert; Hannah Kermes

2003-01-01

146

Kriging and splines with derivative information  

Microsoft Academic Search

SUMMARY Spline fitting is a popular method of interpolating a real-valued function given its values at a set of points in W. Other linear constraints such as derivative information can also be incorporated as we show here. Spline fitting is well known to be a special case of kriging. Using the kriging framework we give a full description of the

K. V. MARDIA; J. T. KENT; C. R. GOODALL; J. A. LITTLE

1996-01-01

147

Paying Heed to Collocations.  

National Technical Information Service (NTIS)

In this paper, we introduce a system, Sentence Planning Using Description, which generates collocations within the paradigm of sentence planning SPUD simultaneously constructs the semantics and syntax of a sentence using a Lexicalized Tree Adjoining Gramm...

C. Doran M. Stone

1996-01-01

148

Cubic splines for image interpolation and digital filtering  

Microsoft Academic Search

This paper presents the use of B-splines as a tool in various digital signal processing applications. The theory of B-splines is briefly reviewed, followed by discussions on B-spline interpolation and B-spline filtering. Computer implementation using both an efficient software viewpoint and a hardware method are discussed. Finally, experimental results are presented for illustrative purposes in two-dimensional image format. Applications to

Hsieh Hou; H. C. Andrews

1978-01-01

149

Interpolating splines with local tension, continuity, and bias control  

Microsoft Academic Search

This paper presents a new method for using cubic interpolating splines in a key frame animation system. Three control parameters allow the animator to change the tension, continuity, and bias of the splines. Each of these three parameters can be used for either local or global control. Our technique produces a very general class of interpolating cubic splines which includes

Doris H. U. Kochanek; Richard H. Bartels

1984-01-01

150

Small and large deformation analysis with the p- and B-spline versions of the Finite Cell Method  

NASA Astrophysics Data System (ADS)

The Finite Cell Method (FCM) is an embedded domain method, which combines the fictitious domain approach with high-order finite elements, adaptive integration, and weak imposition of unfitted Dirichlet boundary conditions. For smooth problems, FCM has been shown to achieve exponential rates of convergence in energy norm, while its structured cell grid guarantees simple mesh generation irrespective of the geometric complexity involved. The present contribution first unhinges the FCM concept from a special high-order basis. Several benchmarks of linear elasticity and a complex proximal femur bone with inhomogeneous material demonstrate that for small deformation analysis, FCM works equally well with basis functions of the p-version of the finite element method or high-order B-splines. Turning to large deformation analysis, it is then illustrated that a straightforward geometrically nonlinear FCM formulation leads to the loss of uniqueness of the deformation map in the fictitious domain. Therefore, a modified FCM formulation is introduced, based on repeated deformation resetting, which assumes for the fictitious domain the deformation-free reference configuration after each Newton iteration. Numerical experiments show that this intervention allows for stable nonlinear FCM analysis, preserving the full range of advantages of linear elastic FCM, in particular exponential rates of convergence. Finally, the weak imposition of unfitted Dirichlet boundary conditions via the penalty method, the robustness of FCM under severe mesh distortion, and the large deformation analysis of a complex voxel-based metal foam are addressed.

Schillinger, Dominik; Ruess, Martin; Zander, Nils; Bazilevs, Yuri; Düster, Alexander; Rank, Ernst

2012-10-01

151

Implementation of Free-Surface Condition for Finite-Difference Time-Domain Method Using a Staggered Grid with the Collocated Grid Points of Velocities  

NASA Astrophysics Data System (ADS)

The finite-difference time-domain (FD-TD) method using a staggered grid with the collocated grid points of velocities (SGCV) in two dimensions was applied to Lamé mode resonators on an isotropic solid. Their resonance frequencies of the fundamental Lamé mode were examined to confirm the validity of the SGCV models of the free surfaces. The resonance frequency obtained with an SGCV, which uses bipolynomial interpolation with values of velocity on six adjoining grids to evaluate the derivatives of velocity vector fields on a grid, showed good agreement with the analytical resonance frequency.

Yasui, Takashi; Hasegawa, Koji; Hirayama, Koichi

2013-07-01

152

47 CFR 51.323 - Standards for physical collocation and virtual collocation.  

Code of Federal Regulations, 2012 CFR

...2012-10-01 false Standards for physical collocation and virtual collocation...Carriers § 51.323 Standards for physical collocation and virtual collocation...An incumbent LEC shall provide physical collocation and virtual...

2012-10-01

153

47 CFR 51.323 - Standards for physical collocation and virtual collocation.  

Code of Federal Regulations, 2011 CFR

...2011-10-01 false Standards for physical collocation and virtual collocation...Carriers § 51.323 Standards for physical collocation and virtual collocation...An incumbent LEC shall provide physical collocation and virtual...

2011-10-01

154

47 CFR 51.323 - Standards for physical collocation and virtual collocation.  

Code of Federal Regulations, 2010 CFR

...2009-10-01 false Standards for physical collocation and virtual collocation...51.323 Standards for physical collocation and virtual collocation...k) An incumbent LEC's physical collocation offering must...prorate the charge for site conditioning and preparation...

2009-10-01

155

47 CFR 51.323 - Standards for physical collocation and virtual collocation.  

Code of Federal Regulations, 2010 CFR

...2010-10-01 false Standards for physical collocation and virtual collocation...51.323 Standards for physical collocation and virtual collocation...k) An incumbent LEC's physical collocation offering must...prorate the charge for site conditioning and preparation...

2010-10-01

156

Splines as Linear Combinations of B-Splines. A Survey.  

National Technical Information Service (NTIS)

This paper is intended to promote the point of view that B-splines are truly basic splines: B-splines express the essentially local, but not completely local, character of splines; certain facts about splines take on their most striking form when put into...

C. de Boor

1976-01-01

157

Quasi interpolation with Voronoi splines.  

PubMed

We present a quasi interpolation framework that attains the optimal approximation-order of Voronoi splines for reconstruction of volumetric data sampled on general lattices. The quasi interpolation framework of Voronoi splines provides an unbiased reconstruction method across various lattices. Therefore this framework allows us to analyze and contrast the sampling-theoretic performance of general lattices, using signal reconstruction, in an unbiased manner. Our quasi interpolation methodology is implemented as an efficient FIR filter that can be applied online or as a preprocessing step. We present visual and numerical experiments that demonstrate the improved accuracy of reconstruction across lattices, using the quasi interpolation framework. PMID:22034300

Mirzargar, Mahsa; Entezari, Alireza

2011-12-01

158

Numerical Discretization-Based Estimation Methods for Ordinary Differential Equation Models via Penalized Spline Smoothing with Applications in Biomedical Research  

PubMed Central

Summary Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this paper, we propose a novel class of methods for estimating parameters in ordinary differential equation (ODE) models, which is motivated by HIV dynamics modeling. The new methods exploit the form of numerical discretization algorithms for an ODE solver to formulate estimating equations. First a penalized-spline approach is employed to estimate the state variables and the estimated state variables are then plugged in a discretization formula of an ODE solver to obtain the ODE parameter estimates via a regression approach. We consider three different order of discretization methods, Euler’s method, trapezoidal rule and Runge-Kutta method. A higher order numerical algorithm reduces numerical error in the approximation of the derivative, which produces a more accurate estimate, but its computational cost is higher. To balance the computational cost and estimation accuracy, we demonstrate, via simulation studies, that the trapezoidal discretization-based estimate is the best and is recommended for practical use. The asymptotic properties for the proposed numerical discretization-based estimators (DBE) are established. Comparisons between the proposed methods and existing methods show a clear benefit of the proposed methods in regards to the trade-off between computational cost and estimation accuracy. We apply the proposed methods to an HIV study to further illustrate the usefulness of the proposed approaches.

Wu, Hulin; Xue, Hongqi; Kumar, Arun

2012-01-01

159

Splines as linear combinations of B-splines. A Survey  

Microsoft Academic Search

This paper is intended to serve as a postscript to the fundamental 1966 paper by Curry and Schoenberg on B-splines. Itis also intended to promote the point of view that B-splines are truly basic splines: B-splines express the essentially local, butnot completely local, character of splines; certain facts about splines take on their most striking form when put into B-splineterms,

Carl de Boor

1986-01-01

160

An efficient, high-order probabilistic collocation method on sparse grids for three-dimensional flow and solute transport in randomly heterogeneous porous media  

SciTech Connect

In this study, a probabilistic collocation method (PCM) on sparse grids was used to solve stochastic equations describing flow and transport in three-dimensional in saturated, randomly heterogeneous porous media. Karhunen-Lo\\`{e}ve (KL) decomposition was used to represent the three-dimensional log hydraulic conductivity $Y=\\ln K_s$. The hydraulic head $h$ and average pore-velocity $\\bf v$ were obtained by solving the three-dimensional continuity equation coupled with Darcy's law with random hydraulic conductivity field. The concentration was computed by solving a three-dimensional stochastic advection-dispersion equation with stochastic average pore-velocity $\\bf v$ computed from Darcy's law. PCM is an extension of the generalized polynomial chaos (gPC) that couples gPC with probabilistic collocation. By using the sparse grid points, PCM can handle a random process with large number of random dimensions, with relatively lower computational cost, compared to full tensor products. Monte Carlo (MC) simulations have also been conducted to verify accuracy of the PCM. By comparing the MC and PCM results for mean and standard deviation of concentration, it is evident that the PCM approach is computational more efficient than Monte Carlo simulations. Unlike the conventional moment-equation approach, there is no limitation on the amplitude of random perturbation in PCM. Furthermore, PCM on sparse grids can efficiently simulate solute transport in randomly heterogeneous porous media with large variances.

Lin, Guang; Tartakovsky, Alexandre M.

2009-05-01

161

A Collocational Dictionary of Russian.  

ERIC Educational Resources Information Center

|Describes an adequate collocational dictionary for learners of Russian. Recommendations are made regarding what should and should not be included in a collocational dictionary, and a discussion looks at under which headwords collocations should be entered in the dictionary. (44 references) (GLR)|

Benson, Morton

1989-01-01

162

Coupling of the mesh-free finite cloud method with the boundary element method: a collocation approach  

Microsoft Academic Search

Meshless and mesh-based methods are among the tools frequently applied in the numerical treatment of partial differential equations (PDEs). This paper presents a coupling of the meshless finite cloud method (FCM) and the standard (mesh-based) boundary element method (BEM), which is motivated by the complementary properties of both methods. While the BEM is appropriate for solving linear PDEs with constant

Gang Li; Glaucio H. Paulino; N. R. Aluru

2003-01-01

163

Product integration methods based on discrete spline quasi-interpolants and application to weakly singular integral equations  

NASA Astrophysics Data System (ADS)

Quadrature formulae are established for product integration rules based on discrete spline quasi-interpolants on a bounded interval. The integrand considered may have algebraic or logarithmic singularities. These formulae are then applied to the numerical solution of integral equations with weakly singular kernels.

Allouch, C.; Sablonnière, P.; Sbibih, D.; Tahrichi, M.

2010-04-01

164

A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method  

Microsoft Academic Search

The Element free Galerkin method, which is based on the Moving Least Squares approximation, re- quires only nodal data and no element connectivity, and therefore is more flexible than the conventional finite el- ement method. Direct imposition of essential boundary conditions for the element free Galerkin (EFG) method is always difficult because the shape functions from the Moving Least Squares

T. Zhu; S. N. Atluri

2007-01-01

165

A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method  

Microsoft Academic Search

The Element free Galerkin method, which is based on the Moving Least Squares approximation, requires only nodal data and\\u000a no element connectivity, and therefore is more flexible than the conventional finite element method. Direct imposition of\\u000a essential boundary conditions for the element free Galerkin (EFG) method is always difficult because the shape functions from\\u000a the Moving Least Squares approximation do

T. Zhu; S. N. Atluri

1998-01-01

166

Fast and Stable Vector Spline Method for Fluid Apparent Motion Estimation  

Microsoft Academic Search

Apparent motion estimated on satellite data is used for ex- ample to compute the wind field in meteorology, and surface currents in oceanography. The satellite images display tur- bulent fluids with strong rotational patterns at different spa- tial and temporal scales. This specificity necessitates devis- ing adapted methods, allowing to control the divergence and curl of the retrieved motion field.

Till Isambert; Jean-paul Berroir; Isabelle Herlin

2007-01-01

167

Detection of defects on apple using B-spline lighting correction method  

NASA Astrophysics Data System (ADS)

To effectively extract defective areas in fruits, the uneven intensity distribution that was produced by the lighting system or by part of the vision system in the image must be corrected. A methodology was used to convert non-uniform intensity distribution on spherical objects into a uniform intensity distribution. A basically plane image with the defective area having a lower gray level than this plane was obtained by using proposed algorithms. Then, the defective areas can be easily extracted by a global threshold value. The experimental results with a 94.0% classification rate based on 100 apple images showed that the proposed algorithm was simple and effective. This proposed method can be applied to other spherical fruits.

Li, Jiangbo; Huang, Wenqian; Guo, Zhiming

168

Modeling elastic beams using dynamic splines  

Microsoft Academic Search

In this paper, the authors present the description and an application of the theory of dynamic splines for the modeling of\\u000a very flexible beams in multibody systems. The use of spline formalism reveals an alternative method for the description of\\u000a continuum flexibility by using discrete parameters. The proposed approach is discussed in general terms and a specific example\\u000a is presented

Pier Paolo Valentini; Ettore Pennestrì

2011-01-01

169

An Adaptive B-Spline Method for Low-order Image Reconstruction Problems - Final Report - 09/24/1997 - 09/24/2000  

SciTech Connect

A common problem in signal processing is to estimate the structure of an object from noisy measurements linearly related to the desired image. These problems are broadly known as inverse problems. A key feature which complicates the solution to such problems is their ill-posedness. That is, small perturbations in the data arising e.g. from noise can and do lead to severe, non-physical artifacts in the recovered image. The process of stabilizing these problems is known as regularization of which Tikhonov regularization is one of the most common. While this approach leads to a simple linear least squares problem to solve for generating the reconstruction, it has the unfortunate side effect of producing smooth images thereby obscuring important features such as edges. Therefore, over the past decade there has been much work in the development of edge-preserving regularizers. This technique leads to image estimates in which the important features are retained, but computationally the y require the solution of a nonlinear least squares problem, a daunting task in many practical multi-dimensional applications. In this thesis we explore low-order models for reducing the complexity of the re-construction process. Specifically, B-Splines are used to approximate the object. If a ''proper'' collection B-Splines are chosen that the object can be efficiently represented using a few basis functions, the dimensionality of the underlying problem will be significantly decreased. Consequently, an optimum distribution of splines needs to be determined. Here, an adaptive refining and pruning algorithm is developed to solve the problem. The refining part is based on curvature information, in which the intuition is that a relatively dense set of fine scale basis elements should cluster near regions of high curvature while a spares collection of basis vectors are required to adequately represent the object over spatially smooth areas. The pruning part is a greedy search algorithm to find and delete redundant knots based on the estimation of a weight associated with each basis vector. The overall algorithm iterates by inserting and deleting knots and end up with much fewer knots than pixels to represent the object, while the estimation error is within a certain tolerance. Thus, an efficient reconstruction can be obtained which significantly reduces the complexity of the problem. In this thesis, the adaptive B-Spline method is applied to a cross-well tomography problem. The problem comes from the application of finding underground pollution plumes. Cross-well tomography method is applied by placing arrays of electromagnetic transmitters and receivers along the boundaries of the interested region. By utilizing inverse scattering method, a linear inverse model is set up and furthermore the adaptive B-Spline method described above is applied. The simulation results show that the B-Spline method reduces the dimensional complexity by 90%, compared with that o f a pixel-based method, and decreases time complexity by 50% without significantly degrading the estimation.

Li, Xin; Miller, Eric L.; Rappaport, Carey; Silevich, Michael

2000-04-11

170

On unsymmetric collocation by radial basis functions  

Microsoft Academic Search

Solving partial differential equations by collocation with radial basis functions can be efficiently done by a technique first proposed by Kansa in 1990. It rewrites the problem as a generalized interpolation problem, and the solution is obtained by solving a (possibly large) linear system. The method has been used successfully in a variety of applications, but a proof of nonsingularity

Y. C. Hon; R. Schaback

2001-01-01

171

Survival Estimation Using Splines.  

National Technical Information Service (NTIS)

A nonparametric maximum likelihood procedure is given for estimating the survivor function from right-censored data. It approximates the hazard rate by a simple function such as a spline, with different approximations yielding different estimators. A spec...

A. S. Whittemore J. B. Keller

1986-01-01

172

SCMCRYS: Predicting Protein Crystallization Using an Ensemble Scoring Card Method with Estimating Propensity Scores of P-Collocated Amino Acid Pairs  

PubMed Central

Existing methods for predicting protein crystallization obtain high accuracy using various types of complemented features and complex ensemble classifiers, such as support vector machine (SVM) and Random Forest classifiers. It is desirable to develop a simple and easily interpretable prediction method with informative sequence features to provide insights into protein crystallization. This study proposes an ensemble method, SCMCRYS, to predict protein crystallization, for which each classifier is built by using a scoring card method (SCM) with estimating propensity scores of p-collocated amino acid (AA) pairs (p?=?0 for a dipeptide). The SCM classifier determines the crystallization of a sequence according to a weighted-sum score. The weights are the composition of the p-collocated AA pairs, and the propensity scores of these AA pairs are estimated using a statistic with optimization approach. SCMCRYS predicts the crystallization using a simple voting method from a number of SCM classifiers. The experimental results show that the single SCM classifier utilizing dipeptide composition with accuracy of 73.90% is comparable to the best previously-developed SVM-based classifier, SVM_POLY (74.6%), and our proposed SVM-based classifier utilizing the same dipeptide composition (77.55%). The SCMCRYS method with accuracy of 76.1% is comparable to the state-of-the-art ensemble methods PPCpred (76.8%) and RFCRYS (80.0%), which used the SVM and Random Forest classifiers, respectively. This study also investigates mutagenesis analysis based on SCM and the result reveals the hypothesis that the mutagenesis of surface residues Ala and Cys has large and small probabilities of enhancing protein crystallizability considering the estimated scores of crystallizability and solubility, melting point, molecular weight and conformational entropy of amino acids in a generalized condition. The propensity scores of amino acids and dipeptides for estimating the protein crystallizability can aid biologists in designing mutation of surface residues to enhance protein crystallizability. The source code of SCMCRYS is available at http://iclab.life.nctu.edu.tw/SCMCRYS/.

Charoenkwan, Phasit; Shoombuatong, Watshara; Lee, Hua-Chin; Chaijaruwanich, Jeerayut; Huang, Hui-Ling; Ho, Shinn-Ying

2013-01-01

173

An alternative local collocation strategy for high-convergence meshless PDE solutions, using radial basis functions  

NASA Astrophysics Data System (ADS)

This work proposes an alternative decomposition for local scalable meshless RBF collocation. The proposed method operates on a dataset of scattered nodes that are placed within the solution domain and on the solution boundary, forming a small RBF collocation system around each internal node. Unlike other meshless local RBF formulations that are based on a generalised finite difference (RBF-FD) principle, in the proposed "finite collocation" method the solution of the PDE is driven entirely by collocation of PDE governing and boundary operators within the local systems. A sparse global collocation system is obtained not by enforcing the PDE governing operator, but by assembling the value of the field variable in terms of the field value at neighbouring nodes. In analogy to full-domain RBF collocation systems, communication between stencils occurs only over the stencil periphery, allowing the PDE governing operator to be collocated in an uninterrupted manner within the stencil interior.

Stevens, D.; Power, H.; Meng, C. Y.; Howard, D.; Cliffe, K. A.

2013-12-01

174

Retrieving Collocations from Text: Xtract  

Microsoft Academic Search

Natural languages are full of collocations, recurrent combinations of words that co-occur more often than expected by chance and that correspond to arbitrary word usages. Recent work in lexicography indicates that collocations are pervasive in English; apparently, they are common in all types of writing, including both technical and nontechnical genres. Several approaches have been proposed to retrieve various types

Frank A. Smadja

1993-01-01

175

Solving Partial Differential Equations by Collocation with Radial Basis Functions  

Microsoft Academic Search

. Motivated by [5] we describe a method related to scatteredHermite interpolation for which the solution of elliptic partial differentialequations by collocation is well-posed. We compare the method of [5] withour method.x1. IntroductionIn this paper we discuss the numerical solution of elliptic partial differentialequations using a collocation approach based on radial basis functions. Tomake the discussion transparent we will focus

Gregory E. Fasshauer

1997-01-01

176

Numerical Dynamic Programming with Shape-Preserving Splines  

Microsoft Academic Search

Parametric approximations of the value function are a critical feature of the value function iteration method for solving dynamic programming problems with continuous states. Simple approximation methods such as polynomial or spline interpolation may cause value function iteration to diverge. We show that shape-preserving splines can avoid divergence problems while producing a smooth approximation to the value function. Dynamic programming

Kenneth L. Judd; Andrew Solnick

177

Spline Potential Eigenfunctions Model  

NSDL National Science Digital Library

The Spline Potential Eigenfunctions Model computes the Schrödinger equation energy eigenvalues and eigenfunctions for a particle confined to a potential well with hard walls at -a/2 and a/2 and a smooth potential energy function between these walls. The potential energy function is a third-order piecewise continuous polynomial (cubic spline) that connects N draggable control points. Cubic-spline coefficients are chosen such that the resulting potential energy function and its first derivative is smooth throughout the interior and has zero curvature at the endpoints. Users can vary the number of control points and can drag the control points to study level splitting in multi-well systems. Additional windows show a table of energy eigenvalues and their corresponding energy eigenfunctions. The Spline Potential Eigenfunctions Model was created using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_qm_SplinePotentialEigenfunctions.jar file will run the program if Java is installed.

Christian, Wolfgang

2012-01-09

178

Solving partial differential equations by collocation using radial basis functions  

Microsoft Academic Search

After a series of application papers have proven the approach to be numerically effective, this paper gives the first theoretical foundation for methods solving partial differential equations by collocation with (possibly radial) basis functions.

C. Franke; R. Schaback

1998-01-01

179

Cardinal t-Perfect Splines.  

National Technical Information Service (NTIS)

Cardinal t-perfect splines are introduced here as cardinal splines of degree m with leading term in (nu,nu + 1) equal to (t sup nu)(x sup m), all nu, as a connection between cardinal monosplines (t = 1) and cardinal perfect splines (t = -1). A cardinal t-...

A. Sharma J. Tzimbalario

1975-01-01

180

Discrete Simplex Splines and Subdivision.  

National Technical Information Service (NTIS)

A convenient way of approaching the problem of subdividing polynomial splines is to define the so-called discrete splines. This was successfully done in the univariate case and also in the multivariate case for polynomial splines on uniform grids, so call...

M. Neamtu

1990-01-01

181

Spline-Locking Payload Fastener.  

National Technical Information Service (NTIS)

The invention consists of a locking spline payload fastener comprised of a spring-loaded male spline nut located at the tip of a threaded male positioning member that is affixed to a body being fastened. A complimentary female type spline fitting adapted ...

J. M. Vranish

1991-01-01

182

Learning Collocations: Do the Number of Collocates, Position of the Node Word, and Synonymy Affect Learning?  

ERIC Educational Resources Information Center

This study investigated the effects of three factors (the number of collocates per node word, the position of the node word, synonymy) on learning collocations. Japanese students studying English as a foreign language learned five sets of 12 target collocations. Each collocation was presented in a single glossed sentence. The number of collocates

Webb, Stuart; Kagimoto, Eve

2011-01-01

183

Learning Collocations: Do the Number of Collocates, Position of the Node Word, and Synonymy Affect Learning?  

ERIC Educational Resources Information Center

|This study investigated the effects of three factors (the number of collocates per node word, the position of the node word, synonymy) on learning collocations. Japanese students studying English as a foreign language learned five sets of 12 target collocations. Each collocation was presented in a single glossed sentence. The number of collocates

Webb, Stuart; Kagimoto, Eve

2011-01-01

184

Teaching Collocations for Productive Vocabulary Development.  

ERIC Educational Resources Information Center

|One important but undervalued aspect of productive vocabulary is collocation--the ways in which words are combined with one another. To move from receptive to productive vocabulary, students need to learn a wide variety of ways that words collocate with each other. This paper describes the major types of collocations, typical collocational errors…

Wei, Yong

185

A preliminary harmonic spline model from Magsat data  

Microsoft Academic Search

A preliminary main field model for 1980 derived from a carefully selected subset of Magsat vector measurements, using the method of harmonic splines, is presented. This model (PHS \\/80\\/) for preliminary harmonic splines is the smoothest model (in the sense that the rms radial field at the core surface is minimum) consistent with the measurements (with an rms misfit of

L. Shure; R. L. Parker; R. A. Langel

1985-01-01

186

SURVIVAL ESTIMATION USING SPLINES  

EPA Science Inventory

A non parametric maximum likelihood procedure is given for estimating the survivor function from right-censored data. t approximates the hazard rate by a simple function such as a spline, with different approximations yielding different estimators. pecial case is that proposed by...

187

Smoothing spline primordial power spectrum reconstruction  

SciTech Connect

We reconstruct the shape of the primordial power spectrum (PPS) using a smoothing spline. Our adapted smoothing spline technique provides a complementary method to existing efforts to search for smooth features in the PPS, such as a running spectral index. With this technique we find no significant indication with Wilkinson Microwave Anisotropy Probe first-year data that the PPS deviates from a Harrison-Zeldovich spectrum and no evidence for loss of power on large scales. We also examine the effect on the cosmological parameters of the additional PPS freedom. Smooth variations in the PPS are not significantly degenerate with other cosmological parameters, but the spline reconstruction greatly increases the errors on the optical depth and baryon fraction.

Sealfon, Carolyn; Verde, Licia; Jimenez, Raul [Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (United States)

2005-11-15

188

Spline Approximation of Thin Shell Dynamics.  

National Technical Information Service (NTIS)

A spline-based method for approximating thin shell dynamics is presented here. While the method is developed in the context of the Donnell-Mushtari thin shell equations, it can be easily extended to the Byrne-Flugge-Lur'ye equations or other models for sh...

R. C. H. Delrosario R. C. Smith

1996-01-01

189

Deconvolution of Microfluorometric Histograms with B Splines  

Microsoft Academic Search

We consider the problem of estimating a probability density from observations from that density which are further contaminated by random errors. We propose a method of estimation using spline functions, discuss the numerical implementation of the method, and prove its consistency. The problem is motivated by the analysis of DNA content obtained by microfluorometry, and an example of such an

John Mendelsohn; John Rice

1982-01-01

190

Accuracy of a mitral valve segmentation method using J-splines for real-time 3D echocardiography data.  

PubMed

Patient-specific models of the heart's mitral valve (MV) exhibit potential for surgical planning. While advances in 3D echocardiography (3DE) have provided adequate resolution to extract MV leaflet geometry, no study has quantitatively assessed the accuracy of their modeled leaflets vs. a ground-truth standard for temporal frames beyond systolic closure or for differing valvular dysfunctions. The accuracy of a 3DE-based segmentation methodology based on J-splines was assessed for porcine MVs with known 4D leaflet coordinates within a pulsatile simulator during closure, peak closure, and opening for a control, prolapsed, and billowing MV model. For all time points, the mean distance error between the segmented models and ground-truth data were 0.40 ± 0.32 mm, 0.52 ± 0.51 mm, and 0.74 ± 0.69 mm for the control, flail, and billowing models. For all models and temporal frames, 95% of the distance errors were below 1.64 mm. When applied to a patient data set, segmentation was able to confirm a regurgitant orifice and post-operative improvements in coaptation. This study provides an experimental platform for assessing the accuracy of an MV segmentation methodology at phases beyond systolic closure and for differing MV dysfunctions. Results demonstrate the accuracy of a MV segmentation methodology for the development of future surgical planning tools. PMID:23460042

Siefert, Andrew W; Icenogle, David A; Rabbah, Jean-Pierre M; Saikrishnan, Neelakantan; Rossignac, Jarek; Lerakis, Stamatios; Yoganathan, Ajit P

2013-03-05

191

Examination of Absorbing Boundary Condition Using Perfectly Matched Layer for Collocated Orthogonal Grid in Method of Characteristics  

NASA Astrophysics Data System (ADS)

The time domain numerical analysis of sound wave propagation has been performed widely as a result of computer development. The method of characteristics (MOC) is used as a time domain numerical analysis method. In multidimensional MOC sound wave analysis, the so-called automatically absorbing boundary (without additional outer boundary treatment) does not have excellent absorbing performance. To overcome this problem, we introduce the perfectly matched layer (PML) technique into MOC simulation. Through this study, it is clarified that the PML (L = 16) reflection at a vertical incidence is approximately 22 dB lower than the automatically absorbing boundary (without PML) in the simulation by the QUICKEST method.

Adachi, Junpei; Okubo, Kan; Tagawa, Norio; Tsuchiya, Takao; Ishizuka, Takashi

2013-07-01

192

Animation of a B-Spline figure  

Microsoft Academic Search

Summary In this paper we describe how the use of B-Spline surfaces allows lissom movements of body and face. Our method is empirical, based on a parametrical animation. It can be combined with a muscles model for facial animation as we illustrated for the speech.

Monique Nahas; Hervé Huitric; Michel Saintourens

1988-01-01

193

Cartesian spline interpolation for industrial robots  

Microsoft Academic Search

We describe an algorithm for interpolation of positions by a rational spline motion. A reparameterization of the resulting motion is applied in order to achieve the desired distribution of the velocity. For the ease of presentation we discuss trapezoidal velocity profiles, i.e. piecewise constant and linear velocity distribution. The method can be generalized to more general velocity profiles. The whole

Thomas Horsch; Bert Jüttler

1998-01-01

194

WFSFIT. Wilson-Fowler Spline Fit Algorithm  

SciTech Connect

WFSFIT is a legacy algorithm introduced in the early 1960`s for passing a smooth curve through a planar set of design points. WFSFIT predates b-spline methods, but is still used in some numeric control systems, e.g. APT.

Fritsch, F [Lawrence Livermore National Lab, CA (United States)

1992-01-01

195

Spline screw payload fastening system  

NASA Astrophysics Data System (ADS)

A system for coupling an orbital replacement unit (ORU) to a space station structure via the actions of a robot and/or astronaut is described. This system provides mechanical and electrical connections both between the ORU and the space station structure and between the ORU and the ORU and the robot/astronaut hand tool. Alignment and timing features ensure safe, sure handling and precision coupling. This includes a first female type spline connector selectively located on the space station structure, a male type spline connector positioned on the orbital replacement unit so as to mate with and connect to the first female type spline connector, and a second female type spline connector located on the orbital replacement unit. A compliant drive rod interconnects the second female type spline connector and the male type spline connector. A robotic special end effector is used for mating with and driving the second female type spline connector. Also included are alignment tabs exteriorally located on the orbital replacement unit for berthing with the space station structure. The first and second female type spline connectors each include a threaded bolt member having a captured nut member located thereon which can translate up and down the bolt but are constrained from rotation thereabout, the nut member having a mounting surface with at least one first type electrical connector located on the mounting surface for translating with the nut member. At least one complementary second type electrical connector on the orbital replacement unit mates with at least one first type electrical connector on the mounting surface of the nut member. When the driver on the robotic end effector mates with the second female type spline connector and rotates, the male type spline connector and the first female type spline connector lock together, the driver and the second female type spline connector lock together, and the nut members translate up the threaded bolt members carrying the first type electrical connector up to the complementary second type connector for interconnection therewith.

Vranish, John M.

1992-09-01

196

Spline screw payload fastening system  

NASA Astrophysics Data System (ADS)

A system for coupling an orbital replacement unit (ORU) to a space station structure via the actions of a robot and/or astronaut is described. This system provides mechanical and electrical connections both between the ORU and the space station structure and between the ORU and the ORU and the robot/astronaut hand tool. Alignment and timing features ensure safe, sure handling and precision coupling. This includes a first female type spline connector selectively located on the space station structure, a male type spline connector positioned on the orbital replacement unit so as to mate with and connect to the first female type spline connector, and a second female type spline connector located on the orbital replacement unit. A compliant drive rod interconnects the second female type spline connector and the male type spline connector. A robotic special end effector is used for mating with and driving the second female type spline connector. Also included are alignment tabs exteriorally located on the orbital replacement unit for berthing with the space station structure. The first and second female type spline connectors each include a threaded bolt member having a captured nut member located thereon which can translate up and down the bolt but are constrained from rotation thereabout, the nut member having a mounting surface with at least one first type electrical connector located on the mounting surface for translating with the nut member. At least one complementary second type electrical connector on the orbital replacement unit mates with at least one first type electrical connector on the mounting surface of the nut member. When the driver on the robotic end effector mates with the second female type spline connector and rotates, the male type spline connector and the first female type spline connector lock together, the driver and the second female type spline connector lock together, and the nut members translate up the threaded bolt members carrying the first type electrical connector up to the complementary second type connector for interconnection therewith.

Vranish, John M.

1993-09-01

197

Bayesian B-spline mapping for dynamic quantitative traits.  

PubMed

Owing to their ability and flexibility to describe individual gene expression at different time points, random regression (RR) analyses have become a popular procedure for the genetic analysis of dynamic traits whose phenotypes are collected over time. Specifically, when modelling the dynamic patterns of gene expressions in the RR framework, B-splines have been proved successful as an alternative to orthogonal polynomials. In the so-called Bayesian B-spline quantitative trait locus (QTL) mapping, B-splines are used to characterize the patterns of QTL effects and individual-specific time-dependent environmental errors over time, and the Bayesian shrinkage estimation method is employed to estimate model parameters. Extensive simulations demonstrate that (1) in terms of statistical power, Bayesian B-spline mapping outperforms the interval mapping based on the maximum likelihood; (2) for the simulated dataset with complicated growth curve simulated by B-splines, Legendre polynomial-based Bayesian mapping is not capable of identifying the designed QTLs accurately, even when higher-order Legendre polynomials are considered and (3) for the simulated dataset using Legendre polynomials, the Bayesian B-spline mapping can find the same QTLs as those identified by Legendre polynomial analysis. All simulation results support the necessity and flexibility of B-spline in Bayesian mapping of dynamic traits. The proposed method is also applied to a real dataset, where QTLs controlling the growth trajectory of stem diameters in Populus are located. PMID:22624568

Xing, Jun; Li, Jiahan; Yang, Runqing; Zhou, Xiaojing; Xu, Shizhong

2012-04-01

198

Isotonic, Convex and Related Splines  

Microsoft Academic Search

In this paper, we consider the estimation of isotonic, convex or related functions by means of splines. It is shown that certain classes of isotone or convex functions can be represented as a positive cone embedded in a Hilbert space. Using this representation, we give an existence and characterization theorem for isotonic or convex splines. Two special cases are examined

Ian W. Wright; Edward J. Wegman

1980-01-01

199

Approximation by Discrete GB-Splines  

NASA Astrophysics Data System (ADS)

This paper addresses the definition and the study of discrete generalized splines. Discrete generalized splines are continuous piecewise defined functions which meet some smoothness conditions for the first and second divided differences at the knots. They provide a generalization both of smooth generalized splines and of the classical discrete cubic splines. Completely general configurations for steps in divided differences are considered. Direct algorithms are proposed for constructing discrete generalized splines and discrete generalized B-splines (discrete GB-splines for short). Explicit formulae and recurrence relations are obtained for discrete GB-splines. Properties of discrete GB-splines and their series are studied. It is shown that discrete GB-splines form weak Chebyshev systems and that series of discrete GB-splines have a variation diminishing property.

Kvasov, Boris I.

2001-06-01

200

Ray Tracing Free-Form B-Spline Surfaces  

Microsoft Academic Search

We present a method for using ray tracing to render spline surfaces¿one that is suitable for any object generated from control vertices via tensor-product B-splines. The method derives from kajiya's work on ray tracing procedurally defined surfaces1 and makes use of two preprocessing steps. One involves the controlvertex refinement recurrences due to Riesenfeld et. al.2, and the second generates a

M. A. J. Sweeney; R. H. Bartels

1986-01-01

201

Frequency Tracking with Spline Based Chirp Atoms  

Microsoft Academic Search

\\u000a The tracking of prominent oscillations with time-varying frequencies is a common task in many signal processing applications.\\u000a Therefore, efficient methods are needed to meet precision and run-time requirements. We propose two methods that extract the\\u000a energy of the time frequency plane along a cubic spline trajectory. To raise efficiency, a sparse sampling method with dynamically\\u000a shaped atoms is developed for

Matthias Wacker; Miroslaw Galicki; Herbert Witte

2010-01-01

202

Mr. Stockdale's Dictionary of Collocations.  

ERIC Educational Resources Information Center

|This dictionary of collocations was compiled by an English-as-a-Second-Language (ESL) teacher in Saudi Arabia who teaches adult, native speakers of Arabic. The dictionary is practical in teaching English because it helps to focus on everyday events and situations. The dictionary works as follows: the teacher looks up a word, such as "talk"; next…

Stockdale, Joseph Gagen, III

203

Interlanguage Development and Collocational Clash  

ERIC Educational Resources Information Center

Background: Persian English learners committed mistakes and errors which were due to insufficient knowledge of different senses of the words and collocational structures they formed. Purpose: The study reported here was conducted for a thesis submitted in partial fulfillment of the requirements for The Master of Arts degree, School of Graduate…

Shahheidaripour, Gholamabbass

2000-01-01

204

Which Models for Collocated Cokriging?  

Microsoft Academic Search

When a target variable is sparsely sampled, compared to a densely sampled auxiliary variable, cokriging requires simplifications. In its strict sense, collocated cokriging makes use of the auxiliary variable only at the current point where the target variable is to be estimated; in the multicollocated form, it also makes use of the auxiliary variable at all points where the target

Jacques Rivoirard

2001-01-01

205

5-axis polynomial spline interpolation in an open CNC system  

Microsoft Academic Search

Using the advantage of polynomial spline interpolation to represent spatial curves with good approximation effect and mature technology, an instruction format with polynomial spline curves, which is suitability for five axes coordinated real-time interpolation, is presented against the current five axes coordinated linear interpolation method with drawbacks of low-speed, low-accuracy and great NC files in sculptured surface machining. Structure of

Yuan Liu; Yong-zhang Wang; Zhen-yu Han

2008-01-01

206

Using parametric {ital B} splines to fit specular reflectivities  

SciTech Connect

Parametric {ital B}-spline curves offer a flexible and appropriate mathematical description of scattering length density profiles in specular reflectivity analysis. Profiles combining smooth and sharp features can be defined in low dimensional representations using control points in the density-depth plane which provide graded local influence on profile shape. These profiles exist in vector spaces defined by {ital B}-spline order and parameter knot set, which can be systematically densified during analysis. Such profiles can easily be rendered as adaptive histograms for reflectivity computation. {ital B}-spline order can be chosen to accommodate the asymptotic (large-{ital Q}) behavior indicated by reflectivity data. We describe an interactive fitting strategy in which the Nelder and Mead simplex method is used in the {ital B}-spline control point space to guide the discovery of profiles that can produce given reflectivity data. Examples using actual and simulated spectra are discussed.

Berk, N.F.; Majkrzak, C.F. [Materials Science and Engineering Laboratory, National Insitute of Standards and Technology, Gaithersburg, Maryland 20899-0001 (United States)

1995-05-01

207

Quadratic spline subroutine package  

USGS Publications Warehouse

A continuous piecewise quadratic function with continuous first derivative is devised for approximating a single-valued, but unknown, function represented by a set of discrete points. The quadratic is proposed as a treatment intermediate between using the angular (but reliable, easily constructed and manipulated) piecewise linear function and using the smoother (but occasionally erratic) cubic spline. Neither iteration nor the solution of a system of simultaneous equations is necessary to determining the coefficients. Several properties of the quadratic function are given. A set of five short FORTRAN subroutines is provided for generating the coefficients (QSC), finding function value and derivatives (QSY), integrating (QSI), finding extrema (QSE), and computing arc length and the curvature-squared integral (QSK). (USGS)

Rasmussen, L. A.

1982-01-01

208

Hyperbolic spline interpolation algorithms  

NASA Astrophysics Data System (ADS)

Isogeometric interpolation by hyperbolic splines is formulated as a differential multipoint boundary value problem. A discretization of this problem results in the necessity of solving a linear system with a five-diagonal matrix. This system can be ill-conditioned if the data are nonuniformly distributed. It is shown that this system can be split into tridiagonal systems with the property of diagonal dominance. The latter do not require that hyperbolic functions be evaluated. Their solution is numerically stable and can be efficiently parallelized on the basis of the superposition principle. For quasiuniform grids, these systems have positive definite matrices. Algorithms for parallelizing calculations in the case of tri- and five-diagonal systems are given.

Kvasov, B. I.

2011-05-01

209

Automatic clustering of collocation for detecting practical sense boundary  

Microsoft Academic Search

This paper talks about the deciding practical sense boundary of homonymous words. The important problem in dictionaries or thesauri is the confusion of the sense boundary by each resource. This also becomes a bottleneck in the practical language processing systems. This paper proposes the method about discovering sense boundary using the collocation from the large corpora and the clustering methods.

Saim Shin; Key-Sun Choi

210

Locating CVBEM collocation points for steady state heat transfer problems  

NASA Astrophysics Data System (ADS)

The Complex Variable Boundary Element Method or CVBEM provides a highly accurate means of developing numerical solutions to steady state two-dimensional heat transfer problems. The numerical approach exactly solves the Laplace equation and satisfies the boundary conditions at specified points on the boundary by means of collocation. The accuracy of the approximation depends upon the nodal point distribution specified by the numerical analyst. In order to develop subsequent, refined approximation functions, four techniques for selecting additional collocation points are presented. The techniques are compared as to the governing theory, representation of the error of approximation on the problem boundary, the computational costs, and the ease of use by the numerical analyst.

Hromadka, T. V., II

1985-06-01

211

Collocation analysis for UMLS knowledge-based word sense disambiguation  

PubMed Central

Background The effectiveness of knowledge-based word sense disambiguation (WSD) approaches depends in part on the information available in the reference knowledge resource. Off the shelf, these resources are not optimized for WSD and might lack terms to model the context properly. In addition, they might include noisy terms which contribute to false positives in the disambiguation results. Methods We analyzed some collocation types which could improve the performance of knowledge-based disambiguation methods. Collocations are obtained by extracting candidate collocations from MEDLINE and then assigning them to one of the senses of an ambiguous word. We performed this assignment either using semantic group profiles or a knowledge-based disambiguation method. In addition to collocations, we used second-order features from a previously implemented approach. Specifically, we measured the effect of these collocations in two knowledge-based WSD methods. The first method, AEC, uses the knowledge from the UMLS to collect examples from MEDLINE which are used to train a Naïve Bayes approach. The second method, MRD, builds a profile for each candidate sense based on the UMLS and compares the profile to the context of the ambiguous word. We have used two WSD test sets which contain disambiguation cases which are mapped to UMLS concepts. The first one, the NLM WSD set, was developed manually by several domain experts and contains words with high frequency occurrence in MEDLINE. The second one, the MSH WSD set, was developed automatically using the MeSH indexing in MEDLINE. It contains a larger set of words and covers a larger number of UMLS semantic types. Results The results indicate an improvement after the use of collocations, although the approaches have different performance depending on the data set. In the NLM WSD set, the improvement is larger for the MRD disambiguation method using second-order features. Assignment of collocations to a candidate sense based on UMLS semantic group profiles is more effective in the AEC method. In the MSH WSD set, the increment in performance is modest for all the methods. Collocations combined with the MRD disambiguation method have the best performance. The MRD disambiguation method and second-order features provide an insignificant change in performance. The AEC disambiguation method gives a modest improvement in performance. Assignment of collocations to a candidate sense based on knowledge-based methods has better performance. Conclusions Collocations improve the performance of knowledge-based disambiguation methods, although results vary depending on the test set and method used. Generally, the AEC method is sensitive to query drift. Using AEC, just a few selected terms provide a large improvement in disambiguation performance. The MRD method handles noisy terms better but requires a larger set of terms to improve performance.

2011-01-01

212

Parametres de delimitation des collocations du francais courant (Parameters for Delimiting Collocations in Contemporary French).  

ERIC Educational Resources Information Center

|Discusses the definition of collocation, demonstrates that associative word combinations do form a continuum, and proposes some parameters to help delimit the scope of collocations in everyday contemporary French. (Author/VWL)|

Bosse-Andrieu, J.; Mareschal, G.

1998-01-01

213

Fuzzy B-spline membership function (BMF) and its applications in fuzzy-neural control  

Microsoft Academic Search

A general methodology for constructing fuzzy membership functions via B-spline curves is proposed. By using the method of least-squares, the authors translate the empirical data into the form of the control points of B-spline curves to construct fuzzy membership functions. This unified form of fuzzy membership functions is called a B-spline membership function (BMF). By using the local control property

Chi-Hsu Wang; Wei-Yen Wang; Tsu-Tian Lee; Pao-Shun Tseng

1995-01-01

214

GEE-Smoothing Spline in Semiparametric Model with Correlated Nominal Data  

NASA Astrophysics Data System (ADS)

In this paper we propose GEE-Smoothing spline in the estimation of semiparametric models with correlated nominal data. The method can be seen as an extension of parametric generalized estimating equation to semiparametric models. The nonparametric component is estimated using smoothing spline specifically the natural cubic spline. We use profile algorithm in the estimation of both parametric and nonparametric components. The properties of the estimators are evaluated using simulation studies.

Ibrahim, Noor Akma; Suliadi, Suliadi

2010-11-01

215

Three-dimensional myocardial strain reconstruction from tagged MRI using a cylindrical B-spline model  

Microsoft Academic Search

Abstract, In this paper, we present a new method for recon-structing three-dimensional (3-D) left ventricular myocardial strain from tagged magnetic resonance (MR) image data with a 3-D B-spline deformation model. The B-spline model is based on a cylindrical coordinate system that more closely fits the mor-phology of the myocardium than previously proposed Cartesian B-spline models and does not require explicit

Xiang Deng

2004-01-01

216

3D myocardial strain strain reconstruction from tagged MRI using a cylindrical B-spline model  

Microsoft Academic Search

In this paper, we present a new method for reconstructing 3D left ventricular myocardial strain from tagged magnetic resonance (MR) image data with a 3D B-spline deformation model. The B-spline model is based on a cylindrical coordinate system that more closely fits the morphology of the myocardium than previously proposed Cartesian B-spline models and does not require explicit regularization. Simulation

Xiang Deng; Thomas S. Denney Jr.

2002-01-01

217

Efficient volume rendering on the body centered cubic lattice using box splines  

Microsoft Academic Search

We demonstrate that non-separable box splines deployed on body centered cubic lattices (BCC) are suitable for fast evaluation on present graphics hardware. Therefore, we develop the linear and quintic box splines using a piecewise polynomial (pp)-form as opposed to their currently known basis (B)-form. The pp-form lends itself to efficient evaluation methods such as de Boor's algorithm for splines in

Bernhard Finkbeiner; Alireza Entezari; Dimitri Van De Ville; Torsten Möller

2010-01-01

218

Image reconstruction of impenetrable cylinders using cubic B-splines and genetic algorithms  

Microsoft Academic Search

We discuss a new method for the shape reconstruction of perfectly conducting cylinders from measured data based on cubic uniform B-splines and genetic algorithms. The perimeter of the cylinder is modeled by cubic B-splines. A B-spline is defined by an ordered set of control points which determine the shape of the corresponding curve. With an appropriate choice of control points,

K. Barkeshli; M. Mokhtari; N. Mahdavi Amiri

2001-01-01

219

Investigating ESL Learners' Lexical Collocations: The Acquisition of Verb + Noun Collocations by Japanese Learners of English  

ERIC Educational Resources Information Center

|Although it is widely acknowledged that collocations play an important part in second language learning, especially at intermediate-advanced levels, learners' difficulties with collocations have not been investigated in much detail so far. The present study examines ESL learners' use of verb-noun collocations, such as "take notes," "place an…

Miyakoshi, Tomoko

2009-01-01

220

Investigation of Grease-Lubricated Expendable Spline Connections.  

National Technical Information Service (NTIS)

The objective of this program was to evaluate the feasibility of three basic arrangements of expendable spline connections, namely, the 'standard,' the 'dogbone,' and the 'muff' splines. Spline wear tests were performed with three SwRI spline wear testers...

M. L. Valtierra

1976-01-01

221

Maternal MCG interference cancellation using splined independent component subtraction.  

PubMed

Signal distortion is commonly observed when using independent component analysis (ICA) to remove maternal cardiac interference from the fetal magnetocardiogram. This can be seen even in the most conservative case where only the independent components dominated by maternal interference are subtracted from the raw signal, a procedure we refer to as independent component subtraction (ICS). Distortion occurs when the subspaces of the fetal and maternal signals have appreciable overlap. To overcome this problem, we employed splining to remove the fetal signal from the maternal source component. The maternal source components were downsampled and then interpolated to their original sampling rate using a cubic spline. A key aspect of the splining procedure is that the maternal QRS complexes are downsampled much less than the rest of the maternal signal so that they are not distorted, despite their higher bandwidth. The splined maternal source components were projected back onto the magnetic field measurement space and then subtracted from the raw signal. The method was evaluated using data from 24 subjects. We compared the results of conventional, i.e., unsplined, ICS with our method, splined ICS, using matched filtering as a reference. Correlation and subjective assessment of the P-wave and QRS complex were used to assess the performance. Using ICS, we found that the P-wave was adversely affected in 7 of 24 (29%) subjects, all having correlations less than 0.8. Splined ICS showed negligible distortion and improved the signal fidelity to some extent in all subjects. We also demonstrated that maternal T-wave interference could be problematic when the fetal and maternal heartbeats were synchronous. In these instances, splined ICS was more effective than matched filtering. PMID:21712157

Yu, Suhong; Wakai, Ronald T

2011-06-27

222

Properties of the Wilson-Fowler Spline.  

National Technical Information Service (NTIS)

The Wilson-Fowler spline, a piecewise cubic curve with continuous tangent and curvature, is described. The spline is used in the APT numerical machining program and several CAD-CAM systems. This report gives information on existence, uniqueness, invarianc...

J. D. Emery

1982-01-01

223

Supporting collocation learning with a digital library  

Microsoft Academic Search

Extensive knowledge of collocations is a key factor that distinguishes learners from fluent native speakers. Such knowledge is difficult to acquire simply because there is so much of it. This paper describes a system that exploits the facilities offered by digital libraries to provide a rich collocation-learning environment. The design is based on three processes that have been identified as

Shaoqun Wu; Margaret Franken; Ian H. Witten

2010-01-01

224

Collocation and Technicality in EAP Engineering  

ERIC Educational Resources Information Center

|This article explores how collocation relates to lexical technicality, and how the relationship can be exploited for teaching EAP to second-year engineering students. First, corpus data are presented to show that complex noun phrase formation is a ubiquitous feature of engineering text, and that these phrases (or collocations) are highly…

Ward, Jeremy

2007-01-01

225

Supporting Collocation Learning with a Digital Library  

ERIC Educational Resources Information Center

|Extensive knowledge of collocations is a key factor that distinguishes learners from fluent native speakers. Such knowledge is difficult to acquire simply because there is so much of it. This paper describes a system that exploits the facilities offered by digital libraries to provide a rich collocation-learning environment. The design is based…

Wu, Shaoqun; Franken, Margaret; Witten, Ian H.

2010-01-01

226

Rapid Software Development through Team Collocation  

Microsoft Academic Search

In a field study conducted at a leading Fortune 100 company, we examined how having development teams reside in their own large room (an arrangement called radical collocation) affected system development. The collocated projects had significantly higher productivity and shorter schedules than both the industry benchmarks and the performance of past similar projects within the firm. The teams reported high

Stephanie D. Teasley; Lisa A. Covi; Mayuram S. Krishnan; Judith S. Olson

2002-01-01

227

Wavefront reconstruction in adaptive optics systems using nonlinear multivariate splines.  

PubMed

This paper presents a new method for zonal wavefront reconstruction (WFR) with application to adaptive optics systems. This new method, indicated as Spline based ABerration REconstruction (SABRE), uses bivariate simplex B-spline basis functions to reconstruct the wavefront using local wavefront slope measurements. The SABRE enables WFR on nonrectangular and partly obscured sensor grids and is not subject to the waffle mode. The performance of SABRE is compared to that of the finite difference (FD) method in numerical experiments using data from a simulated Shack-Hartmann lenslet array. The results show that SABRE offers superior reconstruction accuracy and noise rejection capabilities compared to the FD method. PMID:23456004

de Visser, Cornelis C; Verhaegen, Michel

2013-01-01

228

A box spline calculus for computed tomography  

Microsoft Academic Search

B-splines are attractive basis functions for the continuous- domain representation of biomedical images and volumes. In this paper, we prove that the extended family of box splines are closed under the Radon transform and derive explicit for- mulae for their transforms. Our results are general; they cover all known brands of compactly-supported box splines (tensor- product B-splines, separable or not)

Alireza Entezari; Michael Unser

2010-01-01

229

History of the Wilson-Fowler spline  

SciTech Connect

The Wilson-Fowler spline (abbreviated WF-spline) was introduced in the early 1960's as a means for drawing a smooth curve through a planar set of data. It has been used as the spline entity in the APT system's TABCYL since its inception. The history of the WF-spline is briefly described and a chronologically arranged annotated bibliography of all known references to it are featured. 6 refs.

Fritsch, F.N.

1986-04-01

230

History of the Wilson-Fowler Spline.  

National Technical Information Service (NTIS)

The Wilson-Fowler spline (abbreviated WF-spline) was introduced in the early 1960's as a means for drawing a smooth curve through a planar set of data. It has been used as the spline entity in the APT system's TABCYL since its inception. The history of th...

F. N. Fritsch

1986-01-01

231

Tesseral Harmonic Coefficients and Station Coordinates from Satellite Observations by Collocation.  

National Technical Information Service (NTIS)

The usual formulation of the least squares collocation method requires the inversion of matrices with dimensions equal to the number of observations. Such a procedure poses difficult numerical problems when large numbers of observations are involved. It i...

K. P. Schwarz

1974-01-01

232

Robust Tensor Splines for Approximation of Diffusion Tensor MRI Data.  

PubMed

In this paper, we present a novel and robust spline approximation algorithm given a noisy symmetric positive definite (SPD) tensor field. Such tensor fields commonly arise in the field of Medical Imaging in the form of Diffusion Tensor (DT) MRI data sets. We develop a statistically robust algorithm for constructing a tensor product of B-splines - for approximating and interpolating these data - using the Riemannian metric of the manifold of SPD tensors. Our method involves a two step procedure wherein the first step uses Riemannian distances in order to evaluate a tensor spline by computing a weighted intrinsic average of diffusion tensors and the second step involves minimization of the Riemannian distance between the evaluated spline curve and the given data. These two steps are alternated to achieve the desired tensor spline approximation to the given tensor field. We present comparisons of our algorithm with four existing methods of tensor interpolation applied to DT-MRI data from fixed heart slices of a rabbit, and show significantly improved results in the presence of noise and outliers. We also present validation results for our algorithm using synthetically generated noisy tensor field data with outliers. This interpolation work has many applications e.g., in DT-MRI registration, in DT-MRI Atlas construction etc. This research was in part funded by the NIH ROI NS42075 and the Department of Radiology, University of Florida. PMID:20454465

Barmpoutis, Angelos; Vemuri, Baba C; Forder, John R

2006-06-17

233

Euler's Contribution to Cardinal Spline Interpolation: The Exponential Euler Splines.  

National Technical Information Service (NTIS)

This paper is the author's contribution to the volume Leonardt Euler-Gedenkband 1983 to be published in Basel, Switzerland, in 1983 in honor of Euler's bicentenial. It is mainly devoted to the exponential Euler spline Sn(x ;t) of degree n to the base t, a...

I. J. Schoenberg

1982-01-01

234

Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities  

ERIC Educational Resources Information Center

|The purpose of this paper is to introduce a new method for fitting item response theory models with the latent population distribution estimated from the data using splines. A spline-based density estimation system provides a flexible alternative to existing procedures that use a normal distribution, or a different functional form, for the…

Woods, Carol M.; Thissen, David

2006-01-01

235

Simulation of switched reluctance motor drives using two-dimensional bicubic spline  

Microsoft Academic Search

In this paper, a novel simulation algorithm of switched reluctance motor drives is presented. With the proposed algorithm the two-dimensional (2-D) bicubic spline interpolation is used to describe the nonlinear magnetic characteristics in switched reluctance motors. The corresponding computational method of 2-D bicubic spline function is described in detail. The simulation results are also compared with and validated by experimental

Xiang-Dang Xue; K. W. E. Cheng; S. L. Ho

2002-01-01

236

Discrete polynomial splines: Applications in computer graphics and digital signal processing  

SciTech Connect

The author provides a theoretical framework for the development of extremely efficient algorithms and hardware for the computation of discrete polynomial spline functions. Computer graphics and digital signal processing fields are investigated for the potential use of discrete splines. The new method is proposed to compute parametric discrete spline curves and surfaces, which decreases computational complexity by orders of magnitude. The method is based on the fact that the k{sup th} order difference of a one-sided factorial function of degree (k-1) is a Kronecker delta function and that successive summations of the delta function can be used to obtain the factorial functions. A discrete polynomial spline is obtained from {kappa} successive summations of its {kappa}{sup th} order difference which is a spare set of delta functions. A recurrence relation is introduced which computes the {kappa}{sup th} order difference of a {kappa}{sup th} order discrete spline. It is shown that this computation approach also provides a very efficient representation for parametric discrete spline curves and surfaces. An equation is derived for the Z transform of discrete splines for the general case of nonuniform knots. Two filter structures are provided for computation and analysis of discrete splines; one for the one-sided factorial function representation and one for the B-spline representation. The filter structures supply the input-output relations which can be used to analyze the effects of different patterns of knot nonuniformities given the coefficients, or vice versa. Then, filters with discrete spline unit-sample responses are analyzed. It is shown that a discrete spline filter can be implemented in two stages: the first stage is an MA filter with as many nodes as there are knots, and the second stage is an AR filter which performs successive summations.

Uestuener, K.F.

1989-01-01

237

Beamforming with collocated microphone arrays  

NASA Astrophysics Data System (ADS)

A collocated microphone array, including three gradient microphones with different orientations and one omnidirectional microphone, was used to acquire data in a sound-treated room and in an outdoor environment. This arrangement of gradient microphones represents an acoustic vector sensor used in air. Beamforming techniques traditionally associated with much larger uniformly spaced arrays of omnidirectional sensors are extended to this compact array (1 cm3) with encouraging results. A frequency-domain minimum-variance beamformer was developed to work with this array. After a calibration of the array, the recovery of sources from any direction is achieved with high fidelity, even in the presence of multiple interferers. SNR gains of 5-12 dB with up to four speech sources were obtained with both indoor and outdoor recordings. This algorithm has been developed for new MEMS-type microphones that further reduce the size of the sensor array.

Lockwood, Michael E.; Jones, Douglas L.; Su, Quang; Miles, Ronald N.

2003-10-01

238

Analysis of Pairwise Preference Data Using Integrated B-SPLINES.  

ERIC Educational Resources Information Center

A general method of scaling pairwise preference data is presented that may be used without prior knowledge about the nature of the relationship between an observation and the process giving rise to it. The method involves a monotone transformation and is similar to the B-SPLINE approach. (Author/JKS)

Winsberg, Suzanne; Ramsay, James O.

1981-01-01

239

B-LUT: Fast and low memory B-spline image interpolation.  

PubMed

We propose a fast alternative to B-splines in image processing based on an approximate calculation using precomputed B-spline weights. During B-spline indirect transformation, these weights are efficiently retrieved in a nearest-neighbor fashion from a look-up table, greatly reducing overall computation time. Depending on the application, calculating a B-spline using a look-up table, called B-LUT, will result in an exact or approximate B-spline calculation. In case of the latter the obtained accuracy can be controlled by the user. The method is applicable to a wide range of B-spline applications and has very low memory requirements compared to other proposed accelerations. The performance of the proposed B-LUTs was compared to conventional B-splines as implemented in the popular ITK toolkit for the general case of image intensity interpolation. Experiments illustrated that highly accurate B-spline approximation can be obtained all while computation time is reduced with a factor of 5-6. The B-LUT source code, compatible with the ITK toolkit, has been made freely available to the community. PMID:20034697

Sarrut, David; Vandemeulebroucke, Jef

2010-01-19

240

Extensions of the Zwart-Powell box spline for volumetric data reconstruction on the cartesian lattice.  

PubMed

In this article we propose a box spline and its variants for reconstructing volumetric data sampled on the Cartesian lattice. In particular we present a tri-variate box spline reconstruction kernel that is superior to tensor product reconstruction schemes in terms of recovering the proper Cartesian spectrum of the underlying function. This box spline produces a C2 reconstruction that can be considered as a three dimensional extension of the well known Zwart-Powell element in 2D. While its smoothness and approximation power are equivalent to those of the tri-cubic B-spline, we illustrate the superiority of this reconstruction on functions sampled on the Cartesian lattice and contrast it to tensor product B-splines. Our construction is validated through a Fourier domain analysis of the reconstruction behavior of this box spline. Moreover, we present a stable method for evaluation of this box spline by means of a decomposition. Through a convolution, this decomposition reduces the problem to evaluation of a four directional box spline that we previously published in its explicit closed form. PMID:17080870

Entezari, Alireza; Möller, Torsten

241

Converting an unstructured quadrilateral/hexahedral mesh to a rational T-spline  

NASA Astrophysics Data System (ADS)

This paper presents a novel method for converting any unstructured quadrilateral or hexahedral mesh to a generalized T-spline surface or solid T-spline, based on the rational T-spline basis functions. Our conversion algorithm consists of two stages: the topology stage and the geometry stage. In the topology stage, the input quadrilateral or hexahedral mesh is taken as the initial T-mesh. To construct a gap-free T-spline, templates are designed for each type of node and applied to elements in the input mesh. In the geometry stage, an efficient surface fitting technique is developed to improve the surface accuracy with sharp feature preservation. The constructed T-spline surface and solid T-spline interpolate every boundary node in the input mesh, with C 2-continuity everywhere except the local region around irregular nodes. Finally, a Bézier extraction technique is developed and linear independence of the constructed T-splines is studied to facilitate T-spline based isogeometric analysis.

Wang, Wenyan; Zhang, Yongjie; Xu, Guoliang; Hughes, Thomas J. R.

2012-07-01

242

Derivative unfolding by spline techniques  

NASA Astrophysics Data System (ADS)

This paper presents some possible improvements to the derivative unfolding scheme employed in processing recoil proton data to obtain the neutron spectra. The scheme is based on representing the recoil proton spectrum by means of equally spaced cubic bell-splines. The finite spread in the detector response to monoenergetic protons is accounted for by folding the splines suitably. A code based on this formulation has been tested with trial spectra pertaining to standard neutron sources such as Pu-Be and has performed better in terms of resolution and of accuracy of the predicted peak positions. The current formulation is flexible for adding constraints using a priori information. This is demonstrated with respect to the suppression of spurious oscillations occurring near the high energy end of the spectra. This scheme is restricted to continuous spectra, however.

Subbaiah, K. V.; Natarajan, A.

1985-01-01

243

Construction of hyperbolic interpolation splines  

NASA Astrophysics Data System (ADS)

The problem of constructing a hyperbolic interpolation spline can be formulated as a differential multipoint boundary value problem. Its discretization yields a linear system with a five-diagonal matrix, which may be ill-conditioned for unequally spaced data. It is shown that this system can be split into diagonally dominant tridiagonal systems, which are solved without computing hyperbolic functions and admit effective parallelization.

Kvasov, B. I.

2008-04-01

244

Multivariate Interpolation of Precipitation Using Regularized Spline with Tension  

Microsoft Academic Search

Abstract Regularized Spline with Tension (RST) is an accurate, flexible and efficient method for multivariate interpolation of scattered data. This study evaluates its capabilities to interpolate daily and annual mean,precipitation in regions with complex,terrain. Tension, smoothing and anisotropy parameters are optimized using the crossvalidation technique. In addition, smoothing and rescaling of the third variable (elevation) is used to minimize the

Jaroslav Hofierka; Juraj Parajka; Helena Mitásová; Lubos Mitas

2002-01-01

245

Multifractional splines: from seismic singularities to geological transitions  

Microsoft Academic Search

A matching pursuit technique in conjunction with an imaging method is used to obtain quantitative information on geological records from seismic data. The technique is based on a greedy, non-linear search algorithm decomposing data into atoms. These atoms are drawn from a redundant dictionary of seismic waveforms. Fractional splines are used to define this dictionary, whose elements are not only

Felix Herrmann

246

Least-Squares Fitting of Algebraic Spline Surfaces  

Microsoft Academic Search

We present an algorithm for fitting implicitly defined algebraic spline surfaces to given scattered data. By simultaneously approximating points and associated normal vectors, we obtain a method which is computationally simple, as the result is obtained by solving a system of linear equations. In addition, the result is geometrically invariant, as no artificial normalization is introduced. The potential applications of

Bert Jüttler; Alf Felis

2002-01-01

247

Spline screw multiple rotations mechanism  

NASA Astrophysics Data System (ADS)

A system for coupling two bodies together and for transmitting torque from one body to another with mechanical timing and sequencing is reported. The mechanical timing and sequencing is handled so that the following criteria are met: (1) the bodies are handled in a safe manner and nothing floats loose in space, (2) electrical connectors are engaged as long as possible so that the internal processes can be monitored throughout by sensors, and (3) electrical and mechanical power and signals are coupled. The first body has a splined driver for providing the input torque. The second body has a threaded drive member capable of rotation and limited translation. The embedded drive member will mate with and fasten to the splined driver. The second body has an embedded bevel gear member capable of rotation and limited translation. This bevel gear member is coaxial with the threaded drive member. A compression spring provides a preload on the rotating threaded member, and a thrust bearing is used for limiting the translation of the bevel gear member so that when the bevel gear member reaches the upward limit of its translation the two bodies are fully coupled and the bevel gear member then rotates due to the input torque transmitted from the splined driver through the threaded drive member to the bevel gear member. An output bevel gear with an attached output drive shaft is embedded in the second body and meshes with the threaded rotating bevel gear member to transmit the input torque to the output drive shaft.

Vranish, John M.

1993-12-01

248

Modeling with triangular B-splines  

Microsoft Academic Search

Triangular B-splines are a new tool for the modelingof complex objects with non-rectangulartopology. The new B-spline scheme is based onblending functions and control points and allowsmodeling piecewise polynomial surfaces over arbitrarytriangulations with an optimal degree ofsmoothness.This paper discusses applications of triangularB-splines in solid modeling. The new schemeis well-suited for modeling applications since itallows the construction of smooth surfaces withlowest degree...

Günther Greiner; Hans-Peter Seidel

1993-01-01

249

B-spline signal processing. I. Theory  

Microsoft Academic Search

The use of continuous B-spline representations for signal processing applications such as interpolation, differentiation, filtering, noise reduction, and data compressions is considered. The B-spline coefficients are obtained through a linear transformation, which unlike other commonly used transforms is space invariant and can be implemented efficiently by linear filtering. The same property also applies for the indirect B-spline transform as well

M. Unser; A. Aldroubi; M. Eden

1993-01-01

250

Algorithms for degree-raising of splines  

Microsoft Academic Search

Stable and efficient algorithms for degree-raising of curves (or surfaces) represented as arbitrary B-splines are presented as a application of the solution to the theoretical problem of rewriting a curve written as a linear combination of mth order B-splines as a linear combination of (m + 1)st order B-splines with a minimal number of knot insertions. This approach can be

Elaine Cohen; Tom Lyche; Larry L. Schumaker

1985-01-01

251

An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations  

SciTech Connect

In recent years, there has been a growing interest in analyzing and quantifying the effects of random inputs in the solution of ordinary/partial differential equations. To this end, the spectral stochastic finite element method (SSFEM) is the most popular method due to its fast convergence rate. Recently, the stochastic sparse grid collocation method has emerged as an attractive alternative to SSFEM. It approximates the solution in the stochastic space using Lagrange polynomial interpolation. The collocation method requires only repetitive calls to an existing deterministic solver, similar to the Monte Carlo method. However, both the SSFEM and current sparse grid collocation methods utilize global polynomials in the stochastic space. Thus when there are steep gradients or finite discontinuities in the stochastic space, these methods converge very slowly or even fail to converge. In this paper, we develop an adaptive sparse grid collocation strategy using piecewise multi-linear hierarchical basis functions. Hierarchical surplus is used as an error indicator to automatically detect the discontinuity region in the stochastic space and adaptively refine the collocation points in this region. Numerical examples, especially for problems related to long-term integration and stochastic discontinuity, are presented. Comparisons with Monte Carlo and multi-element based random domain decomposition methods are also given to show the efficiency and accuracy of the proposed method.

Ma Xiang [Materials Process Design and Control Laboratory, Sibley School of Mechanical and Aerospace Engineering, 101 Frank H.T. Rhodes Hall, Cornell University, Ithaca, NY 14853-3801 (United States); Zabaras, Nicholas [Materials Process Design and Control Laboratory, Sibley School of Mechanical and Aerospace Engineering, 101 Frank H.T. Rhodes Hall, Cornell University, Ithaca, NY 14853-3801 (United States)], E-mail: zabaras@cornell.edu

2009-05-01

252

An adaptive three-dimensional RHT-splines formulation in linear elasto-statics and elasto-dynamics  

NASA Astrophysics Data System (ADS)

An adaptive three-dimensional isogeometric formulation based on rational splines over hierarchical T-meshes (RHT-splines) for problems in elasto-statics and elasto-dynamics is presented. RHT-splines avoid some short-comings of NURBS-based formulations; in particular they allow for adaptive h-refinement with ease. In order to drive the adaptive refinement, we present a recovery-based error estimator for RHT-splines. The method is applied to several problems in elasto-statics and elasto-dynamics including three-dimensional modeling of thin structures. The results are compared to analytical solutions and results of NURBS based isogeometric formulations.

Nguyen-Thanh, N.; Muthu, J.; Zhuang, X.; Rabczuk, T.

2013-08-01

253

A mixed model for investigating a population of asymptotic growth curves using restricted B -splines  

Microsoft Academic Search

We introduce a new method for modeling a population of growth curves with B-splines, adapting the usual regression spline basis to ensure a horizontal upper asymptote in all fitted curves. The new\\u000a method is easily implemented in standard statistical software. We motivate and illustrate our method using data on the growth\\u000a of Brown Kiwi (Apteryx mantelli) in the North Island

Geoffrey Jones; Joyce Leung; Hugh Robertson

2009-01-01

254

Adaptive sampling approach based on cubic-spline for fast monostatic RCS calculation  

Microsoft Academic Search

An adaptive sampling method is proposed in this paper to efficiently calculate the scattering from electrically large objects. This cubic-spline-based sampling method is developed by combining Hermite model and spline technique to approximate a C1-continous curve through a set of arbitrarily discrete points, which adaptively generated by a coarse-to-fine strategy. Numerical results demonstrate that this method is able to rigorously

Z. W. Liu; J. Q. Chen; R. S. Chen

2007-01-01

255

Static polarizabilities of hydrogen in the B-spline basis set  

SciTech Connect

The static polarizability of the 1s, 2p, and 3d states of the hydrogen atom has been calculated using the B-splines basis set method, and the portion of the polarizability without poles has been calculated using the B-splines Galerkin method. Excellent agreement with exact values has been obtained. The current algorithm improves the efficiency and accuracy over the finite perturbation method. In addition, closure rules are obtained for the static polarizability of these states.

Bhatti, Mohammad I.; Coleman, Kevin D.; Perger, Warren F. [Department of Physics and Geology, University of Texas-Pan American, Edinburg, Texas 78539-2999 (United States); Physics Department, Michigan Technological University, Houghton, Michigan 49931-1295 (United States)

2003-10-01

256

Spline solution of the generalized Burgers'Fisher equation  

Microsoft Academic Search

A numerical method based on exponential spline and finite difference approximations is developed to solve the generalized Burgers'-Fisher equation. The error analysis, stability and convergence properties of the method are studied via energy method. The method is shown to be unconditionally stable and accurate of orders 𝒪(k?+?kh?+?h ) and 𝒪(k?+?kh?+?h ). Some test problems are given to demonstrate the applicability

Reza Mohammadi

2011-01-01

257

Multivariate adaptive regression splines models for the prediction of energy expenditure in children and adolescents  

Technology Transfer Automated Retrieval System (TEKTRAN)

Advanced mathematical models have the potential to capture the complex metabolic and physiological processes that result in heat production, or energy expenditure (EE). Multivariate adaptive regression splines (MARS), is a nonparametric method that estimates complex nonlinear relationships by a seri...

258

Splines and Efficiency in Dynamic Programming.  

National Technical Information Service (NTIS)

It is shown how one can use splines, represented in the B-spline basis, to reduce the difficulties of large storage requirements in dynamic programming via approximations to the minimum-return function without the inefficiency associated with using polyno...

J. W. Daniel

1973-01-01

259

A New Approach to Euler Splines II.  

National Technical Information Service (NTIS)

In a previous paper on the subject, the new recursive approach to the exponential Euler splines was used to derive the known properties and some new ones, of these most attractive among cardinal splines. In the present short note, written for Euler's bice...

I. J. Schoenberg

1981-01-01

260

Knowledge of English Collocations: An Analysis of Taiwanese EFL Learners.  

ERIC Educational Resources Information Center

|This study investigated Taiwanese English as a Foreign Language (EFL) students knowledge of English collocations and the collocational errors they made. The subjects were 60 students from a college in Taiwan. The research instrument was a self-designed Simple Completion Test that measured students knowledge of four types of lexical collocations:…

Huang, Li-Szu

261

A weighted collocation on the strong form with mixed radial basis approximations for incompressible linear elasticity  

NASA Astrophysics Data System (ADS)

A weighted strong form collocation framework with mixed radial basis approximations for the pressure and displacement fields is proposed for incompressible and nearly incompressible linear elasticity. It is shown that with the proper choice of independent source points and collocation points for the radial basis approximations in the pressure and displacement fields, together with the analytically derived weights associated with the incompressibility constraint and boundary condition collocation equations, optimal convergence can be achieved. The optimal weights associated with the collocation equations are derived based on achieving balanced errors resulting from domain, boundaries, and constraint equations. Since in the proposed method the overdetermined system of the collocation equations is solved by a least squares method, independent pressure and displacement approximations can be selected without suffering from instability due to violation of the LBB stability condition. The numerical solutions verify that the solution of the proposed method does not exhibit volumetric locking and pressure oscillation, and that the solution converges exponentially in both L2 norm and H1 semi-norm, consistent with the error analysis results presented in this paper.

Chi, Sheng-Wei; Chen, Jiun-Shyan; Hu, Hsin-Yun

2013-08-01

262

Septic spline solutions of sixth-order boundary value problems  

NASA Astrophysics Data System (ADS)

Septic spline is used for the numerical solution of the sixth-order linear, special case boundary value problem. End conditions for the definition of septic spline are derived, consistent with the sixth-order boundary value problem. The algorithm developed approximates the solution and their higher-order derivatives. The method has also been proved to be second-order convergent. Three examples are considered for the numerical illustrations of the method developed. The method developed in this paper is also compared with that developed in [M. El-Gamel, J.R. Cannon, J. Latour, A.I. Zayed, Sinc-Galerkin method for solving linear sixth order boundary-value problems, Mathematics of Computation 73, 247 (2003) 1325-1343], as well and is observed to be better.

Siddiqi, Shahid S.; Akram, Ghazala

2008-05-01

263

Registration of sliding objects using direction dependent B-splines decomposition  

NASA Astrophysics Data System (ADS)

Sliding motion is a challenge for deformable image registration because it leads to discontinuities in the sought deformation. In this paper, we present a method to handle sliding motion using multiple B-spline transforms. The proposed method decomposes the sought deformation into sliding regions to allow discontinuities at their interfaces, but prevents unrealistic solutions by forcing those interfaces to match. The method was evaluated on 16 lung cancer patients against a single B-spline transform approach and a multi B-spline transforms approach without the sliding constraint at the interface. The target registration error (TRE) was significantly lower with the proposed method (TRE = 1.5 mm) than with the single B-spline approach (TRE = 3.7 mm) and was comparable to the multi B-spline approach without the sliding constraint (TRE = 1.4 mm). The proposed method was also more accurate along region interfaces, with 37% less gaps and overlaps when compared to the multi B-spline transforms without the sliding constraint. This work was presented in part at the 4th International Workshop on Pulmonary Image Analysis during the Medical Image Computing and Computer Assisted Intervention (MICCAI) in Toronto, Canada (2011).

Delmon, V.; Rit, S.; Pinho, R.; Sarrut, D.

2013-03-01

264

Registration of sliding objects using direction dependent B-splines decomposition.  

PubMed

Sliding motion is a challenge for deformable image registration because it leads to discontinuities in the sought deformation. In this paper, we present a method to handle sliding motion using multiple B-spline transforms. The proposed method decomposes the sought deformation into sliding regions to allow discontinuities at their interfaces, but prevents unrealistic solutions by forcing those interfaces to match. The method was evaluated on 16 lung cancer patients against a single B-spline transform approach and a multi B-spline transforms approach without the sliding constraint at the interface. The target registration error (TRE) was significantly lower with the proposed method (TRE = 1.5 mm) than with the single B-spline approach (TRE = 3.7 mm) and was comparable to the multi B-spline approach without the sliding constraint (TRE = 1.4 mm). The proposed method was also more accurate along region interfaces, with 37% less gaps and overlaps when compared to the multi B-spline transforms without the sliding constraint. PMID:23388109

Delmon, V; Rit, S; Pinho, R; Sarrut, D

2013-02-07

265

A menagerie of rational B-spline circles  

Microsoft Academic Search

The article was motivated by J. Blinn's column on the many ways to draw a circle (see ibid., vol.7, no.8, p.39-44, 1987). The authors have found several other ways to represent the circle as a nonuniform rational B-spline curve, which they present. Square-based methods, infinite control points, triangle-based methods, general circular arcs and rational cubic circles are some of the

Leslie Piegl; Wayne Tiller

1989-01-01

266

Translating Collocations for Use in Bilingual Lexicons.  

National Technical Information Service (NTIS)

Collocations are notoriously difficult for non-native speakers to translate, primarily because they are opaque and can not be translated on a word by word basis. We describe a program named Champollion which, given a pair of parallel corpora in two differ...

F. Smadja K. McKeown

1994-01-01

267

Selection of smoothing parameters in B -spline nonparametric regression models using information criteria  

Microsoft Academic Search

We consider the use ofB-spline nonparametric regression models estimated by the maximum penalized likelihood method for extracting information from\\u000a data with complex nonlinear structure. Crucial points inB-spline smoothing are the choices of a smoothing parameter and the number of basis functions, for which several selectors\\u000a have been proposed based on cross-validation and Akaike information criterion known as AIC. It might

Seiya Imoto; Sadanori Konishi

2003-01-01

268

Staggered Grid with Collocated Grid Points of Velocities for Modeling Propagation of Elastic Waves in Anisotropic Solids by Finite-Difference Time Domain Method  

NASA Astrophysics Data System (ADS)

A staggered grid for velocity--stress formulation is presented for modeling elastic waves in anisotropic solids by the finite-difference time domain method. To simply impose boundary conditions on numerical models, our grid is derived by applying a finite integration technique to a single control volume satisfying Newton's law instead of interleaved control volumes for conventional staggered grids. Computed results for the numerical dispersions of the new grid for propagating vertically polarized shear and longitudinal waves in an isotropic solid show that the numerical dispersions of the new grid can be suppressed to the same levels as those of the conventional staggered grids by using a third-degree bi-polynomial interpolation.

Hasegawa, Koji; Shimada, Takao

2012-07-01

269

Some identities for products and degree raising of splines  

Microsoft Academic Search

In this paper it is shown how the algebraic product of two spline functions, each represented in terms of B-splines, can again be represented as a linear combination of suitable B-splines. As a corollary to this result we obtain an explicit representation of a given B-spline function in terms of B-splines of some arbitrary higher degree. This generalizes some known

K. Mørken

1991-01-01

270

B-Spline Signal Processing: Part I-Theory  

Microsoft Academic Search

This paper describes a set of efficient filtering techniques for the processing and representation of signals in terms of continuous B-spline basis functions. We first consider the problem of determining the spline coefficients for an exact signal interpolation (direct B-spline transform). The reverse operation is the signal reconstruction from its spline coefficients with an optional zooming factor rn (indirect B-spline

Michael Unser; Akram Aldroubi; Murray Eden

1993-01-01

271

Interpolation by spline spaces on classes of triangulations  

Microsoft Academic Search

We describe a general method for constructing triangulations ? which are suitable for interpolation by Sqr(?),r=1,2, where Sqr(?) denotes the space of splines of degree q and smoothness r. The triangulations ? are obtained inductively by adding a subtriangulation of locally chosen scattered points in each step. By using Bézier–Bernstein techniques, we determine the dimension and construct Lagrange and Hermite

G. Nürnberger; F. Zeilfelder

2000-01-01

272

Spatial group delay patterns for three ultra wideband spline antennas  

Microsoft Academic Search

The IEEE ultra wideband (UWB) standard includes both a multiple frequency carrier (MB-OFDM) and an impulse spectrum (DS-UWB) method, for which application antennas should be appropriately optimized. Small printed monopoles with outline features that can be defined by a Bezier-spline [1] have good matched impedance performance across the 3.1 - 10.6 GHz band. For communications applications, an omni-directional pattern, where

Patrick McEvoy; Matthias John; Sergio Curto; Max J Ammann

2008-01-01

273

CNC tool path in terms of B-spline curves  

Microsoft Academic Search

We present an accurate and efficient method to generate a CNC tool path for a smooth free-form surface in terms of planar cubic B-spline curves which will be fed into a free-form curve interpolator. We assume the use of a three-axis CNC machine tool with a ball end-mill cutter. We first interpolate break points, which are generated by computing the

Claire Lartigue; François Thiebaut; Takashi Maekawa

2001-01-01

274

Minimum energy control and ARMA splines  

Microsoft Academic Search

This paper considers the problem of exact minimum energy control of linear systems with linear functional constraints on the output. An explicit correspondence is established between constrained minimum energy control and interpolation with ARMA (autoregressive-moving average) splines, and then used to obtain a formula for the optimal control. The control-spline correspondence is an input-output duality: if the system is driven

Howard L. Weinert; G. S. Sidhu

1975-01-01

275

Computationally Efficient Spline-Based Time Delay Estimation  

PubMed Central

We have previously presented a highly accurate, spline-based time delay estimator (TDE) that directly determines sub-sample time delay estimates from sampled data. The algorithm uses cubic splines to produce a continuous time representation of a reference signal, then computes an analytical matching function between this reference and a delayed signal. The location of the minima of this function yields estimates of the time delay. In this paper we present more computationally efficient formulations of this algorithm. We present the results of computer simulations and ultrasound experiments which indicate that the bias and the standard deviation of the proposed algorithms are comparable to those of the original method, and thus superior to other published algorithms.

Viola, Francesco; Walker, William F.

2008-01-01

276

A B-spline Hartree-Fock program  

NASA Astrophysics Data System (ADS)

A B-spline version of a Hartree-Fock program is described. The usual differential equations are replaced by systems of non-linear equations and generalized eigenvalue problems of the form (Ha-?B)P=0, where a designates the orbital. When orbital a is required to be orthogonal to a fixed orbital, this form assumes that a projection operator has been applied to eliminate the Lagrange multiplier. When two orthogonal orbitals are both varied, the energy must also be stationary with respect to orthogonal transformations. At such a stationary point, the matrix of Lagrange multipliers, ?=(P|Ha|P), is symmetric and the off-diagonal Lagrange multipliers may again be eliminated through projection operators. For multiply occupied shells, convergence problems are avoided by the use of a single-orbital Newton-Raphson method. A self-consistent field procedure based on these two possibilities exhibits excellent convergence. A Newton-Raphson method for updating all orbitals simultaneously has better numerical properties and a more rapid rate of convergence but requires more computer processing time. Both ground and excited states may be computed using a default universal grid. Output from a calculation for Al 3s23pP2 shows the improvement in accuracy that can be achieved by mapping results from low-order splines on a coarse grid to splines of higher order onto a refined grid. The program distribution contains output from additional test cases.

Froese Fischer, Charlotte

2011-06-01

277

Estimation of musculotendon kinematics in large musculoskeletal models using multidimensional B-splines.  

PubMed

We present a robust and computationally inexpensive method to estimate the lengths and three-dimensional moment arms for a large number of musculotendon actuators of the human lower limb. Using a musculoskeletal model of the lower extremity, a set of values was established for the length of each musculotendon actuator for different lower limb generalized coordinates (joint angles). A multidimensional spline function was then used to fit these data. Muscle moment arms were obtained by differentiating the musculotendon length spline function with respect to the generalized coordinate of interest. This new method was then compared to a previously used polynomial regression method. Compared to the polynomial regression method, the multidimensional spline method produced lower errors for estimating musculotendon lengths and moment arms throughout the whole generalized coordinate workspace. The fitting accuracy was also less affected by the number of dependent degrees of freedom and by the amount of experimental data available. The spline method only required information on musculotendon lengths to estimate both musculotendon lengths and moment arms, thus relaxing data input requirements, whereas the polynomial regression requires different equations to be used for both musculotendon lengths and moment arms. Finally, we used the spline method in conjunction with an electromyography driven musculoskeletal model to estimate muscle forces under different contractile conditions, which showed that the method is suitable for the integration into large scale neuromusculoskeletal models. PMID:22176708

Sartori, Massimo; Reggiani, Monica; van den Bogert, Antonie J; Lloyd, David G

2011-12-15

278

The Sense Boundary Decision and the Sense Labeling from Collocation Clustering  

Microsoft Academic Search

Abstract This paper discusses the deciding practical sense boundary of homonymous words. One of the serious problems in making dictionaries or thesauri is in the vague boundary of senses. This also becomes a bottleneck in sense disambiguation for practical language processing systems. This paper proposes a deciding method,for sense boundary discovery of homonyms,using collocation from large corpora and automatic clustering.

SAIM SHIN; KEY-SUN CHOI

2004-01-01

279

A collocation model for water-hammer dynamics with application to leak detection  

Microsoft Academic Search

This paper presents a new model for so-called water hammer equations based on a collocation method. This model is shown to fairly represent possible leak effects in a pipeline and thus to be useful in the purpose of leak detection. This is illustrated in simulation by an example of observer-based leak detector relying on this model.

Flor Lizeth Torres Ortiz; Gildas Besancon; Didier Georges

2008-01-01

280

The research on collocation networks of relation words in modern Chinese language  

Microsoft Academic Search

Complex networks is a new method to research complicated system from the global perspective. The relation words is the important role in complex sentences. This paper uses complex networks to research the relation words in modern Chinese complex sentences. It finds that complex sentences are linked by the relation words' collocation, so the complex networks which the relations words built

Hu Quan; Jinzhu Hu; Xie Fang

2011-01-01

281

Multi-leak estimator for pipelines based on an orthogonal collocation model  

Microsoft Academic Search

The orthogonal collocation method (OCM) is used to obtain an approximate solution of the water hammer equations which represent one-phase water flow transients in pipeline systems. The OCM provides solutions over the entire spatial domain, therefore it can be used to obtain an accurate model with possible leaks spatially distributed. An estimator can be designed based on the spatially-discretized model

Flor Lizeth Torres Ortiz; Gildas Besançon; Didier Georges

2009-01-01

282

Spline trigonometric bases and their properties  

SciTech Connect

A family of pairs of biorthonormal systems is constructed such that for each p element of (1,{infinity}) one of these systems is a basis in the space L{sub p}(a,b), while the other is the dual basis in L{sub q}(a,b) (here 1/p+1/q=1). The functions in the first system are products of trigonometric and algebraic polynomials; the functions in the second are products of trigonometric polynomials and the derivatives of B-splines. The asymptotic behaviour of the Lebesgue functions of the constructed systems is investigated. In particular, it is shown that the dominant terms of pointwise asymptotic expansions for the Lebesgue functions have everywhere (except at certain singular points) the form 4/{pi}{sup 2} ln n (that is, the same as in the case of an orthonormal trigonometric system). Interpolation representations with multiple nodes for entire functions of exponential type {sigma} are obtained. These formulae involve a uniform grid; however, by contrast with Kotel'nikov's theorem, where the mesh of the grid is {pi}/{sigma} and decreases as the type of the entire function increases, in the representations obtained the nodes of interpolation can be kept independent of {sigma}, and their multiplicity increases as the type of the interpolated function increases. One possible application of such representations (particularly, their multidimensional analogues) is an effective construction of asymptotically optimal approximation methods by means of scaling and argument shifts of a fixed function (wavelets, grid projection methods, and so on)

Strelkov, N A [P.G. Demidov Yaroslavl State University, Yaroslavl (Russian Federation)

2001-08-31

283

47 CFR Appendix B to Part 1 - Nationwide Programmatic Agreement for the Collocation of Wireless Antennas  

Code of Federal Regulations, 2010 CFR

...Nationwide Programmatic Agreement for the Collocation of Wireless Antennas B Appendix...Nationwide Programmatic Agreement for the Collocation of Wireless Antennas Nationwide Programmatic Agreement for the Collocation of Wireless Antennas...

2010-10-01

284

47 CFR Appendix B to Part 1 - Nationwide Programmatic Agreement for the Collocation of Wireless Antennas  

Code of Federal Regulations, 2010 CFR

...Nationwide Programmatic Agreement for the Collocation of Wireless Antennas B Appendix...Nationwide Programmatic Agreement for the Collocation of Wireless Antennas Nationwide Programmatic Agreement for the Collocation of Wireless Antennas...

2009-10-01

285

47 CFR Appendix B to Part 1 - Nationwide Programmatic Agreement for the Collocation of Wireless Antennas  

Code of Federal Regulations, 2010 CFR

...Nationwide Programmatic Agreement for the Collocation of Wireless Antennas B Appendix...Nationwide Programmatic Agreement for the Collocation of Wireless Antennas Nationwide Programmatic Agreement for the Collocation of Wireless Antennas...

2011-10-01

286

Finite Element Analysis for Mass-Lumped Three-Step Taylor Galerkin Method for Time Dependent Singularly Perturbed Problems with Exponentially Fitted Splines  

Microsoft Academic Search

The motive of the current study is to derive pointwise error estimates for the three-step Taylor Galerkin finite element method for singularly perturbed problems. Pointwise error estimates have not been derived so far for the said method in the finite element framework. Singularly perturbed problems represent a class of problems containing a very sharp boundary layer in their solution. A

Vivek Sangwan; B. V. Rathish Kumar

2012-01-01

287

Two different forms of C-B-splines  

Microsoft Academic Search

In a recent paper (Zhang, 1996), C-B-splines are introduced as extensions of cubic uniform B-splines. A new reparametrized form of C-B-splines, which is defined on the interval [0,1], is proposed here. From this form, a third form that could have different parameters ? in a curve is derived. These new forms give an efficient algorithm for C-B-splines with any parameter

Jiwen Zhang

1997-01-01

288

Knot insertion for Beta-spline curves and surfaces  

Microsoft Academic Search

Discrete Beta-splines arise when a Beta-spline curve is subdivided; that is, extra knots are inserted so that the curve is expressed in terms of a larger number of control vertices and Beta-splines. Their properties and an algorithm for their computation are given in “Discrete Beta-Splines” by Joe (Computer Graphics, vol. 21, pp. 137-144). We prove a stronger version of one

Barry Joe

1990-01-01

289

Multiresolution image retrieval using B-splines  

NASA Astrophysics Data System (ADS)

We propose a technique to search through large image collections. Each database image is stored as a combination of potential query terms and non-query terms. The query terms are represented by affine-invariant B-spline moments and wavelet transform subbands. The dual representation supports a two-stage image retrieval system. A user-posed query is first mapped to a dictionary of prototype object contours represented by B-spline moments. The B-spline mapping reduces the query search space to a subset of the original database. Furthermore, it provides an estimate of the affine transformation between the query and the prototypes. The second stage consist of a set of embedded VQ dictionaries of multiresolution subbands of image objects. The estimated affine transformation is employed as a correction factor for the multiresolution VQ mapping. A simple bit string matching algorithm compares the resulting query VQ codewords with the codewords of the database images for retrieval.

Swanson, Mitchell D.; Tewfik, Ahmed H.

1997-10-01

290

Procedure for converting a Wilson-Fowler spline to a cubic B-spline with double knots  

SciTech Connect

The Wilson-Fowler spline (WF-spline) has been used by the DOE Weapons Complex for over twenty years to represent point-defined smooth curves. Most modern CADCAM systems use parametric B-spline curves (or, more recently, rational B-splines) for this same purpose. The WF-spline is a parametric piecewise cubic curve. It has been shown that a WF-spline can be reparametrized so that its components are C/sup 1/ piecewise cubic functions (functions that are cubic polynomials on each parameter interval, joined so the function and first derivative are continuous). The purpose of these notes is to show explicitly how to convert a given WF-spline to a cubic B-spline with double knots. 7 refs.

Fritsch, F.N.

1987-10-14

291

Optimal trajectory planning with quintic G2-splines  

Microsoft Academic Search

This paper deals with the generation of optimal paths for the automated steering of autonomous vehicles. The path is parametrized by quintic G2-splines, or ?-spline, devised to guarantee the overall second order geometric continuity of a composite path interpolating an arbitrary sequence of points. Starting from the closed-form ?-parametrization of the spline an optimization criterion is proposed to design smooth

C. Guarino Lo Bianco; Aurelio PIAZZI

2000-01-01

292

Restricted trivariate polycube splines for volumetric data modeling.  

PubMed

This paper presents a volumetric modeling framework to construct a novel spline scheme called restricted trivariate polycube splines (RTP-splines). The RTP-spline aims to generalize both trivariate T-splines and tensor-product B-splines; it uses solid polycube structure as underlying parametric domains and strictly bounds blending functions within such domains. We construct volumetric RTP-splines in a top-down fashion in four steps: 1) Extending the polycube domain to its bounding volume via space filling; 2) building the B-spline volume over the extended domain with restricted boundaries; 3) inserting duplicate knots by adding anchor points and performing local refinement; and 4) removing exterior cells and anchors. Besides local refinement inherited from general T-splines, the RTP-splines have a few attractive properties as follows: 1) They naturally model solid objects with complicated topologies/bifurcations using a one-piece continuous representation without domain trimming/patching/merging. 2) They have guaranteed semistandardness so that the functions and derivatives evaluation is very efficient. 3) Their restricted support regions of blending functions prevent control points from influencing other nearby domain regions that stay opposite to the immediate boundaries. These features are highly desirable for certain applications such as isogeometric analysis. We conduct extensive experiments on converting complicated solid models into RTP-splines, and demonstrate the proposed spline to be a powerful and promising tool for volumetric modeling and other scientific/engineering applications where data sets with multiattributes are prevalent. PMID:22442125

Wang, Kexiang; Li, Xin; Li, Bo; Xu, Huanhuan; Qin, Hong

2012-05-01

293

Deconvolution using thin-plate splines  

SciTech Connect

The ubiquitous problem of estimating 2-dimensional profile information from a set of line integrated measurements is tackled with Bayesian probability theory by exploiting prior information about local smoothness. For this purpose thin-plate-splines (the 2-D minimal curvature analogue of cubic-splines in 1-D) are employed. The optimal number of support points required for inversion of 2-D tomographic problems is determined using model comparison. Properties of this approach are discussed and the question of suitable priors is addressed. Finally, we illustrated the properties of this approach with 2-D inversion results using data from line-integrated measurements from fusion experiments.

Toussaint, Udo v.; Gori, Silvio [Max-Planck-Institut fuer Plasmaphysik, 85748 Garching (Germany)

2007-11-13

294

A Study of Strategy Use in Producing Lexical Collocations.  

ERIC Educational Resources Information Center

|This study examined strategy use in producing lexical collocations among freshman English majors at the Chinese Culture University. Divided into two groups by English writing proficiency, students completed three tasks: a collocation test, an optimal revision task, and a task-based structured questionnaire regarding their actions and mental…

Liu, Candi Chen-Pin

295

The Repetition of Collocations in EFL Textbooks: A Corpus Study  

ERIC Educational Resources Information Center

|The importance of repetition in the acquisition of lexical items has been widely acknowledged in single-word vocabulary research but has been relatively neglected in collocation studies. Since collocations are considered one key to achieving language fluency, and because learners spend a great amount of time interacting with their textbooks, the…

Wang, Jui-hsin Teresa; Good, Robert L.

2007-01-01

296

The discourse function of collocation in research article introductions  

Microsoft Academic Search

The increasing use of computer-held text corpora containing many millions of words has allowed linguists to establish lexico-grammatical patterns in language that were previously unavailable to observers. Such patterns range from lexical collocations and idioms to the phraseology of grammatical items. Recently, collocations of high frequency words in medical research abstracts and articles have been found to be useful indicators

Chris Gledhill

2000-01-01

297

Quantifying cervical-spine curvature using Be?zier splines.  

PubMed

Knowledge of the distributions of cervical-spine curvature is needed for computational studies of cervical-spine injury in motor-vehicle crashes. Many methods of specifying spinal curvature have been proposed, but they often involve qualitative assessment or a large number of parameters. The objective of this study was to develop a quantitative method of characterizing cervical-spine curvature using a small number of parameters. 180 sagittal X-rays of subjects seated in automotive posture with their necks in neutral, flexed, and extended postures were collected in the early 1970s. Subjects were selected to represent a range of statures and ages for each gender. X-rays were reanalyzed using advanced technology and statistical methods. Coordinates of the posterior margins of the vertebral bodies and dens were digitized. Be?zier splines were fit through the coordinates of these points. The interior control points that define the spline curvature were parameterized as a vector angle and length. By defining the length as a function of the angle, cervical-spine curvature was defined with just two parameters: superior and inferior Be?zier angles. A classification scheme was derived to sort each curvature by magnitude and type of curvature (lordosis versus S-shaped versus kyphosis; inferior or superior location). Cervical-spine curvature in an automotive seated posture varies with gender and age but not stature. Average values of superior and inferior Be?zier angles for cervical spines in flexion, neutral, and extension automotive postures are presented for each gender and age group. Use of Be?zier splines fit through posterior margins offers a quantitative method of characterizing cervical-spine curvature using two parameters: superior and inferior Be?zier angles. PMID:23387791

Klinich, Kathleen D; Ebert, Sheila M; Reed, Matthew P

2012-11-01

298

SMOOTHING SPLINE ANOVA MODELS FOR LARGE DATA SETS WITH BERNOULLI OBSERVATIONS AND THE RANDOMIZED GACV  

Microsoft Academic Search

We propose the randomized Generalized Approximate Cross Valida- tion (ranGACV) method for choosing multiple smoothing parameters in penalized likelihood estimates for Bernoulli data. The method is intended for application with penalized likelihood smoothing spline ANOVA models. In addition we propose a class of approximate numerical methods for solv- ing the penalized likelihood variational problem which, in conjunction with the ranGACV

Xiwu Lin; Grace Wahba; Dong Xiang; Fangyu Gao

2000-01-01

299

A multiresolution analysis for tensor-product splines using weighted spline wavelets  

NASA Astrophysics Data System (ADS)

We construct biorthogonal spline wavelets for periodic splines which extend the notion of "lazy" wavelets for linear functions (where the wavelets are simply a subset of the scaling functions) to splines of higher degree. We then use the lifting scheme in order to improve the approximation properties with respect to a norm induced by a weighted inner product with a piecewise constant weight function. Using the lifted wavelets we define a multiresolution analysis of tensor-product spline functions and apply it to image compression of black-and-white images. By performing-as a model problem-image compression with black-and-white images, we demonstrate that the use of a weight function allows to adapt the norm to the specific problem.

Kapl, Mario; Jüttler, Bert

2009-09-01

300

Error Estimates Derived from the Data for Least-Squares Spline Fitting  

SciTech Connect

The use of least-squares fitting by cubic splines for the purpose of noise reduction in measured data is studied. Splines with variable mesh size are considered. The error, the difference between the input signal and its estimate, is divided into two sources: the R-error, which depends only on the noise and increases with decreasing mesh size, and the Ferror, which depends only on the signal and decreases with decreasing mesh size. The estimation of both errors as a function of time is demonstrated. The R-error estimation requires knowledge of the statistics of the noise and uses well-known methods. The primary contribution of the paper is a method for estimating the F-error that requires no prior knowledge of the signal except that it has four derivatives. It is calculated from the difference between two different spline fits to the data and is illustrated with Monte Carlo simulations and with an example.

Jerome Blair

2007-06-25

301

Bernuau Spline Wavelets andSturmian Sequences  

Microsoft Academic Search

We present spline wavelets of class C n( R) supported by sequences of aperiodic discretizations of R. The construction is based on multiresolution analysis recently elaborated by G. Bernuau. At a given scale, we consider discretizations that are sets of left-hand ends of tiles in a self-similar tiling of the real line with finite local complexity. Corresponding tilings are determined

Miroslav Andrle; Cestmír Burdík; Jean-Pierre Gazeau

2004-01-01

302

Maxentropic reconstruction by first order splines  

NASA Astrophysics Data System (ADS)

We present a way of combining maximum entropy in the mean with first order spline interpolation to obtain solutions to generalized moment problems or Fredholm integral equations of the first kind. An application to numerical inversion of Laplace transform is tried. .

Gzyl, Henryk; Velasquez, Yurayh

2001-05-01

303

Smooth, Easy to Compute Interpolating Splines.  

National Technical Information Service (NTIS)

The authors present a system of interpolating splines with first and approximate second order geometric continuity. The curves are easily computed in linear time by solving a system of linear equations without the need to resort to any kind of successive ...

J. D. Hobby

1985-01-01

304

Smoothing Splines: Regression, Derivatives and Deconvolution  

Microsoft Academic Search

The statistical properties of a cubic smoothing spline and its derivative are analyzed. It is shown that unless unnatural boundary conditions hold, the integrated squared bias is dominated by local effects near the boundary. Similar effects are shown to occur in the regularized solution of a translation-kernel integral equation. These results are derived by developing a Fourier representation for a

John Rice; Murray Rosenblatt

1983-01-01

305

Document segmentation using polynomial spline wavelets  

Microsoft Academic Search

Wavelet transforms have been widely used as effective tools in texture segmentation in the past decade. Segmentation of document images, which usually contain three types of texture information: text, picture and background, can be regarded as a special case of texture segmentation. B-spline wavelets possess some desirable properties such as being well localized in time and frequency, and being compactly

Shulan Deng; Shahram Latifi; Emma Regentova

2001-01-01

306

Marginal longitudinal semiparametric regression via penalized splines  

Microsoft Academic Search

We study the marginal longitudinal nonparametric regression problem and some of its semiparametric extensions. We point out that, while several elaborate proposals for efficient estimation have been proposed, a relative simple and straightforward one, based on penalized splines, has not. After describing our approach, we then explain how Gibbs sampling and the BUGS software can be used to achieve quick

M. Al Kadiri; R. J. Carroll; M. P. Wand

2010-01-01

307

Dynamic B-spline surface reconstruction: Closing the sensing-and-modeling loop in 3D digitization  

Microsoft Academic Search

In this paper, we present a new B-spline surface reconstruction approach, called dynamic surface reconstruction, aiming to close the sensing- and-modeling loop in 3D digitization. At its core, this approach uses a recursive least squares method, the Kalman filter, to dynamically reconstruct the B-spline surface as the surface data are acquired. That is, the acquired data are dynamically incorporated into

Yunbao Huang; Xiaoping Qian

2007-01-01

308

Subspace identification of Hammerstein systems using B-splines.  

PubMed

This paper presents an algorithm for the identification of Hammerstein cascades with hard nonlinearities. The nonlinearity of the cascade is described using a B-spline basis with fixed knot locations; the linear dynamics are described using a state-space model. The algorithm automatically estimates both the order of the linear system and the number and locations of the knots used to characterize the nonlinearity. Therefore, it significantly reduces the a priori knowledge about the underlying system required for identification. A simulation study on a model of reflex stiffness shows that the new method estimates the nonlinearity accurately in the presence of output noise. PMID:23366635

Jalaleddini, K; Westwick, D T; Kearney, R E

2012-01-01

309

Penalised regression splines: theory and application to medical research.  

PubMed

Generalised additive models (GAMs) allow for flexible functional dependence of a response variable on covariates. The aim of this article is to provide an accessible overview of GAMs based on the penalised likelihood approach with regression splines. In contrast to the classical backfitting, the penalised likelihood framework taken here provides researchers with an efficient computational method for automatic multiple smoothing parameter selection, which can determine the functional form of any relationship from the data. We illustrate through an example how the use of this methodology can help to gain insights into medical research. PMID:18815162

Marra, Giampiero; Radice, Rosalba

2008-09-24

310

B-spline design of digital FIR filter using evolutionary computation techniques  

NASA Astrophysics Data System (ADS)

In the forth coming era, digital filters are becoming a true replacement for the analog filter designs. Here in this paper we examine a design method for FIR filter using global search optimization techniques known as Evolutionary computation via genetic algorithm and bacterial foraging, where the filter design considered as an optimization problem. In this paper, an effort is made to design the maximally flat filters using generalized B-spline window. The key to our success is the fact that the bandwidth of the filer response can be modified by changing tuning parameters incorporated well within the B-spline function. This is an optimization problem. Direct approach has been deployed to design B-spline window based FIR digital filters. Four parameters (order, width, length and tuning parameter) have been optimized by using GA and EBFS. It is observed that the desired response can be obtained with lower order FIR filters with optimal width and tuning parameters.

Swain, Manorama; Panda, Rutuparna

2011-10-01

311

Torque ripple minimization in switched reluctance motors via bi-cubic spline interpolation  

Microsoft Academic Search

A method for minimizing the instantaneous torque ripple in switched reluctance (SR) machines is investigated and implemented. The method is based on estimating the instantaneous SR motor torque from the flux linkage versus current and rotor position characteristic curves via a bi-cubic spline interpolation. These coefficients are computed offline, stored in a given memory location of the control processor, and

Julio C. Moreira

1992-01-01

312

Developing and Evaluating a Web-Based Collocation Retrieval Tool for EFL Students and Teachers  

ERIC Educational Resources Information Center

The development of adequate collocational knowledge is important for foreign language learners; nonetheless, learners often have difficulties in producing proper collocations in the target language. Among the various ways of learning collocations, the DDL (data-driven learning) approach encourages independent learning of collocations and allows…

Chen, Hao-Jan Howard

2011-01-01

313

Developing and Evaluating a Web-Based Collocation Retrieval Tool for EFL Students and Teachers  

ERIC Educational Resources Information Center

|The development of adequate collocational knowledge is important for foreign language learners; nonetheless, learners often have difficulties in producing proper collocations in the target language. Among the various ways of learning collocations, the DDL (data-driven learning) approach encourages independent learning of collocations and allows…

Chen, Hao-Jan Howard

2011-01-01

314

Adaptive Predistortion Using Cubic Spline Nonlinearity Based Hammerstein Modeling  

NASA Astrophysics Data System (ADS)

In this paper, a new Hammerstein predistorter modeling for power amplifier (PA) linearization is proposed. The key feature of the model is that the cubic splines, instead of conventional high-order polynomials, are utilized as the static nonlinearities due to the fact that the splines are able to represent hard nonlinearities accurately and circumvent the numerical instability problem simultaneously. Furthermore, according to the amplifier's AM/AM and AM/PM characteristics, real-valued cubic spline functions are utilized to compensate the nonlinear distortion of the amplifier and the following finite impulse response (FIR) filters are utilized to eliminate the memory effects of the amplifier. In addition, the identification algorithm of the Hammerstein predistorter is discussed. The predistorter is implemented on the indirect learning architecture, and the separable nonlinear least squares (SNLS) Levenberg-Marquardt algorithm is adopted for the sake that the separation method reduces the dimension of the nonlinear search space and thus greatly simplifies the identification procedure. However, the convergence performance of the iterative SNLS algorithm is sensitive to the initial estimation. Therefore an effective normalization strategy is presented to solve this problem. Simulation experiments were carried out on a single-carrier WCDMA signal. Results show that compared to the conventional polynomial predistorters, the proposed Hammerstein predistorter has a higher linearization performance when the PA is near saturation and has a comparable linearization performance when the PA is mildly nonlinear. Furthermore, the proposed predistorter is numerically more stable in all input back-off cases. The results also demonstrate the validity of the convergence scheme.

Wu, Xiaofang; Shi, Jianghong

315

Optimized Construction of Biorthogonal Spline-Wavelets  

NASA Astrophysics Data System (ADS)

The paper is concerned with the construction of wavelet bases on the interval derived from B-splines. The resulting bases generate multiresolution analyses on the unit interval with the desired number of vanishing wavelet moments for primal and dual wavelets. Inner wavelets are translated and dilated versions of well-known wavelets designed by Cohen, Daubechies, Feauveau [5] while the construction of boundary wavelets is along the lines of [6]. The disadvantage of popular bases from [6] is their bad condition which cause problems in practical applications. Some modifications which lead to better conditioned bases were proposed in [1, 7, 8, 9, 10]. In this contribution, we further improve the condition of spline-wavelet bases on the interval. Quantitative properties of these bases are presented.

?erná, Dana; Fin?k, Václav

2008-09-01

316

Representing flexible endoscope shapes with hermite splines  

NASA Astrophysics Data System (ADS)

Navigation of a flexible endoscope is a challenging surgical task: the shape of the end effector of the endoscope, interacting with surrounding tissues, determine the surgical path along which the endoscope is pushed. We present a navigational system that visualized the shape of the flexible endoscope tube to assist gastrointestinal surgeons in performing Natural Orifice Translumenal Endoscopic Surgery (NOTES). The system used an electromagnetic positional tracker, a catheter embedded with multiple electromagnetic sensors, and graphical user interface for visualization. Hermite splines were used to interpret the position and direction outputs of the endoscope sensors. We conducted NOTES experiments on live swine involving 6 gastrointestinal and 6 general surgeons. Participants who used the device first were 14.2% faster than when not using the device. Participants who used the device second were 33.6% faster than the first session. The trend suggests that spline-based visualization is a promising adjunct during NOTES procedures.

Chen, Elvis C. S.; Fowler, Sharyle A.; Hookey, Lawrence C.; Ellis, Randy E.

2010-03-01

317

A family of spline finite elements  

Microsoft Academic Search

In this paper, a new family of plane quadrilateral spline elements is proposed. Four quadrilateral elements with 4,8,12 and 17 nodes are constructed, which possess completeness of orders 1,2,3 and 4 in the Cartesian coordinates, respectively. The displacement interpolation functions of the 8,12 and 17-node elements possess higher order completeness than the corresponding quadrilateral isoparametric elements with the same nodes,

Juan Chen; Chong-Jun Li; Wan-Ji Chen

2010-01-01

318

Marginal longitudinal semiparametric regression via penalized splines  

PubMed Central

We study the marginal longitudinal nonparametric regression problem and some of its semiparametric extensions. We point out that, while several elaborate proposals for efficient estimation have been proposed, a relative simple and straightforward one, based on penalized splines, has not. After describing our approach, we then explain how Gibbs sampling and the BUGS software can be used to achieve quick and effective implementation. Illustrations are provided for nonparametric regression and additive models.

Kadiri, M. Al; Carroll, R.J.; Wand, M.P.

2010-01-01

319

Research Article Multivariate Interpolation of Precipitation Using Regularized Spline with Tension  

Microsoft Academic Search

Regularized Spline with Tension (RST) is an accurate, flexible and efficient method for multivariate interpolation of scattered data. This study evaluates its capabilities to interpolate daily and annual mean precipitation in regions with complex terrain. Tension, smoothing and anisotropy parameters are optimized using the cross- validation technique. In addition, smoothing and rescaling of the third variable (elevation) is used to

Jaroslav Hofierka; Juraj Parajka; Helena Mitasova; Lubos Mitas

320

Interobserver reproducibility of quantitative cartilage measurements: comparison of B-spline snakes and manual segmentation  

Microsoft Academic Search

The objective of this work was to develop a segmentation technique for thickness measurements of the articular cartilage in MR images and to assess the interobserver reproducibility of the method in comparison with manual segmentation. The algorithm is based on a B-spline snakes approach and is able to delineate the cartilage boundaries in real time and with minimal user interaction.

Tobias Stammberger; Felix Eckstein; Markus Michaelis; Karl-Hans Englmeier; Maximilian Reiser

1999-01-01

321

Constructing fuzzy controllers with B-spline models?Principles and applications  

Microsoft Academic Search

In this paper we present an approach to designing a novel type of fuzzy controller. B-spline basis functions are used for input variables and fuzzy singletons for output variables to specify linguistic terms. "Product" is chosen as the fuzzy conjunction, and "centroid" as the defuzzification method. By appropriately designing the rule base, a fuzzy controller can be interpreted as a

Jianwei Zhang; Alois Knoll

1998-01-01

322

Cartographic generalisation of lines based on a B-spline snake model  

Microsoft Academic Search

The automation of cartographic map production is still an important research field in Geographical Information Systems (GIS). With the increasing development of monitoring and decision?aid systems either on computer networks or wireless networks, efficient methods are needed to visualise geographical data while respecting some application constraints (accuracy, legibility, security, etc.). This paper introduces a B?spline snake model to deal with

Eric Guilbert; Eric Saux

2008-01-01

323

Scattered Data Interpolation with Multilevel B-Splines  

Microsoft Academic Search

This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel B-splines areintroduced to compute a C2-continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarse-tofinehierarchy of control lattices to generate a sequence of bicubic B-spline functions whose sum approaches the desiredinterpolation function. Large performance gains are realized by using B-spline refinement

Seungyong Lee; George Wolberg; Sung Yong Shin

1997-01-01

324

Generalized B-spline surfaces of arbitrary topology  

Microsoft Academic Search

B-spline surfaces, although widely used, are incapable of describing surfaces of arbitrary topology. It is not possible to model a general closed surface or a surface with handles as a single non-degenerate B-spline. In practice such surfaces are often needed. In this paper, we present generalizations of biquadratic and bicubic B-spline surfaces that are capable of capturing surfaces of arbitrary

Charles T. Loop; Tony DeRose

1990-01-01

325

B-spline signal processing. II. Efficiency design and applications  

Microsoft Academic Search

For pt.I see ibid., vol.41, no.2, p.821-33 (1993). A class of recursive filtering algorithms for the efficient implementation of B-spline interpolation and approximation techniques is described. In terms of simplicity of realization and reduction of computational complexity, these algorithms compare favorably with conventional matrix approaches. A filtering interpretation (low-pass filter followed by an exact polynomial spline interpolator) of smoothing spline

Michael Unser; Akram Aldroubi; Murray Eden

1993-01-01

326

Analysis of Three-Dimensional Splines and Their Application to the Initial Graphics Exchange Specification.  

National Technical Information Service (NTIS)

This research develops the fundamental theories associated with three-dimensional splines and the philosophies underlying the Initial Graphics Exchange Specification (IGES). Splines have been classified into three main categories: polynomial splines, spli...

R. M. Dolin

1985-01-01

327

Box spline reconstruction on the face-centered cubic lattice.  

PubMed

We introduce and analyze an efficient reconstruction algorithm for FCC-sampled data. The reconstruction is based on the 6-direction box spline that is naturally associated with the FCC lattice and shares the continuity and approximation order of the triquadratic B-spline. We observe less aliasing for generic level sets and derive special techniques to attain the higher evaluation efficiency promised by the lower degree and smaller stencil-size of the C1 6-direction box spline over the triquadratic B-spline. PMID:18989005

Kim, Minho; Entezari, Alireza; Peters, Jörg

328

Subcell resolution in simplex stochastic collocation for spatial discontinuities  

NASA Astrophysics Data System (ADS)

Subcell resolution has been used in the Finite Volume Method (FVM) to obtain accurate approximations of discontinuities in the physical space. Stochastic methods are usually based on local adaptivity for resolving discontinuities in the stochastic dimensions. However, the adaptive refinement in the probability space is ineffective in the non-intrusive uncertainty quantification framework, if the stochastic discontinuity is caused by a discontinuity in the physical space with a random location. The dependence of the discontinuity location in the probability space on the spatial coordinates then results in a staircase approximation of the statistics, which leads to first-order error convergence and an underprediction of the maximum standard deviation. To avoid these problems, we introduce subcell resolution into the Simplex Stochastic Collocation (SSC) method for obtaining a truly discontinuous representation of random spatial discontinuities in the interior of the cells discretizing the probability space. The presented SSC-SR method is based on resolving the discontinuity location in the probability space explicitly as function of the spatial coordinates and extending the stochastic response surface approximations up to the predicted discontinuity location. The applications to a linear advection problem, the inviscid Burgers' equation, a shock tube problem, and the transonic flow over the RAE 2822 airfoil show that SSC-SR resolves random spatial discontinuities with multiple stochastic and spatial dimensions accurately using a minimal number of samples.

Witteveen, Jeroen A. S.; Iaccarino, Gianluca

2013-10-01

329

Integration by cell algorithm for Slater integrals in a spline basis  

SciTech Connect

An algorithm for evaluating Slater integrals in a B-spline basis is introduced. Based on the piecewise property of the B-splines, the algorithm divides the two-dimensional (r{sub 1}, r{sub 2}) region into a number of rectangular cells according to the chosen grid and implements the two-dimensional integration over each individual cell using Gaussian quadrature. Over the off-diagonal cells, the integrands are separable so that each two-dimensional cell-integral is reduced to a product of two one-dimensional integrals. Furthermore, the scaling invariance of the B-splines in the logarithmic region of the chosen grid is fully exploited such that only some of the cell integrations need to be implemented. The values of given Slater integrals are obtained by assembling the cell integrals. This algorithm significantly improves the efficiency and accuracy of the traditional method that relies on the solution of differential equations and renders the B-spline method more effective when applied to multi-electron atomic systems.

Qiu, Y.; Fischer, C.F.

1999-12-10

330

Novel approaches to the parametric cubic-spline interpolation.  

PubMed

The cubic-spline interpolation (CSI) scheme can be utilized to obtain a better quality reconstructed image. It is based on the least-squares method with cubic convolution interpolation (CCI) function. Within the parametric CSI scheme, it is difficult to determine the optimal parameter for various target images. In this paper, a novel method involving the concept of opportunity costs is proposed to identify the most suitable parameter for the CCI function needed in the CSI scheme. It is shown that such an optimal four-point CCI function in conjunction with the least-squares method can achieve a better performance with the same arithmetic operations in comparison with the existing CSI algorithm. In addition, experimental results show that the optimal six-point CSI scheme together with cross-zonal filter is superior in performance to the optimal four-point CSI scheme without increasing the computational complexity. PMID:23192562

Hong, Shao-Hua; Wang, Lin; Truong, Trieu-Kien; Lin, Tsung-Ching; Wang, Lung-Jen

2012-11-22

331

Software for plotting Wilson-Fowler and nu-splines. [WFVPLT and NUPLOT  

SciTech Connect

This report describes two Fortran programs for plotting Wilson-Fowler splines (WF-splines) and other nu-splines. WFVPLT computes the WF-spline through a given data set, converts it to an equivalent nu-spline, and computes other comparison nu-splines. NUPLOT computes only nu-splines with specified nu's. Optional plots of the component functions and curvature vs arc length are available. Both codes also print approximations to the arc length and energy of each spline. 14 refs.

Fritsch, F.N.; Springmeyer, R.R.

1985-12-01

332

B-spline parametrization of the dielectric function applied to spectroscopic ellipsometry on amorphous carbon  

SciTech Connect

The remote plasma deposition of hydrogenated amorphous carbon (a-C:H) thin films is investigated by in situ spectroscopic ellipsometry (SE). The dielectric function of the a-C:H film is in this paper parametrized by means of B-splines. In contrast with the commonly used Tauc-Lorentz oscillator, B-splines are a purely mathematical description of the dielectric function. We will show that the B-spline parametrization, which requires no prior knowledge about the film or its interaction with light, is a fast and simple-to-apply method that accurately determines thickness, surface roughness, and the dielectric constants of hydrogenated amorphous carbon thin films. Analysis of the deposition process provides us with information about the high deposition rate, the nucleation stage, and the homogeneity in depth of the deposited film. Finally, we show that the B-spline parametrization can serve as a stepping stone to physics-based models, such as the Tauc-Lorentz oscillator.

Weber, J. W.; Hansen, T. A. R.; Sanden, M. C. M. van de; Engeln, R. [Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands)

2009-12-15

333

Cardiac motion tracking with multilevel B-splines and SinMod from tagged MRI  

NASA Astrophysics Data System (ADS)

Cardiac motion analysis can play an important role in cardiac disease diagnosis. Tagged magnetic resonance imaging (MRI) has the ability to directly and non-invasively alter tissue magnetization and produce tags on the deforming tissue. This paper proposes an approach to analysis of tagged MR images using a multilevel B-splines fitting model incorporating phase information. The novelty of the proposed technique is that phase information is extracted from SinMod.1 By using real tag intersections extracted directly from tagged MR image data and virtual tag intersections extracted from phase information, both considered to be scattered data, multilevel B-spline fitting can result in accurate displacement motion fields. The B-spline approximation which also serves to remove noise in the displacement measurements is performed without specifying control point locations explicitly and is very fast. Dense virtual tag intersections based on SinMod were created and incorporated into the multilevel B-spline fitting process. Experimental results on simulated data from the 13- parameter kinematic model of Arts et al.2 and in vivo canine data demonstrate further improvement in accuracy and effectiveness of the proposed method.

Wang, Hui; Amini, Amir A.

2011-03-01

334

Quantitative analysis of dynamic contrast-enhanced MR images based on Bayesian P-splines.  

PubMed

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is an important tool for detecting subtle kinetic changes in cancerous tissue. Quantitative analysis of DCE-MRI typically involves the convolution of an arterial input function (AIF) with a nonlinear pharmacokinetic model of the contrast agent concentration. Parameters of the kinetic model are biologically meaningful, but the optimization of the nonlinear model has significant computational issues. In practice, convergence of the optimization algorithm is not guaranteed and the accuracy of the model fitting may be compromised. To overcome these problems, this paper proposes a semi-parametric penalized spline smoothing approach, where the AIF is convolved with a set of B-splines to produce a design matrix using locally adaptive smoothing parameters based on Bayesian penalized spline models (P-splines). It has been shown that kinetic parameter estimation can be obtained from the resulting deconvolved response function, which also includes the onset of contrast enhancement. Detailed validation of the method, both with simulated and in vivo data, is provided. PMID:19272996

Schmid, Volker J; Whitcher, Brandon; Padhani, Anwar R; Yang, Guang-Zhong

2008-10-31

335

Comparison Between the Wilson-Fowler Spline and the Circle Spline Routines.  

National Technical Information Service (NTIS)

The Nuclear Weapons Complex has used the Wilson-Fowler Spline as its standard curve-fitting routine. This routine can be used effectively only in two dimensions since it requires an unacceptable amount of computer power to be adapted for use in three dime...

R. M. Dolin W. R. Oakes

1985-01-01

336

Chebyshev collocation benchmark for natural convection flow in differentially heated cavity  

NASA Astrophysics Data System (ADS)

In this paper we in part recreate simulations in the 8:1 differentially heated cavity that were carried out by Xin and Le Quéré [1]. Their method uses second order time stepping scheme and Chebyshev collocation method for spatial dimensions. Our results with the same method differ for about 10-4 from theirs. We further performed simulations using a method based on trigonometric functions for spatial dimensions. Results using the latter method differ for about few percent compared to results in [1].

Oder, J.; Tiselj, I.

2013-10-01

337

Fusion of panchromatic and multispectral images using B-spline tight frame  

NASA Astrophysics Data System (ADS)

Fusion of panchromatic image with multispectral image provides high-resolution data for geographical information system (GIS). This paper presents a method to fuse panchromatic image with multispectral image using B-spline tight frame. The fused image is obtained by processing the B-spline discrete tight frame transform subimages. Fusion of QuickBird remote sensing images is carried out. The spectral resolution of the fused image is high, and the spatial resolution is superior to the one corresponding to discrete wavelet transform (DWT) method as well as a recently reported discrete tight frame transform (DTFT) method. Moreover, this method almost removes the ring artifacts existing in DWT method and DTFT method, thus remarkably improving the visual effects of the fused images.

Gao, Xing; Li, Bodong

2011-10-01

338

Local Control of Bias and Tension in Beta-splines  

Microsoft Academic Search

The Beta-spline introduced recently by Barsky is a generalization of the uniform cubic B-spline: parametric discontinuities are introduced in such a way as to preserve continuity of the unit tangent and curvature vectors at joints (geometric continuity) while providing bias and tension parameters, independent of the position of control vertices, by which the shape of a curve or surface can

Brian A. Barsky; John C. Beatty

1983-01-01

339

Cardinal exponential splines: part I - theory and filtering algorithms  

Microsoft Academic Search

Causal exponentials play a fundamental role in classical system theory. Starting from those elementary building blocks, we propose a complete and self-contained signal processing formulation of exponential splines defined on a uniform grid. We specify the corresponding B-spline basis functions and investigate their reproduction properties (Green function and exponential polynomials); we also characterize their stability (Riesz bounds). We show that

Michael Unser; Thierry Blu

2005-01-01

340

Developable rational Bézier and B-spline surfaces  

Microsoft Academic Search

A constructive geometric approach to developable rational Bézier and B-spline surfaces is presented. It is based on the dual representation in the sense of projective geometry. By the principle of duality, projective algorithms for NURBS curves can be transferred to constructions for developable NURBS surfaces in dual rational B-spline form. We discuss the conversion to the usual tensor product representation

Helmut Pottmann; Gerald E. Farin

1995-01-01

341

Flexible smoothing with B-splines and penalties  

Microsoft Academic Search

B-splines are attractive for nonparametric modelling, but choosing the optimal number and positions of knots is a complex task. Equidistant knots can be used, but their small and discrete number allows only limited control over smoothness and fit. We propose to use a relatively large number of knots and a difference penalty on coefficients of adjacent B-splines. We show connections

Paul H. C. Eilers; Brian D. Marx

1996-01-01

342

Affine-invariant B-spline moments for curve matching  

Microsoft Academic Search

The article deals with the problem of matching and recognizing planar curves that are modeled by B-splines, independently of possible affine transformations to which the original curve has been subjected (for example, rotation, translation, scaling, orthographic, and semiperspective projections), and possible occlusion. It presents a fast algorithm for estimating the B-spline control points that is robust to nonuniform sampling, noise,

Zhaohui Huang; Fernand S. Cohen

1996-01-01

343

Algorithms for spline wavelet packets on an interval  

Microsoft Academic Search

The aim of this paper is to describe decomposition and reconstruction algorithms for spline wavelet packets on a closed interval.\\u000a In order to generate packet spaces of dyadic dimensions, it is necessary to modify the approach for spline wavelets on an\\u000a interval as studied by Chui, Quak and Weyrich in [3, 11].

Ewald Quak; Norman Weyrich

1997-01-01

344

Spline approximation of random processes and design problems  

Microsoft Academic Search

We consider the spline approximation of a continuous (continuously differentiable) random process with finite second moments based on n observations of the process (and its derivatives). The performance of the approximation is measured by mean errors (e.g., integrated or maximal quadratic mean errors). For Hermite interpolation splines, an optimal rule sets n observation locations (i.e., a design, a mesh). While,

Oleg Seleznjev

2000-01-01

345

Interpolation with Splines in Tension: A Green's Function Approach  

Microsoft Academic Search

Interpolation and gridding of data are procedures in the physical sciences and are accomplished typically using an averaging or finite difference scheme on an equidistant grid. Cubic splines are popular because of their smooth appearances; however, these functions can have undesirable oscillations between data points. Adding tension to the spline overcomes this deficiency. Here, we derive a technique for interpolation

Paul Wessel; David Bercovici

1998-01-01

346

Natural Cubic Spline Coalescence Hidden Variable Fractal Interpolation Surfaces  

NASA Astrophysics Data System (ADS)

Fractal interpolation functions provide a new light to the natural deterministic approximation and modeling of complex phenomena. The present paper proposes construction of natural cubic spline coalescence hidden variable fractal interpolation surfaces (CHFISs) over a rectangular grid {R} through the tensor product of univariate bases of cardinal natural cubic spline coalescence hidden variable fractal interpolation functions (CHFIFs). Natural cubic CHFISs are self-affine or non-self-affine in nature depending on the IFS parameters of univariate natural cubic spline CHFIFs. An upper bound of the error between the natural cubic spline blended coalescence fractal interpolant and the original function is deduced. Convergence of the natural cubic CHFIS to the original function f \\in C4[{R}], and their derivatives are deduced. The effects free variables, constrained free variables and hidden variables are discussed on the natural cubic spline CHFIS with suitably chosen examples.

Chand, A. K. B.

2012-06-01

347

Metal flowing of involute spline cold roll-beating forming  

NASA Astrophysics Data System (ADS)

The present research on involute spline cold roll-beating forming is mainly about the principles and motion relations of cold roll-beating, the theory of roller design, and the stress and strain field analysis of cold roll-beating, etc. However, the research on law of metal flow in the forming process of involute spline cold roll-beating is rare. According to the principle of involute spline cold roll-beating, the contact model between the rollers and the spline shaft blank in the process of cold roll-beating forming is established, and the theoretical analysis of metal flow in the cold roll-beating deforming region is proceeded. A finite element model of the spline cold roll-beating process is established, the formation mechanism of the involute spline tooth profile in cold roll-beating forming process is studied, and the node flow tracks of the deformation area are analyzed. The experimental research on the metal flow of cold roll-beating spline is conducted, and the metallographic structure variation, grain characteristics and metal flow line of the different tooth profile area are analyzed. The experimental results show that the particle flow directions of the deformable bodies in cold roll-beating deformation area are determined by the minimum moving resistance. There are five types of metal flow rules of the deforming region in the process of cold roll-beating forming. The characteristics of involute spline cold roll-beating forming are given, and the forming mechanism of involute spline cold roll-beating is revealed. This paper researches the law of metal flow in the forming process of involute spline cold roll-beating, which provides theoretical supports for solving the tooth profile forming quality problem.

Cui, Fengkui; Wang, Xiaoqiang; Zhang, Fengshou; Xu, Hongyu; Quan, Jianhui; Li, Yan

2013-09-01

348

Maxentropic interpolation by cubic splines with possibly noisy data  

NASA Astrophysics Data System (ADS)

The gist of this note is to present a procedure for obtaining numerical solutions of Fredholm equations of the first kind of the type ?01K(s,t)x(t)dt+?(s)=y(s), where K:V-->W is a linear operator mapping V=C([0,1]), the continuous functions on [0, 1], into some other Banach space of functions W, and ? is a W-valued random process. The procedure followed consists of partitioning [0, 1] and leaving the values of x(t) at the points of the partitions as unknowns to be found by the method of maximum entropy in the mean. The data vector is also approximated by a finitely dimensional vector, and at the end we obtain an algebraic problem Ax+?=ywhere the matrix A is obtained from the kernel K applied to the cubic spline that approximates x. .

Gzyl, H.; Velasquez, Y.

2001-05-01

349

Improving the Health of Infants on Medicaid by Collocating Special Supplemental Nutrition Clinics With Managed Care Provider Sites  

PubMed Central

Objectives. This study tested whether collocation of Special Supplemental Nutrition Program for Women, Infants, and Children (WIC) clinics at managed care provider sites improved health care for infants enrolled in Medicaid and WIC. Methods. Weights and immunization rates were studied for the 1997 birth cohort of African American infants enrolled in WIC and Medicaid in Detroit, Mich. Infants using traditional WIC clinics and health services were compared with those enrolled under Medicaid in 2 managed care organizations (MCOs), of whom about half obtained WIC services at MCO provider sites. Results. Compared with other infants, those who used collocated WIC sites either were closer to their age-appropriate weight or had higher immunization rates when recertified by WIC after their first birthday. Specific benefits (weight gain or immunizations) varied according to the priorities at the collocated sites operated by the 2 MCOs. Conclusions. Collocation of WIC clinics at MCO sites can improve health care of low-income infants. However specific procedures for cooperation between WIC staff and other MCO staff are required to achieve this benefit. (Am J Public Health. 2002;92:399–403)

Kendal, Alan P.; Peterson, Alwin; Manning, Claudine; Xu, Fujie; Neville, Loretta J.; Hogue, Carol

2002-01-01

350

Physically Accurate B-Spline Based Non-Rigid Registration Using Variable Spring Model  

Microsoft Academic Search

This paper presents a physically accurate fast parametric non-rigid registration method based on B-spline deformation model. Our method is based on using variable spring model to add a physical constraint to ensure that the deformation does not violate elasticity characteristic of the organs. Using the assumption of human organs as elastic bodies, we modeled the whole volume as 3-D springs

Nicholas Herlambang; Hongen Liao; Kiyoshi Matsumiya; Ken Masamune; Takeyoshi Dohi

2007-01-01

351

English Learners' Knowledge of Prepositions: Collocational Knowledge or Knowledge Based on Meaning?  

ERIC Educational Resources Information Center

Second language (L2) learners' successful performance in an L2 can be partly attributed to their knowledge of collocations. In some cases, this knowledge is accompanied by knowledge of the semantic and/or grammatical patterns that motivate the collocation. At other times, collocational knowledge may serve a compensatory role. To determine the…

Mueller, Charles M.

2011-01-01

352

Collocational Strategies of Arab Learners of English: A Study in Lexical Semantics.  

ERIC Educational Resources Information Center

|Arab learners of English encounter a serious problem with collocational sequences. The present study purports to determine the extent to which university English language majors can use English collocations properly. A two-form translation test of 16 Arabic collocations was administered to both graduate and undergraduate students of English. The…

Muhammad, Raji Zughoul; Abdul-Fattah, Hussein S.

353

An Exploratory Study of Collocational Use by ESL Students--A Task Based Approach  

ERIC Educational Resources Information Center

|Collocation is an aspect of language generally considered arbitrary by nature and problematic to L2 learners who need collocational competence for effective communication. This study attempts, from the perspective of L2 learners, to have a deeper understanding of collocational use and some of the problems involved, by adopting a task based…

Fan, May

2009-01-01

354

L2 Learner Production and Processing of Collocation: A Multi-Study Perspective  

ERIC Educational Resources Information Center

|This article presents a series of studies focusing on L2 production and processing of adjective-noun collocations (e.g., "social services"). In Study 1, 810 adjective-noun collocations were extracted from 31 essays written by Russian learners of English. About half of these collocations appeared frequently in the British National Corpus (BNC);…

Siyanova, Anna; Schmitt, Norbert

2008-01-01

355

English Learners' Knowledge of Prepositions: Collocational Knowledge or Knowledge Based on Meaning?  

ERIC Educational Resources Information Center

|Second language (L2) learners' successful performance in an L2 can be partly attributed to their knowledge of collocations. In some cases, this knowledge is accompanied by knowledge of the semantic and/or grammatical patterns that motivate the collocation. At other times, collocational knowledge may serve a compensatory role. To determine the…

Mueller, Charles M.

2011-01-01

356

The Use of Collocations by Advanced Learners of English and Some Implications for Teaching.  

ERIC Educational Resources Information Center

|Analyzes the use of verb-noun collocations by advanced German speaking students of English in free written production. Types of mistakes that learners make when producing collocations are identified. The influence of the degree of restriction of a combination and of learners' first language on the production of collocations is investigated. (VWL)|

Nesselhauf, Nadja

2003-01-01

357

Comparing measures of model selection for penalized splines in Cox models  

PubMed Central

This article presents an application and a simulation study of model fit criteria for selecting the optimal degree of smoothness for penalized splines in Cox models. The criteria considered were the Akaike information criterion, the corrected AIC, two formulations of the Bayesian information criterion, and a generalized cross-validation method. The estimated curves selected by the five methods were compared to each other in a study of rectal cancer mortality in autoworkers. In the stimulation study, we estimated the fit of the penalized spline models in six exposure-response scenarios, using the five model fit criteria. The methods were compared based on a mean squared-error score and the power and size of hypothesis tests for any effect and for detecting nonlinearity. All comparisons were made across a range in the total sample size and number of cases.

Malloy, Elizabeth J.; Spiegelman, Donna; Eisen, Ellen A.

2009-01-01

358

Left ventricular motion reconstruction with a prolate spheroidal B-spline model.  

PubMed

Tagged cardiac magnetic resonance (MR) imaging can non-invasively image deformation of the left ventricular (LV) wall. Three-dimensional (3D) analysis of tag data requires fitting a deformation model to tag lines in the image data. In this paper, we present a 3D myocardial displacement and strain reconstruction method based on a B-spline deformation model defined in prolate spheroidal coordinates, which more closely matches the shape of the LV wall than existing Cartesian or cylindrical coordinate models. The prolate spheroidal B-spline (PSB) deformation model also enforces smoothness across and can compute strain at the apex. The PSB reconstruction algorithm was evaluated on a previously published data set to allow head-to-head comparison of the PSB model with existing LV deformation reconstruction methods. We conclude that the PSB method can accurately reconstruct deformation and strain in the LV wall from tagged MR images and has several advantages relative to existing techniques. PMID:16424579

Li, Jin; Denney, Thomas S

2006-01-11

359

Using B splines to investigate rectangular-plate flexure  

SciTech Connect

Recently, B splines have been used in solving one-, two-, and three-dimensional problems of shell and plate theory on account of their good approximating properties and convenience in numerical approaches. Researchers have used spline functions with a uniform grid and have only considered certai types of boundary conditions. At the same time, the application of splines to problems described by systems of differential equations with discontinuous coefficients entails a considerable volume of calculations, which raises questions about their applicability to practically important problems of plate and shell statics.

Kryukov, N.N.

1995-08-01

360

Collocation with nonlinear programming for two-sided flight path optimization  

NASA Astrophysics Data System (ADS)

This research successfully develops a new numerical method for the problem of two-sided flight path optimization, that is, a method capable of finding trajectories satisfying the necessary condition of an open-loop representation of a saddle-point trajectory. The method of direct collocation with nonlinear programming is extended to find the solution of a zerosum two-person differential game by incorporating the analytical optimality condition for one player into the system equations. The new method is named semi-direct collocation with nonlinear programming (semi-DCNLP). We apply the new method to a variety of problems of increasing complexity; the dolichobrachistochrone, a problem of ballistic interception, the homicidal chauffeur problem and minimum-time spacecraft interception for optimally evasive target, and thus verify that the method is capable of identifying saddle-point trajectories. While the method is quite robust, ambitious problems require a reasonable initial guess of the discretized solution from which the optimizer may converge. A method for generating a good initial guess, requiring no a priori information about the solution, is developed using genetic algorithms. The semi-DCNLP, in combination with the genetic algorithm-based preprocessor, is then used to solve a very complicated pursuit-evasion problem; optimal air combat for realistic fighter aircraft models in three dimensions. Characteristics of the optimal air combat maneuvers for both aircraft are identified for many different initial conditions.

Horie, Kazuhiro

361

The numerical solution of fifth-order boundary value problems with sixth-degree B-spline functions  

Microsoft Academic Search

The numerical solution of fifth-order, nonlinear boundary-value problems with two-point boundary conditions is considered. A sixth-degree B-spline approximation is used to construct the numerical method, the coefficients of which are detailed in a table. The method is tested on two problems, one linear and one nonlinear.

E. H. Twizell

1999-01-01

362

Quantification of spinal cord atrophy from magnetic resonance images via a B-spline active surface model  

Microsoft Academic Search

A method is presented that aims at segmenting and measuring the surface of the spinal cord from MR images in order to detect and quantify atrophy. A semiautomatic segmentation with very little intervention from an operator is proposed. It is based on the optimization of a B-spline active surface. The method al- lows for the computation of orthogonal cross-sections at

O. Coulon; S. J. Hickman; G. J. Parker; G. J. Barker; D. H. Miller; S. R. Arridge

2002-01-01

363

Parameter estimation in systems biology models using spline approximation  

PubMed Central

Background Mathematical models for revealing the dynamics and interactions properties of biological systems play an important role in computational systems biology. The inference of model parameter values from time-course data can be considered as a "reverse engineering" process and is still one of the most challenging tasks. Many parameter estimation methods have been developed but none of these methods is effective for all cases and can overwhelm all other approaches. Instead, various methods have their advantages and disadvantages. It is worth to develop parameter estimation methods which are robust against noise, efficient in computation and flexible enough to meet different constraints. Results Two parameter estimation methods of combining spline theory with Linear Programming (LP) and Nonlinear Programming (NLP) are developed. These methods remove the need for ODE solvers during the identification process. Our analysis shows that the augmented cost function surfaces used in the two proposed methods are smoother; which can ease the optima searching process and hence enhance the robustness and speed of the search algorithm. Moreover, the cores of our algorithms are LP and NLP based, which are flexible and consequently additional constraints can be embedded/removed easily. Eight system biology models are used for testing the proposed approaches. Our results confirm that the proposed methods are both efficient and robust. Conclusions The proposed approaches have general application to identify unknown parameter values of a wide range of systems biology models.

2011-01-01

364

Collocation: Integrating Child Welfare and Substance Abuse Services  

Microsoft Academic Search

This article presents findings from a process evaluation of a pilot program to address parental substance abuse in the child welfare system. By placing substance abuse counselors in a local child welfare office, the collocation program was designed to facilitate early identification, timely referral to treatment, and improved treatment engagement of substance-abusing parents. Frontline child welfare workers in 6 of

Eunju Lee; Nina Esaki; Rose Greene

2009-01-01

365

Beyond Single Words: The Most Frequent Collocations in Spoken English  

ERIC Educational Resources Information Center

|This study presents a list of the highest frequency collocations of spoken English based on carefully applied criteria. In the literature, more than forty terms have been used for designating multi-word units, which are generally not well defined. To avoid this confusion, six criteria are strictly applied. The ten million word BNC spoken section…

Shin, Dongkwang; Nation, Paul

2008-01-01

366

The Effects of Vocabulary Learning on Collocation and Meaning  

ERIC Educational Resources Information Center

|This study investigates the effects of receptive and productive vocabulary tasks on learning collocation and meaning. Japanese English as a foreign language students learned target words in three glossed sentences and in a cloze task. To determine the effects of the treatments, four tests were used to measure receptive and productive knowledge of…

Webb, Stuart; Kagimoto, Eve

2009-01-01

367

Redefining Creativity--Analyzing Definitions, Collocations, and Consequences  

ERIC Educational Resources Information Center

|How holistically is human creativity defined, investigated, and understood? Until recently, most scientific research on creativity has focused on its positive side. However, creativity might not only be a desirable resource but also be a potential threat. In order to redefine creativity we need to analyze and understand definitions, collocations,…

Kampylis, Panagiotis G.; Valtanen, Juri

2010-01-01

368

The spline probability hypothesis density filter  

NASA Astrophysics Data System (ADS)

The Probability Hypothesis Density Filter (PHD) is a multitarget tracker for recursively estimating the number of targets and their state vectors from a set of observations. The PHD filter is capable of working well in scenarios with false alarms and missed detections. Two distinct PHD filter implementations are available in the literature: the Sequential Monte Carlo Probability Hypothesis Density (SMC-PHD) and the Gaussian Mixture Probability Hypothesis Density (GM-PHD) filters. The SMC-PHD filter uses particles to provide target state estimates, which can lead to a high computational load, whereas the GM-PHD filter does not use particles, but restricts to linear Gaussian mixture models. The SMC-PHD filter technique provides only weighted samples at discrete points in the state space instead of a continuous estimate of the probability density function of the system state and thus suffers from the well-known degeneracy problem. This paper proposes a B-Spline based Probability Hypothesis Density (S-PHD) filter, which has the capability to model any arbitrary probability density function. The resulting algorithm can handle linear, non-linear, Gaussian, and non-Gaussian models and the S-PHD filter can also provide continuous estimates of the probability density function of the system state. In addition, by moving the knots dynamically, the S-PHD filter ensures that the splines cover only the region where the probability of the system state is significant, hence the high efficiency of the S-PHD filter is maintained at all times. Also, unlike the SMC-PHD filter, the S-PHD filter is immune to the degeneracy problem due to its continuous nature. The S-PHD filter derivations and simulations are provided in this paper.

Sithiravel, Rajiv; Tharmarasa, Ratnasingham; McDonald, Mike; Pelletier, Michel; Kirubarajan, Thiagalingam

2012-05-01

369

Semi-parametric analysis of dynamic contrast-enhanced MRI using Bayesian P-splines.  

PubMed

Current approaches to quantitative analysis of DCE-MRI with non-linear models involve the convolution of an arterial input function (AIF) with the contrast agent concentration at a voxel or regional level. Full quantification provides meaningful biological parameters but is complicated by the issues related to convergence, (de-)convolution of the AIF, and goodness of fit. To overcome these problems, this paper presents a penalized spline smoothing approach to model the data in a semi-parametric way. With this method, the AIF is convolved with a set of B-splines to produce the design matrix, and modeling of the resulting deconvolved biological parameters is obtained in a way that is similar to the parametric models. Further kinetic parameters are obtained by fitting a non-linear model to the estimated response function and detailed validation of the method, both with simulated and in vivo data is PMID:17354949

Schmid, Volker J; Whitcher, Brandon; Yang, Guang-Zhong

2006-01-01

370

Isogeometric divergence-conforming B-splines for the unsteady Navier-Stokes equations  

NASA Astrophysics Data System (ADS)

Divergence-conforming B-splines are developed for application to the incompressible Navier-Stokes equations on geometrically mapped domains. These enable smooth, pointwise divergence-free solutions and thus satisfy mass conservation in the strongest possible sense. Semi-discrete methods based on divergence-conforming B-splines are shown to conserve linear and angular momentum and satisfy balance laws for energy, vorticity, enstrophy, and helicity. These are geometric structure-preserving quantities and numerical simulations that are sensitive to them are shown to be qualitatively correct and quantitatively accurate. The methods developed are anticipated to open new doors to the practical calculation of complex flows and to studies of their physical behavior.

Evans, John A.; Hughes, Thomas J. R.

2013-05-01

371

Trajectory Design and Control of a Wheel-type Mobile Robot Using B-spline Curve  

Microsoft Academic Search

In flexible trajectory control of a mobile robot it is preferable to design a smooth trajectory which passes specified points with specified tangents in a two dimensional plane. A trajectory design method which satisfies the above condition is presented using a Bspline curve. In order to use the designed B-spline curve for a two-wheel-driven-type mobile mechanism the possibility of using

Kiyoshi Komoriya; Kazuo Tanie

1989-01-01

372

Realization Methodology of a 5-axis Spline Interpolator in an Open CNC System  

Microsoft Academic Search

By making use of the advantages of non-uniform rational B-spline (NURBS) curves to represent spatial curves, an instruction format with double NURBS curves suitable for 5-axis coordinated real-time interpolation is presented to replace the current 5-axis coordinated linear interpolation method defective in low-speed, low-accuracy and enormous numerical control (NC) files in sculptured surface machining. A generation procedure of the NC

Yongzhang Wang; Xiongbo Ma; Liangji Chen; Zhenyu Han

2007-01-01

373

5Axis A-Spline Iterpolation Function and Its Realization Strategy  

Microsoft Academic Search

The current 5-axis coordinated linear interpolation method results in low-speed, low-accuracy and enormous numerical control (NC) files in sculptured surface machining. An instruction format with AKIMA spline curves suitable for 5-axis coordinated real-time interpolation is presented by making use of the advantages of AKIMA curves to represent spatial curves. Curve through position vectors in the machining path is constructed using

Han Zhen-yu; Liu Yuan; Wang Yong-zhang; Fu Hong-ya

2009-01-01

374

Detail view of redwood spline joinery of woodframe section against ...  

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

Detail view of redwood spline joinery of wood-frame section against adobe addition (measuring tape denotes plumb line from center of top board) - First Theatre in California, Southwest corner of Pacific & Scott Streets, Monterey, Monterey County, CA

375

L1 Influence on the Acquisition of L2 Collocations: Japanese ESL Users and EFL Learners Acquiring English Collocations  

ERIC Educational Resources Information Center

|This study investigated first language (L1) influence on the acquisition of second language (L2) collocations using a framework based on Kroll and Stewart (1994) and Jiang (2000), by comparing the performance on a phrase-acceptability judgment task among native speakers of English, Japanese English as a second language (ESL) users, and Japanese…

Yamashita, Junko; Jiang, Nan

2010-01-01

376

Trivariate spline approximations of 3D Navier-Stokes equations  

Microsoft Academic Search

We present numerical approximations of the 3D steady state Nav- ier-Stokes equations in velocity-pressure formulation using trivariate splines of arbitrary degree d and arbitrary smoothness r with rsplines over a tetrahedral partition of any given polyg- onal domain. Smoothness conditions, boundary

Gerard Awanou; Ming-Jun Lai

2005-01-01

377

TURBS—Topologically Unrestricted Rational B-Splines  

Microsoft Academic Search

.    We present a new approach to the construction of piecewise polynomial or rational C\\u000a \\u000a k\\u000a -spline surfaces of arbitrary topological structure. The basic idea is to use exclusively parametric smoothness conditions,\\u000a and to solve the well-known problems at extraordinary points by admitting singular parametrizations. The smoothness of the\\u000a spline surfaces is guaranteed by specifying a regular smooth reparametrization

Ulrich Reif

1998-01-01

378

Simple Algorithms and Architectures for B-spline Interpolation  

Microsoft Academic Search

It is proved that the Toeplitz binary value matrix inversion associated with mth-order B-spline interpolation can be implemented using only 2(m+1) additions. Pipelined architectures are developed for real-time B-spline interpolation based on simple running average filters. It is shown that an ideal interpolating function, which is approximated by a truncated sinc function with M half cycles, can be implemented using

P. V. Sankar; Leonard A. Ferrari

1988-01-01

379

Scale-Space Derived From B-Splines  

Microsoft Academic Search

It is well-known that the linear scale-space theory in computer vision is mainly based on the Gaussian kernel. The purpose of the paper is to propose a scale-space theory based on B-spline kernels. Our aim is twofold. On one hand, we present a general framework and show how B-splines provide a flexible tool to design various scale-space representations: continuous scale-

Yu-ping Wang; Seng Luan Lee

1998-01-01

380

Hybrid physics-based elastic image registration using approximating splines  

Microsoft Academic Search

We introduce a new hybrid physics-based approach for elastic image registration using approximating splines. As underlying deformation model we employ Gaussian elastic body splines (GEBS), which are an analytic solution of the Navier equation under Gaussian forces and are represented by matrix-valued basis functions. Our approach is formulated as an energy-minimizing functional that incorporates both landmark and intensity information as

Stefan Wörz; Karl Rohr

2008-01-01

381

Global and regional surface-wave inversions: A spherical-spline parameterization  

NASA Astrophysics Data System (ADS)

A surface-wave phase-velocity inversion scheme based upon a compactly supported cubic B-spline basis on a triangular grid of knots with approximately equal inter-knot spacing is implemented to perform global, regional and variable resolution inversions. Numerical results show that the inverted phase-velocity maps based upon this method are similar to those obtained using a global spherical-harmonic representation. Nonlinear inversions incorporating ray refraction are feasible based upon the spherical-spline model parameterization and the resulting maps are only slightly different from those based upon the great-circle approximation. A multiresolution analysis is introduced to obtain finer resolution in regions with good ray coverage and lower resolution in regions with poor coverage.

Wang, Zheng; Tromp, Jeroen; Ekström, Göran

382

Cubic Spline Wavelets Satisfying Homogeneous Boundary Conditions for Fourth-Order Problems  

NASA Astrophysics Data System (ADS)

The paper is concerned with a construction of cubic spline wavelet bases on the interval which are adapted to homogeneous Dirichlet boundary conditions for fourth-order problems. The resulting bases generate multiresolution analyses on the unit interval with the desired number of vanishing wavelet moments. Inner wavelets are translated and dilated versions of well-known wavelets designed by Cohen, Daubechies, and Feauveau. The construction of boundary scaling functions and wavelets is a delicate task, because they may significantly worsen conditions of resulting bases as well as condition numbers of corresponding stiffness matrices. We present quantitative properties of the constructed bases and we show superiority of our construction in comparison to some other known spline wavelet bases in an adaptive wavelet method for the partial differential equation with the biharmonic operator.

?erná, Dana; Fin?k, Václav

2009-09-01

383

B-spline goal-oriented error estimators for geometrically nonlinear rods  

NASA Astrophysics Data System (ADS)

We consider goal-oriented a posteriori error estimators for the evaluation of the errors on quantities of interest associated with the solution of geometrically nonlinear curved elastic rods. For the numerical solution of these nonlinear one-dimensional problems, we adopt a B-spline based Galerkin method, a particular case of the more general isogeometric analysis. We propose error estimators using higher order "enhanced" solutions, which are based on the concept of enrichment of the original B-spline basis by means of the "pure" k-refinement procedure typical of isogeometric analysis. We provide several numerical examples for linear and nonlinear output functionals, corresponding to the rotation, displacements and strain energy of the rod, and we compare the effectiveness of the proposed error estimators.

Dedè, L.; Santos, H. A. F. A.

2012-01-01

384

On developing B-spline registration algorithms for multi-core processors.  

PubMed

Spline-based deformable registration methods are quite popular within the medical-imaging community due to their flexibility and robustness. However, they require a large amount of computing time to obtain adequate results. This paper makes two contributions towards accelerating B-spline-based registration. First, we propose a grid-alignment scheme and associated data structures that greatly reduce the complexity of the registration algorithm. Based on this grid-alignment scheme, we then develop highly data parallel designs for B-spline registration within the stream-processing model, suitable for implementation on multi-core processors such as graphics processing units (GPUs). Particular attention is focused on an optimal method for performing analytic gradient computations in a data parallel fashion. CPU and GPU versions are validated for execution time and registration quality. Performance results on large images show that our GPU algorithm achieves a speedup of 15 times over the single-threaded CPU implementation whereas our multi-core CPU algorithm achieves a speedup of 8 times over the single-threaded implementation. The CPU and GPU versions achieve near-identical registration quality in terms of RMS differences between the generated vector fields. PMID:20938071

Shackleford, J A; Kandasamy, N; Sharp, G C

2010-10-12

385

Smoothing in occupational cohort studies: an illustration based on penalised splines  

PubMed Central

Aims: To illustrate the contribution of smoothing methods to modelling exposure-response data, Cox models with penalised splines were used to reanalyse lung cancer risk in a cohort of workers exposed to silica in California's diatomaceous earth industry. To encourage application of this approach, computer code is provided. Methods: Relying on graphic plots of hazard ratios as smooth functions of exposure, the sensitivity of the curve to amount of smoothing, length of the exposure lag, and the influence of the highest exposures was evaluated. Trimming and data transformations were used to down-weight influential observations. Results: The estimated hazard ratio increased steeply with cumulative silica exposure before flattening and then declining over the sparser regions of exposure. The curve was sensitive to changes in degrees of freedom, but insensitive to the number or location of knots. As the length of lag increased, so did the maximum hazard ratio, but the shape was similar. Deleting the two highest exposed subjects eliminated the top half of the range and allowed the hazard ratio to continue to rise. The shape of the splines suggested a parametric model with log hazard as a linear function of log transformed exposure would fit well. Conclusions: This flexible statistical approach reduces the dependence on a priori assumptions, while pointing to a suitable parametric model if one exists. In the absence of an appropriate parametric form, however, splines can provide exposure-response information useful for aetiological research and public health intervention.

Eisen, E; Agalliu, I; Thurston, S; Coull, B; Checkoway, H

2004-01-01

386

Three-dimensional stress analysis in laminated composites with fasteners based on the B-spline approximation  

Microsoft Academic Search

A three dimensional contact problem describing the interaction between a composite plate with a circular hole and elastic fastener has been solved by using the displacement spline approximation and Lagrangian multiplier method. An algorithm capable of adjusting the nonuniform through the thickness contact zone was developed. The converged contact conditions: radial stress and displacement continuity are shown in each ply

Endel Iarve

1997-01-01

387

The Feature Extraction Based on Nonlinear Partial Orthogonal Analysis with B-Spline Function for Signal of Vibrational Sensors  

Microsoft Academic Search

The new method of feature extraction based on nonlinear partial orthogonal analysis with B-spline function for signal of vibrational sensors is proposed in the paper. Firstly, the nonlinear signal is mapped into linear space; then, the signal is analyzed in the linear space; finally, a set of eigenvalue vectors are obtained with nonlinear partial orthogonal analysis. The vectors reflect a

Liu Gui-Guo; Yue Bin; Huang Dao; Huang Hai-Yan

2008-01-01

388

A Corpus-Based Study of the Linguistic Features and Processes Which Influence the Way Collocations Are Formed: Some Implications for the Learning of Collocations  

ERIC Educational Resources Information Center

|In this article I examine the collocational behaviour of groups of semantically related verbs (e.g., "head, run, manage") and nouns (e.g., "issue, factor, aspect") from the domain of business English. The results of this corpus-based study show that much of the collocational behaviour exhibited by these lexical items can be explained by examining…

Walker, Crayton Phillip

2011-01-01

389

Beta-function B-spline smoothing on triangulations  

NASA Astrophysics Data System (ADS)

In this work we investigate a novel family of Ck-smooth rational basis functions on triangulations for fitting, smoothing, and denoising geometric data. The introduced basis function is closely related to a recently introduced general method introduced in utilizing generalized expo-rational B-splines, which provides Ck-smooth convex resolutions of unity on very general disjoint partitions and overlapping covers of multidimensional domains with complex geometry. One of the major advantages of this new triangular construction is its locality with respect to the star-1 neighborhood of the vertex on which the said base is providing Hermite interpolation. This locality of the basis functions can be in turn utilized in adaptive methods, where, for instance a local refinement of the underlying triangular mesh affects only the refined domain, whereas, in other method one needs to investigate what changes are occurring outside of the refined domain. Both the triangular and the general smooth constructions have the potential to become a new versatile tool of Computer Aided Geometric Design (CAGD), Finite and Boundary Element Analysis (FEA/BEA) and Iso-geometric Analysis (IGA).

Dechevsky, Lubomir T.; Zanaty, Peter

2013-03-01

390

User's guide for Wilson-Fowler spline software: SPLPKG, WFCMPR, WFAPPX - CADCAM-010  

SciTech Connect

The Wilson-Fowler spline is widely used in computer aided manufacturing, but is not available in all commercial CAD/CAM systems. These three programs provide a capability for generating, comparing, and approximating Wilson-Fowler splines. SPLPKG generates a spline passing through given nodes, and computes a piecewise linear approximation to the spline. WFCMPR computes the difference between two splines with common nodes. WFAPPX computes the difference between a spline and a piecewise linear curve. The programs are in Fortran 77 and are machine independent.

Fletcher, S.K.

1985-02-01

391

Converting an unstructured quadrilateral mesh to a standard T-spline surface  

NASA Astrophysics Data System (ADS)

This paper presents a novel method for converting any unstructured quadrilateral mesh to a standard T-spline surface, which is C 2-continuous except for the local region around each extraordinary node. There are two stages in the algorithm: the topology stage and the geometry stage. In the topology stage, we take the input quadrilateral mesh as the initial T-mesh, design templates for each quadrilateral element type, and then standardize the T-mesh by inserting nodes. One of two sufficient conditions is derived to guarantee the generated T-mesh is gap-free around extraordinary nodes. To obtain a standard T-mesh, a second sufficient condition is provided to decide what T-mesh configuration yields a standard T-spline. These two sufficient conditions serve as a theoretical basis for our template development and T-mesh standardization. In the geometry stage, an efficient surface fitting technique is developed to improve the geometric accuracy. In addition, the surface continuity around extraordinary nodes can be improved by adjusting surrounding control nodes. The algorithm can also preserve sharp features in the input mesh, which are common in CAD (Computer Aided Design) models. Finally, a Bézier extraction technique is used to facilitate T-spline based isogeometric analysis. Several examples are tested to show the robustness of the algorithm.

Wang, Wenyan; Zhang, Yongjie; Scott, Michael A.; Hughes, Thomas J. R.

2011-10-01

392

TableTops: Worthwhile Experiences of Collocated and Remote Collaboration  

Microsoft Academic Search

Tabletops incite people to collaborate around shared documents. We propose DigiTable, a platform for collocated and remote collaboration which attempts to preserve the fluidity of interactions and the mutual awareness of co- presence. DigiTable combines a multiuser tactile table- top, a video-communication system and a robust computer vision module for distant users' gesture visualization. From an experiment, we show that

A. Pauchet; F. Coldefy; L. Lefebvre; S. Louis Dit Picard; L. Perron; A. Bouguet; M. Collobert; J. Guerin; D. Corvaisier

2007-01-01

393

BOX SPLINE BASED 3D TOMOGRAPHIC RECONSTRUCTION OF DIFFUSION PROPAGATORS FROM MRI DATA.  

PubMed

This paper introduces a tomographic approach for reconstruction of diffusion propagators, P( r ), in a box spline framework. Box splines are chosen as basis functions for high-order approximation of P( r ) from the diffusion signal. Box splines are a generalization of B-splines to multivariate setting that are particularly useful in the context of tomographic reconstruction. The X-Ray or Radon transform of a (tensor-product B-spline or a non-separable) box spline is a box spline - the space of box splines is closed under the Radon transform.We present synthetic and real multi-shell diffusion-weighted MR data experiments that demonstrate the increased accuracy of P( r ) reconstruction as the order of basis functions is increased. PMID:23459604

Ye, Wenxing; Portnoy, Sharon; Entezari, Alireza; Vemuri, Baba C; Blackband, Stephen J

2011-03-30

394

BOX SPLINE BASED 3D TOMOGRAPHIC RECONSTRUCTION OF DIFFUSION PROPAGATORS FROM MRI DATA  

PubMed Central

This paper introduces a tomographic approach for reconstruction of diffusion propagators, P(r), in a box spline framework. Box splines are chosen as basis functions for high-order approximation of P(r) from the diffusion signal. Box splines are a generalization of B-splines to multivariate setting that are particularly useful in the context of tomographic reconstruction. The X-Ray or Radon transform of a (tensor-product B-spline or a non-separable) box spline is a box spline – the space of box splines is closed under the Radon transform. We present synthetic and real multi-shell diffusion-weighted MR data experiments that demonstrate the increased accuracy of P(r) reconstruction as the order of basis functions is increased.

Ye, Wenxing; Portnoy, Sharon; Entezari, Alireza; Vemuri, Baba C.; Blackband, Stephen J.

2011-01-01

395

Growth curve analysis for plasma profiles using smoothing splines  

SciTech Connect

We are developing a profile analysis code for the statistical estimation of the parametric dependencies of the temperature and density profiles in tokamaks. Our code uses advanced statistical techniques to determine the optimal fit, i.e. the fit which minimized the predictive error. For a forty TFTR Ohmic profile dataset, our preliminary results indicate that the profile shape depends almost exclusively on q[sub a][prime] but that the shape dependencies are not Gaussian. We are now comparing various shape models on the TFTR data. In the first six months, we have completed the core modules of the code, including a B-spline package for variable knot locations, a data-based method to determine the optimal smoothing parameters, self-consistent estimation of the bias errors, and adaptive fitting near the plasma edge. Visualization graphics already include three dimensional surface plots, and discharge by discharge plots of the predicted curves with error bars together with the actual measurements values, and plots of the basis functions with errors.

Imre, K.

1993-05-01

396

Spline-based models for predictiveness curves and surfaces  

PubMed Central

A biomarker is defined to be a biological characteristic that is objectively measured and evaluated as an indicator of normal biologic processes, pathogenic processes, or pharmacologic responses to a therapeutic intervention. The use of biomarkers in cancer has been advocated for a variety of purposes, which include use as surrogate endpoints, early detection of disease, proxies for environmental exposure and risk prediction. We deal with the latter issue in this paper. Several authors have proposed use of the predictiveness curve for assessing the capacity of a biomarker for risk prediction. For most situations, it is reasonable to assume monotonicity of the biomarker effects on disease risk. In this article, we propose the use of flexible modelling of the predictiveness curve and its bivariate analogue, the predictiveness surface, through the use of spline algorithms that incorporate the appropriate monotonicity constraints. Estimation proceeds through use of a two-step algorithm that represents the “smooth, then monotonize” approach. Subsampling procedures are used for inference. The methods are illustrated to data from a melanoma study.

Ghosh, Debashis; Sabel, Michael

2010-01-01

397

Polynomial spline signal approximations: Filter design and asymptotic equivalence with Shannon's sampling theorem  

Microsoft Academic Search

The least-squares polynomial spline approximation of a signal g(t) ? L2(R) is obtained by projecting g(t) on Sn( R) (the space of polynomial splines of order n). It is shown that this process can be linked to the classical problem of cardinal spline interpolation by first convolving g(t) with a B-spline of order n. More specifically, the coefficients of the

Michael Unser; Akram Aldroubi; Murray Eden

1992-01-01

398

Fast B-spline Transforms for Continuous Image Representation and Interpolation  

Microsoft Academic Search

Efficient algorithms for the continuous representation of a discrete signal in terms of B-splines (direct B-spline transform) and for interpolative signal reconstruction (indirect B-spline transform) with an expansion factor m are described. Expressions for the z-transforms of the sampled B-spline functions are determined and a convolution property of these kernels is established. It is shown that both the direct and

Michael Unser; Akram Aldroubi; Murray Eden

1991-01-01

399

Minimal multi-element stochastic collocation for uncertainty quantification of discontinuous functions  

NASA Astrophysics Data System (ADS)

We propose a multi-element stochastic collocation method that can be applied in high-dimensional parameter space for functions with discontinuities lying along manifolds of general geometries. The key feature of the method is that the parameter space is decomposed into multiple elements defined by the discontinuities and thus only the minimal number of elements are utilized. On each of the resulting elements the function is smooth and can be approximated using high-order methods with fast convergence properties. The decomposition strategy is in direct contrast to the traditional multi-element approaches which define the sub-domains by repeated splitting of the axes in the parameter space. Such methods are more prone to the curse-of-dimensionality because of the fast growth of the number of elements caused by the axis based splitting. The present method is a two-step approach. Firstly a discontinuity detector is used to partition parameter space into disjoint elements in each of which the function is smooth. The detector uses an efficient combination of the high-order polynomial annihilation technique along with adaptive sparse grids, and this allows resolution of general discontinuities with a smaller number of points when the discontinuity manifold is low-dimensional. After partitioning, an adaptive technique based on the least orthogonal interpolant is used to construct a generalized Polynomial Chaos surrogate on each element. The adaptive technique reuses all information from the partitioning and is variance-suppressing. We present numerous numerical examples that illustrate the accuracy, efficiency, and generality of the method. When compared against standard locally-adaptive sparse grid methods, the present method uses many fewer number of collocation samples and is more accurate.

Jakeman, John D.; Narayan, Akil; Xiu, Dongbin

2013-06-01

400

On the asymptotic convergence of B-spline wavelets to Gabor functions  

Microsoft Academic Search

A family of nonorthogonal polynomial spline wavelet transforms is considered. These transforms are fully reversible and can be implemented efficiently. The corresponding wavelet functions have a compact support. It is proven that these B-spline wavelets converge to Gabor functions (modulated Gaussian) pointwise and in all Lp -norms with 1⩽p+? as the order of the spline ( n) tends to infinity.

Michael Unser; Akram Aldroubi; Murray Eden

1992-01-01

401

Elastic Body Splines: A Physics Based Approach to Coordinate Transformation in Medical Image Matching  

Microsoft Academic Search

In a landmark based medical image matching scheme, a coordinate transformation maps a set of landmark locations in one image onto a corresponding set in a second image. A novel approach to this transformation, the elastic body spline, is introduced. The development of the spline is outlined. An example of using the spline to match 3D magnetic resonance images (MRIs)

Malcolm H. Davis; Alireza Khotanzad; Duane P. Flamig; Steven E. Harms

1995-01-01

402

A New Class of Elastic Body Splines for Nonrigid Registration of Medical Images  

Microsoft Academic Search

We introduce a new point-based elastic registration scheme for medical images which is based on elastic body splines (EBS). Since elastic body splines result from a physical model in form of analytical solutions of the Navier equation these splines describe elastic deformations of physical objects. This property is advantageous in medical registration applications, in which the geometric differences between the

Jan Kohlrausch; Karl Rohr; H. Siegfried Stiehl

2001-01-01

403

Image Morphing of Facial Images Transformation based on Navier Elastic Body Splines  

Microsoft Academic Search

We propose an image morphing algorithm which uses Navier elastic body splines to generate warp functions for interpolating scattered data points. The spline is based on a partial differential equation proposed by Navier that describes the equilibrium displacement of an elastic body subjected to forces. The spline maps can be expressed as the linear combination of an affine transformation and

Aboul Ella Hassanien; Masayuki Nakajima

1998-01-01

404

Image metamorphosis transformation of facial images based on elastic body splines  

Microsoft Academic Search

In this paper, we propose a new image metamorphosis algorithm which uses elastic body splines to generate warp functions for interpolating scattered data points. The spline is based on a partial differential equation proposed by Navier that describes the equilibrium displacement of an elastic body subjected to forces. The spline maps can be expressed as the linear combination of an

Hassanien Aboul-Ella; Masayuki Nakajima

1998-01-01

405

Extensions of the Zwart-Powell Box Spline for Volumetric Data Reconstruction on the Cartesian Lattice  

Microsoft Academic Search

In this article we propose a box spline and its variants for reconstructing volumetric data sampled on the Cartesian lattice. In particular we present a tri-variate box spline reconstruction kernel that is superior to tensor product reconstruction schemes in terms of recovering the proper Cartesian spectrum of the underlying function. This box spline produces a C2 reconstruction that can be

Alireza Entezari; Torsten Möller

2006-01-01

406

Box Spline Reconstruction On The Face-Centered Cubic Lattice  

Microsoft Academic Search

Abstract—We introduce and analyze,an efficient reconstruction,algorithm for FCC-sampled data. The reconstruction,is based,on the 6-direction box spline that is naturally associated,with the FCC lattice and shares the continuity and approximation order of the triquadratic B-spline. We observe,less aliasing for generic level sets and,derive special techniques,to attain the higher evaluation efficiency promised,by the lower degree,and smaller stencil-size of the C, 6-direction box

Inho Kim; Alireza Entezari

2008-01-01

407

Joint image and motion reconstruction for PET using a B-spline motion model  

NASA Astrophysics Data System (ADS)

We present a novel joint image and motion reconstruction method for PET. The method is based on gated data and reconstructs an image together with a motion function. The motion function can be used to transform the reconstructed image to any of the input gates. All available events (from all gates) are used in the reconstruction. The presented method uses a B-spline motion model, together with a novel motion regularization procedure that does not need a regularization parameter (which is usually extremely difficult to adjust). Several image and motion grid levels are used in order to reduce the reconstruction time. In a simulation study, the presented method is compared to a recently proposed joint reconstruction method. While the presented method provides comparable reconstruction quality, it is much easier to use since no regularization parameter has to be chosen. Furthermore, since the B-spline discretization of the motion function depends on fewer parameters than a displacement field, the presented method is considerably faster and consumes less memory than its counterpart. The method is also applied to clinical data, for which a novel purely data-driven gating approach is presented.

Blume, Moritz; Navab, Nassir; Rafecas, Magdalena

2012-12-01

408

Joint image and motion reconstruction for PET using a B-spline motion model.  

PubMed

We present a novel joint image and motion reconstruction method for PET. The method is based on gated data and reconstructs an image together with a motion function. The motion function can be used to transform the reconstructed image to any of the input gates. All available events (from all gates) are used in the reconstruction. The presented method uses a B-spline motion model, together with a novel motion regularization procedure that does not need a regularization parameter (which is usually extremely difficult to adjust). Several image and motion grid levels are used in order to reduce the reconstruction time. In a simulation study, the presented method is compared to a recently proposed joint reconstruction method. While the presented method provides comparable reconstruction quality, it is much easier to use since no regularization parameter has to be chosen. Furthermore, since the B-spline discretization of the motion function depends on fewer parameters than a displacement field, the presented method is considerably faster and consumes less memory than its counterpart. The method is also applied to clinical data, for which a novel purely data-driven gating approach is presented. PMID:23190499

Blume, Moritz; Navab, Nassir; Rafecas, Magdalena

2012-11-29

409

Improved statistical models for limited datasets in uncertainty quantification using stochastic collocation  

NASA Astrophysics Data System (ADS)

This paper presents a data-driven framework for performing uncertainty quantification (UQ) by choosing a stochastic model that accurately describes the sources of uncertainty in a system. This model is propagated through an appropriate response surface function that approximates the behavior of this system using stochastic collocation. Given a sample of data describing the uncertainty in the inputs, our goal is to estimate a probability density function (PDF) using the kernel moment matching (KMM) method so that this PDF can be used to accurately reproduce statistics like mean and variance of the response surface function. Instead of constraining the PDF to be optimal for a particular response function, we show that we can use the properties of stochastic collocation to make the estimated PDF optimal for a wide variety of response functions. We contrast this method with other traditional procedures that rely on the Maximum Likelihood approach, like kernel density estimation (KDE) and its adaptive modification (AKDE). We argue that this modified KMM method tries to preserve what is known from the given data and is the better approach when the available data is limited in quantity. We test the performance of these methods for both univariate and multivariate density estimation by sampling random datasets from known PDFs and then measuring the accuracy of the estimated PDFs, using the known PDF as a reference. Comparing the output mean and variance estimated with the empirical moments using the raw data sample as well as the actual moments using the known PDF, we show that the KMM method performs better than KDE and AKDE in predicting these moments with greater accuracy. This improvement in accuracy is also demonstrated for the case of UQ in electrostatic and electrothermomechanical microactuators. We show how our framework results in the accurate computation of statistics in micromechanical systems.

Alwan, Aravind; Aluru, N. R.

2013-12-01

410

B-spline active rays segmentation of microcalcifications in mammography  

SciTech Connect

Accurate segmentation of microcalcifications in mammography is crucial for the quantification of morphologic properties by features incorporated in computer-aided diagnosis schemes. A novel segmentation method is proposed implementing active rays (polar-transformed active contours) on B-spline wavelet representation to identify microcalcification contour point estimates in a coarse-to-fine strategy at two levels of analysis. An iterative region growing method is used to delineate the final microcalcification contour curve, with pixel aggregation constrained by the microcalcification contour point estimates. A radial gradient-based method was also implemented for comparative purposes. The methods were tested on a dataset consisting of 149 mainly pleomorphic microcalcification clusters originating from 130 mammograms of the DDSM database. Segmentation accuracy of both methods was evaluated by three radiologists, based on a five-point rating scale. The radiologists' average accuracy ratings were 3.96{+-}0.77, 3.97{+-}0.80, and 3.83{+-}0.89 for the proposed method, and 2.91{+-}0.86, 2.10{+-}0.94, and 2.56{+-}0.76 for the radial gradient-based method, respectively, while the differences in accuracy ratings between the two segmentation methods were statistically significant (Wilcoxon signed-ranks test, p<0.05). The effect of the two segmentation methods in the classification of benign from malignant microcalcification clusters was also investigated. A least square minimum distance classifier was employed based on cluster features reflecting three morphological properties of individual microcalcifications (area, length, and relative contrast). Classification performance was evaluated by means of the area under ROC curve (A{sub z}). The area and length morphologic features demonstrated a statistically significant (Mann-Whitney U-test, p<0.05) higher patient-based classification performance when extracted from microcalcifications segmented by the proposed method (0.82{+-}0.06 and 0.86{+-}0.05, respectively), as compared to segmentation by the radial gradient-based method (0.71{+-}0.08 and 0.75{+-}0.08). The proposed method demonstrates improved segmentation accuracy, fulfilling human visual criteria, and enhances the ability of morphologic features to characterize microcalcification clusters.

Arikidis, Nikolaos S.; Skiadopoulos, Spyros; Karahaliou, Anna; Likaki, Eleni; Panayiotakis, George; Costaridou, Lena [Department of Medical Physics, School of Medicine, University of Patras, 265 00 Patras (Greece); Department of Radiology, School of Medicine, University of Patras, 265 00 Patras (Greece); Department of Medical Physics, School of Medicine, University of Patras, 265 00 Patras (Greece)

2008-11-15

411

Communication: favorable dimensionality scaling of rectangular collocation with adaptable basis functions up to 7 dimensions.  

PubMed

We show that by using a rectangular collocation method with a small basis of parameterized functions, it is possible to compute a vibrational spectrum by solving the Schro?dinger equation in 7D from a small number of ab initio calculations without a potential surface. The method is ideal for spectra of molecules adsorbed on a surface. In this paper, it is applied to calculate experimentally relevant energy levels of acetic acid adsorbed on the (101) surface of anatase TiO2. In this case, to obtain levels of experimental accuracy, increasing the number of dimensions from 4 to 7 increases the number of required potential points from about 1000 to about 10,000 and the number of basis functions from 126 to 792: the scaling is very attractive. PMID:23927236

Manzhos, Sergei; Chan, Matthew; Carrington, Tucker

2013-08-01

412

A spline relaxation procedure for calculating axisymmetric flow fields about body\\/propeller combinations. 1: Frozen vorticity and potential flows  

Microsoft Academic Search

A general numerical solution method is presented for calculating incompressible axisymmetric viscous\\/turbulent flow in the tail-near wake region of a body-propeller combination. The method makes use of the parabolic vorticity transport approximation in conjunction with polynomial splines to achieve sufficient accuracy in high flow gradient regions with as few grid points as possible. A sheared body fitted coordinate system is

G. H. Hoffman

1980-01-01

413

Optimal Path Planning for Autonomous Airship Based on Clonal Selection and Direct Collocation Algorithm  

Microsoft Academic Search

A novel algorithm, based on clonal selection and direct collocation theories, is introduced to solve the three-dimensional optimal path problem of airship. Firstly, the six-DOF (Degree of Freedom) nonlinear dynamic model for a special kind of airship is presented. Then, the model of novel algorithm is designed from clonal selection and direct collocation aspects respectively, and the dissipative energy function

Yu Liu; Yachen Zhang; Yueming Hu

2008-01-01

414

Effects of Web-Based Concordancing Instruction on EFL Students' Learning of Verb-Noun Collocations  

ERIC Educational Resources Information Center

|This study investigates the influence of using five web-based practice units on English verb-noun collocations with the design of a web-based Chinese-English bilingual concordancer (keyword retrieval program) on collocation learning. Thirty-two college EFL students participated by taking a pre-test and two post-tests, and responding to a…

Chan, Tun-pei; Liou, Hsien-Chin

2005-01-01

415

Investigating the Viability of a Collocation List for Students of English for Academic Purposes  

ERIC Educational Resources Information Center

|A number of researchers are currently attempting to create listings of important collocations for students of EAP. However, so far these attempts have (1) failed to include positionally-variable collocations, and (2) not taken sufficient account of variation across disciplines. The present paper describes the creation of one listing of…

Durrant, Philip

2009-01-01

416

Collocation, Semantic Prosody, and Near Synonymy: A Cross-Linguistic Perspective  

ERIC Educational Resources Information Center

|This paper explores the collocational behaviour and semantic prosody of near synonyms from a cross-linguistic perspective. The importance of these concepts to language learning is well recognized. Yet while collocation and semantic prosody have recently attracted much interest from researchers studying the English language, there has been little…

Xiao, Richard; McEnery, Tony

2006-01-01

417

English Collocation Learning through Corpus Data: On-Line Concordance and Statistical Information  

ERIC Educational Resources Information Center

|We developed an English Collocations On Demand system offering on-line corpus and concordance information to help Japanese researchers acquire a better command of English collocation patterns. The Life Science Dictionary Corpus consists of approximately 90,000,000 words collected from life science related research papers published in academic…

Ohtake, Hiroshi; Fujita, Nobuyuki; Kawamoto, Takeshi; Morren, Brian; Ugawa, Yoshihiro; Kaneko, Shuji

2012-01-01

418

Collocational Links in the L2 Mental Lexicon and the Influence of L1 Intralexical Knowledge  

ERIC Educational Resources Information Center

|This article assesses the influence of L1 intralexical knowledge on the formation of L2 intralexical collocations. Two tests, a primed lexical decision task (LDT) and a test of receptive collocational knowledge, were administered to a group of non-native speakers (NNSs) (L1 Swedish), with native speakers (NSs) of English serving as controls on…

Wolter, Brent; Gyllstad, Henrik

2011-01-01

419

A modal filter approach to non-collocated vibration control of structures  

NASA Astrophysics Data System (ADS)

This paper employs modal filters for simultaneous and independent control of multiple vibration modes of a flexible structure embedded with a non-collocated pair of sensor and actuator. Each modal filter of second order is designed to be sensitive to the target mode for control while insensitive to the others. Based on the fact that there are only in- and out-of-phase modes in lightly and proportionally damped finite structures, those in-phase modes are controlled in the same way as that for collocated control using negative feedback, while those out-of-phase modes are controlled exactly in the opposite way using positive feedback. These two are equivalent as far as single mode control is concerned and are electrical realizations of a mechanical dynamic vibration absorber. Feedback control experiments were conducted on a cantilever beam embedded with a piezoelectric actuator at the root and an accelerometer at the end tip. The results reveal a number of peculiar advantages of using non-collocated control over collocated control. Non-collocated plants generally exhibit better high-frequency roll-off characteristics because there are weaker mechanical and electrical feedthrough couplings between non-collocated transducers. Furthermore, the high frequency control spillover can be greatly eliminated by appropriately adjusting the gains of modal filters. It is thus often possible to make the performance and robustness of non-collocated control as well as or even better than those using collocated control.

Kim, Sang-Myeong; Oh, Jae-Eung

2013-04-01

420

Going beyond Patterns: Involving Cognitive Analysis in the Learning of Collocations  

ERIC Educational Resources Information Center

|Since the late 1980s, collocations have received increasing attention in applied linguistics, especially language teaching, as is evidenced by the many publications on the topic. These works fall roughly into two lines of research (a) those focusing on the identification and use of collocations (Benson, 1989; Hunston, 2002; Hunston & Francis,…

Liu, Dilin

2010-01-01

421

Location Choices Across the Value Chain: How Activity and Capability Influence Collocation  

Microsoft Academic Search

There has been a recent revival of interest in the geographic component of firm strategy. Recent research suggests that two opposing forces--competition costs and agglomeration benefits--determine whether firms collocate in a given geographic market. Unexplored is (1) whether these forces have different impacts on R& D, production, and sales subsidiaries, leading to diverse collocation levels, and (2) how firm capabilities

Juan Alcácer

2006-01-01

422

Interpolating Mean Rainfall Using Thin Plate Smoothing Splines  

Microsoft Academic Search

Thin plate smoothing splines provide accurate, operationally straightforward and computationally efficient solutions to the problem of the spatial interpolation of annual mean rainfall for a standard period from point data which contains many short period rainfall means. The analyses depend on developing a statistical model of the spatial variation of the observed rainfall means, considered as noisy estimates of standard

M. F. Hutchinson

1995-01-01

423

Image interpolation using adaptive fast B-spline filtering  

Microsoft Academic Search

An adaptive version of a B-spline interpolation algorithm is proposed. Adaptivity is used in two different phases: (1) adaptive zero order interpolation is realized by considering directional edge information, and (2) adaptive length of the moving average filter in four directions is obtained by computing the local image statistics. The proposed algorithm exhibits significant improvements in image quality compared with

Seong Won Lee; Joon Ki Paik

1993-01-01

424

Shear flexible curved spline beam element for static analysis  

Microsoft Academic Search

In this paper, an efficient curved cubic B-spline beam element is developed based on field consistency principle, for the static analysis. The formulation is general in the sense that it includes anisotropy, transverse shear deformation, in-plane and rotary inertia effects. The element is based on laminated beam theory, which satisfies the interface stress and displacement continuity, and has a vanishing

M. Ganapathi; B. P. Patel; J. Saravanan; M. Touratier

1999-01-01

425

Group-Lasso on Splines for Spectrum Cartography  

Microsoft Academic Search

The unceasing demand for continuous situational awareness calls for innovative and large-scale signal processing algorithms, complemented by collaborative and adaptive sensing platforms to accomplish the objectives of layered sensing and con- trol. Towards this goal, the present paper develops a spline-based approach to field estimation, which relies on a basis expan- sion model of the field of interest. The model

Juan Andrés Bazerque; Gonzalo Mateos; Georgios B. Giannakis

2011-01-01

426

Window functions represented by B-spline functions  

Microsoft Academic Search

Characteristics of window functions provided by B-spline functions are analyzed in comparison to other known windows. For the same highest-sidelobe level, those windows have a mainlobe bandwidth between those of Gaussian and cosa x windows are as good as those of cosa x ones in the sidelobe falloff

K. Toraichi; M. Kamada; S. Itahashi; R. Mori

1989-01-01

427

Viscous Flow Solutions with a Cubic Spline Approximation.  

National Technical Information Service (NTIS)

A cubic spline approximation is used for the solution of several problems in fluid mechanics. This procedure provides a high degree of accuracy even with a non-uniform mesh, and leads to a more accurate treatment of derivative boundary conditions. The tru...

S. G. Rubin R. A. Graves

1974-01-01

428

B-Splines and Linear Combinations of Uniform Order Statistics.  

National Technical Information Service (NTIS)

It is shown in this document that the density of the sum of n independent random variables uniformly distributed on unequal intervals is given by a linear combination of n B-splines with constant coefficients. Another useful representation of the same den...

A. G. Ignatov V. K. Kaishev

1985-01-01

429

B-Spline Filtering for Automatic Detection of Calcification Lesions in Mammograms  

SciTech Connect

Breast cancer continues to be an important health problem between women population. Early detection is the only way to improve breast cancer prognosis and significantly reduce women mortality. It is by using CAD systems that radiologist can improve their ability to detect, and classify lesions in mammograms. In this study the usefulness of using B-spline based on a gradient scheme and compared to wavelet and adaptative filtering has been investigated for calcification lesion detection and as part of CAD systems. The technique has been applied to different density tissues. A qualitative validation shows the success of the method.

Bueno, G. [E.T.S. Ingenieros Industrials. Universidad de Castilla-La Mancha. Ciudad Real (Spain); Ruiz, M. [Servicio de Patologia Mamaria. Fundacion Rioja Salud (Spain); Sanchez, S

2006-10-04

430

An Automatic Collocation Writing Assistant for Taiwanese EFL Learners: A Case of Corpus-Based NLP Technology  

ERIC Educational Resources Information Center

Previous work in the literature reveals that EFL learners were deficient in collocations that are a hallmark of near native fluency in learner's writing. Among different types of collocations, the verb-noun (V-N) one was found to be particularly difficult to master, and learners' first language was also found to heavily influence their collocation

Chang, Yu-Chia; Chang, Jason S.; Chen, Hao-Jan; Liou, Hsien-Chin

2008-01-01

431

Flexible estimation of covariance function by penalized spline with application to longitudinal family data.  

PubMed

Longitudinal data are routinely collected in biomedical research studies. A natural model describing longitudinal data decomposes an individual's outcome as the sum of a population mean function and random subject-specific deviations. When parametric assumptions are too restrictive, methods modeling the population mean function and the random subject-specific functions nonparametrically are in demand. In some applications, it is desirable to estimate a covariance function of random subject-specific deviations. In this work, flexible yet computationally efficient methods are developed for a general class of semiparametric mixed effects models, where the functional forms of the population mean and the subject-specific curves are unspecified. We estimate nonparametric components of the model by penalized spline (P-spline, Biometrics 2001; 57:253-259), and reparameterize the random curve covariance function by a modified Cholesky decomposition (Biometrics 2002; 58:121-128) which allows for unconstrained estimation of a positive-semidefinite matrix. To provide smooth estimates, we penalize roughness of fitted curves and derive closed-form solutions in the maximization step of an EM algorithm. In addition, we present models and methods for longitudinal family data where subjects in a family are correlated and we decompose the covariance function into a subject-level source and observation-level source. We apply these methods to the multi-level Framingham Heart Study data to estimate age-specific heritability of systolic blood pressure nonparametrically. PMID:21491474

Wang, Yuanjia

2011-04-13

432

Fast simulation of x-ray projections of spline-based surfaces using an append buffer  

NASA Astrophysics Data System (ADS)

Many scientists in the field of x-ray imaging rely on the simulation of x-ray images. As the phantom models become more and more realistic, their projection requires high computational effort. Since x-ray images are based on transmission, many standard graphics acceleration algorithms cannot be applied to this task. However, if adapted properly, the simulation speed can be increased dramatically using state-of-the-art graphics hardware. A custom graphics pipeline that simulates transmission projections for tomographic reconstruction was implemented based on moving spline surface models. All steps from tessellation of the splines, projection onto the detector and drawing are implemented in OpenCL. We introduced a special append buffer for increased performance in order to store the intersections with the scene for every ray. Intersections are then sorted and resolved to materials. Lastly, an absorption model is evaluated to yield an absorption value for each projection pixel. Projection of a moving spline structure is fast and accurate. Projections of size 640 × 480 can be generated within 254 ms. Reconstructions using the projections show errors below 1 HU with a sharp reconstruction kernel. Traditional GPU-based acceleration schemes are not suitable for our reconstruction task. Even in the absence of noise, they result in errors up to 9 HU on average, although projection images appear to be correct under visual examination. Projections generated with our new method are suitable for the validation of novel CT reconstruction algorithms. For complex simulations, such as the evaluation of motion-compensated reconstruction algorithms, this kind of x-ray simulation will reduce the computation time dramatically.

Maier, Andreas; Hofmann, Hannes G.; Schwemmer, Chris; Hornegger, Joachim; Keil, Andreas; Fahrig, Rebecca

2012-10-01

433

Fast Simulation of X-ray Projections of Spline-based Surfaces using an Append Buffer  

PubMed Central

Many scientists in the field of x-ray imaging rely on the simulation of x-ray images. As the phantom models become more and more realistic, their projection requires high computational effort. Since x-ray images are based on transmission, many standard graphics acceleration algorithms cannot be applied to this task. However, if adapted properly, simulation speed can be increased dramatically using state-of-the-art graphics hardware. A custom graphics pipeline that simulates transmission projections for tomographic reconstruction was implemented based on moving spline surface models. All steps from tessellation of the splines, projection onto the detector, and drawing are implemented in OpenCL. We introduced a special append buffer for increased performance in order to store the intersections with the scene for every ray. Intersections are then sorted and resolved to materials. Lastly, an absorption model is evaluated to yield an absorption value for each projection pixel. Projection of a moving spline structure is fast and accurate. Projections of size 640×480 can be generated within 254 ms. Reconstructions using the projections show errors below 1 HU with a sharp reconstruction kernel. Traditional GPU-based acceleration schemes are not suitable for our reconstruction task. Even in the absence of noise, they result in errors up to 9 HU on average, although projection images appear to be correct under visual examination. Projections generated with our new method are suitable for the validation of novel CT reconstruction algorithms. For complex simulations, such as the evaluation of motion-compensated reconstruction algorithms, this kind of x-ray simulation will reduce the computation time dramatically. Source code is available at http://conrad.stanford.edu/

Maier, Andreas; Hofmann, Hannes G.; Schwemmer, Chris; Hornegger, Joachim; Keil, Andreas; Fahrig, Rebecca

2012-01-01

434

Fast simulation of x-ray projections of spline-based surfaces using an append buffer.  

PubMed

Many scientists in the field of x-ray imaging rely on the simulation of x-ray images. As the phantom models become more and more realistic, their projection requires high computational effort. Since x-ray images are based on transmission, many standard graphics acceleration algorithms cannot be applied to this task. However, if adapted properly, the simulation speed can be increased dramatically using state-of-the-art graphics hardware. A custom graphics pipeline that simulates transmission projections for tomographic reconstruction was implemented based on moving spline surface models. All steps from tessellation of the splines, projection onto the detector and drawing are implemented in OpenCL. We introduced a special append buffer for increased performance in order to store the intersections with the scene for every ray. Intersections are then sorted and resolved to materials. Lastly, an absorption model is evaluated to yield an absorption value for each projection pixel. Projection of a moving spline structure is fast and accurate. Projections of size 640 × 480 can be generated within 254 ms. Reconstructions using the projections show errors below 1 HU with a sharp reconstruction kernel. Traditional GPU-based acceleration schemes are not suitable for our reconstruction task. Even in the absence of noise, they result in errors up to 9 HU on average, although projection images appear to be correct under visual examination. Projections generated with our new method are suitable for the validation of novel CT reconstruction algorithms. For complex simulations, such as the evaluation of motion-compensated reconstruction algorithms, this kind of x-ray simulation will reduce the computation time dramatically. PMID:22975431

Maier, Andreas; Hofmann, Hannes G; Schwemmer, Chris; Hornegger, Joachim; Keil, Andreas; Fahrig, Rebecca

2012-09-14

435

Fourth-order B-spline wavelet multiscale local modulus maxima for edge detection in identification of pipeline fault  

Microsoft Academic Search

In this paper, for the actual in-service pipeline detection, an edge detection method based on fourth-order B-spline wavelet multi-scale local modulus maxima is proposed. We extract defect edge using wavelet maximum algorithm, select fine length, invariant moment, gray scale energy and so on, several key characteristic parameters that are good for defect identification, and use BP neural network of single-output

Peixin Yuan; Jun Tan; Jiahui Cong

2009-01-01

436

A GENERALIZED STOCHASTIC COLLOCATION APPROACH TO CONSTRAINED OPTIMIZATION FOR RANDOM DATA IDENTIFICATION PROBLEMS  

SciTech Connect

We present a scalable, parallel mechanism for stochastic identification/control for problems constrained by partial differential equations with random input data. Several identification objectives will be discussed that either minimize the expectation of a tracking cost functional or minimize the difference of desired statistical quantities in the appropriate $L^p$ norm, and the distributed parameters/control can both deterministic or stochastic. Given an objective we prove the existence of an optimal solution, establish the validity of the Lagrange multiplier rule and obtain a stochastic optimality system of equations. The modeling process may describe the solution in terms of high dimensional spaces, particularly in the case when the input data (coefficients, forcing terms, boundary conditions, geometry, etc) are affected by a large amount of uncertainty. For higher accuracy, the computer simulation must increase the number of random variables (dimensions), and expend more effort approximating the quantity of interest in each individual dimension. Hence, we introduce a novel stochastic parameter identification algorithm that integrates an adjoint-based deterministic algorithm with the sparse grid stochastic collocation FEM approach. This allows for decoupled, moderately high dimensional, parameterized computations of the stochastic optimality system, where at each collocation point, deterministic analysis and techniques can be utilized. The advantage of our approach is that it allows for the optimal identification of statistical moments (mean value, variance, covariance, etc.) or even the whole probability distribution of the input random fields, given the probability distribution of some responses of the system (quantities of physical interest). Our rigorously derived error estimates, for the fully discrete problems, will be described and used to compare the efficiency of the method with several other techniques. Numerical examples illustrate the theoretical results and demonstrate the distinctions between the various stochastic identification objectives.

Webster, Clayton G [ORNL; Gunzburger, Max D [ORNL

2013-01-01

437

BSR: B-spline atomic R-matrix codes  

NASA Astrophysics Data System (ADS)

BSR is a general program to calculate atomic continuum processes using the B-spline R-matrix method, including electron atom and electron ion scattering, and radiative processes such as bound bound transitions, photoionization and polarizabilities. The calculations can be performed in LS-coupling or in an intermediate-coupling scheme by including terms of the Breit Pauli Hamiltonian.New version program summaryTitle of program: BSR Catalogue identifier: ADWY Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWY Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computers on which the program has been tested: Microway Beowulf cluster; Compaq Beowulf cluster; DEC Alpha workstation; DELL PC Operating systems under which the new version has been tested: UNIX, Windows XP Programming language used: FORTRAN 95 Memory required to execute with typical data: Typically 256 512 Mwords. Since all the principal dimensions are allocatable, the available memory defines the maximum complexity of the problem No. of bits in a word: 8 No. of processors used: 1 Has the code been vectorized or parallelized?: no No. of lines in distributed program, including test data, etc.: 69?943 No. of bytes in distributed program, including test data, etc.: 746?450 Peripherals used: scratch disk store; permanent disk store Distribution format: tar.gz Nature of physical problem: This program uses the R-matrix method to calculate electron atom and electron ion collision processes, with options to calculate radiative data, photoionization, etc. The calculations can be performed in LS-coupling or in an intermediate-coupling scheme, with options to include Breit Pauli terms in the Hamiltonian. Method of solution: The R-matrix method is used [P.G. Burke, K.A. Berrington, Atomic and Molecular Processes: An R-Matrix Approach, IOP Publishing, Bristol, 1993; P.G. Burke, W.D. Robb, Adv. At. Mol. Phys. 11 (1975) 143; K.A. Berrington, W.B. Eissner, P.H. Norrington, Comput. Phys. Comm. 92 (1995) 290].

Zatsarinny, Oleg

2006-02-01

438

Optimal spacecraft attitude control using collocation and nonlinear programming  

NASA Astrophysics Data System (ADS)

Direct collocation with nonlinear programming (DCNLP) is employed to find the optimal open-loop control histories for detumbling a disabled satellite. The controls are torques and forces applied to the docking arm and joint and torques applied about the body axes of the OMV. Solutions are obtained for cases in which various constraints are placed on the controls and in which the number of controls is reduced or increased from that considered in Conway and Widhalm (1986). DCLNP works well when applied to the optimal control problem of satellite attitude control. The formulation is straightforward and produces good results in a relatively small amount of time on a Cray X/MP with no a priori information about the optimal solution. The addition of joint acceleration to the controls significantly reduces the control magnitudes and optimal cost. In all cases, the torques and acclerations are modest and the optimal cost is very modest.

Herman, A. L.; Conway, B. A.

1992-10-01

439

Segmentation of ultrasound images of the carotid using RANSAC and cubic splines.  

PubMed

A new algorithm is proposed for the semi-automatic segmentation of the near-end and the far-end adventitia boundary of the common carotid artery in ultrasound images. It uses the random sample consensus method to estimate the most significant cubic splines fitting the edge map of a longitudinal section. The consensus of the geometric model (a spline) is evaluated through a new gain function, which integrates the responses to different discriminating features of the carotid boundary: the proximity of the geometric model to any edge or to valley shaped edges; the consistency between the orientation of the normal to the geometric model and the intensity gradient; and the distance to a rough estimate of the lumen boundary. A set of 50 longitudinal B-mode images of the common carotid and their manual segmentations performed by two medical experts were used to assess the performance of the method. The image set was taken from 25 different subjects, most of them having plaques of different classes (class II to class IV), sizes and shapes. The quantitative evaluation showed promising results, having detection errors similar to the ones observed in manual segmentations for 95% of the far-end boundaries and 73% of the near-end boundaries. PMID:20554343

Rocha, Rui; Campilho, Aurélio; Silva, Jorge; Azevedo, Elsa; Santos, Rosa

2010-06-15

440

On the spectral methods for population balance problems  

NASA Astrophysics Data System (ADS)

Numerical methods in the weighted residual framework have been evaluated for three population balance (PB) problems. Based on the present solution results, the orthogonal collocation method is recommended above the tau and least-squares methods. The orthogonal collocation method holds the simplest algebra theory, obtains high accuracy, and is more computational efficient compared to the other methods evaluated.

Solsvik, J.; Jakobsen, H. A.

2013-10-01

441

Adaptation of a cubic smoothing spline algorithm for multi-channel data stitching at the National Ignition Facility  

NASA Astrophysics Data System (ADS)

Some diagnostics at the National Ignition Facility (NIF), including the Gamma Reaction History (GRH) diagnostic, require multiple channels of data to achieve the required dynamic range. These channels need to be stitched together into a single time series, and they may have non-uniform and redundant time samples. We chose to apply the popular cubic smoothing spline technique to our stitching problem because we needed a general non-parametric method. We adapted one of the algorithms in the literature, by Hutchinson and deHoog, to our needs. The modified algorithm and the resulting code perform a cubic smoothing spline fit to multiple data channels with redundant time samples and missing data points. The data channels can have different, timevarying, zero-mean white noise characteristics. The method we employ automatically determines an optimal smoothing level by minimizing the Generalized Cross Validation (GCV) score. In order to automatically validate the smoothing level selection, the Weighted Sum-Squared Residual (WSSR) and zero-mean tests are performed on the residuals. Further, confidence intervals, both analytical and Monte Carlo, are also calculated. In this paper, we describe the derivation of our cubic smoothing spline algorithm. We outline the algorithm and test it with simulated and experimental data.

Brown, Charles G., Jr.; Adcock, Aaron B.; Azevedo, Stephen G.; Liebman, Judith A.; Bond, Essex J.

2011-02-01

442

Smoothing and interpolation by kriging and with splines  

Microsoft Academic Search

Let scalar measurements at distinct points x1, , xn\\u000abe y1, , yn.We may look for a smooth function f(x)that goes through or near the points (xi, yi).Kriging assumes f(x)is a random function with known (possibly estimable) covariance function (in the simplest case). Splines assume a definition of the smoothness of a nonrandom function f(x).An elementary explanation is given of

G. S. Watson

1984-01-01

443

Reconstruction of nonuniformly sampled images in spline spaces.  

PubMed

This paper presents a novel approach to the reconstruction of images from nonuniformly spaced samples. This problem is often encountered in digital image processing applications. Nonrecursive video coding with motion compensation, spatiotemporal interpolation of video sequences, and generation of new views in multicamera systems are three possible applications. We propose a new reconstruction algorithm based on a spline model for images. We use regularization, since this is an ill-posed inverse problem. We minimize a cost function composed of two terms: one related to the approximation error and the other related to the smoothness of the modeling function. All the processing is carried out in the space of spline coefficients; this space is discrete, although the problem itself is of a continuous nature. The coefficients of regularization and approximation filters are computed exactly by using the explicit expressions of B-spline functions in the time domain. The regularization is carried out locally, while the computation of the regularization factor accounts for the structure of the nonuniform sampling grid. The linear system of equations obtained is solved iteratively. Our results show a very good performance in motion-compensated interpolation applications. PMID:15971771

Vázquez, Carlos; Dubois, Eric; Konrad, Janusz

2005-06-01

444

Railroad inspection based on ACFM employing a non-uniform B-spline approach  

NASA Astrophysics Data System (ADS)

The stresses sustained by rails have increased in recent years due to the use of higher train speeds and heavier axle loads. For this reason surface and near-surface defects generate by Rolling Contact Fatigue (RCF) have become particularly significant as they can cause unexpected structural failure of the rail, resulting in severe derailments. The accident that took place in Hatfield, UK (2000), is an example of a derailment caused by the structural failure of a rail section due to RCF. Early detection of RCF rail defects is therefore of paramount importance to the rail industry. The performance of existing ultrasonic and magnetic flux leakage techniques in detecting rail surface-breaking defects, such as head checks and gauge corner cracking, is inadequate during high-speed inspection, while eddy current sensors suffer from lift-off effects. The results obtained through rail inspection experiments under simulated conditions using Alternating Current Field Measurement (ACFM) probes, suggest that this technique can be applied for the accurate and reliable detection of surface-breaking defects at high inspection speeds. This paper presents the B-Spline approach used for the accurate filtering the noise of the raw ACFM signal obtained during high speed tests to improve the reliability of the measurements. A non-uniform B-spline approximation is employed to calculate the exact positions and the dimensions of the defects. This method generates a smooth approximation similar to the ACFM dataset points related to the rail surface-breaking defect.

Chacón Muñoz, J. M.; García Márquez, F. P.; Papaelias, M.

2013-11-01

445

B-spline snakes: a flexible tool for parametric contour detection  

Microsoft Academic Search

Abstract, We present a novel formulation for B-spline snakes that can be used as a tool for fast and intuitive contour outlining. We start with a theoretical argument in favor of splines in the tra-ditional formulation by showing that the optimal, curvature-con-strained snake is a cubic spline, irrespective of the form of the ex-ternal energy field. Unfortunately, such regularized snakes

Patrick Brigger; Jeff Hoeg; Michael Unser

2000-01-01

446

Variational Splines and Paley–Wiener Spaces on Combinatorial Graphs  

Microsoft Academic Search

Notions of interpolating variational splines and Paley–Wiener spaces are introduced on a combinatorial graph G. Both of these definitions explore existence of a combinatorial Laplace operator on G. The existence and uniqueness of interpolating variational splines on a graph is shown. As an application of variational\\u000a splines, the paper presents a reconstruction algorithm of Paley–Wiener functions on graphs from their

Isaac Pesenson

2009-01-01

447

High-speed contouring control with NURBS-based C 2 PH spline curves  

Microsoft Academic Search

This paper presents a C2 Pythagorean hodograph (PH) spline curve constructed by the non-uniform rational B-spline (NURBS) curve for high-speed contouring\\u000a control. With the knot vector, weights, and control points given, the C2 PH spline curve is defined to be a “good” interpolant for Hermit data obtained from a NURBS curve of degree 3 specified by\\u000a the same control polygon,

Javad Jahanpour; Mi-Ching Tsai; Ming-Yang Cheng

2010-01-01

448

Chinese typeface generation and composition using B-spline wavelet transform  

Microsoft Academic Search

In this paper, a new approach is introduced to generate and compose CHinese typefaces employing B-spline wavelet transform. Firstly, we model each area-based curved outline of the Chinese characters using a B-spline curve, which is determined by a set of control points. Secondly, the B- spline wavelet transform is used to represent the control points with several sequences of wavelet

Feng Yang; Zhou Wang; Ying Lin Yu

1998-01-01

449

Tensor splines for interpolation and approximation of DT-MRI with applications to segmentation of isolated rat hippocampi.  

PubMed

In this paper, we present novel algorithms for statistically robust interpolation and approximation of diffusion tensors-which are symmetric positive definite (SPD) matrices-and use them in developing a significant extension to an existing probabilistic algorithm for scalar field segmentation, in order to segment diffusion tensor magnetic resonance imaging (DT-MRI) datasets. Using the Riemannian metric on the space of SPD matrices, we present a novel and robust higher order (cubic) continuous tensor product of B-splines algorithm to approximate the SPD diffusion tensor fields. The resulting approximations are appropriately dubbed tensor splines. Next, we segment the diffusion tensor field by jointly estimating the label (assigned to each voxel) field, which is modeled by a Gauss Markov measure field (GMMF) and the parameters of each smooth tensor spline model representing the labeled regions. Results of interpolation, approximation, and segmentation are presented for synthetic data and real diffusion tensor fields from an isolated rat hippocampus, along with validation. We also present comparisons of our algorithms with existing methods and show significantly improved results in the presence of noise as well as outliers. PMID:18041268

Barmpoutis, Angelos; Vemuri, Baba C; Shepherd, Timothy M; Forder, John R

2007-11-01

450

Tensor Splines for Interpolation and Approximation of DT-MRI With Applications to Segmentation of Isolated Rat Hippocampi  

PubMed Central

In this paper, we present novel algorithms for statistically robust interpolation and approximation of diffusion tensors—which are symmetric positive definite (SPD) matrices—and use them in developing a significant extension to an existing probabilistic algorithm for scalar field segmentation, in order to segment diffusion tensor magnetic resonance imaging (DT-MRI) datasets. Using the Riemannian metric on the space of SPD matrices, we present a novel and robust higher order (cubic) continuous tensor product of B-splines algorithm to approximate the SPD diffusion tensor fields. The resulting approximations are appropriately dubbed tensor splines. Next, we segment the diffusion tensor field by jointly estimating the label (assigned to each voxel) field, which is modeled by a Gauss Markov measure field (GMMF) and the parameters of each smooth tensor spline model representing the labeled regions. Results of interpolation, approximation, and segmentation are presented for synthetic data and real diffusion tensor fields from an isolated rat hippocampus, along with validation. We also present comparisons of our algorithms with existing methods and show significantly improved results in the presence of noise as well as outliers.

Barmpoutis, Angelos; Shepherd, Timothy M.; Forder, John R.

2009-01-01

451

A box spline calculus for the discretization of computed tomography reconstruction problems.  

PubMed

B-splines are attractive basis functions for the continuous-domain representation of biomedical images and volumes. In this paper, we prove that the extended family of box splines are closed under the Radon transform and derive explicit formulae for their transforms. Our results are general; they cover all known brands of compactly-supported box splines (tensor-product B-splines, separable or not) in any number of dimensions. The proposed box spline approach extends to non-Cartesian lattices used for discretizing the image space. In particular, we prove that the 2-D Radon transform of an N-direction box spline is generally a (nonuniform) polynomial spline of degree N-1. The proposed framework allows for a proper discretization of a variety of tomographic reconstruction problems in a box spline basis. It is of relevance for imaging modalities such as X-ray computed tomography and cryo-electron microscopy. We provide experimental results that demonstrate the practical advantages of the box spline formulation for improving the quality and efficiency of tomographic reconstruction algorithms. PMID:22453611

Entezari, Alireza; Nilchian, Masih; Unser, Michael

2012-03-20

452

[Choices of proper words and word collocations in English medical papers].  

PubMed

On reviewing recurrent problems in English medical papers written by Chinese authors concerning the usage of words and word collocations, the authors of this article call for careful evaluation between possible choices of words and expressions. PMID:12297461

Wang, Zheng-ai; Song, Jian-wu

2002-09-01

453

A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions  

Microsoft Academic Search

The nonlinear sine-Gordon equation arises in various problems in science and engineering. In this paper, we propose a numerical scheme to solve the two-dimensional damped\\/undamped sine-Gordon equation. The proposed scheme is based on using collocation points and approximating the solution employing the thin plate splines (TPS) radial basis function (RBF). The new scheme works in a similar fashion as finite

Mehdi Dehghan; Ali Shokri

2008-01-01

454

A numerical solution of the linear Boltzmann equation using cubic B-splines.  

PubMed

A numerical method using cubic B-splines is presented for solving the linear Boltzmann equation. The collision kernel for the system is chosen as the Wigner-Wilkins kernel. A total of three different representations for the distribution function are presented. Eigenvalues and eigenfunctions of the collision matrix are obtained for various mass ratios and compared with known values. Distribution functions, along with first and second moments, are evaluated for different mass and temperature ratios. Overall it is shown that the method is accurate and well behaved. In particular, moments can be predicted with very few points if the representation is chosen well. This method produces sparse matrices, can be easily generalized to higher dimensions, and can be cast into efficient parallel algorithms. PMID:22401425

Khurana, Saheba; Thachuk, Mark

2012-03-01

455

3-D Face Reconstruction Using RBF and B Spline Method  

Microsoft Academic Search

3-D specific face model construction by way of 2-D face image is an active topic in 3-D face modeling research. In this paper, stereoscopic sense of vision is used to reconstruct 3-D feature points. Then multi-layer and multi-region RBF (radial basis function) based on feature points of frontal and profile face image is adopted for reconstructing the generic face model

Guo-hui He; Bin Zhu; Jun-ying Gan

2008-01-01

456

Collocated sensor/actuator positioning and feedback design in the control of flexible structure system  

NASA Astrophysics Data System (ADS)

This paper presents a new control design method for the control of flexible systems that not only guarantees closed-loop asymptotic stability but also effectively suppresses vibration. This method allows integrated determination of actuator/sensor locations and feedback gain via minimization of an energy criterion, which is chosen as the integrated total energy stored in the system. The energy criterion is determined via an efficient solution of the Lyapunov equation and minimized with a quasi-Newton or recursive quadratic programming algorithm. The prerequisite for this optimal design method is that the controlled system be asymptotically stable. This study shows that when the controller structure is a collocated direct velocity feedback design with positive definite feedback gain, the number and placement of actuators/sensors are the only factors needed to determine necessary and sufficient conditions for ensuring closed-loop asymptotic stability. The application of this method to a simple flexible structure confirms the direct relationship between our optimization criterion and effectiveness in vibration suppression.

Lee, An-Chen; Chen, Song-Tsuen

1994-04-01

457

Computationally Efficient Models of Urban and Natural Terrain by Non- Iterative Domain Decomposition for L1 Smoothing Splines.  

National Technical Information Service (NTIS)

In this paper, we propose and validate a computationally efficient non-iterative domain decomposition procedure for calculating bivariate cubic L1 smoothing splines. This domain decomposition procedure involves calculating local L1 smoothing splines indiv...

J. E. Lavery S. Fang W. Zhang Y. Lin Y. Wang

2006-01-01

458

Finite nucleus Dirac mean field theory and random phase approximation using finite /ital B/ splines  

SciTech Connect

We calculate the finite nucleus Dirac mean field spectrum in a Galerkinapproach using finite basis splines. We review the method and present resultsfor the relativistic sigma-..omega.. model for the closed-shell nuclei/sup 16/O and /sup 40/Ca. We study the convergence of themethod as a function of the size of the basis and the closure properties of thespectrum using an energy-weighted dipole sum rule. We apply the method to theDirac random-phase-approximation response and present results for the isoscalar1/sup /minus// and 3/sup /minus// longitudinal form factors of/sup 16/O and /sup 40/Ca. We also use a /ital B/-splinespectral representation of the positive-energy projector to evaluate partialenergy-weighted sum rules and compare with nonrelativistic sum rule results.

McNeil, J. A.; Furnstahl, R. J.; Rost, E.; Shepard, J. R.

1989-07-01

459

Exploiting spatial diversity in MIMO radars with collocated antennas  

NASA Astrophysics Data System (ADS)

MIMO systems have revolutionized wireless communications resulting in unprecedented channel capacity. This breakthrough led researchers in radar as well as wireless communications communities to investigate the applicability of MIMO systems to radar. Preliminary research is showing that the full benefits of MIMO technology is realized when antenna spacing results in a decorrelated target scattering matrix. This requires antenna placement such that each receiver is observing an independent view of the target. Research is also showing that suboptimal improvements can be attained when the scattering matrix is partially correlated. This situation arises when antennas are collocated. In this work, we investigate the feasibility of MIMO Radar technology when antenna placement is quite restricted, such as in phased-array antennas. We extend the theoretical results for the correlation coefficients derived for statistical MIMO radar. We apply these results to assess the degree of decorrelation that can be achieved with Phase-Array antennas. We quantify our results as a function of antenna element spacing, frequency band and target RCS. In addition, we quantify the degree of decorrelation that is achievable by antennas that are typical in a tactical missile environment. Our results show that even when the antennas are quite small, it is possible to achieve a significant degree of decorrelation for a certain class of targets and certain frequency bands.

Maalouli, Ghassan; Rosser, Daniel; Stratis, Glafkos

2011-05-01

460

Unintended consequences of collocation: using agent-based modeling to untangle effects of communication delay and in-group favor  

Microsoft Academic Search

In studies about office arrangements that have individuals working from remote locations, researchers usually hypothesize\\u000a advantages for collocators and disadvantages for remote workers. However, empirical findings have not shown consistent support\\u000a for the hypothesis. We suspect that there are unintended consequences of collocation, which can offset well-recognized advantages\\u000a of being collocated. To explain these unintended consequences, we developed a multi-agent

Ning Nan; Erik W. Johnston; Judith S. Olson

2008-01-01

461

Spline-based modelling of trends in the force of HIV infection, with application to the UNAIDS Estimation and Projection Package  

PubMed Central

Objective We previously developed a flexible specification of the UNAIDS Estimation and Projection Package (EPP) that relied on splines to generate time-varying values for the force of infection parameter. Here, we test the feasibility of this approach for concentrated HIV/AIDS epidemics with very sparse data and compare two methods for making short-term future projections with the spline-based model. Methods Penalised B-splines are used to model the average infection risk over time within the EPP 2011 modelling framework, which includes antiretroviral treatment effects and CD4 cell count progression, and is fit to sentinel surveillance prevalence data with a Bayesian algorithm. We compare two approaches for future projections: (1) an informative prior related to equilibrium prevalence and (2) a random walk formulation. Results The spline-based model produced plausible fits across a range of epidemics, which included 87 subpopulations from 14 countries with concentrated epidemics and 75 subpopulations from 33 countries with generalised epidemics. The equilibrium prior and random walk approaches to future projections yielded similar prevalence estimates, and both performed well in tests of out-of-sample predictive validity for prevalence. In contrast, in some cases the two approaches varied substantially in estimates of incidence, with the random walk formulation avoiding extreme changes in incidence. Conclusions A spline-based approach to allowing the force of infection parameter to vary over time within EPP 2011 is robust across a diverse array of epidemics, including concentrated ones with limited surveillance data. Future work on the EPP model should consider the impact that different modelling approaches have on estimates of HIV incidence.

Hogan, Daniel R; Salomon, Joshua A

2012-01-01

462

Use of tensor product splines in magnet optimization  

SciTech Connect

Variational Metrics and other direct search techniques have proved useful in magnetic optimization. At least one technique used in magnetic optimization is to first fit the data of the desired optimization parameter to the data. If this fit is smoothly differentiable, a number of powerful techniques become available for the optimization. The author shows the usefulness of tensor product splines in accomplishing this end. Proper choice of augmented knot placement not only makes the fit very accurate, but allows for differentiation. Thus the gradients required with direct optimization in divariate and trivariate applications are robustly generated.

Davey, K.R. (American Maglev, Inc., New Smyrna Beach, FL (United States))

1999-05-01

463

Target characterization by using B-spline curves for infrared image segmentation algorithms evaluation  

Microsoft Academic Search

This paper deals with the automatic evaluation of segmentation algorithms; the application framework is automatic target recognition within the specific case of infrared images of military vehicles. The approach consists in approximating the edges with generic B-spline functions; since the problem stated like this is too general, we use a spline template which has to be matched with the approximation

Jerome Caporossi; Philippe Bolon; Jacques Blanc-Talon

2001-01-01

464

Invariant matching and identification of curves using B-splines curve representation  

Microsoft Academic Search

There have been many techniques for curve shape representation and analysis, ranging from Fourier descriptors, to moments, to implicit polynomials, to differential geometry features, to time series models, to B-splines, etc. The B-splines stand as one of the most efficient curve (surface) representations and possess very attractive properties such as spatial uniqueness, boundedness and continuity, local shape controllability, and invariance

Fernand S. Cohen; Zhaohui Huang; Zhengwei Yang

1995-01-01

465

G1 continuity of B-spline surface patches in reverse engineering  

Microsoft Academic Search

When a clay model or industrial part is reverse engineered, B-spline surfaces are typically fitted to surface data points collected by a coordinate measuring machine, or, in more recent times, a laser scanner. The surface fitting procedure results in a patchwork of B-spline surfaces. Some of these patches may be required to blend smoothly with their neighbours to a specified

Michael J. Milroy; Colin Bradley; Geoffrey W. Vickers; D. J. Weir

1995-01-01

466

Formulation of Joint Trajectories for Industrial Robots Using B-Splines  

Microsoft Academic Search

In this paper, we describe a new procedure for constructing robot trajectories. The procedure uses the theory of B-splines. The motion of the robot, as specified by a time sequence of position and orientation knots of the end effector, is first transformed into sets of joint displacements. B-splines are then used to fit these sequences for each joint. The procedure

Stuart E. Thompson; Rajnikant V. Patel

1987-01-01

467

Wilson-Fowler Spline in a Global IGES (Initial Graphics Exchange Specification) Coordinate Frame.  

National Technical Information Service (NTIS)

This report re-examines the original Wilson-Fowler spline. The Wilson-Fowler spline is a two-dimensional, cubic, piecewise-smooth, curve-fitting algorithm. Its defining equations are redeveloped. The intended application of the redevelopment is the Initia...

R. M. Dolin

1987-01-01

468

The effects of friction in axial splines on rotor system stability  

Microsoft Academic Search

An in-depth parametric evaluation of the effects of Coulomb friction in an axial spline joint on the stability of the rotor-bearing system was conducted through time transient integration of the equations of motion. The effects of spin speed, friction coefficient, spline torque, external damping, imbalance, and side load as well as asymmetric bearing stiffnesses were investigated. A subnsynchrounous instability is

A. F. Artiles

1993-01-01

469

Hybrid Spline-Based Elastic Image Registration Using Analytic Solutions of the Navier Equation  

Microsoft Academic Search

We introduce a new hybrid approach for spline-based elastic image registration using both point landmarks and intensity information. As underlying deformation model we use Gaussian elastic body splines (GEBS), which are solutions of the Navier equation of linear elasticity under Gaussian forces. We also incorporate landmark localization uncer- tainties represented by weight matrices to cope with anisotropic errors. The hybrid

Stefan Wörz; Karl Rohr

2007-01-01

470

Spline-based elastic image registration using solutions of the Navier equation  

Microsoft Academic Search

We introduce a new hybrid approach for spline-based elastic image registration using both landmarks and intensity information. As underlying deformation model we use Gaussian elastic body splines (GEBS), which are solutions of the Navier equation of linear elasticity under Gaussian forces. We also incorporate landmark localization uncertainties, which are characterized by weight matrices representing anisotropic errors. To combine landmarks and

Stefan Wörz; Karl Rohr

2007-01-01

471

Practical Box Splines for Reconstruction on the Body Centered Cubic Lattice  

Microsoft Academic Search

We introduce a family of box splines for efficient, accurate and smooth reconstruction of volumetric data sampled on the Body Centered Cubic (BCC) lattice, which is the favorable volumetric sampling pattern due to its optimal spectral sphere packing property. First, we construct a box spline based on the four principal directions of the BCC lattice that allows for a linear

Alireza Entezari; Dimitri Van De Ville; Torsten Möller

2008-01-01

472

Free vibration of rotating non-uniform discs: Spline interpolation technique calculations  

Microsoft Academic Search

Stress distributions and flexural vibration of rotating annular discs with radially varying thickness are calculated by means of a spline interpolation technique. For this purpose, the disc is divided into many ring-shaped elements and the radial displacement is expressed as a cubic spline function, which satisfies the equation of equilibrium of force at all the knots and also satisfies boundary

T. Irie; G. Yamada; R. Kanda

1979-01-01

473

A few remarks on recurrence relations for geometrically continuous piecewise Chebyshevian B-splines  

NASA Astrophysics Data System (ADS)

This works complements a recent article (Mazure, J. Comp. Appl. Math. 219(2):457-470, 2008) in which we showed that T. Lyche's recurrence relations for Chebyshevian B-splines (Lyche, Constr. Approx. 1:155-178, 1985) naturally emerged from blossoms and their properties via de Boor type algorithms. Based on Chebyshevian divided differences, T. Lyche's approach concerned splines with all sections in the same Chebyshev space and with ordinary connections at the knots. Here, we consider geometrically continuous piecewise Chebyshevian splines, namely, splines with sections in different Chebyshev spaces, and with geometric connections at the knots. In this general framework, we proved in (Mazure, Constr. Approx. 20:603-624, 2004) that existence of B-spline bases could not be separated from existence of blossoms. Actually, the present paper enhances the powerfulness of blossoms in which not only B-splines are inherent, but also their recurrence relations. We compare this fact with the work by G. Mühlbach and Y. Tang (Mühlbach and Tang, Num. Alg. 41:35-78, 2006) who obtained the same recurrence relations via generalised Chebyshevian divided differences, but only under some total positivity assumption on the connexion matrices. We illustrate this comparison with splines with four-dimensional sections. The general situation addressed here also enhances the differences of behaviour between B-splines and the functions of smaller and smaller supports involved in the recurrence relations.

Mazure, Marie-Laurence

2009-08-01

474

Determination of loose spline coupling coefficients of rotor bearing systems in turbomachinery  

NASA Astrophysics Data System (ADS)

Analytical and experimental studies have been carried out to determine the stiffness and damping coefficients of loose spline couplings used in high speed rotating machinery from which a realistic assessment of rotor stability can be made at the turbomachinery design stage. This is believed to be the first attempt ever to determine these coefficients experimentally. Experimental modal parameters of the rotor bearing system with a spline coupling are found using modal testing for given spline geometry, misalignment, lubrication condition, torque, and rotational speeds. A dual rotor computer algorithm which contains a spline coupling model is developed in order to calculate the analytical modal parameters. Support bearing coefficients are obtained using a pressure dam bearing computer code which employs lubrication theory. Spline coupling coefficients are determined by adjusting the model until the analytical modal parameters match the experimental modal parameters. Both computer simulations and impact testing show that shaft speed and torque are the most important parameters which affect the system natural frequency and logarithmic decrement. However, the modal parameters are not very sensitive to the spine coupling coefficients. Only the second natural frequency shows any sensitivity to the spline angular stiffness. The lateral stiffness coefficient of the spline coupling decreases as rotational speed increases. Lateral and angular damping do not influence the modal parameter until unreasonably large values are considered. This is due to the large value of damping in the pressure dam bearings. Since the modal parameters are insensitive to the spline coefficients, a set of error bounds for the experimental values are chosen to determine the ranges of the loose spline coupling coefficients. The results show that the value of the spline lateral stiffness is between 2.0 x10(exp 7) and 8.0 x 10(exp 8) N/m and the spline angular stiffness is between 2.0 x 10(exp 5) and 8.0 x 10(exp 8) N/m, and the spline angular stiffness is between 2.0 x 10(exp 6) Nm/rad. However, it is impossible to identify the spline damping coefficients because the effect of the support bearing damping coefficients suppress the nonsynchronous whirling motion due to the spline friction even at speeds above the first critical speed.

Park, Sang Kyu

475

TWO-LEVEL TIME MARCHING SCHEME USING SPLINES FOR SOLVING THE ADVECTION EQUATION. (R826371C004)  

EPA Science Inventory

A new numerical algorithm using quintic splines is developed and analyzed: quintic spline Taylor-series expansion (QSTSE). QSTSE is an Eulerian flux-based scheme that uses quintic splines to compute space derivatives and Taylor series expansion to march in time. The new scheme...

476

Reconstruction of irregularly-sampled volumetric data in efficient box spline spaces.  

PubMed

We present a variational framework for the reconstruction of irregularly-sampled volumetric data in, nontensor-product, spline spaces. Motivated by the sampling-theoretic advantages of body centered cubic (BCC) lattice, this paper examines the BCC lattice and its associated box spline spaces in a variational setting. We introduce a regularization scheme for box splines that allows us to utilize the BCC lattice in a variational reconstruction framework. We demonstrate that by choosing the BCC lattice over the commonly-used Cartesian lattice, as the shift-invariant representation, one can increase the quality of signal reconstruction. Moreover, the computational cost of the reconstruction process is reduced in the BCC framework due to the smaller bandwidth of the system matrix in the box spline space compared to the corresponding tensor-product B-spline space. The improvements in accuracy are quantified numerically and visualized in our experiments with synthetic as well as real biomedical datasets. PMID:22434796

Xu, Xie; Alvarado, Alexander Singh; Entezari, Alireza

2012-03-12

477

Recommended practices for spline usage in CAD/CAM systems: CADCAM-007  

SciTech Connect

Sandia National Laboratories has been assigned Lead Lab responsibility for integrating CAD/CAM activities throughout the DOE Nuclear Weapons Complex (NWC) and automating exchange of product definition. Transfer of splines between CAD/CAM systems presents a special problem due to the use of different spline interpolation schemes in these systems. Automated exchange via IGES (Initial Graphics Exchange Specification, ANSI Y14.26M-1981) shows promise but does not yet provide a usable data path for NWC spline needs. Data exchange today is primarily via hard copy drawings with manual data reentry and spline recomputation. In this environment, spline problems can be minimized by following the recommended practices set forth in this report.

Fletcher, S.K.

1984-04-01

478

Trajectory Planning of Satellite Formation Flying using Nonlinear Programming and Collocation  

NASA Astrophysics Data System (ADS)

Recently, satellite formation flying has been a topic of significant research interest in aerospace society because it provides potential benefits compared to a large spacecraft. Some techniques have been proposed to design optimal formation trajectories minimizing fuel consumption in the process of formation configuration or reconfiguration. In this study, a method is introduced to build fuel-optimal trajectories minimizing a cost function that combines the total fuel consumption of all satellites and assignment of fuel consumption rate for each satellite. This approach is based on collocation and nonlinear programming to solve constraints for collision avoidance and the final configuration. New constraints of nonlinear equality or inequality are derived for final configuration, and nonlinear inequality constraints are established for collision avoidance. The final configuration constraints are that three or more satellites should form a projected circular orbit and make an equilateral polygon in the horizontal plane. Example scenarios, including these constraints and the cost function, are simulated by the method to generate optimal trajectories for the formation configuration and reconfiguration of multiple satellites.

Lim, Hyung-Chu; Bang, Hyochoong

2008-12-01

479

Simplex stochastic collocation with ENO-type stencil selection for robust uncertainty quantification  

NASA Astrophysics Data System (ADS)

Multi-element uncertainty quantification approaches can robustly resolve the high sensitivities caused by discontinuities in parametric space by reducing the polynomial degree locally to a piecewise linear approximation. It is important to extend the higher degree interpolation in the smooth regions up to a thin layer of linear elements that contain the discontinuity to maintain a highly accurate solution. This is achieved here by introducing Essentially Non-Oscillatory (ENO) type stencil selection into the Simplex Stochastic Collocation (SSC) method. For each simplex in the discretization of the parametric space, the stencil with the highest polynomial degree is selected from the set of candidate stencils to construct the local response surface approximation. The application of the resulting SSC-ENO method to a discontinuous test function shows a sharper resolution of the jumps and a higher order approximation of the percentiles near the singularity. SSC-ENO is also applied to a chemical model problem and a shock tube problem to study the impact of uncertainty both on the formation of discontinuities in time and on the location of discontinuities in space.

Witteveen, Jeroen A. S.; Iaccarino, Gianluca

2013-04-01

480

The construction of operational matrix of fractional derivatives using B-spline functions  

NASA Astrophysics Data System (ADS)

Fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. For that reason we need a reliable and efficient technique for the solution of fractional differential equations. Here we construct the operational matrix of fractional derivative of order ? in the Caputo sense using the linear B-spline functions. The main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of algebraic equations thus we can solve directly the problem. The method is applied to solve two types of fractional differential equations, linear and nonlinear. Illustrative examples are included to demonstrate the validity and applicability of the new technique presented in the current paper.

Lakestani, Mehrdad; Dehghan, Mehdi; Irandoust-Pakchin, Safar

2012-03-01