Leuven 2000 Tension spline collocation methods for singularly
Rogina, Mladen
Leuven 2000 July 2000 pp. 1{26 Tension spline collocation methods for singularly perturbed Volterra Abstract. We consider the numerical discretization of singularly perturbed Volterra integro{ di#11;erential spline collo- cation solution for 0 singularly perturbed VIDE and VIE, thus extending
Optimal Quadratic Spline Collocation Methods for the Shallow Water Equations on the Sphere
Christara, Christina C.
Optimal Quadratic Spline Collocation Methods for the Shallow Water Equations on the Sphere Anita T, for solving the shallow water equations (SWEs) in spherical co ordinates. A quadratic spline collocation formulation, the quadratic spline is computed by making the residual of the differential equations zero
Basis spline collocation method for solving the Schroedinger equation in axillary symmetric systems
Kegley, D.R. Jr.; Oberacker, V.E.; Umar, A.S. [Oak Ridge National Lab., TN (United States)]|[Vanderbilt Univ., Nashville, TN (United States)] [and others
1996-10-01
We use basis spline collocation to solve the Schroedinger equation on a lattice for axially symmetric systems, with and without spin. The focus of the present work is on systems which have continuum states, weakly bound states, or strong spin-orbit coupling, since these are the most difficult to solve on the lattice. A brief overview of the basis spline collocation method is included which concentrates primarily on those aspects of the theory which are relevant to its application in cylindrical coordinates. To demonstrate the method, we solve several model problems selected from the fields of atomic and nuclear physics. 25 refs., 6 figs., 5 tabs.
Z. Mahmoodi; J. Rashidinia; E. Babolian
2012-01-01
A numerical method based on quintic B-spline has been developed to solve the linear and nonlinear Fredholm and Volterra integro-differential equations up to order 4. The solution and its derivatives are collocated by quintic B-spline and then the integral equation is approximated by the 4-points GaussTurán quadrature formula with respect to the weight function Legendre. The error analysis of proposed
Rogina, Mladen
Tension spline collocation methods for singularly perturbed Volterra integro-di#11;erential of the singularly perturbed Volterra integro- di#11;erential equations (VIDE) "y 0 (t) = q(t) p(t)y(t) + Z t 0 K to the singularly perturbed case, and the numerical examples support the theoretical results. References [1] J
Basis Spline Collocation Method for Solving the Schrödinger Equation in Axillary Symmetric Systems
D. R. Jr. Kegley; V. E. Oberacker; M. R. Strayer; A. S. Umar; J. C. Wells
1996-01-01
We use basis spline collocation to solve the Schrödinger equation on a lattice for axially symmetric systems, with and without spin. The focus of the present work is on systems which have continuum states, weakly bound states, or strong spinorbit coupling, since these are the most difficult to solve on the lattice. A brief overview of the basis spline collocation
Analysis of Iterative Line Spline Collocation Methods for Elliptic Partial Differential Equations
A. Hadjidimos; E. N. Houstis; J. r. Rice E. Vavalis; E. Vavalis
2000-01-01
.In this paper we present the convergence analysis of iterative schemes for solving linear systemsresulting from discretizing multidimensional linear second order elliptic partial differential equations(PDEs) defined in ahyper-parallelepiped\\\\Omegaand subject to Dirichlet boundary conditions onsome facesof\\\\Omegaand Neumann on the others, using line cubic spline collocation (LCSC) methods.Specifically, we derive analytic expressions or obtain sharp bounds for the spectral radius of the...
Orthogonal spline collocation method for the two-dimensional fractional sub-diffusion equation
NASA Astrophysics Data System (ADS)
Yang, Xuehua; Zhang, Haixiang; Xu, Da
2014-01-01
The aim of this paper is to develop a novel numerical techniques for the solution of the two-dimensional fractional sub-diffusion equation. The proposed technique is based on orthogonal spline collocation (OSC) method in space and a finite difference method (FDM) in time. Stability and convergence of the proposed method are rigorously discussed and theoretically proven. We present the results of numerical experiments in one and two space variables, which confirm the predicted convergence rates and exhibit optimal accuracy in various norms.
NASA Astrophysics Data System (ADS)
Fernandes, Ryan I.; Fairweather, Graeme
2012-08-01
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.
Quartic B-spline collocation method applied to Korteweg de Vries equation
NASA Astrophysics Data System (ADS)
Zin, Shazalina Mat; Majid, Ahmad Abd; Ismail, Ahmad Izani Md
2014-07-01
The Korteweg de Vries (KdV) equation is known as a mathematical model of shallow water waves. The general form of this equation is ut+?uux+?uxxx = 0 where u(x,t) describes the elongation of the wave at displacement x and time t. In this work, one-soliton solution for KdV equation has been obtained numerically using quartic B-spline collocation method for displacement x and using finite difference approach for time t. Two problems have been identified to be solved. Approximate solutions and errors for these two test problems were obtained for different values of t. In order to look into accuracy of the method, L2-norm and L?-norm have been calculated. Mass, energy and momentum of KdV equation have also been calculated. The results obtained show the present method can approximate the solution very well, but as time increases, L2-norm and L?-norm are also increase.
Christara, Christina C.
1 Quadratic spline collocation for onedimensional linear parabolic partial differential equations general linear parabolic partial differential equations (PDEs) in one space dimen sion are developed. The methods combine quadraticspline collocation for the space discretization and classical finite differences
Collocation and Galerkin Time-Stepping Methods
NASA Technical Reports Server (NTRS)
Huynh, H. T.
2011-01-01
We study the numerical solutions of ordinary differential equations by one-step methods where the solution at tn is known and that at t(sub n+1) is to be calculated. The approaches employed are collocation, continuous Galerkin (CG) and discontinuous Galerkin (DG). Relations among these three approaches are established. A quadrature formula using s evaluation points is employed for the Galerkin formulations. We show that with such a quadrature, the CG method is identical to the collocation method using quadrature points as collocation points. Furthermore, if the quadrature formula is the right Radau one (including t(sub n+1)), then the DG and CG methods also become identical, and they reduce to the Radau IIA collocation method. In addition, we present a generalization of DG that yields a method identical to CG and collocation with arbitrary collocation points. Thus, the collocation, CG, and generalized DG methods are equivalent, and the latter two methods can be formulated using the differential instead of integral equation. Finally, all schemes discussed can be cast as s-stage implicit Runge-Kutta methods.
Numerical Methods Using B-Splines
NASA Technical Reports Server (NTRS)
Shariff, Karim; Merriam, Marshal (Technical Monitor)
1997-01-01
The seminar will discuss (1) The current range of applications for which B-spline schemes may be appropriate (2) The property of high-resolution and the relationship between B-spline and compact schemes (3) Comparison between finite-element, Hermite finite element and B-spline schemes (4) Mesh embedding using B-splines (5) A method for the incompressible Navier-Stokes equations in curvilinear coordinates using divergence-free expansions.
Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's
NASA Technical Reports Server (NTRS)
Cai, Wei; Wang, Jian-Zhong
1993-01-01
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 constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.
Stochastic Collocation Method for Three-dimensional Groundwater Flow
NASA Astrophysics Data System (ADS)
Shi, L.; Zhang, D.
2008-12-01
The stochastic collocation method (SCM) has recently gained extensive attention in several disciplines. The numerical implementation of SCM only requires repetitive runs of an existing deterministic solver or code as in the Monte Carlo simulation. But it is generally much more efficient than the Monte Carlo method. In this paper, the stochastic collocation method is used to efficiently qualify uncertainty of three-dimensional groundwater flow. We introduce the basic principles of common collocation methods, i.e., the tensor product collocation method (TPCM), Smolyak collocation method (SmCM), Stround-2 collocation method (StCM), and probability collocation method (PCM). Their accuracy, computational cost, and limitation are discussed. Illustrative examples reveal that the seamless combination of collocation techniques and existing simulators makes the new framework possible to efficiently handle complex stochastic problems.
B-spline Method in Fluid Dynamics
NASA Technical Reports Server (NTRS)
Botella, Olivier; Shariff, Karim; Mansour, Nagi N. (Technical Monitor)
2001-01-01
B-spline functions are bases for piecewise polynomials that possess attractive properties for complex flow simulations : they have compact support, provide a straightforward handling of boundary conditions and grid nonuniformities, and yield numerical schemes with high resolving power, where the order of accuracy is a mere input parameter. This paper reviews the progress made on the development and application of B-spline numerical methods to computational fluid dynamics problems. Basic B-spline approximation properties is investigated, and their relationship with conventional numerical methods is reviewed. Some fundamental developments towards efficient complex geometry spline methods are covered, such as local interpolation methods, fast solution algorithms on cartesian grid, non-conformal block-structured discretization, formulation of spline bases of higher continuity over triangulation, and treatment of pressure oscillations in Navier-Stokes equations. Application of some of these techniques to the computation of viscous incompressible flows is presented.
Multivariate spline methods in surface fitting
NASA Technical Reports Server (NTRS)
Guseman, L. F., Jr. (principal investigator); Schumaker, L. L.
1984-01-01
The use of spline functions in the development of classification algorithms is examined. In particular, a method is formulated for producing spline approximations to bivariate density functions where the density function is decribed by a histogram of measurements. The resulting approximations are then incorporated into a Bayesiaan classification procedure for which the Bayes decision regions and the probability of misclassification is readily computed. Some preliminary numerical results are presented to illustrate the method.
Testing Generalized Linear Models Using Smoothing Spline Methods
Meiring, Wendy
Testing Generalized Linear Models Using Smoothing Spline Methods Anna Liu, Wendy Meiring and Yuedong Wang University of California, Santa Barbara Abstract This article considers testing exponential families. The tests developed are based on the connection between the smoothing spline models
Collocation method for fractional quantum mechanics
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
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.
Collocation Method for Numerical Solution of Coupled Nonlinear Schroedinger Equation
Ismail, M. S. [Department of Mathematics, College of Science, P.O.Box 80203, King Abdulaziz University, Jeddah (Saudi Arabia)
2010-09-30
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.
Comparison of Implicit Collocation Methods for the Heat Equation
NASA Technical Reports Server (NTRS)
Kouatchou, Jules; Jezequel, Fabienne; Zukor, Dorothy (Technical Monitor)
2001-01-01
We combine a high-order compact finite difference scheme to approximate spatial derivatives arid collocation techniques for the time component to numerically solve the two dimensional heat equation. We use two approaches to implement the collocation methods. The first one is based on an explicit computation of the coefficients of polynomials and the second one relies on differential quadrature. We compare them by studying their merits and analyzing their numerical performance. All our computations, based on parallel algorithms, are carried out on the CRAY SV1.
Collocation Model Reduction for Moving-least-square method
Paris-Sud XI, Université de
Collocation Model Reduction for Moving-least-square method B. Khoshnoudirad,P.Joyot,F. Chinesta, P. Villon December 2, 2008 Abstract Proper orthogonal decomposition (POD) and moving least-square- square data in a certain least-square optimal sense. In addition to being optimal in a least-square sense, POD
Stable spline methods for parabolic partial differential equations
NASA Astrophysics Data System (ADS)
Lippolis, A.; Napolitano, M.
A classical spline-Crank Nicolson approach (Rubin and Khosla, 1977) applied to a linear parabolic partial differential equation is considered. The marching technique of Napolitano and Vacca (1980) is considered with a view to further developments. A stability analysis is used to verify that a technique of this type is unconditionally unstable and to indicate possible ways of removing the cause of the instability. Two new stable marching techniques, which employ spline interpolating concepts in both the marching and the nonmarching directions, are then presented. A different approach to obtaining stability is then followed, and two stable two-sweep procedures are presented. These use the spline-Crank Nicolson approach as the first step and a spline-spline method, for improving the accuracy of the first-step solution, in the second and final sweep. The case of a three-dimensional and nonlinear parabolic partial differential equation is addressed, and numerial results for the classical Burgers equation are presented.
Adaptive Collocation Methods for the Solution of Partial Differential Equations
Paulo Brito; António Portugal
2009-01-01
\\u000a An integration algorithm that conjugates a Method of Lines (MOL) strategy based on finite differences space discretizations,\\u000a with a collocation strategy based on increasing level dyadic grids is presented. It reveals potential either as a grid generation\\u000a procedure and a Partial Differential Equation (PDE) integration scheme. It copes satisfactorily with a example characterized\\u000a by a steep travelling wave and a
Pseudospectral collocation methods for fourth order differential equations
NASA Technical Reports Server (NTRS)
Malek, Alaeddin; Phillips, Timothy N.
1994-01-01
Collocation schemes are presented for solving linear fourth order differential equations in one and two dimensions. The variational formulation of the model fourth order problem is discretized by approximating the integrals by a Gaussian quadrature rule generalized to include the values of the derivative of the integrand at the boundary points. Collocation schemes are derived which are equivalent to this discrete variational problem. An efficient preconditioner based on a low-order finite difference approximation to the same differential operator is presented. The corresponding multidomain problem is also considered and interface conditions are derived. Pseudospectral approximations which are C1 continuous at the interfaces are used in each subdomain to approximate the solution. The approximations are also shown to be C3 continuous at the interfaces asymptotically. A complete analysis of the collocation scheme for the multidomain problem is provided. The extension of the method to the biharmonic equation in two dimensions is discussed and results are presented for a problem defined in a nonrectangular domain.
The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
Jasmine Foo; Xiaoliang Wan; George Em Karniadakis
2008-01-01
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
Lianghui Tu; Jianping Yuan; Jianjun Luo; Xin Ning; Ruiwu Zhou
2007-01-01
Direct collocation method has been widely used for trajectory optimization. In this paper, the application of direct optimization method (direct collocation method & nonlinear programming (NLP)) to lunar probe soft-landing trajectory optimization is introduced. Firstly, the model of trajectory optimization control problem to lunar probe soft landing trajectory is established and the equations of motion are simplified respectively based on
An efficient method for calculating smoothing splines using orthogonal transformations
F. R. de Hoog; M. F. Hutchinson
1986-01-01
Summary A procedure for calculating the mean squared residual and the trace of the influence matrix associated with a polynomial smoothing spline of degree 2m-1 using an orthogonal factorization is presented. The procedure substantially overcomes the problem of ill-conditioning encountered by a recently developed method which employs a Cholesky factorization, but still requires only orderm2n operations and ordermn storage.
ERIC Educational Resources Information Center
Cui, Zhongmin; Kolen, Michael J.
2009-01-01
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
Direct methods for solving singular integral equations with shifts in the unit circle
F. Feras
1998-01-01
The computation schemes of spline-collocation methods for solving singular integral equations. A theoretical foundation of these two methods is obtained in space L2: In the present paper we give theoreticaly justification of the nu- merical schemes of spline-collocation method for solving the singular integral equations (SIE) of the following form
A multidomain spectral collocation method for the Stokes problem
NASA Technical Reports Server (NTRS)
Landriani, G. Sacchi; Vandeven, H.
1989-01-01
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 pressure.
Webster, Clayton G [ORNL; Tran, Hoang A [ORNL; Trenchea, Catalin S [ORNL
2013-01-01
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.
A method fortting regression splines with varying polynomial order in the linear mixed model
Lloyd J. Edwards; Paul W. Stewart; James E. MacDougall; Ronald W. Helms
2005-01-01
SUMMARY The linear mixed model has become a widely used tool for longitudinal analysis of continuous variables. The use of regression splines in these models oers the analyst additionalexibility in the formulation of descriptive analyses, exploratory analyses and hypothesis-driven conrmatory analyses. We propose a method fortting piecewise polynomial regression splines with varying polynomial order in the ?xed eects and =or
GRADUAL GENERALIZATION OF NAUTICAL CHART CONTOURS WITH A B-SPLINE SNAKE METHOD
New Hampshire, University of
GRADUAL GENERALIZATION OF NAUTICAL CHART CONTOURS WITH A B-SPLINE SNAKE METHOD BY DANDAN MIAO BS...............................................................................................39 2.2 Snake Method....................................................................................................................40 2.2.1 Snake Method Definition...............................................
Fast Spectral Collocation Method for Surface Integral Equations of Potential Problems in a Spheroid
Xu, Zhenli; Cai, Wei
2009-01-01
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. PMID:20414359
Spectral collocation methods for polymer brushes Tanya L. Chantawansri,1, 2
Bigelow, Stephen
methods associated with modeling the self-assembly of molten mixed polymer brushes in the frameworkSpectral collocation methods for polymer brushes Tanya L. Chantawansri,1, 2 Su-Mi Hur,1 Carlos J of self-consistent field theory (SCFT). SCFT of molten polymer brushes has proved numerically challenging
Point interpolation collocation method for the solution of partial differential equations
Xin Liu; K. Tai
2006-01-01
This paper presents a truly meshless method for solving partial differential equations based on point interpolation collocation method (PICM). This method is different from the previous Galerkin-based point interpolation method (PIM) investigated in the papers [G.R. Liu, (2002), mesh free methods, Moving beyond the Finite Element Method, CRC Press. G.R. Liu, Y.T. Gu, A point interpolation method for two-dimension solids,
ADAPTIVE WAVELET COLLOCATION METHODS FOR IMAGE SEGMENTATION USING TV-ALLEN-CAHN TYPE MODELS
Soatto, Stefano
algorithm integrates (i) grid adaptation based on a threshold of the sparse wavelet representation of wavelets [18] and dynamically evolves the sparse representation of the locally-structured solution throughADAPTIVE WAVELET COLLOCATION METHODS FOR IMAGE SEGMENTATION USING TV-ALLEN-CAHN TYPE MODELS ZHIJIAN
Fast split-step wavelet collocation method for WDM system parameter optimization
Tristan Kremp; Wolfgang Freude
2005-01-01
To meet rapidly increasing bandwidth requirements, extensive numerical simulations are an important optimization step for optical networks. Using a basis of cardinal functions with compact support, a new split-step wavelet collocation method (SSWCM) was developed as a general solver for the nonlinear Schrödinger equation describing pulse propagation in nonlinear optical fibers. With N as the number of discretization points, this
NASA Technical Reports Server (NTRS)
Rubin, S. G.; Khosla, P. K.
1980-01-01
The coupled strongly implicit (CSIP) method described previously is combined with a deferred-corrector spline solver for the vorticity-stream function form of the Navier-Stokes equations. Solutions for cavity, channel and cylinder flows are obtained with the fourth-order spline 4 procedure. The strongly coupled spline corrector method converges as rapidly as the finite difference calculations and also allows for arbitrary large time increments for the Reynolds numbers considered (equal to or less than 1000). In some cases fourth-order smoothing or filtering is required in order to suppress high frequency oscillations.
Navier-Stokes calculations with a coupled strongly implicit method. Part 2: Spline solutions
NASA Technical Reports Server (NTRS)
Rubin, S. G.; Khosla, P. K.
1978-01-01
A coupled strongly implicit method is combined with a deferred-corrector spline solver for the vorticity-stream function form of the Navier-Stokes equation. Solutions for cavity, channel and cylinder flows are obtained with the fourth-order spline 4 procedure. The strongly coupled spline corrector method converges as rapidly as the finite difference calculations and also allows for arbitrary large time increments for the Reynolds numbers considered. In some cases fourth-order smoothing or filtering is required in order to suppress high frequency oscillations.
Spline methods for the comparison of physical and genetic maps.
Berloff, Natalia; Perola, Markus; Lange, Kenneth
2002-01-01
The first genetic maps were constructed by linkage analysis. Physical mapping techniques, such as radiation hybrids and complete sequencing, produce a different picture. For the purposes of population genetics, clinical genetics, and genetic epidemiology, it is important to harmonize and amalgamate existing genetic and physical maps. Among other things, comparisons of the two kinds of maps promotes better understanding of the wide variation in local recombination rates per unit physical length of DNA. The current paper presents methods for estimating recombination intensity as a function of physical distance along a chromosome. Genetic map distance is the integral of intensity. We derive fast reliable estimation algorithms based on a Poisson process model, penalized likelihoods, and cubic spline interpolation. Our methods provide a rigorous and statistically sound foundation for comparing physical and genetic maps. To illustrate the possibilities, we apply the methods to published recombination data on CEPH families and the complete sequences of chromosomes 21 and 22. Our results are in good agreement with previous studies and the biological data. PMID:12162886
Parallel Implementation of a High Order Implicit Collocation Method for the Heat Equation
NASA Technical Reports Server (NTRS)
Kouatchou, Jules; Halem, Milton (Technical Monitor)
2000-01-01
We combine a high order compact finite difference approximation and collocation techniques to numerically solve the two dimensional heat equation. The resulting method is implicit arid can be parallelized with a strategy that allows parallelization across both time and space. We compare the parallel implementation of the new method with a classical implicit method, namely the Crank-Nicolson method, where the parallelization is done across space only. Numerical experiments are carried out on the SGI Origin 2000.
B-spline approximation methods for digital image reconstruction in strain measurement
H. Deng; A. Ben-Zvi; J. B. Wiskel; H. Henein
2010-01-01
A non-invasive digital imaging procedure has been successfully developed to quantify the strain history during electric resistance welded (ERW) pipe forming. A curve fitting method was used to reconstruct a continuous and smooth pipe profile from digital image data. Three B-spline approximation methods (one-dimensional, two-dimensional, and trigonometric B-spline) were evaluated using the same set of digital image data, and validated
E. J. Kansa; M FRIEDMAN
2002-01-01
The multiquadric radial basis function (MQ) method is a recent meshless collocation method with global basis functions. It was introduced for discretizing partial differential equations (PDEs) by Kansa in the early 1990s. The MQ method was originally used for interpolation of scattered data, and it was shown to have exponential convergence for interpolation problems.In [1], we have extended the Kansa-MQ
Adaptive Wavelet Collocation Method for Simulation of Time Dependent Maxwell's Equations
Haojun Li; Kirankumar R. Hiremath; Andreas Rieder; Wolfgang Freude
2012-04-05
This paper investigates an adaptive wavelet collocation time domain method for the numerical solution of Maxwell's equations. In this method a computational grid is dynamically adapted at each time step by using the wavelet decomposition of the field at that time instant. In the regions where the fields are highly localized, the method assigns more grid points; and in the regions where the fields are sparse, there will be less grid points. On the adapted grid, update schemes with high spatial order and explicit time stepping are formulated. The method has high compression rate, which substantially reduces the computational cost allowing efficient use of computational resources. This adaptive wavelet collocation method is especially suitable for simulation of guided-wave optical devices.
A numerical solution of Falkner-Skan equation via a shifted Chebyshev collocation method
NASA Astrophysics Data System (ADS)
Kajani, M. T.; Maleki, M.; Allame, M.
2014-11-01
The Falkner-Skan equation is a nonlinear third-order boundary value problem defined on the semi-infinite interval [0,?). This equation plays an important role to illustrate the main physical features of boundary layer phenomena. This paper presents a new collocation method for solving the Falkner-Skan equation. The proposed approach is equipped by the orthogonal Chebyshev polynomials that have perfect properties to achieve this goal. The shifted Chebyshev-Gauss points are utilized as collocation points. In addition, this method reduces solution of the problem to solution of a system of algebraic equations. Comparisons with other methods show that the proposed method is highly accurate and its convergence is very rapid.
Domain decomposition methods for systems of conservation laws: Spectral collocation approximations
NASA Technical Reports Server (NTRS)
Quarteroni, Alfio
1989-01-01
Hyperbolic systems of conversation laws are considered which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level a domain deposition method based on an iteration by subdomain procedure was introduced yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The method is set for a general nonlinear problem in several space variables. The convergence analysis, however, is carried out only for a linear one-dimensional system with continuous solutions. A precise form of the error reduction factor at each iteration is derived. Although the method is applied here to the case of spectral collocation approximation only, the idea is fairly general and can be used in a different context as well. For instance, its application to space discretization by finite differences is straight forward.
T. Kremp; A. Killi; W. Freude; A. Rieder
2002-01-01
Summary form only given. Pulse propagation in a nonlinear optical medium is described by the nonlinear Schrodinger equation (NLSE). For large wavelength division multiplexing (WDM) systems, the simulation time can run into weeks. We developed a new, flexible, fast and adaptive split-step wavelet collocation method (SSWCM) which provides a substantial speed-up compared to the standard split-step Fourier method (SSFM).
Fractional spectral collocation methods for linear and nonlinear variable order FPDEs
NASA Astrophysics Data System (ADS)
Zayernouri, Mohsen; Karniadakis, George Em
2015-07-01
While several high-order methods have been developed for fractional PDEs (FPDEs) with fixed order, there are no such methods for FPDEs with field-variable order. These equations allow multiphysics simulations seamlessly, e.g. from diffusion to sub-diffusion or from wave dynamics transitioning to diffusion, by simply varying the fractional order as a function of space or time. We develop an exponentially accurate fractional spectral collocation method for solving linear/nonlinear FPDEs with field-variable order. Following the spectral theory, developed in [1] for fractional Sturm-Liouville eigenproblems, we introduce a new family of interpolants, called left-/right-sided and central fractional Lagrange interpolants. We employ the fractional derivatives of (left-/right-sided) Riemann-Liouville and Riesz type and obtain the corresponding fractional differentiation matrices by collocating the field-variable fractional orders. We solve several FPDEs including time- and space-fractional advection-equation, time- and space-fractional advection-diffusion equation, and finally the space-fractional Burgers' equation to demonstrate the performance of the method. In addition, we develop a spectral penalty method for enforcing inhomogeneous initial conditions. Our numerical results confirm the exponential-like convergence of the proposed fractional collocation methods.
Higher-order numerical solutions using cubic splines. [for partial differential equations
NASA Technical Reports Server (NTRS)
Rubin, S. G.; Khosla, P. K.
1975-01-01
A cubic spline collocation procedure has recently been developed for the numerical solution of partial differential equations. In the present paper, this spline procedure is reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a non-uniform mesh and overall fourth-order accuracy for a uniform mesh. Solutions using both spline procedures, as well as three-point finite difference methods, will be presented for several model problems.-
Global collocation methods for approximation and the solution of partial differential equations
NASA Technical Reports Server (NTRS)
Solomonoff, A.; Turkel, E.
1986-01-01
Polynomial interpolation methods are applied both to the approximation of functions and to the numerical solutions of hyperbolic and elliptic partial differential equations. The derivative matrix for a general sequence of the collocation points is constructed. The approximate derivative is then found by a matrix times vector multiply. The effects of several factors on the performance of these methods including the effect of different collocation points are then explored. The resolution of the schemes for both smooth functions and functions with steep gradients or discontinuities in some derivative are also studied. The accuracy when the gradients occur both near the center of the region and in the vicinity of the boundary is investigated. The importance of the aliasing limit on the resolution of the approximation is investigated in detail. Also examined is the effect of boundary treatment on the stability and accuracy of the scheme.
Solar Convection Simulations using a B-spline method
Thomas Hartlep; Nagi N. Mansour
2008-05-05
This report outlines the development of a B-spline--spectral numerical code for the simulation of convection flows. It allows changing the spatial resolution in all three coordinates as a function of depth, which is especially advantageous for simulations of solar convection.
A Survey of Symplectic and Collocation Integration Methods for Orbit Propagation
NASA Technical Reports Server (NTRS)
Jones, Brandon A.; Anderson, Rodney L.
2012-01-01
Demands on numerical integration algorithms for astrodynamics applications continue to increase. Common methods, like explicit Runge-Kutta, meet the orbit propagation needs of most scenarios, but more specialized scenarios require new techniques to meet both computational efficiency and accuracy needs. This paper provides an extensive survey on the application of symplectic and collocation methods to astrodynamics. Both of these methods benefit from relatively recent theoretical developments, which improve their applicability to artificial satellite orbit propagation. This paper also details their implementation, with several tests demonstrating their advantages and disadvantages.
Webster, Clayton G [ORNL; Zhang, Guannan [ORNL; Gunzburger, Max D [ORNL
2012-10-01
Accurate predictive simulations of complex real world applications require numerical approximations to first, oppose the curse of dimensionality and second, converge quickly in the presence of steep gradients, sharp transitions, bifurcations or finite discontinuities in high-dimensional parameter spaces. In this paper we present a novel multi-dimensional multi-resolution adaptive (MdMrA) sparse grid stochastic collocation method, that utilizes hierarchical multiscale piecewise Riesz basis functions constructed from interpolating wavelets. The basis for our non-intrusive method forms a stable multiscale splitting and thus, optimal adaptation is achieved. Error estimates and numerical examples will used to compare the efficiency of the method with several other techniques.
Some Optimal Runge-Kutta Collocation Methods for Stiff Problems and DAEs
NASA Astrophysics Data System (ADS)
Gonzalez-Pinto, S.; Hernández-Abreu, D.; Montijano, J. I.
2008-09-01
A new family of implicit Runge-Kutta methods was introduced at ICCAM 2008 (Gent) by the present authors. This family of methods is intended to solve numerically stiff problems and DAEs. The s-stage method (for s?3) has the following features: it is a collocation method depending on a real free parameter ?, has classical convergence order 2s-3 and is strongly A-stable for ? ranging in some nonempty open interval Is = (-?s,0). In addition, for ??Is, all the collocation nodes fall in the interval [0,1]. Moreover, these methods also involve a similar computational cost as that of the corresponding counterpart in the Runge-Kutta Radau IIA family (the method having the same classical order) when solving for their stage values. However, our methods have the additional advantage of possessing a higher stage order than the respective Radau IIA counterparts. This circumstance is important when integrating stiff problems in which case most of numerical methods are affected by an order reduction. In this talk we discuss how to optimize the free parameter depending on the special features of the kind of stiff problems and DAEs to be solved. This point is highly important in order to make competitive our methods when compared with those of the Radau IIA family.
The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
NASA Astrophysics Data System (ADS)
Foo, Jasmine; Wan, Xiaoliang; Karniadakis, George Em
2008-11-01
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 L2 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.
Numerical Algorithm Based on Haar-Sinc Collocation Method for Solving the Hyperbolic PDEs
Javadi, H. H. S.; Navidi, H. R.
2014-01-01
The present study investigates the Haar-Sinc collocation method for the solution of the hyperbolic partial telegraph equations. The advantages of this technique are that not only is the convergence rate of Sinc approximation exponential but the computational speed also is high due to the use of the Haar operational matrices. This technique is used to convert the problem to the solution of linear algebraic equations via expanding the required approximation based on the elements of Sinc functions in space and Haar functions in time with unknown coefficients. To analyze the efficiency, precision, and performance of the proposed method, we presented four examples through which our claim was confirmed. PMID:25485295
Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation
NASA Technical Reports Server (NTRS)
Kouatchou, Jules
1999-01-01
In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.
Hill, G.R.
1987-11-10
A power transmission member is described comprising a radially-extending end wall and a cylindrical axially-extending sleeve connected to the end wall and terminating remote from the end wall in an open end. The sleeve has pressure formed internal and external axially-extending splines formed therein by intermeshing of teeth of a mandrel on which the sleeve is mounted and teeth of a pair of racks slidable therepast. The splines terminate short of the open sleeve end in an unsplined cylindrical ring-shaped lip portion which reduced bellmouth of the splines to within about 0.010 inch along their length.
NASA Astrophysics Data System (ADS)
Lang, A. W.; Sloan, D. M.
2002-03-01
A coordinate transformation approach is described that enables Hermite collocation methods to be applied efficiently in one space dimension to steady and unsteady differential problems with steep solutions. The work is an extension of earlier work by Mulholland et al. (J. Comput. Phys. 131 (1997) 280). A coarse grid is generated by an adaptive finite difference method and this grid is used to construct a steady or unsteady coordinate transformation that is based on monotonic cubic spline approximation. An uneven grid is generated by means of the coordinate transformation and the differential problem is solved on this grid using Hermite collocation. Numerical results are presented for steady and unsteady problems.
B-spline one-center method for molecular Hartree-Fock calculations
Hu, Shi-lin; Shi, Ting-yun
2013-01-01
We introduce one-center method in spherical coordinates to carry out Hartree-Fock calculations. Both the radial wave function and the angular wave function are expanded by B-splines, and the radial knots and angular knots are adjusted to deal with cusps properly, resulting in the significant improvement of convergence for several typical closed-shell diatomic molecules. B-splines could represent both the bound state and continuum state wave function properly, and the present approach has been applied to investigating ionization dynamics for H$_2$ in the intense laser field adopting single-active-electron model.
A semi-implicit collocation method - Application to thermal convection in 2D compressible fluids
NASA Astrophysics Data System (ADS)
Gauthier, Serge
1991-06-01
A semiimplicit pseudo-spectral collocation method using a third-order Runge-Kutta numerical scheme for the full Navier-Stokes equations is described. The Courant-Friedrichs-Lewy condition is overcome by the implicit handling of a diffusive term. All such terms are solved with an iterative scheme in the Fourier space. Simulation of thermal convection in 2D compressible fluids is made by expanding variables on a Fourier-Chebyshev basis. Examples of subsonic and supersonic steady solutions are given in the case where the heat flux at the upper boundary is governed by a black body.
Sinc-Chebyshev Collocation Method for a Class of Fractional Diffusion-Wave Equations
Mao, Zhi; Xiao, Aiguo; Yu, Zuguo; Shi, Long
2014-01-01
This paper is devoted to investigating the numerical solution for a class of fractional diffusion-wave equations with a variable coefficient where the fractional derivatives are described in the Caputo sense. The approach is based on the collocation technique where the shifted Chebyshev polynomials in time and the sinc functions in space are utilized, respectively. The problem is reduced to the solution of a system of linear algebraic equations. Through the numerical example, the procedure is tested and the efficiency of the proposed method is confirmed. PMID:24977177
Motsa, S. S.; Magagula, V. M.; Sibanda, P.
2014-01-01
This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature. PMID:25254252
NASA Astrophysics Data System (ADS)
Tirani, M. D.; Maleki, M.; Kajani, M. T.
2014-11-01
A numerical method for solving the Lane-Emden equations of the polytropic index ? when 4.75 ? ? ? 5 is introduced. The method is based upon nonclassical Gauss-Radau collocation points and Freud type weights. Nonclassical orthogonal polynomials, nonclassical Radau points and weighted interpolation are introduced and are utilized in the interval [0,1]. A smooth, strictly monotonic transformation is used to map the infinite domain x ? [0,?) onto a half-open interval t ? [0,1). The resulting problem on the finite interval is then transcribed to a system of nonlinear algebraic equations using collocation. The method is easy to implement and yields very accurate results.
MULTILEVEL ACCELERATION OF STOCHASTIC COLLOCATION METHODS FOR PDE WITH RANDOM INPUT DATA
Webster, Clayton G [ORNL; Jantsch, Peter A [ORNL; Teckentrup, Aretha L [ORNL; Gunzburger, Max D [ORNL
2013-01-01
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.
Interpolation of Superconducting Gravity Observations Using Least-Squares Collocation Method
NASA Astrophysics Data System (ADS)
Habel, Branislav; Janak, Juraj
2014-05-01
A pre-processing of the gravity data measured by superconducting gravimeter involves removing of spikes, offsets and gaps. Their presence in observations can limit the data analysis and degrades the quality of obtained results. Short data gaps are filling by theoretical signal in order to get continuous records of gravity. It requires the accurate tidal model and eventually atmospheric pressure at the observed site. The poster presents a design of algorithm for interpolation of gravity observations with a sampling rate of 1 min. Novel approach is based on least-squares collocation which combines adjustment of trend parameters, filtering of noise and prediction. It allows the interpolation of missing data up to a few hours without necessity of any other information. Appropriate parameters for covariance function are found using a Bayes' theorem by modified optimization process. Accuracy of method is improved by the rejection of outliers before interpolation. For filling of longer gaps the collocation model is combined with theoretical tidal signal for the rigid Earth. Finally, the proposed method was tested on the superconducting gravity observations at several selected stations of Global Geodynamics Project. Testing demonstrates its reliability and offers results comparable with the standard approach implemented in ETERNA software package without necessity of an accurate tidal model.
Solving non-linear Lane-Emden type equations using Bessel orthogonal functions collocation method
NASA Astrophysics Data System (ADS)
Parand, Kourosh; Nikarya, Mehran; Rad, Jamal Amani
2013-05-01
The Lane-Emden type equations are employed in the modeling of several phenomena in the areas of mathematical physics and astrophysics. These equations are categorized as non-linear singular ordinary differential equations on the semi-infinite domain [0,infty ). In this research we introduce the Bessel orthogonal functions as new basis for spectral methods and also, present an efficient numerical algorithm based on them and collocation method for solving these well-known equations. We compare the obtained results with other results to verify the accuracy and efficiency of the presented scheme. To obtain the orthogonal Bessel functions we need their roots. We use the algorithm presented by Glaser et al. (SIAM J Sci Comput 29:1420-1438, 2007) to obtain the N roots of Bessel functions.
Split-step spline method for modeling optical fiber communications systems
Malin Premaratne
2004-01-01
Operator splitting techniques such as the split-step Fourier method or the split-step wavelet method have been successfully used for numerical simulation of uniformly time-sampled pulses along nonlinear optical fibers. In this letter, we extend the operator splitting technique to derive a novel numerical algorithm based on cubic B-splines for simulating propagation of nonuniformly sampled optical pulses along nonlinear optical fiber.
Direct Numerical Simulation of Incompressible Pipe Flow Using a B-Spline Spectral Method
NASA Technical Reports Server (NTRS)
Loulou, Patrick; Moser, Robert D.; Mansour, Nagi N.; Cantwell, Brian J.
1997-01-01
A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field.
The Hydrogen Molecular Ion in Strong Fields Using the B-Spline Method
NASA Astrophysics Data System (ADS)
Zhang, Yue-Xia; Liu, Qiang; Shi, Ting-Yun
2013-04-01
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.
Smith, Cherri Imelda
1987-01-01
of the requirements for the degree of MASTER OF SCIENCE August 1987 Major Subject: Chemical Engineering INVERSE SENSITIVITY ANALYSIS OF SISO AND MIMO SYSTEMS USING MALETINSKY'S SPLINE-TYPE MODULATION FUNCTION METHOD A Thesis by CHERRI IMELDA SMITH Approved... in which inverse sensitivity analysis could advantageously be applied. In the design of automatic control systems the engineer relies on a number of resources (e. g. previous experience, mathematical models, laboratory data) to realize the desired...
Two-dimensional mesh embedding for Galerkin B-spline methods
NASA Technical Reports Server (NTRS)
Shariff, Karim; Moser, Robert D.
1995-01-01
A number of advantages result from using B-splines as basis functions in a Galerkin method for solving partial differential equations. Among them are arbitrary order of accuracy and high resolution similar to that of compact schemes but without the aliasing error. This work develops another property, namely, the ability to treat semi-structured embedded or zonal meshes for two-dimensional geometries. This can drastically reduce the number of grid points in many applications. Both integer and non-integer refinement ratios are allowed. The report begins by developing an algorithm for choosing basis functions that yield the desired mesh resolution. These functions are suitable products of one-dimensional B-splines. Finally, test cases for linear scalar equations such as the Poisson and advection equation are presented. The scheme is conservative and has uniformly high order of accuracy throughout the domain.
NASA Astrophysics Data System (ADS)
Soghrati, Soheil; Mai, Weijie; Liang, Bowen; Buchheit, Rudolph G.
2015-01-01
A new meshfree method based on a discrete transformation of Green's basis functions is introduced to simulate Poisson problems with complex morphologies. The proposed Green's Discrete Transformation Method (GDTM) uses source points that are located along a virtual boundary outside the problem domain to construct the basis functions needed to approximate the field. The optimal number of Green's functions source points and their relative distances with respect to the problem boundaries are evaluated to obtain the best approximation of the partition of unity condition. A discrete transformation technique together with the boundary point collocation method is employed to evaluate the unknown coefficients of the solution series via satisfying the problem boundary conditions. A comprehensive convergence study is presented to investigate the accuracy and convergence rate of the GDTM. We will also demonstrate the application of this meshfree method for simulating the conductive heat transfer in a heterogeneous materials system and the dissolved aluminum ions concentration in the electrolyte solution formed near a passive corrosion pit.
[Baseline correction method for Raman spectroscopy based on B-spline fitting].
Wang, Xin; Fan, Xian-guang; Xu, Ying-jie; Wu, Jing-lin; Liang, Jun; Zuo, Yong
2014-08-01
Baseline drift is a widespread phenomenon in modern spectroscopy instrumentation, which would bring a very negative impact to the feature extraction of spectrum signal, and the baseline correction method is an important means to solve the problem, which is also the important part of Raman signal preprocessing. The general principle of baseline drift elimination is using the fitting method to the fit the baseline. The traditional fitting method is polynomial fitting, but this method is prone to over-fitting and under-fitting, and the fitting order is difficult to be determined. In this paper, the traditional method is improved; the B-spline fitting method is used to approach the baseline of Raman signal through constant iteration The advantages of B-spline, namely low-order and smoothness, can help the method overcome the shortcomings of polynomial method. In the experiments, the Raman signal of malachite green and rhodamine B were detected, and then the proposed method and traditional method were applied to perform baseline correction Experimental results showed that the proposed method can eliminate the Raman signal baseline drift effectively without over- and under-fitting, and the same order can be used in both positions where large or small baseline drift occurred. Therefore, the proposed method provided more accurate and reliable information for the further analysis of spectral data. PMID:25508725
[Baseline correction method for Raman spectroscopy based on B-spline fitting].
Wang, Xin; Fan, Xian-guang; Xu, Ying-jie; Wu, Jing-lin; Liang, Jun; Zuo, Yong
2014-08-01
Baseline drift is a widespread phenomenon in modern spectroscopy instrumentation, which would bring a very negative impact to the feature extraction of spectrum signal, and the baseline correction method is an important means to solve the problem, which is also the important part of Raman signal preprocessing. The general principle of baseline drift elimination is using the fitting method to the fit the baseline. The traditional fitting method is polynomial fitting, but this method is prone to over-fitting and under-fitting, and the fitting order is difficult to be determined. In this paper, the traditional method is improved; the B-spline fitting method is used to approach the baseline of Raman signal through constant iteration The advantages of B-spline, namely low-order and smoothness, can help the method overcome the shortcomings of polynomial method. In the experiments, the Raman signal of malachite green and rhodamine B were detected, and then the proposed method and traditional method were applied to perform baseline correction Experimental results showed that the proposed method can eliminate the Raman signal baseline drift effectively without over- and under-fitting, and the same order can be used in both positions where large or small baseline drift occurred. Therefore, the proposed method provided more accurate and reliable information for the further analysis of spectral data. PMID:25474946
NASA Astrophysics Data System (ADS)
Kondaxakis, Dimitrios; Tsangaris, Sokrates
2008-05-01
A numerical methodology is presented for the coupled aerodynamic and aeroacoustic analysis of time dependent laminar viscous flows in general two-dimensional geometries. The overall procedure is constituted firstly by the solution of the incompressible Navier-Stokes equations and secondly by the solution of a linear evolution equation of second order in space and time which originates from Lighthill's acoustic analogy. A semi-implicit projection method is utilized for the time integration of the incompressible Navier-Stokes system, while a choice between a second order implicit Newmark scheme and a fourth order explicit Runge-Kutta-Nyström method is offered for the temporal discretization of the wave equation. The multidomain weak Legendre collocation spectral method on quadrilateral subdomain topologies is employed for the spatial approximation of both the fluid dynamic and the acoustic problems. A specific pulsating internal flow inside a plane constricted channel is selected as a representative application for the assessment of the capabilities of the proposed discrete algorithm. Numerous results are presented and discussed, so as to thoroughly demonstrate the behavior of the numerical procedure.
Thermoacoustic wave propagation modeling using a dynamically adaptive wavelet collocation method
Vasilyev, O.V.; Paolucci, S. [Univ. of Notre Dame, IN (United States). Dept. of Aerospace and Mechanical Engineering
1996-12-31
When a localized region of a solid wall surrounding a compressible medium is subjected to a sudden temperature change, the medium in the immediate neighborhood of that region expands. This expansion generates pressure waves. These thermally-generated waves are referred to as thermoacoustic (TAC) waves. The main interest in thermoacoustic waves is motivated by their property to enhance heat transfer by inducing convective motion away from the heated area. Thermoacoustic wave propagation in a two-dimensional rectangular cavity is studied numerically. The thermoacoustic waves are generated by raising the temperature locally at the walls. The waves, which decay at large time due to thermal and viscous diffusion, propagate and reflect from the walls creating complicated two-dimensional patterns. The accuracy of numerical simulation is ensured by using a highly accurate, dynamically adaptive, multilevel wavelet collocation method, which allows local refinements to adapt to local changes in solution scales. Subsequently, high resolution computations are performed only in regions of large gradients. The computational cost of the method is independent of the dimensionality of the problem and is O(N), where N is the total number of collation points.
Simulating the focusing of light onto 1D nanostructures with a B-spline modal method
NASA Astrophysics Data System (ADS)
Bouchon, P.; Chevalier, P.; Héron, S.; Pardo, F.; Pelouard, J.-L.; Haďdar, R.
2015-03-01
Focusing the light onto nanostructures thanks to spherical lenses is a first step to enhance the field, and is widely used in applications, in particular for enhancing non-linear effects like the second harmonic generation. Nonetheless, the electromagnetic response of such nanostructures, which have subwavelength patterns, to a focused beam can not be described by the simple ray tracing formalism. Here, we present a method to compute the response to a focused beam, based on the B-spline modal method. The simulation of a gaussian focused beam is obtained thanks to a truncated decomposition on plane waves computed on a single period, which limits the computation burden.
NASA Astrophysics Data System (ADS)
Cherry, M. R.; Knopp, J. S.; Blodgett, M. P.
2012-05-01
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.
NASA Astrophysics Data System (ADS)
Sun, Alexander Y.; Zeidouni, Mehdi; Nicot, Jean-Philippe; Lu, Zhiming; Zhang, Dongxiao
2013-06-01
We present an efficient methodology for assessing leakage detectability at geologic carbon sequestration sites under parameter uncertainty. Uncertainty quantification (UQ) and risk assessment are integral and, in many countries, mandatory components of geologic carbon sequestration projects. A primary goal of risk assessment is to evaluate leakage potential from anthropogenic and natural features, which constitute one of the greatest threats to the integrity of carbon sequestration repositories. The backbone of our detectability assessment framework is the probability collocation method (PCM), an efficient, nonintrusive, uncertainty-quantification technique that can enable large-scale stochastic simulations that are based on results from only a small number of forward-model runs. The metric for detectability is expressed through an extended signal-to-noise ratio (SNR), which incorporates epistemic uncertainty associated with both reservoir and aquifer parameters. The spatially heterogeneous aquifer hydraulic conductivity is parameterized using Karhunen-Ločve (KL) expansion. Our methodology is demonstrated numerically for generating probability maps of pressure anomalies and for calculating SNRs. Results indicate that the likelihood of detecting anomalies depends on the level of uncertainty and location of monitoring wells. A monitoring well located close to leaky locations may not always yield the strongest signal of leakage when the level of uncertainty is high. Therefore, our results highlight the need for closed-loop site characterization, monitoring network design, and leakage source detection.
NASA Astrophysics Data System (ADS)
Vasilyev, Oleg V.; Gazzola, Mattia; Koumoutsakos, Petros
2010-11-01
In this talk we discuss preliminary results for the use of hybrid wavelet collocation - Brinkman penalization approach for shape optimization for drag reduction in flows past linked bodies. This optimization relies on Adaptive Wavelet Collocation Method along with the Brinkman penalization technique and the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). Adaptive wavelet collocation method tackles the problem of efficiently resolving a fluid flow on a dynamically adaptive computational grid, while a level set approach is used to describe the body shape and the Brinkman volume penalization allows for an easy variation of flow geometry without requiring body-fitted meshes. We perform 2D simulations of linked bodies in order to investigate whether flat geometries are optimal for drag reduction. In order to accelerate the costly cost function evaluations we exploit the inherent parallelism of ES and we extend the CMA-ES implementation to a multi-host framework. This framework allows for an easy distribution of the cost function evaluations across several parallel architectures and it is not limited to only one computing facility. The resulting optimal shapes are geometrically consistent with the shapes that have been obtained in the pioneering wind tunnel experiments for drag reduction using Evolution Strategies by Ingo Rechenberg.
Butcher, Eric A.
Free Vibration Analysis of Kirchoff Plates with Damaged Boundaries by the Chebyshev Collocation for the free vibration analysis of slender Kirchoff plates with both mixed and damaged boundaries an important role in applications of mechanical, aerospace and civil engineering. Studying the free vibration
High-order numerical solutions using cubic splines
NASA Technical Reports Server (NTRS)
Rubin, S. G.; Khosla, P. K.
1975-01-01
The cubic spline collocation procedure for the numerical solution of partial differential equations was reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a nonuniform mesh and overall fourth-order accuracy for a uniform mesh. Application of the technique was made to the Burger's equation, to the flow around a linear corner, to the potential flow over a circular cylinder, and to boundary layer problems. The results confirmed the higher-order accuracy of the spline method and suggest that accurate solutions for more practical flow problems can be obtained with relatively coarse nonuniform meshes.
NASA Astrophysics Data System (ADS)
Mai-Duy, N.; Tanner, R. I.
2007-04-01
This paper reports a new spectral collocation method for numerically solving two-dimensional biharmonic boundary-value problems. The construction of the Chebyshev approximations is based on integration rather than conventional differentiation. This use of integration allows: (i) the imposition of the governing equation at the whole set of grid points including the boundary points and (ii) the straightforward implementation of multiple boundary conditions. The performance of the proposed method is investigated by considering several biharmonic problems of first and second kinds; more accurate results and higher convergence rates are achieved than with conventional differential methods.
NASA Astrophysics Data System (ADS)
Loukopoulos, V. C.; Bourantas, G. C.; Skouras, E. D.; Nikiforidis, G. C.
2011-02-01
In this article a numerical solution of the time dependent, coupled system equations of magnetohydrodynamics (MHD) flow is obtained, using the strong-form local meshless point collocation (LMPC) method. The approximation of the field variables is obtained with the moving least squares (MLS) approximation. Regular and irregular nodal distributions are used. Thus, a numerical solver is developed for the unsteady coupled MHD problems, using the collocation formulation, for regular and irregular cross sections, as are the rectangular, triangular and circular. Arbitrary wall conductivity conditions are applied when a uniform magnetic field is imposed at characteristic directions relative to the flow one. Velocity and induced magnetic field across the section have been evaluated at various time intervals for several Hartmann numbers (up to 105) and wall conductivities. The numerical results of the strong-form MPC method are compared with those obtained using two weak-form meshless methods, that is, the local boundary integral equation (LBIE) meshless method and the meshless local Petrov-Galerkin (MLPG) method, and with the analytical solutions, where they are available. Furthermore, the accuracy of the method is assessed in terms of the error norms L 2 and L ?, the number of nodes in the domain of influence and the time step length depicting the convergence rate of the method. Run time results are also presented demonstrating the efficiency and the applicability of the method for real world problems.
NASA Astrophysics Data System (ADS)
Doha, Eid; Bhrawy, Ali; Abdelkawy, Mohammed
2014-09-01
In this paper, we propose an efficient spectral collocation algorithm to solve numerically wave type equations subject to initial, boundary and non-local conservation conditions. The shifted Jacobi pseudospectral approximation is investigated for the discretization of the spatial variable of such equations. It possesses spectral accuracy in the spatial variable. The shifted Jacobi-Gauss-Lobatto (SJ-GL) quadrature rule is established for treating the non-local conservation conditions, and then the problem with its initial and non-local boundary conditions are reduced to a system of second-order ordinary differential equations in temporal variable. This system is solved by two-stage forth-order A-stable implicit RK scheme. Five numerical examples with comparisons are given. The computational results demonstrate that the proposed algorithm is more accurate than finite difference method, method of lines and spline collocation approach
NASA Astrophysics Data System (ADS)
Chen, Shang-Shang; Li, Ben-Wen
2014-12-01
A collocation spectral domain decomposition method (CSDDM) based on the influence matrix technique is developed to solve radiative transfer problems within a participating medium of 2D partitioned domains. In this numerical approach, the spatial domains of interest are decomposed into rectangular sub-domains. The radiative transfer equation (RTE) in each sub-domain is angularly discretized by the discrete ordinates method (DOM) with the SRAPN quadrature scheme and then is solved by the CSDDM directly. Three test geometries that include square enclosure and two enclosures with one baffle and one centered obstruction are used to validate the accuracy of the developed method and their numerical results are compared to the data obtained by other researchers. These comparisons indicate that the CSDDM has a good accuracy for all solutions. Therefore this method can be considered as a useful approach for the solution of radiative heat transfer problems in 2D partitioned domains.
NASA Technical Reports Server (NTRS)
Rosen, I. G.
1985-01-01
Rayleigh-Ritz methods for the approximation of the natural modes for a class of vibration problems involving flexible beams with tip bodies using subspaces of piecewise polynomial spline functions are developed. An abstract operator theoretic formulation of the eigenvalue problem is derived and spectral properties investigated. The existing theory for spline-based Rayleigh-Ritz methods applied to elliptic differential operators and the approximation properties of interpolatory splines are useed to argue convergence and establish rates of convergence. An example and numerical results are discussed.
Dorje C. Brody; Darryl D. Holm; David M. Meier
2012-09-04
A quantum spline is a smooth curve parameterised by time in the space of unitary transformations, whose associated orbit on the space of pure states traverses a designated set of quantum states at designated times, such that the trace norm of the time rate of change of the associated Hamiltonian is minimised. The solution to the quantum spline problem is obtained, and is applied in an example that illustrates quantum control of coherent states. An efficient numerical scheme for computing quantum splines is discussed and implemented in the examples.
NASA Astrophysics Data System (ADS)
Hagan, Jonathan; Priede, J?nis
2013-04-01
We present a simple technique for avoiding physically spurious eigenmodes that often occur in the solution of hydrodynamic stability problems by the Chebyshev collocation method. The method is demonstrated on the solution of the Orr-Sommerfeld equation for plane Poiseuille flow. Following the standard approach, the original fourth-order differential equation is factorised into two second-order equations using a vorticity-type auxiliary variable with unknown boundary values which are then eliminated by a capacitance matrix approach. However the elimination is constrained by the conservation of the structure of matrix eigenvalue problem, it can be done in two basically different ways. A straightforward application of the method results in a couple of physically spurious eigenvalues which are either huge or close to zero depending on the way the vorticity boundary conditions are eliminated. The zero eigenvalues can be shifted to any prescribed value and thus removed by a slight modification of the second approach.
Multiresolution B-spline Radiosity
Yizhou Yu; Qunsheng Peng
1995-01-01
This paper introduces a kind of new wavelet radiosity method called multiresolution B-spline radiosity, which uses B-splines of different scales to represent radiosity distribution functions. A set of techniques and algo- rithms, such as function extrapolation, adaptive quadrature, scale adjustment and octree, are proposed to im- plement it. This method sets up hierarchical structures on surfaces, keeps radiosity distribution continuous
NASA Astrophysics Data System (ADS)
Bhrawy, A. H.; Doha, E. H.; Ezz-Eldien, S. S.; Van Gorder, Robert A.
2014-12-01
The Jacobi spectral collocation method (JSCM) is constructed and used in combination with the operational matrix of fractional derivatives (described in the Caputo sense) for the numerical solution of the time-fractional Schrödinger equation (T-FSE) and the space-fractional Schrödinger equation (S-FSE). The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations, which greatly simplifies the solution process. In addition, the presented approach is also applied to solve the time-fractional coupled Schrödinger system (T-FCSS). In order to demonstrate the validity and accuracy of the numerical scheme proposed, several numerical examples with their approximate solutions are presented with comparisons between our numerical results and those obtained by other methods.
NASA Astrophysics Data System (ADS)
Shukla, H. S.; Tamsir, Mohammad; Srivastava, Vineet K.
2015-01-01
In this paper, a modified cubic B-spline differential quadrature method (MCB-DQM) is employed for the numerical simulation of two-space dimensional nonlinear sine-Gordon equation with appropriate initial and boundary conditions. The modified cubic B-spline works as a basis function in the differential quadrature method to compute the weighting coefficients. Accordingly, two dimensional sine-Gordon equation is transformed into a system of second order ordinary differential equations (ODEs). The resultant system of ODEs is solved by employing an optimal five stage and fourth-order strong stability preserving Runge-Kutta scheme (SSP-RK54). Numerical simulation is discussed for both damped and undamped cases. Computational results are found to be in good agreement with the exact solution and other numerical results available in the literature.
NASA Astrophysics Data System (ADS)
Zhu, W.; Sommar, J.; Lin, C.-J.; Feng, X.
2015-01-01
Reliable quantification of air-biosphere exchange flux of elemental mercury vapor (Hg0) is crucial for understanding the global biogeochemical cycle of mercury. However, there has not been a standard analytical protocol for flux quantification, and little attention has been devoted to characterize the temporal variability and comparability of fluxes measured by different methods. In this study, we deployed a collocated set of micrometeorological (MM) and dynamic flux chamber (DFC) measurement systems to quantify Hg0 flux over bare soil and low standing crop in an agricultural field. The techniques include relaxed eddy accumulation (REA), modified Bowen ratio (MBR), aerodynamic gradient (AGM) as well as dynamic flux chambers of traditional (TDFC) and novel (NDFC) designs. The five systems and their measured fluxes were cross-examined with respect to magnitude, temporal trend and correlation with environmental variables. Fluxes measured by the MM and DFC methods showed distinct temporal trends. The former exhibited a highly dynamic temporal variability while the latter had much more gradual temporal features. The diurnal characteristics reflected the difference in the fundamental processes driving the measurements. The correlations between NDFC and TDFC fluxes and between MBR and AGM fluxes were significant (R>0.8, p<0.05), but the correlation between DFC and MM fluxes were from weak to moderate (R=0.1-0.5). Statistical analysis indicated that the median of turbulent fluxes estimated by the three independent MM techniques were not significantly different. Cumulative flux measured by TDFC is considerably lower (42% of AGM and 31% of MBR fluxes) while those measured by NDFC, AGM and MBR were similar (<10% difference). This suggests that incorporating an atmospheric turbulence property such as friction velocity for correcting the DFC-measured flux effectively bridged the gap between the Hg0 fluxes measured by enclosure and MM techniques. Cumulated flux measured by REA was ~60% higher than the gradient-based fluxes. Environmental factors have different degrees of impacts on the fluxes observed by different techniques, possibly caused by the underlying assumptions specific to each individual method. Recommendations regarding the application of flux quantification methods were made based on the data obtained in this study.
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
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.
NASA Astrophysics Data System (ADS)
Ranjan, Reetesh; Pantano, Carlos
2010-11-01
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.
NASA Astrophysics Data System (ADS)
Ni, Ming-Jiu
2009-10-01
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.
NASA Technical Reports Server (NTRS)
Alexander, J. Iwan; Ouazzani, Jalil
1989-01-01
The problem of determining the sensitivity of Bridgman-Stockbarger directional solidification experiments to residual accelerations of the type associated with spacecraft in low earth orbit is analyzed numerically using a pseudo-spectral collocation method. The approach employs a novel iterative scheme combining the method of artificial compressibility and a generalized ADI method. The results emphasize the importance of the consideration of residual accelerations and careful selection of the operating conditions in order to take full advantages of the low gravity conditions.
NASA Astrophysics Data System (ADS)
Lee, W. M.
2011-09-01
This paper presents a semi-analytical approach to solve the eigenproblem of an acoustic cavity with multiple elliptical boundaries. To satisfy the Helmholtz equation in the elliptical coordinate system, the multipole expansion for the acoustic pressure is formulated in terms of angular and radial Mathieu functions. The boundary conditions are satisfied by uniformly collocating points on the boundaries. The acoustic pressure at each point is directly calculated in each elliptical coordinate system. In different coordinate systems, the normal derivative of the acoustic pressure is calculated by using the appropriate directional derivative, an alternative to the addition theorem. By truncating the multipole expansion, a finite linear algebraic system is derived. The direct searching approach is employed to determine the natural frequencies by using the singular value decomposition (SVD). Numerical results are widely discussed for several examples including an elliptical cavity, a confocal elliptical annulus cavity and an elliptical cavity with two elliptical cylinders. The accuracy and numerical convergence of the presented method is validated by comparison with available results from the analytical method and the commercial finite-element code ABAQUS. No spurious eigensolutions are found in the proposed formulation. Excellent accuracy and fast rate of convergence are the key features of the present method thanks to its semi-analytical feature.
Quirós, Elia; Felicísimo, Ángel M.; Cuartero, Aurora
2009-01-01
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. PMID:22291550
Multivariate Adaptive Regression Splines
Jerome H. Friedman
1991-01-01
A new method is presented for flexible regression modeling of high dimensional data. The model takes the form of an expansion in product spline basis functions, where the number of basis functions as well as the parameters associated with each one (product degree and knot locations) are automatically determined by the data. This procedure is motivated by the recursive partitioning
R. K. Mohanty; M. K. Jain; Deepika Dhall
2011-01-01
In this article, we report an efficient high order numerical method based on cubic spline approximation and application of alternating group explicit method for the solution of two point non-linear boundary value problems, whose forcing functions are in integral form, on a non-uniform mesh. The proposed method is applicable when the internal grid points of solution interval are odd in
Number systems, ?-splines and refinement
NASA Astrophysics Data System (ADS)
Zube, Severinas
2004-12-01
This paper is concerned with the smooth refinable function on a plane relative with complex scaling factor . Characteristic functions of certain self-affine tiles related to a given scaling factor are the simplest examples of such refinable function. We study the smooth refinable functions obtained by a convolution power of such charactericstic functions. Dahlke, Dahmen, and Latour obtained some explicit estimates for the smoothness of the resulting convolution products. In the case ?=1+i, we prove better results. We introduce ?-splines in two variables which are the linear combination of shifted basic functions. We derive basic properties of ?-splines and proceed with a detailed presentation of refinement methods. We illustrate the application of ?-splines to subdivision with several examples. It turns out that ?-splines produce well-known subdivision algorithms which are based on box splines: Doo-Sabin, Catmull-Clark, Loop, Midedge and some -subdivision schemes with good continuity. The main geometric ingredient in the definition of ?-splines is the fundamental domain (a fractal set or a self-affine tile). The properties of the fractal obtained in number theory are important and necessary in order to determine two basic properties of ?-splines: partition of unity and the refinement equation.
Zhang, Guannan [ORNL; Webster, Clayton G [ORNL; Gunzburger, Max D [ORNL
2012-09-01
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.
Regularization of B-Spline Objects*
Xu, Guoliang; Bajaj, Chandrajit
2010-01-01
By a d-dimensional B-spline object (denoted as ), we mean a B-spline curve (d = 1), a B-spline surface (d = 2) or a B-spline volume (d = 3). By regularization of a B-spline object we mean the process of relocating the control points of such that they approximate an isometric map of its definition domain in certain directions and is shape preserving. In this paper we develop an efficient regularization method for , d = 1, 2, 3 based on solving weak form L2-gradient flows constructed from the minimization of certain regularizing energy functionals. These flows are integrated via the finite element method using B-spline basis functions. Our experimental results demonstrate that our new regularization method is very effective. PMID:21218183
A least-squares preconditioner for radial basis functions collocation methods
Leevan Ling; Edward J. Kansa
2005-01-01
Although meshless radial basis function (RBF) methods applied to partial differential equations (PDEs) are not only simple to implement and enjoy exponential convergence rates as compared to standard mesh-based schemes, the system of equations required to find the expansion coefficients are typically badly conditioned and expensive using the global Gaussian elimination (G-GE) method requiring \\u000a$\\\\mathcal{O}(N^{3})$ \\u000aflops. We present a simple
Valilyev, O.V.; Paolucci, S. [Univ. of Notre Dame, IN (United States)
1996-05-01
A dynamically adaptive multilevel structure of the algorithm provides a simple way to adapt computational refinements to local demands of the solution. High resolution computations are performed only in regions where sharp transitions occur. The scheme handles general boundary conditions. The method is applied to the solution of the one-dimensional Burgers equation with small viscosity, a moving shock problem, and a nonlinear thermoacoustic wave problem. The results indicate that the method is very accurate and efficient. 16 refs., 9 figs., 2 tab.
Xiang Ma; Nicholas Zabaras
2009-01-01
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
NASA Astrophysics Data System (ADS)
Martinsson, P. G.
2013-06-01
A numerical method for variable coefficient elliptic problems on two-dimensional domains is presented. The method is based on high-order spectral approximations and is designed for problems with smooth solutions. The resulting system of linear equations is solved using a direct solver with O(N1.5) complexity for the pre-computation and O(NlogN) complexity for the solve. The fact that the solver is direct is a principal feature of the scheme, and makes it particularly well suited to solving problems for which iterative solvers struggle; in particular for problems with highly oscillatory solutions. Numerical examples demonstrate that the scheme is fast and highly accurate. For instance, using a discretization with 12 points per wavelength, a Helmholtz problem on a domain of size 100×100 wavelengths was solved to ten correct digits. The computation was executed on a standard laptop; it involved 1.6 M degrees of freedom and required 100 s for the pre-computation, and 0.3 s for the actual solve.
Collocation Mining: Exploiting Corpora for Collocation Identification and Representation
and tools for represent ing collocations in a relational database integrating competence (collocation and in a large scale combining competencebased descriptions of collocations with ac tual occurrences in text. 1 collocational from noncollocational word combinations. Finally, identifi cation results for German based
A comparative study of spline regression
Nougues, Arnaud
1980-01-01
this thesis work. I am also very greatful to Dr. M. T. Longnecker and Dr. S. B. Childs whose support and suggestions were greatly appreciated. TABLE OF CONTENTS 1. INTRODUCTION 2. SPLINE FUNCTIONS 3. SMOOTHNESS LEAST SQUARES SPLINES ~Pa e 10 4, 1... COMPARISON OF THE COMPUTATIONAL METHODS FOR LEAST SQUARES SPL INES 2B 4. 6 THE CHOICE OF THE NUMBER OF BREAKPOINTS 29 4. 7 POSITIONING THE BREAKPOINTS 5. SMOOTHING SPLINES AND CROSS VALIDATION 33 5. 1 SMOOTHING SPLINES 5. 2 CROSS VALIDATION 5. 3...
NASA Astrophysics Data System (ADS)
Mohd Fauzi, Norizyan Izzati; Sulaiman, Jumat
2013-04-01
The aim of this paper is to describe the application of Quarter-Sweep Gauss-Seidel (QSGS) iterative method using quadratic spline scheme for solving fourth order two-point linear boundary value problems. In the line to derive approximation equations, firstly the fourth order problems need to be reduced onto a system of second-order two-point boundary value problems. Then two linear systems have been constructed via discretization process by using the corresponding quarter-sweep quadratic spline approximation equations. The generated linear systems have been solved using the proposed QSGS iterative method to show the superiority over Full-Sweep Gauss-Seidel (FSGS) and Half-Sweep Gauss-Seidel (HSGS) methods. Computational results are provided to illustrate that the effectiveness of the proposed QSGS method is more superior in terms of computational time and number of iterations as compared to other tested methods.
Cubic splines for image interpolation and digital filtering
Hsieh Hou; H. C. Andrews
1978-01-01
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
-Quaternion Splines for the Smooth Interpolation of Orientations
Frey, Pascal
-Quaternion Splines for the Smooth Interpolation of Orientations Gregory M. Nielson, Senior Member upon quaternions and a particular construction of -spline curves. The new method has tension parameters animations. Index Terms--Animation, key frame, inbetweening, quaternion, splines. ĂŚ 1 INTRODUCTION
Splines and Geometric Modeling Chandrajit L. Bajaj and Susan Evans
Texas at Austin, University of
. Properties of tensor product B ezier patches include a ne invariance, convex hull property, and the variation elements. Splines are used in applications ranging from image processing, computer aided design shalldwellmainly on spline surface tting methods in IR3 Tensor product splines in Section xx.1,..., triangular
Xia Wu; Lezhu Zhou
2008-01-01
A new time-domain finite element method (TDFEM) based on B-spline temporal basis function is presented for the first time in this paper. This approach is motivated by aims of achieving higher computational efficiency. Compared with the reported TDFEM scheme, which is based on Galerldnpsilas method with a piecewise linear temporal expansion of electric field[t], in our scheme, the electric field
Image Denoising Using Orthogonal Spline
NASA Astrophysics Data System (ADS)
Zhou, Kaiting; Zheng, Lixin; Lin, Fuyong
We apply new multiresolution theory based on orthogonal spline to image denoising. Just like spline interpolation, the new theory can well approximate any function. It also integrates symmetry, therefore there is no loss or getting and no phase derivation when one reconstruct signal after decomposition. The new method is applied to image denoising via soft-thresholding. Comparing with commonly used wavelets, the new method can well separate noise and image and shows potential application in improving vision quality and preserving edge information for denoised image.
Lin, Guang; Elizondo, Marcelo A.; Lu, Shuai; Wan, Xiaoliang
2014-01-01
This paper proposes a probabilistic collocation method (PCM) to quantify the uncertainties with dynamic simulations in power systems. The appraoch was tested on a single-machine-infinite-bus system and the over 15,000 -bus Western Electricity Coordinating Council (WECC) system. Comparing to classic Monte-Carlo (MC) method, the proposed PCM applies the Smolyak algorithm to reduce the number of simulations that have to be performed. Therefore, the computational cost can be greatly reduced using PCM. The algorithm and procedures are described in the paper. Comparison was made with MC method on the single machine as well as the WECC system. The simulation results shows that using PCM only a small number of sparse grid points need to be sampled even when dealing with systems with a relatively large number of uncertain parameters. PCM is, therefore, computationally more efficient than MC method.
Time Synchronization In Spline
Richard C. Waters
The Spline scalable platform for interactive environments makes it easy to build virtual worlds where multiple people interact with each other and with computer simulations in a 3D visual and audio environment. A key problem shared by Spline and many other systems is achieving accurate time synchronization of events and data streams. In Spline, synchronization is achieved through the use
Prautzsch, Hartmut
BOX SPLINES Hartmut Prautzsch Universit¨at, 76128 Karlsruhe, Germany Wolfgang Boehm Technische Universit¨at, 38106 Braunschweig, Germany March 28, 2002 This chapter provides a brief introduction to box and half-box splines with particular focus on triangular splines and surface design. A particular exam- ple
NASA Astrophysics Data System (ADS)
Ng, Pin T.; Maechler, Martin
2015-05-01
COBS (COnstrained B-Splines), written in R, creates constrained regression smoothing splines via linear programming and sparse matrices. The method has two important features: the number and location of knots for the spline fit are established using the likelihood-based Akaike Information Criterion (rather than a heuristic procedure); and fits can be made for quantiles (e.g. 25% and 75% as well as the usual 50%) in the response variable, which is valuable when the scatter is asymmetrical or non-Gaussian. This code is useful for, for example, estimating cluster ages when there is a wide spread in stellar ages at a chosen absorption, as a standard regression line does not give an effective measure of this relationship.
NASA Astrophysics Data System (ADS)
Wang, Chunpeng; Luo, Zhengzhao Johnny; Huang, Xianglei
2011-09-01
Parallax is associated with an apparent shift of the position of an object when viewed from different angles. For satellite observations, especially observations with clouds, it affects collocation of measurements from different platforms. In this study, we investigate how the parallax problem affects the collocation of CloudSat and Moderate Resolution Imaging Spectroradiometer (MODIS) observations of tropical convective clouds by examining the impact of parallax correction on statistics of convective cloud properties such as cloud top temperature (CTT) and buoyancy. Previous studies circumvented the parallax problem by imposing a "flat-top" condition on the selection of convective clouds, but it inadvertently biases the statistics toward convections at mature or dissipating stages when convective plumes cease to grow but flatten out to form cirrus anvils. The main findings of this study are the following: (1) Parallax correction reduces CTT of convective clouds; the magnitude of the reduction increases with cloud top height (CTH). (2) Parallax correction also reduces the spread of CTT estimates, making it more closely clustered around the corresponding CTH. (3) The fraction of convection with positive buoyancy decreases after the parallax correction. All these changes that are due to parallax correction are most pronounced for convections above 10-12 km, highlighting the importance of parallax correction in satellite-based study of deep convection. With parallax correction applied, we further examine the contrast in convective cloud buoyancy between land and ocean and day and night and the dependence on convective cloud size; results are consistent with our general understanding of tropical convection.
NASA Astrophysics Data System (ADS)
Zhu, W.; Sommar, J.; Lin, C.-J.; Feng, X.
2014-09-01
Reliable quantification of air-biosphere exchange flux of elemental mercury vapor (Hg0) is crucial for understanding global biogeochemical cycle of mercury. However, there has not been a standard analytical protocol for flux quantification, and little attention has been devoted to characterize the temporal variability and comparability of fluxes measured by different methods. In this study, we deployed a collocated set of micro-meteorological (MM) and enclosure measurement systems to quantify Hg0 flux over bare soil and low standing crop in an agricultural field. The techniques include relaxed eddy accumulation (REA), modified Bowen-ratio (MBR), aerodynamic gradient (AGM) as well as dynamic flux chambers of traditional (TDFC) and novel (NDFC) designs. The five systems and their measured fluxes were cross-examined with respect to magnitude, temporal trend and sensitivity to environmental variables. Fluxes measured by the MM and DFC methods showed distinct temporal trends. The former exhibited a highly dynamic temporal variability while the latter had much gradual temporal features. The diurnal characteristics reflected the difference in the fundamental processes driving the measurements. The correlations between NDFC and TDFC fluxes and between MBR and AGM fluxes were significant (R > 0.8, p < 0.05), but the correlation between DFC and MM instantaneous fluxes were from weak to moderate (R = 0.1-0.5). Statistical analysis indicated that the median of turbulent fluxes estimated by the three independent MM-techniques were not significantly different. Cumulative flux measured by TDFC is considerably lower (42% of AGM and 31% of MBR fluxes) while those measured by NDFC, AGM and MBR were similar (< 10% difference). This implicates that the NDFC technique, which accounts for internal friction velocity, effectively bridged the gap in measured Hg0 flux compared to MM techniques. Cumulated flux measured by REA was ~60% higher than the gradient-based fluxes. Environmental factors have different degrees of impacts on the fluxes observed by different techniques, possibly caused by the underlying assumptions specific to each individual method. Recommendations regarding the application of flux quantification methods were made based on the data obtained in this study.
Charoenkwan, Phasit; Shoombuatong, Watshara; Lee, Hua-Chin; Chaijaruwanich, Jeerayut; Huang, Hui-Ling; Ho, Shinn-Ying
2013-01-01
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/. PMID:24019868
Smoothing noisy data with spline functions
M. F. Hutchinson; F. R. de Hoog
1985-01-01
Summary A procedure for calculating the trace of the influence matrix associated with a polynomial smoothing spline of degree2m-1 fitted ton distinct, not necessarily equally spaced or uniformly weighted, data points is presented. The procedure requires orderm2n operations and therefore permits efficient orderm2n calculation of statistics associated with a polynomial smoothing spline, including the generalized cross validation. The method is
Numerical Dynamic Programming with Shape-Preserving Splines
Kenneth L. Judd; Andrew Solnick
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
Multivariate Spline Algorithms for CAGD
NASA Technical Reports Server (NTRS)
Boehm, W.
1985-01-01
Two special polyhedra present themselves for the definition of B-splines: a simplex S and a box or parallelepiped B, where the edges of S project into an irregular grid, while the edges of B project into the edges of a regular grid. More general splines may be found by forming linear combinations of these B-splines, where the three-dimensional coefficients are called the spline control points. Univariate splines are simplex splines, where s = 1, whereas splines over a regular triangular grid are box splines, where s = 2. Two simple facts render the development of the construction of B-splines: (1) any face of a simplex or a box is again a simplex or box but of lower dimension; and (2) any simplex or box can be easily subdivided into smaller simplices or boxes. The first fact gives a geometric approach to Mansfield-like recursion formulas that express a B-spline in B-splines of lower order, where the coefficients depend on x. By repeated recursion, the B-spline will be expressed as B-splines of order 1; i.e., piecewise constants. In the case of a simplex spline, the second fact gives a so-called insertion algorithm that constructs the new control points if an additional knot is inserted.
M Ali, M. K., E-mail: majidkhankhan@ymail.com, E-mail: eutoco@gmail.com; Ruslan, M. H., E-mail: majidkhankhan@ymail.com, E-mail: eutoco@gmail.com [Solar Energy Research Institute (SERI), Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor (Malaysia); Muthuvalu, M. S., E-mail: sudaram-@yahoo.com, E-mail: jumat@ums.edu.my; Wong, J., E-mail: sudaram-@yahoo.com, E-mail: jumat@ums.edu.my [Unit Penyelidikan Rumpai Laut (UPRL), Sekolah Sains dan Teknologi, Universiti Malaysia Sabah, 88400 Kota Kinabalu, Sabah (Malaysia); Sulaiman, J., E-mail: ysuhaimi@ums.edu.my, E-mail: hafidzruslan@eng.ukm.my; Yasir, S. Md., E-mail: ysuhaimi@ums.edu.my, E-mail: hafidzruslan@eng.ukm.my [Program Matematik dengan Ekonomi, Sekolah Sains dan Teknologi, Universiti Malaysia Sabah, 88400 Kota Kinabalu, Sabah (Malaysia)
2014-06-19
The solar drying experiment of seaweed using Green V-Roof Hybrid Solar Drier (GVRHSD) was conducted in Semporna, Sabah under the metrological condition in Malaysia. Drying of sample seaweed in GVRHSD reduced the moisture content from about 93.4% to 8.2% in 4 days at average solar radiation of about 600W/m{sup 2} and mass flow rate about 0.5 kg/s. Generally the plots of drying rate need more smoothing compared moisture content data. Special cares is needed at low drying rates and moisture contents. It is shown the cubic spline (CS) have been found to be effective for moisture-time curves. The idea of this method consists of an approximation of data by a CS regression having first and second derivatives. The analytical differentiation of the spline regression permits the determination of instantaneous rate. The method of minimization of the functional of average risk was used successfully to solve the problem. This method permits to obtain the instantaneous rate to be obtained directly from the experimental data. The drying kinetics was fitted with six published exponential thin layer drying models. The models were fitted using the coefficient of determination (R{sup 2}), and root mean square error (RMSE). The modeling of models using raw data tested with the possible of exponential drying method. The result showed that the model from Two Term was found to be the best models describe the drying behavior. Besides that, the drying rate smoothed using CS shows to be effective method for moisture-time curves good estimators as well as for the missing moisture content data of seaweed Kappaphycus Striatum Variety Durian in Solar Dryer under the condition tested.
Matuschek, Hannes; Kliegl, Reinhold; Holschneider, Matthias
2015-01-01
The Smoothing Spline ANOVA (SS-ANOVA) requires a specialized construction of basis and penalty terms in order to incorporate prior knowledge about the data to be fitted. Typically, one resorts to the most general approach using tensor product splines. This implies severe constraints on the correlation structure, i.e. the assumption of isotropy of smoothness can not be incorporated in general. This may increase the variance of the spline fit, especially if only a relatively small set of observations are given. In this article, we propose an alternative method that allows to incorporate prior knowledge without the need to construct specialized bases and penalties, allowing the researcher to choose the spline basis and penalty according to the prior knowledge of the observations rather than choosing them according to the analysis to be done. The two approaches are compared with an artificial example and with analyses of fixation durations during reading. PMID:25816246
Scalar and planar-valued curve fitting using splines under tension
A. K. Cline
1974-01-01
The spline under tension was introduced by Schweikert in an attempt to imitate cubic splines but avoid the spurious critical points they induce. The defining equations are presented here, together with an efficient method for determining the necessary parameters and computing the resultant spline. The standard scalar-valued curve fitting problem is discussed, as well as the fitting of open and
ECS 178 Course Notes QUADRATIC UNIFORM B-SPLINE CURVE REFINEMENT
California at Davis, University of
by Chaikin's Algorithm [?]. The Matrix Equation for the Quadratic Uniform B-Spline Curve Given a setECS 178 Course Notes QUADRATIC UNIFORM B-SPLINE CURVE REFINEMENT Kenneth I. Joy Institute for Data method for a quadratic uniform B-spline curve and show that the refinement is exactly that speci- fied
On-Line Geometric Modeling Notes QUADRATIC UNIFORM B-SPLINE CURVE REFINEMENT
California at Davis, University of
that specified by Chaikin's Algorithm [1]. The Matrix Equation for the Quadratic Uniform B-Spline Curve GivenOn-Line Geometric Modeling Notes QUADRATIC UNIFORM B-SPLINE CURVE REFINEMENT Kenneth I. Joy the refinement method for a quadratic uniform B-spline curve and show that the refinement is exactly
Cheng, C.Z.
1988-12-01
A nonvariational ideal MHD stability code (NOVA) has been developed. In a general flux coordinate (/psi/, theta, /zeta/) system with an arbitrary Jacobian, the NOVA code employs Fourier expansions in the generalized poloidal angle theta and generalized toroidal angle /zeta/ directions, and cubic-B spline finite elements in the radial /psi/ direction. Extensive comparisons with these variational ideal MHD codes show that the NOVA code converges faster and gives more accurate results. An extended version of NOVA is developed to integrate non-Hermitian eigenmode equations due to energetic particles. The set of non-Hermitian integro-differential eigenmode equations is numerically solved by the NOVA-K code. We have studied the problems of the stabilization of ideal MHD internal kink modes by hot particle pressure and the excitation of ''fishbone'' internal kink modes by resonating with the energetic particle magnetic drift frequency. Comparisons with analytical solutions show that the values of the critical ..beta../sub h/ from the analytical theory can be an order of magnitude different from those computed by the NOVA-K code. 24 refs., 11 figs., 1 tab.
SURVIVAL ESTIMATION USING SPLINES
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...
Polynominal Interpolation Methods for Viscous Flow Calculations
NASA Technical Reports Server (NTRS)
Rubin, S. G.; Khosla, P. K.
1976-01-01
Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and by Hermitian (Taylor series) finite-difference discretization. The similarities and special features of these different developments are discussed. The governing systems apply for both uniform and variable meshes. Hybrid schemes resulting from two different polynomial approximations for the first and second derivatives lead to a nonuniform mesh extension of the so-called compact or Pad? difference technique (Hermite 4). A variety of fourth-order methods are described and the Hermitian approach is extended to sixth-order (Hermite 6). The appropriate spline boundary conditions are derived for all procedures. For central finite differences, this leads to a two-point, second-order accurate generalization of the commonly used three-point end-difference formula. Solutions with several spline and Hermite procedures are presented for the boundary layer equations, with and without mass transfer, and for the incompressible viscous flow in a driven cavity. Divergence and nondivergence equations are considered for the cavity. Among the fourth-order techniques, it is shown that spline 4 has the smallest truncation error. The spline 4 procedure generally requires one-quarter the number of mesh points in a given coordinate direction as a central finite-difference calculation of equal accuracy. The Hermite 6 procedure leads to remarkably accurate boundary layer solutions.
NASA Astrophysics Data System (ADS)
Zhang, Yuexia; Liu, Qiang; Shi, Tingyun
2012-04-01
An accurate one-centre method is here applied to the calculation of the equilibrium distances and the energies for the hydrogen molecular ion in magnetic fields ranging from 109G to 4.414 × 1013 G. Both the radial and angular wavefunctions were expanded in terms of optimization B-splines. The slow convergence problem in the general one-centre method and singularities at the nuclear positions of the H+2 were solved well. The accuracy of the one-centre method has been improved in this way. We compared our results with those generated by high-precision methods from published studies. Equilibrium distances of the 1?g, u, 1?g, u, 1?g, u and 2?g states of the H+2 in strong magnetic fields were found to be accurate to three to four significant digits at least up to 2.35 × 1012 G, even for the antibonding states 1?u, 1?g and 1?u, whose equilibrium distances Req are very large.
Theory, computation, and application of exponential splines
NASA Technical Reports Server (NTRS)
Mccartin, B. J.
1981-01-01
A generalization of the semiclassical cubic spline known in the literature as the exponential spline is discussed. In actuality, the exponential spline represents a continuum of interpolants ranging from the cubic spline to the linear spline. A particular member of this family is uniquely specified by the choice of certain tension parameters. The theoretical underpinnings of the exponential spline are outlined. This development roughly parallels the existing theory for cubic splines. The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data. Next, the numerical computation of the exponential spline is discussed. A variety of numerical devices are employed to produce a stable and robust algorithm. An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed. A sequence of selected curve-fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines.
Optimal spline regression utilizing steepest descent
Flora, Eric Shirley
1975-01-01
fit so that the L2 error as a function of the knots is minimized. The method includes a density method to obtain an original guess for the knot placement. This will then be improved upon by applying steepest descent to the L2 error as a function... special thanks goes to Hew L. Packard for the excellent graphics. TABLE OF CONTENTS CHAPTER I. INTRODUCTION Page II. NORMALIZED B-SPLINES-PROPERTIES AND CALCULATIONS. . . 3 1. Introduction . . . . . , , . . . . , . . . 3 2. Divided Differences 3...
Using parametric {ital B} splines to fit specular reflectivities
Berk, N.F.; Majkrzak, C.F. [Materials Science and Engineering Laboratory, National Insitute of Standards and Technology, Gaithersburg, Maryland 20899-0001 (United States)] [Materials Science and Engineering Laboratory, National Insitute of Standards and Technology, Gaithersburg, Maryland 20899-0001 (United States)
1995-05-01
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.
47 CFR 51.323 - Standards for physical collocation and virtual collocation.
Code of Federal Regulations, 2013 CFR
2013-10-01
...collocation in adjacent controlled environmental vaults, controlled environmental huts, or similar...collocate in any adjacent controlled environmental vault, controlled environmental vault, or similar structure that the carrier has...
47 CFR 51.323 - Standards for physical collocation and virtual collocation.
Code of Federal Regulations, 2012 CFR
2012-10-01
...collocation in adjacent controlled environmental vaults, controlled environmental huts, or similar...collocate in any adjacent controlled environmental vault, controlled environmental vault, or similar structure that the carrier has...
47 CFR 51.323 - Standards for physical collocation and virtual collocation.
Code of Federal Regulations, 2014 CFR
2014-10-01
...collocation in adjacent controlled environmental vaults, controlled environmental huts, or similar...collocate in any adjacent controlled environmental vault, controlled environmental vault, or similar structure that the carrier has...
Polynomial spline-approximation of Clarke's model
Yuriy V. Zakharov; Tim C. Tozer; Jonathan F. Adlard
2004-01-01
We investigate polynomial spline approximation of stationary random processes on a uniform grid applied to Clarke's model of time variations of path amplitudes in multipath fading channels with Doppler scattering. The integral mean square error (MSE) for optimal and interpolation splines is presented as a series of spectral moments. The optimal splines outperform the interpolation splines; however, as the sampling
GEE-Smoothing Spline in Semiparametric Model with Correlated Nominal Data
NASA Astrophysics Data System (ADS)
Ibrahim, Noor Akma; Suliadi
2010-11-01
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.
ERIC Educational Resources Information Center
Miyakoshi, Tomoko
2009-01-01
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
Learning Relations Using Collocations
Gerhard Heyer; Martin Läuter; Uwe Quasthoff; Thomas Wittig; Christian Wolff
2001-01-01
This paper describes the application of statistical analysis of large corpora to the problem of extracting semantic relations from unstructured text. We regard this approach as a viable method for generating input for the construction of ontologies as ontologies use well-defined semantic relations as building blocks (cf. van der Vet & Mars 1998). Starting from a short description of our
Collocation and Technicality in EAP Engineering
ERIC Educational Resources Information Center
Ward, Jeremy
2007-01-01
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
Supporting Collocation Learning with a Digital Library
ERIC Educational Resources Information Center
Wu, Shaoqun; Franken, Margaret; Witten, Ian H.
2010-01-01
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
Validation of significant wave height product from Envisat ASAR using triple collocation
NASA Astrophysics Data System (ADS)
Wang, H.; Shi, C. Y.; Zhu, J. H.; Huang, X. Q.; Chen, C. T.
2014-03-01
Nowadays, spaceborne Synthetic Aperture Radar (SAR) has become a powerful tool for providing significant wave height. Traditionally, validation of SAR derived ocean wave height has been carried out against buoy measurements or model outputs, which only yield a inter-comparison, but not an 'absolute' validation. In this study, the triple collocation error model has been introduced in the validation of Envisat ASAR level 2 data. Significant wave height data from ASAR were validated against in situ buoy data, and wave model hindcast results from WaveWatch III, covering a period of six years. The impact of the collocation distance on the error of ASAR wave height was discussed. From the triple collocation validation analysis, it is found that the error of Envisat ASAR significant wave height product is linear to the collocation distance, and decrease with the decreasing collocation distance. Using the linear regression fit method, the absolute error of Envisat ASAR wave height was obtained with zero collocation distance. The absolute Envisat ASAR wave height error of 0.49m is presented in deep and open ocean from this triple collocation validation work.
Simulation of switched reluctance motor drives using two-dimensional bicubic spline
Xiang-Dang Xue; K. W. E. Cheng; S. L. Ho
2002-01-01
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
CDB --A Database of Lexical Collocations Brigitte Krenn \\Lambda
collocations. The relational model is defined such that competencebased descriptions of collocations (the competence base) and actually occurring collocation examples extracted from text corpora (the example base of German PPverb collocations are given. A number of example queries are presented, and additional
Properties of the Wilson-Fowler spline
Emery, J.D.
1982-07-01
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, invariance properties, and gives some comparison with other spline types. Fortran subroutines are included.
Vertex collocation profiles: theory, computation, and results.
Lichtenwalter, Ryan N; Chawla, Nitesh V
2014-01-01
We describe the vertex collocation profile (VCP) concept. VCPs provide rich information about the surrounding local structure of embedded vertex pairs. VCP analysis offers a new tool for researchers and domain experts to understand the underlying growth mechanisms in their networks and to analyze link formation mechanisms in the appropriate sociological, biological, physical, or other context. The same resolution that gives the VCP method its analytical power also enables it to perform well when used to accomplish link prediction. We first develop the theory, mathematics, and algorithms underlying VCPs. We provide timing results to demonstrate that the algorithms scale well even for large networks. Then we demonstrate VCP methods performing link prediction competitively with unsupervised and supervised methods across different network families. Unlike many analytical tools, VCPs inherently generalize to multirelational data, which provides them with unique power in complex modeling tasks. To demonstrate this, we apply the VCP method to longitudinal networks by encoding temporally resolved information into different relations. In this way, the transitions between VCP elements represent temporal evolutionary patterns in the longitudinal network data. Results show that VCPs can use this additional data, typically challenging to employ, to improve predictive model accuracies. We conclude with our perspectives on the VCP method and its future in network science, particularly link prediction. PMID:25392767
Upsilon-quaternion splines for the smooth interpolation of orientations.
Nielson, Gregory M
2004-01-01
We present a new method for smoothly interpolating orientation matrices. It is based upon quaternions and a particular construction of upsilon-spline curves. The new method has tension parameters and variable knot (time) spacing which both prove to be effective in designing and controlling key frame animations. PMID:15384647
A Two-Timescale Discretization Scheme for Collocation
NASA Technical Reports Server (NTRS)
Desai, Prasun; Conway, Bruce A.
2004-01-01
The development of a two-timescale discretization scheme for collocation is presented. This scheme allows a larger discretization to be utilized for smoothly varying state variables and a second finer discretization to be utilized for state variables having higher frequency dynamics. As such. the discretization scheme can be tailored to the dynamics of the particular state variables. In so doing. the size of the overall Nonlinear Programming (NLP) problem can be reduced significantly. Two two-timescale discretization architecture schemes are described. Comparison of results between the two-timescale method and conventional collocation show very good agreement. Differences of less than 0.5 percent are observed. Consequently. a significant reduction (by two-thirds) in the number of NLP parameters and iterations required for convergence can be achieved without sacrificing solution accuracy.
Bidirectional elastic image registration using B-spline affine transformation.
Gu, Suicheng; Meng, Xin; Sciurba, Frank C; Ma, Hongxia; Leader, Joseph; Kaminski, Naftali; Gur, David; Pu, Jiantao
2014-06-01
A registration scheme termed as B-spline affine transformation (BSAT) is presented in this study to elastically align two images. We define an affine transformation instead of the traditional translation at each control point. Mathematically, BSAT is a generalized form of the affine transformation and the traditional B-spline transformation (BST). In order to improve the performance of the iterative closest point (ICP) method in registering two homologous shapes but with large deformation, a bidirectional instead of the traditional unidirectional objective/cost function is proposed. In implementation, the objective function is formulated as a sparse linear equation problem, and a sub-division strategy is used to achieve a reasonable efficiency in registration. The performance of the developed scheme was assessed using both two-dimensional (2D) synthesized dataset and three-dimensional (3D) volumetric computed tomography (CT) data. Our experiments showed that the proposed B-spline affine model could obtain reasonable registration accuracy. PMID:24530210
ERIC Educational Resources Information Center
Wolter, Brent; Gyllstad, Henrik
2013-01-01
This study investigated the influence of frequency effects on the processing of congruent (i.e., having an equivalent first language [L1] construction) collocations and incongruent (i.e., not having an equivalent L1 construction) collocations in a second language (L2). An acceptability judgment task was administered to native and advanced
The Impact of Corpus-Based Collocation Instruction on Iranian EFL Learners' Collocation Learning
ERIC Educational Resources Information Center
Ashouri, Shabnam; Arjmandi, Masoume; Rahimi, Ramin
2014-01-01
Over the past decades, studies of EFL/ESL vocabulary acquisition have identified the significance of collocations in language learning. Due to the fact that collocations have been regarded as one of the major concerns of both EFL teachers and learners for many years, the present study attempts to shed light on the impact of corpus-based
Smoothing Strange Attractors Using Splines
Junheng Luo; Dominique Thiebaut
1995-12-31
A noise-reduction algorithm for time-series of non-linear systems is presented. The algorithm smoothes the attractors in phase space using B-splines, allowing a more accurate measure of their dynamics. The algorithm is tested on numerical and experimental data. It is linear in complexity, and can be applied to embeddings of any dimension.
Saito, Shiro L. [School of International Liberal Studies, Chukyo University, Toyota 470-0393 (Japan)], E-mail: luna@trinity.lets.chukyo-u.ac.jp
2009-11-15
The ground state energies and expectation values of atoms are given by Hartree-Fock-Roothaan calculations with one B-spline set. For the neutral atoms He to Uuo, the total energies, kinetic energies, potential energies, and virial ratios are tabulated. Our total energies are in excellent agreement with the highly accurate 10-digit numerical Hartree-Fock energies given by Koga and Thakkar [T. Koga, A.J. Thakkar, J. Phys. B 29 (1996) 2973]. The virial ratios are in complete agreement to within 12-digits of the exact value -2. Orbital energies, electron densities at the nucleus, electron-nucleus cusp ratios, and radial expectation values
NASA Astrophysics Data System (ADS)
Nikolopoulos, L. A. A.
2003-02-01
A package is presented for the fully ab-initio calculation of one- and two-photon ionization cross sections for two-electron atomic systems (H -, He, Mg, Ca, ) under strong laser fields, within lowest-order perturbation theory (LOPT) and in the dipole approximation. The atomic structure is obtained through configuration interaction (CI) of antisymmetrized two-electron states expanded in a B-spline finite basis. The formulation of the theory and the relevant codes presented here represent the accumulation of work over the last ten years [1-11,13-15]. Extensions to more than two-photon ionization is straightforward. Calculation is possible for both the length and velocity form of the laser-atom interaction operator. The package is mainly, written in standard FORTRAN language and uses the publicly available libraries SLATEC, LAPACK and BLAS.
Nonparametric Small Area Estimation Using Penalized Spline Regression
inference and estimation of the small area prediction mean squared error. The applicability of the method prediction; bootstrap infer- ence, natural resource survey. Department of Statistics, Iowa State UniversityNonparametric Small Area Estimation Using Penalized Spline Regression J. D. Opsomer Iowa State
Spline interpolation techniques applied to the study of geophysical data
NASA Astrophysics Data System (ADS)
Mariani, Maria C.; Basu, Kanadpriya
2015-06-01
This work is devoted to the study of geophysical data by using different spline interpolation techniques. A spatial analysis of the California earthquakes geological data was performed, some of the methods proved to be more efficient than others depending on the number of data points considered. Overall, this class of interpolation surface proved to be a very powerful tool for analyzing geophysical data.
An inverse algorithm of the cubic B-spline curve
AiLian Leng; HuiXian Yang; WenLong Yue; Qiufang Dai
2010-01-01
Disadvantages of normal boundary conditions and advantages of the combination coefficient method of the adjacent point are analysed. Recursion formulas and algorithms for inverse of the cubic uniform B-spline with different boundary conditions are presented. The algorithms are simple, fast and satisfied with upper designers' demands.
Daly, Don S.; Anderson, Kevin K.; White, Amanda M.; Gonzalez, Rachel M.; Varnum, Susan M.; Zangar, Richard C.
2008-07-14
Background: A microarray of enzyme-linked immunosorbent assays, or ELISA microarray, predicts simultaneously the concentrations of numerous proteins in a small sample. These predictions, however, are uncertain due to processing error and biological variability. Making sound biological inferences as well as improving the ELISA microarray process require require both concentration predictions and creditable estimates of their errors. Methods: We present a statistical method based on monotonic spline statistical models, penalized constrained least squares fitting (PCLS) and Monte Carlo simulation (MC) to predict concentrations and estimate prediction errors in ELISA microarray. PCLS restrains the flexible spline to a fit of assay intensity that is a monotone function of protein concentration. With MC, both modeling and measurement errors are combined to estimate prediction error. The spline/PCLS/MC method is compared to a common method using simulated and real ELISA microarray data sets. Results: In contrast to the rigid logistic model, the flexible spline model gave credible fits in almost all test cases including troublesome cases with left and/or right censoring, or other asymmetries. For the real data sets, 61% of the spline predictions were more accurate than their comparable logistic predictions; especially the spline predictions at the extremes of the prediction curve. The relative errors of 50% of comparable spline and logistic predictions differed by less than 20%. Monte Carlo simulation rendered acceptable asymmetric prediction intervals for both spline and logistic models while propagation of error produced symmetric intervals that diverged unrealistically as the standard curves approached horizontal asymptotes. Conclusions: The spline/PCLS/MC method is a flexible, robust alternative to a logistic/NLS/propagation-of-error method to reliably predict protein concentrations and estimate their errors. The spline method simplifies model selection and fitting, and reliably estimates believable prediction errors. For the 50% of the real data sets fit well by both methods, spline and logistic predictions are practically indistinguishable, varying in accuracy by less than 15%. The spline method may be useful when automated prediction across simultaneous assays of numerous proteins must be applied routinely with minimal user intervention.
NASA Astrophysics Data System (ADS)
Mitra, Jhimli; Marti, Robert; Oliver, Arnau; Llado, Xavier; Vilanova, Joan C.; Meriaudeau, Fabrice
2011-03-01
This paper provides a comparison of spline-based registration methods applied to register interventional Trans Rectal Ultrasound (TRUS) and pre-acquired Magnetic Resonance (MR) prostate images for needle guided prostate biopsy. B-splines and Thin-plate Splines (TPS) are the most prevalent spline-based approaches to achieve deformable registration. Pertaining to the strategic selection of correspondences for the TPS registration, we use an automatic method already proposed in our previous work to generate correspondences in the MR and US prostate images. The method exploits the prostate geometry with the principal components of the segmented prostate as the underlying framework and involves a triangulation approach. The correspondences are generated with successive refinements and Normalized Mutual Information (NMI) is employed to determine the optimal number of correspondences required to achieve TPS registration. B-spline registration with successive grid refinements are consecutively applied for a significant comparison of the impact of the strategically chosen correspondences on the TPS registration against the uniform B-spline control grids. The experimental results are validated on 4 patient datasets. Dice Similarity Coefficient (DSC) is used as a measure of the registration accuracy. Average DSC values of 0.97+/-0.01 and 0.95+/-0.03 are achieved for the TPS and B-spline registrations respectively. B-spline registration is observed to be more computationally expensive than the TPS registration with average execution times of 128.09 +/- 21.7 seconds and 62.83 +/- 32.77 seconds respectively for images with maximum width of 264 pixels and a maximum height of 211 pixels.
J. Reiter
1991-01-01
A biplicit technique is presented for the numerical solution of evolutionary partial differential equations by the method of lines. The derivatives with respect to the discretized variables are approximated explicitly by trial functions which are defined by a set of parameters. These are determined as free parameters in a multipoint boundary-value problem by the requirement that the trial functions should,
Bivariate B-splines and its Applications in Spatial Data Analysis
Pan, Huijun 1987-
2011-08-09
nonparametric spatial surface fitting problems. In particular, the third part develops a penalized B-splines method to reconstruct a smooth surface from noisy observations. A numerical algorithm is derived, implemented, and applied to simulated and real data...
Stochastic dynamic models and Chebyshev splines
Fan, Ruzong; Zhu, Bin; Wang, Yuedong
2015-01-01
In this article, we establish a connection between a stochastic dynamic model (SDM) driven by a linear stochastic differential equation (SDE) and a Chebyshev spline, which enables researchers to borrow strength across fields both theoretically and numerically. We construct a differential operator for the penalty function and develop a reproducing kernel Hilbert space (RKHS) induced by the SDM and the Chebyshev spline. The general form of the linear SDE allows us to extend the well-known connection between an integrated Brownian motion and a polynomial spline to a connection between more complex diffusion processes and Chebyshev splines. One interesting special case is connection between an integrated OrnsteinUhlenbeck process and an exponential spline. We use two real data sets to illustrate the integrated OrnsteinUhlenbeck process model and exponential spline model and show their estimates are almost identical.
Über den Einsatz von Spline-Funktionen zur Glättung von Meßwerten bei der Abel-Inversion
J. V. Calker; D. Fischer
1976-01-01
Durch Anwendung von sogenannten Spline-Funktionen wird die Rauschverstärkung, die bei der Abel-Transformation von verrauschten Meßwerten auftritt, reduziert. Durch die strikte Trennung von Glättung und Abel-Inversion ergeben sich übersichtliche Verhältnisse. Das Verfahren ist übertragbar auf Fälle mit nicht-äquidistanter Stützstellenverteilung.Translated AbstractUse of Spline-function for Smoothing Measured Values by Means of the Abel-inversion MethodThe application of so-called Spline-functions will reduce the noise-amplification, which
Gauging the Effects of Exercises on Verb-Noun Collocations
ERIC Educational Resources Information Center
Boers, Frank; Demecheleer, Murielle; Coxhead, Averil; Webb, Stuart
2014-01-01
Many contemporary textbooks for English as a foreign language (EFL) and books for vocabulary study contain exercises with a focus on collocations, with verb-noun collocations (e.g. "make a mistake") being particularly popular as targets for collocation learning. Common exercise formats used in textbooks and other pedagogic materials
Spline screw multiple rotations mechanism
NASA Technical Reports Server (NTRS)
Vranish, John M. (inventor)
1993-01-01
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.
Image interpolation by multivariate B-splines
Chan, Ki Bun
1986-01-01
support. 2. 2 Octagon support of the bivariate B-spline surface. 2. 3 Bivariate quadratic B-spline. 2. 4 Three-dimensional plot of B-spline approximant. . 2. 5 Preprocessed reduction by ? '. 2. 6 Illustration of overlap interpolants. . 3. 1 Bi...-linear interpolation on & reduction. 3. 2 First iteration on 4 reduction image. 3. 3 Bi-cubic spline on & reduction image. 3. 4 Second iteration on 4 reduction image. 3. 5 Third iteration on 4 reduction image. 3. 6 Original "girl" image. 3. 7 Pre-processed r...
NASA Astrophysics Data System (ADS)
Kuczy?ski, Pawe?; Bia?ecki, Ryszard
2014-06-01
The paper deals with a solution of radiation heat transfer problems in enclosures filled with nonparticipating medium using ray tracing on hierarchical ortho-Cartesian meshes. The idea behind the approach is that radiative heat transfer problems can be solved on much coarser grids than their counterparts from computational fluid dynamics (CFD). The resulting code is designed as an add-on to OpenFOAM, an open-source CFD program. Ortho-Cartesian mesh involving boundary elements is created based upon CFD mesh. Parametric non-uniform rational basis spline (NURBS) surfaces are used to define boundaries of the enclosure, allowing for dealing with domains of complex shapes. Algorithm for determining random, uniformly distributed locations of rays leaving NURBS surfaces is described. The paper presents results of test cases assuming gray diffusive walls. In the current version of the model the radiation is not absorbed within gases. However, the ultimate aim of the work is to upgrade the functionality of the model, to problems in absorbing, emitting and scattering medium projecting iteratively the results of radiative analysis on CFD mesh and CFD solution on radiative mesh.
NASA Astrophysics Data System (ADS)
Wielgus, Maciek; Patorski, Krzysztof
2014-12-01
We discuss a recently proposed method of the implicit smoothing splines in the context of the interferometric fringe pattern processing. The algorithm extends classic smoothing spline method to the case of the measurements being in some non-trivial functional relation to the estimated distribution, i.e., to the case of the implicitly given data. This is the case of the phase estimation based on the intensity of the related fringe pattern. While there are certain preprocessing complications involved in the application of the implicit smoothing splines, the method offers very accurate continuous (unwrapped) phase estimation and outperforms well-established fringe pattern analysis tools. In this paper we present theoretical background of the implicit smoothing splines as well as numerical results related to their application to the fringe pattern phase estimation problem.
47 CFR 51.323 - Standards for physical collocation and virtual collocation.
Code of Federal Regulations, 2010 CFR
2010-10-01
...collocating telecommunications carrier, at which the fiber optic cable carrying an interconnector's circuits can enter...LEC shall provide the connection using copper, dark fiber, lit fiber, or other transmission medium, as requested by...
Septic spline solutions of sixth-order boundary value problems
NASA Astrophysics Data System (ADS)
Siddiqi, Shahid S.; Akram, Ghazala
2008-05-01
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.
Tat-jen Cham; Roberto Cipolla
1999-01-01
The main issues of developing an automatic and reliable scheme for spline-fitting are discussed and addressed in this paper, which are not fully covered in previous papers or algorithms. The proposed method incorporates B-spline active contours, the minimum description length (MDL) principle, and a novel control point insertion strategy based on maximizing the potential for energy-reduction maximization (PERM). A comparison
Splines Covering Polar Configurations Ashish Myles a
Peters, Jörg
-spline, curvature-continuous (a) star-like layout (b) Polar layout Fig. 1. (a) A star-like mesh of the earth. If Email addresses: amyles@cs.nyu.edu (Ashish Myles), jorg@cise.ufl.edu (J¨org Peters in Section 6. Section 7 proves curvature continuity and bi-3 C2 compatibility of C2 polar splines. Section 8
Splines in Higher Order TV Regularization
Gabriele Steidl; Stephan Didas; Julia Neumann
2006-01-01
Splines play an important role as solutions of various interpolation and approximation problems that minimize special functionals in some smoothness spaces. In this paper, we show in a strictly discrete setting that splines of degree m ? 1 solve also a minimization problem with quadratic data term and m-th order total variation (TV) regularization term. In contrast to problems with
Spline-based procedures for dose-finding studies with active control
Helms, Hans-Joachim; Benda, Norbert; Zinserling, Jörg; Kneib, Thomas; Friede, Tim
2015-01-01
In a dose-finding study with an active control, several doses of a new drug are compared with an established drug (the so-called active control). One goal of such studies is to characterize the doseresponse relationship and to find the smallest target dose concentration d*, which leads to the same efficacy as the active control. For this purpose, the intersection point of the mean doseresponse function with the expected efficacy of the active control has to be estimated. The focus of this paper is a cubic spline-based method for deriving an estimator of the target dose without assuming a specific doseresponse function. Furthermore, the construction of a spline-based bootstrap CI is described. Estimator and CI are compared with other flexible and parametric methods such as linear spline interpolation as well as maximum likelihood regression in simulation studies motivated by a real clinical trial. Also, design considerations for the cubic spline approach with focus on bias minimization are presented. Although the spline-based point estimator can be biased, designs can be chosen to minimize and reasonably limit the maximum absolute bias. Furthermore, the coverage probability of the cubic spline approach is satisfactory, especially for bias minimal designs. Š 2014 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd. PMID:25319931
Robust Tessellation of Trimmed Rational B-Spline Surface Patches
Wonjoon Cho; Takashi Maekawa; Nicholas M. Patrikalakis; Jaime Peraire
1997-01-01
We present an unstructured triangular mesh gen- eration algorithm that approximates a set of mutually non-intersecting simple trimmed rational B-spline sur- face patches within a user specied geometric tolerance. The proposed method uses numerically robust interval geometric representations\\/computations and also ad- dresses the problem of topological consistency (homeo- morphism) between the exact geometry and its approx- imation. Those are among
Recognition of Unconstrained Handwritten Numerals using Biorthogonal Spline Wavelets
Suzete E. N. Correia; Joăo Marques De Carvalho
2000-01-01
This work proposes a novel approach for recognition of unconstrained handwritten numerals using the biorthogonal spline wavelets Cohen-Daubechies-Feauveau (CDF) 3\\/7 as a feature extractor and a multilayer cluster neural network as a classifier. Experiments with the database of CENPARMI show that this method yields good results. 1 Objective To develop a system which is able to efficiently extract fea- tures
Fairing Bicubic B-Spline Surfaces using Simulated Annealing
Stefanie Hahmann; Stefan Konz
In this paper we present an automatic fairing algorithm for bicubic B-spline surfaces. The fairing method consists of a knot re- moval and knot reinsertion step which locally smoothes the surface. The simulated-annealing search strategy is used to search for the global mini- mum of the fairing measure. x1. Introduction Free form surfaces are an indispensable part of powerful CAD-systems.
CNC tool path in terms of B-spline curves
Claire Lartigue; François Thiebaut; Takashi Maekawa
2001-01-01
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
A collocation approach to solve the Riccati-type differential equation systems
?uayip Yüzba??
2012-01-01
In this paper, a collocation method is presented for the solutions of the system of the Riccati-type differential equations with variable coefficients. The proposed approach consists of reducing the problem to a nonlinear algebraic equation system by expanding the approximate solutions in terms of the Bessel polynomials with unknown coefficients. The unknown coefficients of the Bessel polynomials are found by
Larry C. Young; Bruce A. Finlayson
1976-01-01
The orthogonal collocation method is applied to solve the mathematical model of a monolith catalytic converter, in which the reaction takes place in a porous catalytic layer deposited on the wall of a tube. A sequence of models is developed, with the most complicated one involving transient heat and mass transfer in three dimensions.
Flight Testing a Real Time Implementation of a UAV Path Planner Using Direct Collocation
Flight Testing a Real Time Implementation of a UAV Path Planner Using Direct Collocation Brian R by tracking a second UAV flying a predefined pattern. Finally, a method of commanding the observation vector ^s UAV sensor line of sight unit vector p Attraction point u UAV Control vector xt Target state
ERIC Educational Resources Information Center
Chatpunnarangsee, Kwanjira
2013-01-01
The purpose of this study is to explore ways of incorporating web-based concordancers for the purpose of teaching English collocations. A mixed-methods design utilizing a case study strategy was employed to uncover four specific dimensions of corpus use by twenty-four students in two classroom sections of a writing course at a university in
B-Spline Signal Processing: Part I-Theory
Michael Unser; Akram Aldroubi; Murray Eden
1993-01-01
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
Analysis of harmonic spline gravity models for Venus and Mars
NASA Technical Reports Server (NTRS)
Bowin, Carl
1986-01-01
Methodology utilizing harmonic splines for determining the true gravity field from Line-Of-Sight (LOS) acceleration data from planetary spacecraft missions was tested. As is well known, the LOS data incorporate errors in the zero reference level that appear to be inherent in the processing procedure used to obtain the LOS vectors. The proposed method offers a solution to this problem. The harmonic spline program was converted from the VAX 11/780 to the Ridge 32C computer. The problem with the matrix inversion routine that improved inversion of the data matrices used in the Optimum Estimate program for global Earth studies was solved. The problem of obtaining a successful matrix inversion for a single rev supplemented by data for the two adjacent revs still remains.
ANALYSIS ON CENSORED QUANTILE RESIDUAL LIFE MODEL VIA SPLINE SMOOTHING
Ma, Yanyuan; Wei, Ying
2013-01-01
We propose a general class of quantile residual life models, where a specific quantile of the residual life time, conditional on an individual has survived up to time t, is a function of certain covariates with their coefficients varying over time. The varying coefficients are assumed to be smooth unspecified functions of t. We propose to estimate the coefficient functions using spline approximation. Incorporating the spline representation directly into a set of unbiased estimating equations, we obtain a one-step estimation procedure, and we show that this leads to a uniformly consistent estimator. To obtain further computational simplification, we propose a two-step estimation approach in which we estimate the coefficients on a series of time points first, and follow this with spline smoothing. We compare the two methods in terms of their asymptotic efficiency and computational complexity. We further develop inference tools to test the significance of the covariate effect on residual life. The finite sample performance of the estimation and testing procedures are further illustrated through numerical experiments. We also apply the methods to a data set from a neurological study. PMID:24478565
Image interpolation by multivariate B-splines
Chan, Ki Bun
1986-01-01
IMAGE INTERPOLATION BY MULTIVARIATE B-SPLINES A Thesis by KI BUN CHAN Submitted to the Graduate College of Texas A&M University in partial fulfillment of the requirement for the degree of MASTER OF SCIENCE August 1986 Major Subject...: Electrical Engineering IMAGE INTERPOLATION BY MULTIVARIATE B-SPLINES A Thesis by KI BUN CHAN Approved as to style and content by: Andrew K. Chan (Chairman of Committee) orman C. Griswold (Member) e@. a (r Charles K. Chui (Member) Chanan Singh...
Optimization of Low-Thrust Spiral Trajectories by Collocation
NASA Technical Reports Server (NTRS)
Falck, Robert D.; Dankanich, John W.
2012-01-01
As NASA examines potential missions in the post space shuttle era, there has been a renewed interest in low-thrust electric propulsion for both crewed and uncrewed missions. While much progress has been made in the field of software for the optimization of low-thrust trajectories, many of the tools utilize higher-fidelity methods which, while excellent, result in extremely high run-times and poor convergence when dealing with planetocentric spiraling trajectories deep within a gravity well. Conversely, faster tools like SEPSPOT provide a reasonable solution but typically fail to account for other forces such as third-body gravitation, aerodynamic drag, solar radiation pressure. SEPSPOT is further constrained by its solution method, which may require a very good guess to yield a converged optimal solution. Here the authors have developed an approach using collocation intended to provide solution times comparable to those given by SEPSPOT while allowing for greater robustness and extensible force models.
Achieving high data reduction with integral cubic B-splines
NASA Technical Reports Server (NTRS)
Chou, Jin J.
1993-01-01
During geometry processing, tangent directions at the data points are frequently readily available from the computation process that generates the points. It is desirable to utilize this information to improve the accuracy of curve fitting and to improve data reduction. This paper presents a curve fitting method which utilizes both position and tangent direction data. This method produces G(exp 1) non-rational B-spline curves. From the examples, the method demonstrates very good data reduction rates while maintaining high accuracy in both position and tangent direction.
A Study of Strategy Use in Producing Lexical Collocations.
ERIC Educational Resources Information Center
Liu, Candi Chen-Pin
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
SPLPKG,WFCMPR,WFAPPX. Wilson-Fowler Spline Use
Fletcher, S.K. [Sandia National Labs., Albuquerque, NM (United States)
1985-02-01
The three programs SPLPKG, WFCMPR, and WFAPPX provide the capability for interactively generating, comparing, and approximating Wilson-Fowler splines. The Wilson-Fowler spline is widely used in Computer Aided Design and Manufacturing (CAD/CAM) systems. It is favored for many applications because it produces a smooth, low curvature fit to planar data points. Program SPLPKG generates a Wilson-Fowler spline passing through given nodes (with given end conditions) and also generates a piecewise linear approximation to that spline within a user-defined tolerance. The program may be used to generate a `desired` spline against which to compare other splines generated by CAD/CAM systems. It may also be used to generate an acceptable approximation to a desired spline in the event that an acceptable spline cannot be generated by the receiving CAD/CAM system. SPLPKG writes an IGES file of points evaluated on the spline and/or a file containing the spline description. Program WFCMPR computes the maximum difference between two Wilson-Fowler splines and may be used to verify the spline recomputed by a receiving system. It compares two Wilson-Fowler splines with common nodes and reports the maximum distance between curves (measured perpendicular to segments) and the maximum difference of their tangents (or normals), both computed along the entire length of the splines. Program WFAPPX computes the maximum difference between a Wilson-Fowler spline and a piecewise linear curve. It may be used to accept or reject a proposed approximation to a desired Wilson-Fowler spline, even if the origin of the approximation is unknown. The maximum deviation between these two curves, and the parameter value on the spline where it occurs are reported.
Polynomial interpolation methods for viscous flow calculations
NASA Technical Reports Server (NTRS)
Rubin, S. G.; Khosla, P. K.
1977-01-01
Higher-order collocation procedures which result in block-tridiagonal matrix systems are derived from (1) Taylor series expansions and from (2) polynomial interpolation, and the relationships between the two formulations, called respectively Hermite and spline collocation, are investigated. A Hermite block-tridiagonal system for a nonuniform mesh is derived, and the Hermite approach is extended in order to develop a variable-mesh sixth-order block-tridiagonal procedure. It is shown that all results obtained by Hermite development can be recovered by appropriate spline polynomial interpolation. The additional boundary conditions required for these higher-order procedures are also given. Comparative solutions using second-order accurate finite difference and spline and Hermite formulations are presented for the boundary layer on a flat plate, boundary layers with uniform and variable mass transfer, and the viscous incompressible Navier-Stokes equations describing flow in a driven cavity.
Yankov, A.; Downar, T. [University of Michigan, 2355 Bonisteel Blvd, Ann Arbor, MI 48109 (United States)
2013-07-01
Recent efforts in the application of uncertainty quantification to nuclear systems have utilized methods based on generalized perturbation theory and stochastic sampling. While these methods have proven to be effective they both have major drawbacks that may impede further progress. A relatively new approach based on spectral elements for uncertainty quantification is applied in this paper to several problems in reactor simulation. Spectral methods based on collocation attempt to couple the approximation free nature of stochastic sampling methods with the determinism of generalized perturbation theory. The specific spectral method used in this paper employs both the Smolyak algorithm and adaptivity by using Newton-Cotes collocation points along with linear hat basis functions. Using this approach, a surrogate model for the outputs of a computer code is constructed hierarchically by adaptively refining the collocation grid until the interpolant is converged to a user-defined threshold. The method inherently fits into the framework of parallel computing and allows for the extraction of meaningful statistics and data that are not within reach of stochastic sampling and generalized perturbation theory. This paper aims to demonstrate the advantages of spectral methods-especially when compared to current methods used in reactor physics for uncertainty quantification-and to illustrate their full potential. (authors)
Truncated Laurent expansions for the fast evaluation of thin plate splines
NASA Astrophysics Data System (ADS)
Powell, M.
1993-02-01
Thin plate splines are highly useful for the approximation of functions of two variables, partly because they provide the interpolant to scattered function values that minimizes a 2-norm of second derivatives. On the other hand, they have the severe disadvantage that the explicit calculation of a thin plate spline approximation requires a log function to be evaluatedm times, wherem is the number of "r2logr2" terms that occur. Therefore we consider a recent technique that saves much work whenm is large by forming sets of terms, and then the total contribution to the thin plate spline from the terms of each set is estimated by a single truncated Laurent expansion. In order to apply this technique, one has to pick the sets, one has to generate the coefficients of the expansions, and one has to decide which expansions give enough accuracy when the value of the spline is required at a general point of ?2. Our answers to these questions are different from those that are given elsewhere, as we prefer to refine sets of terms recursively by splitting them into two rather than four subsets. Some theoretical properties and several numerical results of our method are presented. They show that the work to calculate all the Laurent coefficients is usuallyO(m logm), and then onlyO(logm) operations are needed to estimate the value of the thin plate spline at a typical point of ?2. Thus substantial gains over direct methods are achieved form
?uayip Yüzba??; Ahmet Yildirim
In this study, a collocation method based on the Bessel polynomials is introduced for the approximate solutions of high-order linear FredholmVolterra integro-differential equations (FVIDEs) under mixed conditions. In addition, the method is presented with error and stability analysis. Numerical examples are included to demonstrate the validity and applicability of the technique and comparisons are made with the existing results.
Error Estimates Derived from the Data for Least-Squares Spline Fitting
Jerome Blair
2007-06-25
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.
NASA Technical Reports Server (NTRS)
Gottlieb, David; Shu, Chi-Wang
1994-01-01
The paper presents a method to recover exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of an approximation to the interpolation polynomial (or trigonometrical polynomial). We show that if we are given the collocation point values (or a highly accurate approximation) at the Gauss or Gauss-Lobatto points, we can reconstruct a uniform exponentially convergent approximation to the function f(x) in any sub-interval of analyticity. The proof covers the cases of Fourier, Chebyshev, Legendre, and more general Gegenbauer collocation methods.
Regression spline smoothing using the minimum description length principle
Thomas C. M. Lee; Colorado State
2000-01-01
One approach to estimating a function nonparametrically is to fit an rth-order regression spline to the noisy observations, and one important component of this approach is the choice of the number and the locations of the knots. This article proposes a new regression spline smoothing procedure which automatically chooses: (i) the order r of the regression spline being fitted; (ii)
Exponential box-like splines on nonuniform grids Thomas Kunkle
Kasman, Alex
Exponential box-like splines on nonuniform grids Thomas Kunkle Department of Mathematics, College/home.html In Memory of Prof. Ewa Maria Wojcicka 19551996 Abstract We generalize the exponential box spline. Introduction With the invention of the exponential box spline [23], Ron generalized both the polynomial box
PSEUDO-SPLINES, WAVELETS AND (B.Sc., Peking University)
Zakharov, Vladimir
PSEUDO-SPLINES, WAVELETS AND FRAMELETS DONG BIN (B.Sc., Peking University) A THESIS SUBMITTED help and guidance all along. The topic, i.e. pseudo-splines, that Professor Shen suggested to me properties of pseudo-splines, but also learnt a lot about basic and modern ideas of wavelet theory. Meanwhile
A trans-dimensional polynomial-spline parameterization for gradient-based geoacoustic inversion.
Steininger, Gavin; Dosso, Stan E; Holland, Charles W; Dettmer, Jan
2014-10-01
This paper presents a polynomial spline-based parameterization for trans-dimensional geoacoustic inversion. The parameterization is demonstrated for both simulated and measured data and shown to be an effective method of representing sediment geoacoustic profiles dominated by gradients, as typically occur, for example, in muddy seabeds. Specifically, the spline parameterization is compared using the deviance information criterion (DIC) to the standard stack-of-homogeneous layers parameterization for the inversion of bottom-loss data measured at a muddy seabed experiment site on the Malta Plateau. The DIC is an information criterion that is well suited to trans-D Bayesian inversion and is introduced to geoacoustics in this paper. Inversion results for both parameterizations are in good agreement with measurements on a sediment core extracted at the site. However, the spline parameterization more accurately resolves the power-law like structure of the core density profile and provides smaller overall uncertainties in geoacoustic parameters. In addition, the spline parameterization is found to be more parsimonious, and hence preferred, according to the DIC. The trans-dimensional polynomial spline approach is general, and applicable to any inverse problem for gradient-based profiles. [Work supported by ONR.]. PMID:25324060
Developing and Evaluating a Web-Based Collocation Retrieval Tool for EFL Students and Teachers
ERIC Educational Resources Information Center
Chen, Hao-Jan Howard
2011-01-01
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
Torque ripple minimization in switched reluctance motors via bi-cubic spline interpolation
Julio C. Moreira
1992-01-01
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
NASA Technical Reports Server (NTRS)
Rogers, David
1991-01-01
G/SPLINES are a hybrid of Friedman's Multivariable Adaptive Regression Splines (MARS) algorithm with Holland's Genetic Algorithm. In this hybrid, the incremental search is replaced by a genetic search. The G/SPLINE algorithm exhibits performance comparable to that of the MARS algorithm, requires fewer least squares computations, and allows significantly larger problems to be considered.
Deconvolution using thin-plate splines
Toussaint, Udo v.; Gori, Silvio [Max-Planck-Institut fuer Plasmaphysik, 85748 Garching (Germany)
2007-11-13
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.
A multiresolution analysis for tensor-product splines using weighted spline wavelets
NASA Astrophysics Data System (ADS)
Kapl, Mario; Jüttler, Bert
2009-09-01
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.
Pierson, Jeffery L; Small, Scott R; Rodriguez, Jose A; Kang, Michael N; Glassman, Andrew H
2015-07-01
Design parameters affecting initial mechanical stability of tapered, splined modular titanium stems (TSMTSs) are not well understood. Furthermore, there is considerable variability in contemporary designs. We asked if spline geometry and stem taper angle could be optimized in TSMTS to improve mechanical stability to resist axial subsidence and increase torsional stability. Initial stability was quantified with stems of varied taper angle and spline geometry implanted in a foam model replicating 2cm diaphyseal engagement. Increased taper angle and a broad spline geometry exhibited significantly greater axial stability (+21%-269%) than other design combinations. Neither taper angle nor spline geometry significantly altered initial torsional stability. PMID:25754255
B-Spline Wavelet Paint Luiz Velho
B-Spline Wavelet Paint Luiz Velho Ken Perlin Abstract This paper describes an unbounded resolution paint system. The image is repre- sented using a bi-orthogonal wavelet basis. The wavelet implementation is provided. Keywords: wavelets. IMPA Â Instituto de MatemÂ´atica Pura e Aplicada Estrada Dona
Spline approximations for nonlinear hereditary control systems
P. K. Lamm
1984-01-01
A spline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.
Spline-Based Robot Navigation Evgeni Magid
Rivlin, Ehud
of the path is essential for mobile robot navigation, because non-smooth motions can cause slippage of wheelsSpline-Based Robot Navigation Evgeni Magid Applied Mathematics Technion - Israel Institute]). Other mechanisms of mapping the robot's environment onto a discrete searchable space include visibility
Global Optimization With Multivariate Adaptive Regression Splines
Scott Crino; Donald E. Brown
2007-01-01
This paper presents a novel procedure for approximating the global optimum in structural design by combining multivariate adaptive regression splines (MARS) with a response surface methodology (RSM). MARS is a flexible regression technique that uses a modified recursive partitioning strategy to simplify high-dimensional problems into smaller yet highly accurate models. Combining MARS and RSM improves the conventional RSM by addressing
Computing exact shadow irradiance using splines
Michael M. Stark; Elaine Cohen; Tom Lyche; Richard F. Riesenfeld
1999-01-01
We present a solution to the general problem of characterizing shad- ows in scenes involving a uniform polygonal area emitter and a polygonal occluder in arbitrary position by manifesting shadow irradiance as a spline function. Studying generalized prism-like constructions generated by the emitter and the occluder in a four- dimensional (shadow) space reveals a simpler intrinsic structure of the shadow
A Spline Regression Model for Latent Variables
ERIC Educational Resources Information Center
Harring, Jeffrey R.
2014-01-01
Spline (or piecewise) regression models have been used in the past to account for patterns in observed data that exhibit distinct phases. The changepoint or knot marking the shift from one phase to the other, in many applications, is an unknown parameter to be estimated. As an extension of this framework, this research considers modeling the
Subcell resolution in simplex stochastic collocation for spatial discontinuities
Witteveen, Jeroen A.S., E-mail: jeroen.witteveen@cwi.nl [Center for Turbulence Research, Stanford University, Building 500, Stanford, CA 94305-3035 (United States); Center for Mathematics and Computer Science (CWI), Science Park 123, 1098XG Amsterdam (Netherlands); Iaccarino, Gianluca, E-mail: jops@stanford.edu [Center for Turbulence Research, Stanford University, Building 500, Stanford, CA 94305-3035 (United States)] [Center for Turbulence Research, Stanford University, Building 500, Stanford, CA 94305-3035 (United States)
2013-10-15
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 SSCSR 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 SSCSR resolves random spatial discontinuities with multiple stochastic and spatial dimensions accurately using a minimal number of samples.
Translating Collocations for Bilingual Lexicons: A Statistical Approach
Frank A. Smadja; Kathleen R. Mckeown; Vasileios Hatzivassiloglou
1996-01-01
Collocations are notoriously difficult for non-native speakers to translate, primarily because they are opaque and cannot be translated on a word-by-word basis. We describe a program named Champollion which, given a pair of parallel corpora in two different languages and a list of collocations in one of them, automatically produces their translations. Our goal is to provide a tool for
The Benard problem: A comparison of finite difference and spectral collocation eigen value solutions
NASA Technical Reports Server (NTRS)
Skarda, J. Raymond Lee; Mccaughan, Frances E.; Fitzmaurice, Nessan
1995-01-01
The application of spectral methods, using a Chebyshev collocation scheme, to solve hydrodynamic stability problems is demonstrated on the Benard problem. Implementation of the Chebyshev collocation formulation is described. The performance of the spectral scheme is compared with that of a 2nd order finite difference scheme. An exact solution to the Marangoni-Benard problem is used to evaluate the performance of both schemes. The error of the spectral scheme is at least seven orders of magnitude smaller than finite difference error for a grid resolution of N = 15 (number of points used). The performance of the spectral formulation far exceeded the performance of the finite difference formulation for this problem. The spectral scheme required only slightly more effort to set up than the 2nd order finite difference scheme. This suggests that the spectral scheme may actually be faster to implement than higher order finite difference schemes.
Statistical modelling of collocation uncertainty in atmospheric thermodynamic profiles
NASA Astrophysics Data System (ADS)
Fassň, A.; Ignaccolo, R.; Madonna, F.; Demoz, B. B.; Franco-Villoria, M.
2014-06-01
The quantification of measurement uncertainty of atmospheric parameters is a key factor in assessing the uncertainty of global change estimates given by numerical prediction models. One of the critical contributions to the uncertainty budget is related to the collocation mismatch in space and time among observations made at different locations. This is particularly important for vertical atmospheric profiles obtained by radiosondes or lidar. In this paper we propose a statistical modelling approach capable of explaining the relationship between collocation uncertainty and a set of environmental factors, height and distance between imperfectly collocated trajectories. The new statistical approach is based on the heteroskedastic functional regression (HFR) model which extends the standard functional regression approach and allows a natural definition of uncertainty profiles. Along this line, a five-fold decomposition of the total collocation uncertainty is proposed, giving both a profile budget and an integrated column budget. HFR is a data-driven approach valid for any atmospheric parameter, which can be assumed smooth. It is illustrated here by means of the collocation uncertainty analysis of relative humidity from two stations involved in the GCOS reference upper-air network (GRUAN). In this case, 85% of the total collocation uncertainty is ascribed to reducible environmental error, 11% to irreducible environmental error, 3.4% to adjustable bias, 0.1% to sampling error and 0.2% to measurement error.
Ruberti, M; Averbukh, V; Decleva, P
2014-10-28
We present the first implementation of the ab initio many-body Green's function method, algebraic diagrammatic construction (ADC), in the B-spline single-electron basis. B-spline versions of the first order [ADC(1)] and second order [ADC(2)] schemes for the polarization propagator are developed and applied to the ab initio calculation of static (photoionization cross-sections) and dynamic (high-order harmonic generation spectra) quantities. We show that the cross-section features that pose a challenge for the Gaussian basis calculations, such as Cooper minima and high-energy tails, are found to be reproduced by the B-spline ADC in a very good agreement with the experiment. We also present the first dynamic B-spline ADC results, showing that the effect of the Cooper minimum on the high-order harmonic generation spectrum of Ar is correctly predicted by the time-dependent ADC calculation in the B-spline basis. The present development paves the way for the application of the B-spline ADC to both energy- and time-resolved theoretical studies of many-electron phenomena in atoms, molecules, and clusters. PMID:25362291
Least Committed Splines in 3D Modelling of Free Form Objects from Intensity Images
Kuntal Sengupta; Prabir Burman; Sumit Gupta
2002-01-01
Generating 3D models of objects from video sequences is an important problem in many multimedia applications ranging from teleconferencing to virtual reality. In this paper, we present a method of estimating the 3D face model from a monocular image sequence, using a few standard results from the affine camera geometry literature in computer vision, and spline fitting techniques using a
Triangle Mesh Compression using B-Spline Curves Anshuman Razdan1
Triangle Mesh Compression using B-Spline Curves Anshuman Razdan1 , Vinodth Kumar Mohanam2 , Gerald Farin3 Abstract We present a new method to compress triangle meshes in a lossless manner. Triangle compressed files are roughly 10% smaller than that from Edgebreaker. Keywords: Triangle compression, B
Tobias Stammberger; Felix Eckstein; Markus Michaelis; Karl-Hans Englmeier; Maximilian Reiser
1999-01-01
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.
Mathematical Geology, Vol. 30, No. 1, 1998 Interpolation with Splines in Tension: A Green's
in the earth-science community. This method produces a gridded surface that minimizes the squared curvature, splines. INTRODUCTION In the physical sciences, and in the earth sciences in particular, data may of Ocean and Earth Science and Technology, University of Hawaii at Manoa, 1680 East-West Road, Honolulu
Using P-splines to smooth two-dimensional Poisson data
Maria Durban; Iain Currie; Paul Eilers
Eilers & Marx (1996) used P-splines to smooth one-dimensional count data with Poisson errors. We extend their methods to two dimensions. We con- sider a variety of models and highlight some of the computational problems that arise with large data sets. We illustrate our remarks with the analysis of a large set of mortality data indexed by age of death
A B-spline approach to phase unwrapping in tagged cardiac MRI for motion tracking.
Chiang, Patricia; Cai, Yiyu; Mak, Koon Hou; Zheng, Jianmin
2013-05-01
A novel B-Spline based approach to phase unwrapping in tagged magnetic resonance images is proposed for cardiac motion tracking. A bicubic B-spline surface is used to model the absolute phase. The phase unwrapping problem is formulated as a mixed integer optimization problem that minimizes the sum of the difference between the spatial gradients of absolute and wrapped phases, and the difference between the rewrapped and wrapped phases. In contrast to the existing techniques for motion tracking, the proposed approach can overcome the limitation of interframe half-tag displacement and increase the robustness of motion tracking. The article further presents a hybrid harmonic phase imaging-B-spline method to take the advantage of the harmonic phase imaging method for small motion and the efficiency of the B-Spline approach for large motion. The proposed approach has been successively applied to a full set of cardiac MRI scans in both long and short axis slices with superior performance when compared with the harmonic phase imaging and quality guided path-following methods. PMID:22692944
Trajectory control of an articulated robot with a parallel drive arm based on splines under tension
NASA Astrophysics Data System (ADS)
Yi, Seung-Jong
Today's industrial robots controlled by mini/micro computers are basically simple positioning devices. The positioning accuracy depends on the mathematical description of the robot configuration to place the end-effector at the desired position and orientation within the workspace and on following the specified path which requires the trajectory planner. In addition, the consideration of joint velocity, acceleration, and jerk trajectories are essential for trajectory planning of industrial robots to obtain smooth operation. The newly designed 6 DOF articulated robot with a parallel drive arm mechanism which permits the joint actuators to be placed in the same horizontal line to reduce the arm inertia and to increase load capacity and stiffness is selected. First, the forward kinematic and inverse kinematic problems are examined. The forward kinematic equations are successfully derived based on Denavit-Hartenberg notation with independent joint angle constraints. The inverse kinematic problems are solved using the arm-wrist partitioned approach with independent joint angle constraints. Three types of curve fitting methods used in trajectory planning, i.e., certain degree polynomial functions, cubic spline functions, and cubic spline functions under tension, are compared to select the best possible method to satisfy both smooth joint trajectories and positioning accuracy for a robot trajectory planner. Cubic spline functions under tension is the method selected for the new trajectory planner. This method is implemented for a 6 DOF articulated robot with a parallel drive arm mechanism to improve the smoothness of the joint trajectories and the positioning accuracy of the manipulator. Also, this approach is compared with existing trajectory planners, 4-3-4 polynomials and cubic spline functions, via circular arc motion simulations. The new trajectory planner using cubic spline functions under tension is implemented into the microprocessor based robot controller and motors to produce combined arc and straight-line motion. The simulation and experiment show interesting results by demonstrating smooth motion in both acceleration and jerk and significant improvements of positioning accuracy in trajectory planning.
Higher-order numerical methods derived from three-point polynomial interpolation
NASA Technical Reports Server (NTRS)
Rubin, S. G.; Khosla, P. K.
1976-01-01
Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and Hermitian finite-difference discretization. The equations generally apply for both uniform and variable meshes. Hybrid schemes resulting from different polynomial approximations for first and second derivatives lead to the nonuniform mesh extension of the so-called compact or Pade difference techniques. A variety of fourth-order methods are described and this concept is extended to sixth-order. Solutions with these procedures are presented for the similar and non-similar boundary layer equations with and without mass transfer, the Burgers equation, and the incompressible viscous flow in a driven cavity. Finally, the interpolation procedure is used to derive higher-order temporal integration schemes and results are shown for the diffusion equation.
Development and flight tests of vortex-attenuating splines
NASA Technical Reports Server (NTRS)
Hastings, E. C., Jr.; Patterson, J. C., Jr.; Shanks, R. E.; Champine, R. A.; Copeland, W. L.; Young, D. C.
1975-01-01
The ground tests and full-scale flight tests conducted during development of the vortex-attenuating spline are described. The flight tests were conducted using a vortex generating aircraft with and without splines; a second aircraft was used to probe the vortices generated in both cases. The results showed that splines significantly reduced the vortex effects, but resulted in some noise and climb performance penalties on the generating aircraft.
On the spline-based wavelet differentiation matrix
NASA Technical Reports Server (NTRS)
Jameson, Leland
1993-01-01
The differentiation matrix for a spline-based wavelet basis is constructed. Given an n-th order spline basis it is proved that the differentiation matrix is accurate of order 2n + 2 when periodic boundary conditions are assumed. This high accuracy, or superconvergence, is lost when the boundary conditions are no longer periodic. Furthermore, it is shown that spline-based bases generate a class of compact finite difference schemes.
Continuous Groundwater Monitoring Collocated at USGS Streamgages
NASA Astrophysics Data System (ADS)
Constantz, J. E.; Eddy-Miller, C.; Caldwell, R.; Wheeer, J.; Barlow, J.
2012-12-01
USGS Office of Groundwater funded a 2-year pilot study collocating groundwater wells for monitoring water level and temperature at several existing continuous streamgages in Montana and Wyoming, while U.S. Army Corps of Engineers funded enhancement to streamgages in Mississippi. To increase spatial relevance with in a given watershed, study sites were selected where near-stream groundwater was in connection with an appreciable aquifer, and where logistics and cost of well installations were considered representative. After each well installation and surveying, groundwater level and temperature were easily either radio-transmitted or hardwired to existing data acquisition system located in streamgaging shelter. Since USGS field personnel regularly visit streamgages during routine streamflow measurements and streamgage maintenance, the close proximity of observation wells resulted in minimum extra time to verify electronically transmitted measurements. After field protocol was tuned, stream and nearby groundwater information were concurrently acquired at streamgages and transmitted to satellite from seven pilot-study sites extending over nearly 2,000 miles (3,200 km) of the central US from October 2009 until October 2011, for evaluating the scientific and engineering add-on value of the enhanced streamgage design. Examination of the four-parameter transmission from the seven pilot study groundwater gaging stations reveals an internally consistent, dynamic data suite of continuous groundwater elevation and temperature in tandem with ongoing stream stage and temperature data. Qualitatively, the graphical information provides appreciation of seasonal trends in stream exchanges with shallow groundwater, as well as thermal issues of concern for topics ranging from ice hazards to suitability of fish refusia, while quantitatively this information provides a means for estimating flux exchanges through the streambed via heat-based inverse-type groundwater modeling. In June USGS Fact Sheet 2012-3054 was released online, summarizing the results of the pilot project.
A mixed basis density functional approach for low dimensional systems with B-splines
NASA Astrophysics Data System (ADS)
Ren, Chung-Yuan; Hsue, Chen-Shiung; Chang, Yia-Chung
2015-03-01
A mixed basis approach based on density functional theory is employed for low dimensional systems. The basis functions are taken to be plane waves for the periodic direction multiplied by B-spline polynomials in the non-periodic direction. B-splines have the following advantages: (1) the associated matrix elements are sparse, (2) B-splines possess a superior treatment of derivatives, (3) B-splines are not associated with atomic positions when the geometry structure is optimized, making the geometry optimization easy to implement. With this mixed basis set we can directly calculate the total energy of the system instead of using the conventional supercell model with a slab sandwiched between vacuum regions. A generalized Lanczos-Krylov iterative method is implemented for the diagonalization of the Hamiltonian matrix. To demonstrate the present approach, we apply it to study the C(001)-(2×1) surface with the norm-conserving pseudopotential, the n-type ?-doped graphene, and graphene nanoribbon with Vanderbilt's ultra-soft pseudopotentials. All the resulting electronic structures were found to be in good agreement with those obtained by the VASP code, but with a reduced number of basis.
Kendal, Alan P.; Peterson, Alwin; Manning, Claudine; Xu, Fujie; Neville, Loretta J.; Hogue, Carol
2002-01-01
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;92:399403) PMID:11867319
Acoustic ranging of small arms fire using a single sensor node collocated with the target.
Lo, Kam W; Ferguson, Brian G
2015-06-01
A ballistic model-based method, which builds upon previous work by Lo and Ferguson [J. Acoust. Soc. Am. 132, 2997-3017 (2012)], is described for ranging small arms fire using a single acoustic sensor node collocated with the target, without a priori knowledge of the muzzle speed and ballistic constant of the bullet except that they belong to a known two-dimensional parameter space. The method requires measurements of the differential time of arrival and differential angle of arrival of the muzzle blast and ballistic shock wave at the sensor node. Its performance is evaluated using both simulated and real data. PMID:26093450
Face occlusion detection by using B-spline active contour and skin color information
Gahyun Kim; Jae Kyu Suhr; Ho Gi Jung; Jaihie Kim
2010-01-01
This paper proposes a face occlusion verification method for an automated teller machine (ATM) application. The proposed method mainly consists of three steps. Firstly, a head and shoulder shape is detected by applying B-spline active contour to motion edges. This motion edge is generated by a kurtosis-based frame selection and distance transformation-based motion edge detection. Secondly, a face area is
Instant Trend-Seasonal Decomposition of Time Series with Splines
Krivobokova, Tatyana
Instant Trend-Seasonal Decomposition of Time Series with Splines Luis Francisco Rosales1 Tatyana to decompose a times series into trend, seasonal and remainder components. This fully data-driven technique is based on penalized splines and makes an explicit characterization of the varying seasonality
Regression Spline Smoothing using the Minimum Description Length Principle \\Lambda
Lee, Chun Man "Thomas"
Regression Spline Smoothing using the Minimum Description Length Principle \\Lambda Thomas C. M. Lee of the knots; and (iii) the locations of the knots. This procedure is based on the minimum description length. Keywords: automatic knot selection; minimum description length; regression spline smoothing 1 Introduction
Penalized spline estimation for functional coefficient regression models
Yanrong Cao; Haiqun Lin; Tracy Z. Wu; Yan Yu
2010-01-01
The functional coefficient regression models assume that the regression coefficients vary with some threshold variable, providing appreciable flexibility in capturing the underlying dynamics in data and avoiding the so-called curse of dimensionality in multivariate nonparametric estimation. We first investigate the estimation, inference, and forecasting for the functional coefficient regression models with dependent observations via penalized splines. The P-spline approach, as
B-Splines for Physically-Based Michael M. Stark
Utah, University of
B-Splines for Physically-Based Rendering Michael M. Stark William Martin Elaine Cohen Tom Lyche. #12;B-Splines for Physically-Based Rendering Michael M. Stark William Martin Elaine Cohen Tom Lyche--Three-Dimensional Graphics and Realism Keywords: Curves & Surfaces, Illumination, Numerical Analysis, Ray Tracing, Rendering
Spline transfer through IGES: CADCAM-001
Fletcher, S.K.
1983-10-01
Sandia National Laboratories has been assigned Lead Lab responsibility for integrating CAD/CAM activities throughout the DOE Nuclear Weapons Complex (NWC). Pilot projects involving exchange of actual or artificial data are being used to assess our current capabilities in the areas of electronic data transmission, translations between different CAD/CAM systems, etc. This report is the final report for one pilot project. It assesses the effectiveness of IGES (Initial Graphics Exchange Specification, defined in ANSIY14.26M-1981) in transferring interpolating splines between various CAD/CAM systems used in the NWC. The results are generally encouraging.
The Effects of Vocabulary Learning on Collocation and Meaning
ERIC Educational Resources Information Center
Webb, Stuart; Kagimoto, Eve
2009-01-01
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
Exploratory Collocation Extraction Stefan Evert, University of Osnabrck
cooccurrences (such as "dark"/"night" and "milk"/"cow") that provide information about the objects and concepts approach Type of proposal: full paper Keywords: collocations, cooccurrence, association measures than their actual occurrences in corpora. The goal of such approaches is to extract a specific type
Using job-shop scheduling tasks for evaluating collocated collaboration
Desney S. Tan; Darren Gergle; Regan L. Mandryk; Kori Inkpen; Melanie Kellar; Kirstie Hawkey; Mary Czerwinski
2008-01-01
Researchers have begun to explore tools that allow multiple users to collaborate across multiple devices in collocated environments. These tools often allow users to simultaneously place and interact with information on shared displays. Unfortunately, there is a lack of experi- mental tasks to evaluate the effectiveness of these tools for information coordination in such scenarios. In this article, we introduce
NASA Astrophysics Data System (ADS)
Athanasakis, I. E.; Papadopoulou, E. P.; Saridakis, Y. G.
2014-03-01
Fisher's equation has been widely used to model the biological invasion of single-species communities in homogeneous one dimensional habitats. In this study we develop high order numerical methods to accurately capture the spatiotemporal dynamics of the generalized Fisher equation, a nonlinear reaction-diffusion equation characterized by density dependent non-linear diffusion. Working towards this direction we consider strong stability preserving Runge-Kutta (RK) temporal discretization schemes coupled with the Hermite cubic Collocation (HC) spatial discretization method. We investigate their convergence and stability properties to reveal efficient HC-RK pairs for the numerical treatment of the generalized Fisher equation. The Hadamard product is used to characterize the collocation discretized non linear equation terms as a first step for the treatment of generalized systems of relevant equations. Numerical experimentation is included to demonstrate the performance of the methods.
Sahay, Sundeep
that linear combinations of B-splines have the convex hull property, i.e., any point on a spline curve lies within the convex hull of the B-spline coefficients. There is also a local convex hull property: If we-splines are nonzero so the associated curve segment lies within the convex hull of the corresponding coefficients
Parameter estimation in systems biology models using spline approximation
2011-01-01
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. PMID:21255466
Goh, Joan; Hj. M. Ali, Norhashidah
2015-01-01
Over the last few decades, cubic splines have been widely used to approximate differential equations due to their ability to produce highly accurate solutions. In this paper, the numerical solution of a two-dimensional elliptic partial differential equation is treated by a specific cubic spline approximation in the x-direction and finite difference in the y-direction. A four point explicit group (EG) iterative scheme with an acceleration tool is then applied to the obtained system. The formulation and implementation of the method for solving physical problems are presented in detail. The complexity of computational is also discussed and the comparative results are tabulated to illustrate the efficiency of the proposed method. PMID:26182211
Curvature analysis approach to shape coding using B-splines
NASA Astrophysics Data System (ADS)
Zaletelj, Janez; Tasic, Jurij F.
2000-12-01
This work presents an algorithm for efficient shape coding using cubic B-splines. In the framework of object-based layered coding of image sequences, shape information is essential for content-based access to video objects, and its efficient encoding needs to be investigated. We present a rate and distortion controlled algorithm for vide object shape approximation by variable number of cubic B-spline segments and motion compensated inter-frame coding of B-spline control points. Rate-distortion efficiency of the proposed algorithm is compared to MPEG-4 context arithmetic encoding and two stage motion compensated chain coding.
NASA Astrophysics Data System (ADS)
Li, Shengquan; Li, Juan; Mo, Yueping; Zhao, Rong
2014-01-01
A novel active method for multi-mode vibration control of an all-clamped stiffened plate (ACSP) is proposed in this paper, using the extended-state-observer (ESO) approach based on non-collocated acceleration sensors and piezoelectric actuators. Considering the estimated capacity of ESO for system state variables, output superposition and control coupling of other modes, external excitation, and model uncertainties simultaneously, a composite control method, i.e., the ESO based vibration control scheme, is employed to ensure the lumped disturbances and uncertainty rejection of the closed-loop system. The phenomenon of phase hysteresis and time delay, caused by non-collocated sensor/actuator pairs, degrades the performance of the control system, even inducing instability. To solve this problem, a simple proportional differential (PD) controller and acceleration feed-forward with an output predictor design produce the control law for each vibration mode. The modal frequencies, phase hysteresis loops and phase lag values due to non-collocated placement of the acceleration sensor and piezoelectric patch actuator are experimentally obtained, and the phase lag is compensated by using the Smith Predictor technology. In order to improve the vibration control performance, the chaos optimization method based on logistic mapping is employed to auto-tune the parameters of the feedback channel. The experimental control system for the ACSP is tested using the dSPACE real-time simulation platform. Experimental results demonstrate that the proposed composite active control algorithm is an effective approach for suppressing multi-modal vibrations.
Detection of defects in weld radiographic images by using multi-scale GVF B-spline snake
Y. Boutiche; A. Bessekri
2011-01-01
Inthispaper, weusetheactive contour models (Snakes) for edge detection and segmentation of weld defects in radiographic images. Gradient Vector Flow snakes enhance the concave object extraction capability. However, the GVF snakes are sensitive to noise. Several new snake models were developed by combining different methods with GVF snake. Here, a multiscale GVF and B-spline model is proposed to overcome the traditionnal
Computational dealings in nonlinear spline regression
Hrncir, Stanley Godfrey
1976-01-01
aaa Data points m Knot locations Spline approximation 35 TABLE 3 INPUT DATA FOR TEST CASE 2 N = 8 K = 4 LX = 25 X Values -1. 00000 -0. 52000 -0. 04000 0. 44000 0. 92000 -0. 92000 -0. 84000 -0. 76000 -0. 68000 -0. 60000 -0, 44000 -0... 5 3) (T(1) ~ I=l ~ NKT ) r6) IVERSIs ~ K r N ~ LX s I ENTER ACCELKNQT VERSION Al ~ r ~ I I s r ~ I 3e LX= ~ I4 ) 001 N= EM( N= 0 FNX=246 5MI X=E M KPl=K+I KPN=KAN WRITE(6 FORMAT( WRITE(6 FORMAT ( WRITE(6 FORMAT ( WRITE(6 IF( IKOP IN/(2...
The spline probability hypothesis density filter
NASA Astrophysics Data System (ADS)
Sithiravel, Rajiv; Tharmarasa, Ratnasingham; McDonald, Mike; Pelletier, Michel; Kirubarajan, Thiagalingam
2012-06-01
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.
Error Bounded Regular Algebraic Spline Curves * (Extended Abstract)
Texas at Austin, University of
of Computer Science, University of Texas, Austin, TX 78712 Email: bajajOcs.utexas.edu 1 Introduction We use curve design. (c) The spline curves, for the rectangle scheme, are e-error controllable where Eis
Modeling terminal ballistics using blending-type spline surfaces
NASA Astrophysics Data System (ADS)
Pedersen, Aleksander; Bratlie, Jostein; Dalmo, Rune
2014-12-01
We explore using GERBS, a blending-type spline construction, to represent deform able thin-plates and model terminal ballistics. Strategies to construct geometry for different scenarios of terminal ballistics are proposed.
NASA Astrophysics Data System (ADS)
Calbet, X.
2015-06-01
A method is presented to assess whether a given reference ground based point observation, typically a radiosonde measurement, is adequately collocated and sufficiently representative of space borne hyperspectral infrared instrument measurements. Once this assessment is made, the ground based data can be used to validate and potentially calibrate, with a high degree of accuracy, the hyperspectral retrievals of temperature and water vapour.
On Convergent Numerical Algorithms for Unsymmetric Collocation
Schaback, Robert
, exponential convergence for the multiquadric and Gaussian RBFs. Some numerical algorithms are proposed with the theories that the modified Kansa's method converges faster than the interpolant to the solution; that is RBF shape parameters, we show that the modified Kansa's method, through a subspace selection using
Algebraic grid generation using tensor product B-splines. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Saunders, B. V.
1985-01-01
Finite difference methods are more successful if the accompanying grid has lines which are smooth and nearly orthogonal. The development of an algorithm which produces such a grid when given the boundary description. Topological considerations in structuring the grid generation mapping are discussed. The concept of the degree of a mapping and how it can be used to determine what requirements are necessary if a mapping is to produce a suitable grid is examined. The grid generation algorithm uses a mapping composed of bicubic B-splines. Boundary coefficients are chosen so that the splines produce Schoenberg's variation diminishing spline approximation to the boundary. Interior coefficients are initially chosen to give a variation diminishing approximation to the transfinite bilinear interpolant of the function mapping the boundary of the unit square onto the boundary grid. The practicality of optimizing the grid by minimizing a functional involving the Jacobian of the grid generation mapping at each interior grid point and the dot product of vectors tangent to the grid lines is investigated. Grids generated by using the algorithm are presented.
I. J. Schoenberg
1973-01-01
It is shown that for entire functionsf(x) defined by a Fourier-Stieltjes integral (9) the cardinal splineS\\u000a \\u000a m\\u000a (x) of the odd degree 2m?1, which interpolatesf(x) at all integers, converges tof(x) asm tends to infinity. Properties of the exponential Euler spline are used in the proof.
NASA Astrophysics Data System (ADS)
Tao, Jun; Zeng, Xuan; Cai, Wei; Su, Yangfeng; Zhou, Dian
In this paper, a Stochastic Collocation Algorithm combined with Sparse Grid technique (SSCA) is proposed to deal with the periodic steady-state analysis for nonlinear systems with process variations. Compared to the existing approaches, SSCA has several considerable merits. Firstly, compared with the moment-matching parameterized model order reduction (PMOR) which equally treats the circuit response on process variables and frequency parameter by Taylor approximation, SSCA employs Homogeneous Chaos to capture the impact of process variations with exponential convergence rate and adopts Fourier series or Wavelet Bases to model the steady-state behavior in time domain. Secondly, contrary to Stochastic Galerkin Algorithm (SGA), which is efficient for stochastic linear system analysis, the complexity of SSCA is much smaller than that of SGA for nonlinear case. Thirdly, different from Efficient Collocation Method, the heuristic approach which may result in Rank deficient problem and Runge phenomenon, Sparse Grid technique is developed to select the collocation points needed in SSCA in order to reduce the complexity while guaranteing the approximation accuracy. Furthermore, though SSCA is proposed for the stochastic nonlinear steady-state analysis, it can be applied to any other kind of nonlinear system simulation with process variations, such as transient analysis, etc..
User's guide for Wilson-Fowler spline software: SPLPKG, WFCMPR, WFAPPX - CADCAM-010
Fletcher, S.K.
1985-02-01
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.
A collocation method for certain elliptic boundary-value problems
Hord, Susan Kathleen
1974-01-01
=NN( ) & NP 2) A(1& J )=16. J=NN( I ~ NP 1) A(2&J)=1 J =NN( 2 & N+2) A(I, J)=4. A( I&IRHS)=1 THE BOUNDARY X(K) Y(1) DO 101 K=2 ~ KN1=K-1 6 +D(NPZ) POINT'S MHI CH AREN 7 CORNE R POINTS K =Z & ~ ~ ~ ~ N+1 NP1 KP 1=K+1 I=NA)( Kr 1 ) J=NN( KM1 r I...Xt ~ +t t6Xttt ~ tlTXt t?tt ) OO 9000 NDEX ? 1 t 6 RFAO100 t Ni tE PS 100 FORHAT( I lot I=10, 0) NZ =N't&2 NP 1=N+1 NP2=N+2 NP22= (N+2 )'?2 NP I=N+ I NH l=N-1 H=l. /(N+I ) HZ =H t & 2 ~ IRHS=hi?2+1 XNPI=NiP 1 H= I, /XNP 1 HZ=H'h+2 e...
A collocation method for certain elliptic boundary-value problems
Hord, Susan Kathleen
1974-01-01
&)TERS &F7 ~ 5& & rrI 1& + tE15 ~ 6t t' ~ 13 ~ (3) -I ~ -I 01 01 ? 1. -1 01. 01 ? I ? I Ole01 -1 ~ -I 9. 1 . 01 ? I ~ -I 01 01 ? I -I 01 F 01 -I ? I Glo01 ? I -I ? lo ? I 01. 01 01 01 ? 1. ? I 01 ~ 01 ? I ? I -I ~ -I 01 F 01 01. 01... . ? I ? I 01. 01 . ? 1 ~ ? I ? I ? I , 01 F 01 . 01 01 ~ Gl ~ 01 Ql ~ Ole 01 o 01 Ol 01 ~ OI ~ Ol. 01 o 01 ~ 01 ~ 01 ~ I -I I ~ Gl 1. -1 I . -I I ~ 01 I 01 -I -1 ~ 01 ' 01 ? I ? I ? I F 01 01 . 01 01 ~ ? I -I ? I ? I ? I ~ ~ 01 01 01...
B-spline calculations of oscillator strengths in noble gases
NASA Astrophysics Data System (ADS)
Zatsarinny, Oleg; Bartschat, Klaus
2009-05-01
B-spline box-based multi-channel calculations of transition probabilities in noble gases are reported for energy levels up to n= 12. Energy levels and oscillator strengths for transitions from the p6 ground-state configuration, as well as for transitions between excited states, have been computed in the Breit-Pauli approximation. Individually optimized, term-dependent sets of non-orthogonal valence orbitals are used to account for the strong term dependence in the one-electron orbitals. The agreement in the length and velocity gauges of the transition data and the accuracy of the binding energies are used to estimate the accuracy of our results, which are also compared with experimental and other theoretical data. It is shown that the present method can be used for accurate calculations of oscillator strengths for states with intermediate to high n-values, for which it is difficult to apply standard multi-configuration Hartree-Fock (MCHF) methods. Recent developments based on the extension of our computer codes from the semi-relativistic Breit-Pauli Hamiltonian to the full relativistic Dirac-Breit Hamiltonian are also reported.
Alwan, Aravind; Aluru, N.R.
2013-12-15
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.
Efficient Stochastic Galerkin Methods For Random Diffusion ...
2008-09-16
Further extensions along this line include using piecewise basis functions to deal with discontinuity in ... variables. The resulting deterministic equations from a Galerkin method are a set of ...... A stochastic collocation method for elliptic partial differential ... High-order collocation methods for differential equations with random ...
Growth curve analysis for plasma profiles using smoothing splines
Imre, K.
1993-05-01
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.
False Paraphrase Pairs in Spanish for Verbs and Verb+Noun Collocations
,600 high frequency Spanish nouns and 2,800 high frequency Spanish verbs. The restricted combinatory of both counterpart (to have flu,*to flu); b) verbs that have no verb- noun collocation counterpart (to breath, *to do the breathing); c) verbs and verb- noun collocation counterpart that differ in meaning (to count, to do a count
Going beyond Patterns: Involving Cognitive Analysis in the Learning of Collocations
ERIC Educational Resources Information Center
Liu, Dilin
2010-01-01
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,
Facilitating Non-Collocated Coexistence for WiFi and 4G Wireless Networks
Sahoo, Anirudha
Facilitating Non-Collocated Coexistence for WiFi and 4G Wireless Networks Punit Rathod Department of non- collocated coexistence of WiFi and 4G technologies such as WiMAX and LTE due to adjacent channel.4 GHz ISM band used by WiFi. We show, with measurements on our test-bed and from existing results
English Collocation Learning through Corpus Data: On-Line Concordance and Statistical Information
ERIC Educational Resources Information Center
Ohtake, Hiroshi; Fujita, Nobuyuki; Kawamoto, Takeshi; Morren, Brian; Ugawa, Yoshihiro; Kaneko, Shuji
2012-01-01
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
The Chebyshev-Legendre method: Implementing Legendre methods on Chebyshev points
NASA Technical Reports Server (NTRS)
Don, Wai Sun; Gottlieb, David
1993-01-01
We present a new collocation method for the numerical solution of partial differential equations. This method uses the Chebyshev collocation points, but because of the way the boundary conditions are implemented, it has all the advantages of the Legendre methods. In particular, L2 estimates can be obtained easily for hyperbolic and parabolic problems.
PSEUDO-SPLINES, WAVELETS AND FRAMELETS BIN DONG AND ZUOWEI SHEN
Shen, Zuowei
PSEUDO-SPLINES, WAVELETS AND FRAMELETS BIN DONG AND ZUOWEI SHEN Abstract. The first type of pseudo the unitary extension principle of [22]. In the spirit of the first type of pseudo-splines, we introduce here a new type (the second type) of pseudo-splines to construct symmetric or antisymmetric tight framelets
Computing spline functions using quasi-interpolant techniques
Beacht, Russell Wilson
1975-01-01
). In [3] the k divided difference of th g (s; t) is def ined recursively by k +1' ' '+k' k i' ' '+k-1' (1. 2. 3) g (t , , t. ;t) i+k i The B-spline M. is now defined as i, k (1. 2. 4) (t) g (r, , t. , t) Given this definition for the B-spline, we now... wish to define the normalized B-spline N, in the usual manner, namely i, k (l. 2. 5) N. k(t) = (t. . k-t. )M, (t). Using (1. 2. 4) and (1, 2. 3), we also see (1. 2. 6) N. k(t) = gk(t yi? ' t k', t) ? gk(t. , '' &t. Additionally, de Boor [3] defines...
Error bounded conic spline approximation for NC code
NASA Astrophysics Data System (ADS)
Shen, Liyong
2011-12-01
Curve fitting is an important preliminary work for data compression and path interpolator in numerical control (NC). The paper gives a simple conic spline approximation algorithm for G01 code. The algorithm is mainly formed by three steps: divide the G01 code to subsets by discrete curvature detection, find the polygon line segment approximation for each subset within a given error and finally, fit each polygon line segment approximation with a conic Bezier spline. Naturally, B-spline curve can be obtained by proper knots selection. The algorithm is designed straightforward and efficient without solving any global equation system or optimal problem. It is complete with the selection of curve's weight. To design the curve more suitable for NC, we present an interval for the weight selection and the error is then computed.
Error bounded conic spline approximation for NC code
NASA Astrophysics Data System (ADS)
Shen, Liyong
2012-01-01
Curve fitting is an important preliminary work for data compression and path interpolator in numerical control (NC). The paper gives a simple conic spline approximation algorithm for G01 code. The algorithm is mainly formed by three steps: divide the G01 code to subsets by discrete curvature detection, find the polygon line segment approximation for each subset within a given error and finally, fit each polygon line segment approximation with a conic Bezier spline. Naturally, B-spline curve can be obtained by proper knots selection. The algorithm is designed straightforward and efficient without solving any global equation system or optimal problem. It is complete with the selection of curve's weight. To design the curve more suitable for NC, we present an interval for the weight selection and the error is then computed.
ERIC Educational Resources Information Center
Chang, Yu-Chia; Chang, Jason S.; Chen, Hao-Jan; Liou, Hsien-Chin
2008-01-01
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
B-spline active rays segmentation of microcalcifications in mammography
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
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.
Reconstruction of egg shape using B-spline
NASA Astrophysics Data System (ADS)
Roslan, Nurshazneem; Yahya, Zainor Ridzuan
2015-05-01
In this paper, the reconstruction of egg's outline by using piecewise parametric cubic B-spline is proposed. Reverse engineering process has been used to represent the generic shape of egg in order to acquire its geometric information in form of a two-dimensional set of points. For the curve reconstruction, the purpose is to optimize the control points of all curves such that the distance of the data points to the curve is minimized. Then, the B-spline curve functions were used for the curve fitting between the actual and the reconstructed profiles.
Comparison of various drag coefficient expansions using polynomials and splines
NASA Technical Reports Server (NTRS)
Sabot, S. M.; Winchenbach, G. L.; Chapman, G. T.
1984-01-01
The longitudinal differential equation of motion has been used to investigate various aerodynamic expansion techniques. The total drag coefficient was expanded using conventional polynomials and splines with and without floating knot locations. This paper discusses the various techniques and approaches, compares results obtained from simultaneously fitting four separate flights (time vs distance measurements) and outlines the potential advantages and/or disadvantages of the various aerodynamic expansion techniques. It is believed that this is the first time splines have been used in the aerodynamic coefficient estimation process and that these results and techniques are germane to other applications.
How to fly an aircraft with control theory and splines
NASA Technical Reports Server (NTRS)
Karlsson, Anders
1994-01-01
When trying to fly an aircraft as smoothly as possible it is a good idea to use the derivatives of the pilot command instead of using the actual control. This idea was implemented with splines and control theory, in a system that tries to model an aircraft. Computer calculations in Matlab show that it is impossible to receive enough smooth control signals by this way. This is due to the fact that the splines not only try to approximate the test function, but also its derivatives. A perfect traction is received but we have to pay in very peaky control signals and accelerations.
B-Spline Filtering for Automatic Detection of Calcification Lesions in Mammograms
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
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.
Webster, Clayton G [ORNL; Gunzburger, Max D [ORNL
2013-01-01
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.
Spline smoothing in small area trend estimation and forecasting
Maria Dolores Ugarte; T. Goicoa; Ana F. Militino; Maria Durbán
2009-01-01
Semiparametric models combining both non-parametric trends and small area random effects are now currently being investigated in small area estimation (SAE). These models can prevent bias when the functional form of the relationship between the response and the covariates is unknown. Furthermore, penalized spline regression can be a good tool to incorporate non-parametric regression models into the SAE techniques, as
Odds Ratio Estimation in Bernoulli Smoothing Spline ANOVA Models
Wang, Yuedong
Odds Ratio Estimation in Bernoulli Smoothing Spline ANOVA Models Yuedong Wang \\Lambda Department the odds ratios based on a SS ANOVA model for binary data and construct Bayesian confidence in tervals. We intervals. Our simulations suggest that the odds ratio estimates are quite reasonable in general but may
SPLINE TECHNIQUES FOR GENERATING AIRPLANE WINGS WITH PRACTICAL APPLICATIONS
to achieve realistic results near the root of the airfoil wing. Keywords: B-splines, CAGD, approximation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 INTRODUCTION In the Collaborative Research Center SFB 401, "Modulation of Flow and Fluid with an elastic model have been car- ried out. The experiments were done in the Eu- ropean Transonic Wind
Penalized spline models for functional principal component analysis
Fang Yao; Thomas C. M. Lee
2006-01-01
We propose an iterative estimation procedure for performing functional principal component analysis. The procedure aims at functional or longitudinal data where the repeated measurements from the same subject are correlated. An increasingly popular smoothing approach, penalized spline regression, is used to represent the mean function. This allows straightforward incorporation of covariates and simple implementation of approximate inference procedures for coefficients.
A ternary interpolatory subdivision schemes originated from splines
Amir Z. Averbuch; Valery A. Zheludev; Garry B. Fatakhov; Eduard H. Yakubov
A generic technique for construction of a ternary interpolatory subdivision schemes, which is based on polynomial and discrete splines, is presented. These schemes have rational symbols. The symbols are explicitly presented in the paper. This is accompa- nied by a detailed description of the design of the reflnement masks and by algorithms for verifying the convergence these schemes. In addition,
Spline Estimator for the Functional Linear Regression with Functional Response
Lubo˙s Prchal; Pascal Sarda
2007-01-01
The article is devoted to a regression setting where both, the response and the predictor, are random functions defined on some compact sets of R. We consider functional linear (auto)regression and we face the estimation of a bivariate functional parameter. Conditions for existence and uniqueness of the parameter are given and an estimator based on a B-splines expansion is proposed
date February 17, 1995 CUBIC SPLINE WAVELET BASES OF SOBOLEV
Wang, Jianzhong
of continuous space C0(I). Meanwhile, the orthogonal projections on the wavelet subspaces in H2 0 (I that a fast discrete wavelet transform (FWT) for functions in C0(I) which is different from the pyramid, Interpolation, Multilevel interpolation, Wavelet, Spline wavelets, Fast wavelet transform, Adaptive
Splines, Knots, and Penalties Paul H. C. Eilers
Marx, Brian D.
Splines, Knots, and Penalties Paul H. C. Eilers Department of Biostatistics Erasmus Medical Centre on many aspects: numerical stability, quality of the fit, interpolation/extrapolation, derivative of the basis is reduced to little more than a convenient smooth interpolation device. The penalty is the core
Nonlinear n-term Approximation from Hierarchical Spline Bases
Petrushev, Pencho
Nonlinear n-term Approximation from Hierarchical Spline Bases Pencho Petrushev This article is a survey of some recent developments which concern two multilevel approximation schemes: (a) Nonlinear n-term approximation from piecewise polynomials generated by anisotropic dyadic partitions in Rd , and (b) Nonlinear n
MULTIRESOLUTION DECOMPOSITION BASED DATA COMPRESSION WITH B-SPLINES
Gabbouj, Moncef
MULTIRESOLUTION DECOMPOSITION BASED DATA COMPRESSION WITH B-SPLINES Rusen Oktem1 , Moncef Gabbouj2email: rusen@cs.tut.#12; 2 email: moncef@cs.tut.#12; ABSTRACT A new multiresolution decomposition scheme bit rate compres- sion. 1. INTRODUCTION Multiresolution decomposition refers to analyzing an image
Radial Splines Would Prevent Rotation Of Bearing Race
NASA Technical Reports Server (NTRS)
Kaplan, Ronald M.; Chokshi, Jaisukhlal V.
1993-01-01
Interlocking fine-pitch ribs and grooves formed on otherwise flat mating end faces of housing and outer race of rolling-element bearing to be mounted in housing, according to proposal. Splines bear large torque loads and impose minimal distortion on raceway.
Adaptive knot placement in B-spline curve approximation
Weishi Li; Shuhong Xu; Gang Zhao; Li Ping Goh
2005-01-01
An adaptive knot placement algorithm for B-spline curve approximation to dense and noisy data points is presented in this paper. In this algorithm, the discrete curvature of the points is smoothed to expose the characteristics of the underlying curve. With respect to the integration of the smoothed curvature, knots are placed adaptively to satisfy a heuristic rule. Several experimental results
Driving trajectory generation of electric powered wheelchair using spline curve
Yoshimasa Teruya; Hirokazu Seki; Susumu Tadakuma
2008-01-01
This paper describes a novel smooth and stable driving trajectory generation scheme for electric powered wheelchair based on the third order spline curve. Electric powered wheelchair moved by the right and left electric motors based on the human's joystick input is expected to be widely used as a mobility support system for elderly people and disabled people. As one of
PHYSICALLY-BASED B-SPLINE SURFACE Colette J. Mullenho
Utah, University of
PHYSICALLY-BASED B-SPLINE SURFACE SCULPTING by Colette J. Mullenho A thesis submitted of Science Department of Computer Science The University of Utah December 1998 #12;Copyright c Colette J of a thesis submitted by Colette J. Mullenho This thesis has been read by each member of the following
Thin-plate spline quadrature of geodetic integrals
NASA Technical Reports Server (NTRS)
Vangysen, Herman
1989-01-01
Thin-plate spline functions (known for their flexibility and fidelity in representing experimental data) are especially well-suited for the numerical integration of geodetic integrals in the area where the integration is most sensitive to the data, i.e., in the immediate vicinity of the evaluation point. Spline quadrature rules are derived for the contribution of a circular innermost zone to Stoke's formula, to the formulae of Vening Meinesz, and to the recursively evaluated operator L(n) in the analytical continuation solution of Molodensky's problem. These rules are exact for interpolating thin-plate splines. In cases where the integration data are distributed irregularly, a system of linear equations needs to be solved for the quadrature coefficients. Formulae are given for the terms appearing in these equations. In case the data are regularly distributed, the coefficients may be determined once-and-for-all. Examples are given of some fixed-point rules. With such rules successive evaluation, within a circular disk, of the terms in Molodensky's series becomes relatively easy. The spline quadrature technique presented complements other techniques such as ring integration for intermediate integration zones.
Interpolating Mean Rainfall Using Thin Plate Smoothing Splines
M. F. Hutchinson
1995-01-01
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
Robustness properties of LQG optimized compensators for collocated rate sensors
NASA Technical Reports Server (NTRS)
Balakrishnan, A. V.
1994-01-01
In this paper we study the robustness with respect to stability of the closed-loop system with collocated rate sensor using LQG (mean square rate) optimized compensators. Our main result is that the transmission zeros of the compensator are precisely the structure modes when the actuator/sensor locations are 'pinned' and/or 'clamped': i.e., motion in the direction sensed is not allowed. We have stability even under parameter mismatch, except in the unlikely situation where such a mode frequency of the assumed system coincides with an undamped mode frequency of the real system and the corresponding mode shape is an eigenvector of the compensator transfer function matrix at that frequency. For a truncated modal model - such as that of the NASA LaRC Phase Zero Evolutionary model - the transmission zeros of the corresponding compensator transfer function can be interpreted as the structure modes when motion in the directions sensed is prohibited.
Optimal Computation of Symmetric Boolean Functions in Collocated Networks
Kowshik, Hemant
2011-01-01
We consider collocated wireless sensor networks, where each node has a Boolean measurement and the goal is to compute a given Boolean function of these measurements. We first consider the worst case setting and study optimal block computation strategies for computing symmetric Boolean functions. We study three classes of functions: threshold functions, delta functions and interval functions. We provide exactly optimal strategies for the first two classes, and a scaling law order-optimal strategy with optimal preconstant for interval functions. We also extend the results to the case of integer measurements and certain integer-valued functions. We use lower bounds from communication complexity theory, and provide an achievable scheme using information theoretic tools. Next, we consider the case where nodes measurements are random and drawn from independent Bernoulli distributions. We address the problem of optimal function computation so as to minimize the expected total number of bits that are transmitted. In ...
Defining window-boundaries for genomic analyses using smoothing spline techniques
Beissinger, Timothy M; Rosa, Guilherme JM; Kaeppler, Shawn M; Gianola, Daniel; de Leon, Natalia
2015-12-01
High-density genomic data is often analyzed by combining information over windows of adjacent markers. Interpretation of data grouped in windows versus at individual locations may increase statistical power, simplify computation, reduce sampling noise, and reduce the total number of tests performed. However, use of adjacent marker information can result in over- or under-smoothing, undesirable window boundary specifications, or highly correlated test statistics. We introduce a method for defining windows based on statistically guided breakpoints in the data, as a foundation for the analysis of multiple adjacent data points. This method involves first fitting a cubic smoothing spline to the datamore ťand then identifying the inflection points of the fitted spline, which serve as the boundaries of adjacent windows. This technique does not require prior knowledge of linkage disequilibrium, and therefore can be applied to data collected from individual or pooled sequencing experiments. Moreover, in contrast to existing methods, an arbitrary choice of window size is not necessary, since these are determined empirically and allowed to vary along the genome.Ť less
Defining window-boundaries for genomic analyses using smoothing spline techniques
Beissinger, Timothy M; Rosa, Guilherme JM; Kaeppler, Shawn M; Gianola, Daniel; de Leon, Natalia
2015-12-01
High-density genomic data is often analyzed by combining information over windows of adjacent markers. Interpretation of data grouped in windows versus at individual locations may increase statistical power, simplify computation, reduce sampling noise, and reduce the total number of tests performed. However, use of adjacent marker information can result in over- or under-smoothing, undesirable window boundary specifications, or highly correlated test statistics. We introduce a method for defining windows based on statistically guided breakpoints in the data, as a foundation for the analysis of multiple adjacent data points. This method involves first fitting a cubic smoothing spline to the data and then identifying the inflection points of the fitted spline, which serve as the boundaries of adjacent windows. This technique does not require prior knowledge of linkage disequilibrium, and therefore can be applied to data collected from individual or pooled sequencing experiments. Moreover, in contrast to existing methods, an arbitrary choice of window size is not necessary, since these are determined empirically and allowed to vary along the genome.
NASA Technical Reports Server (NTRS)
Argentiero, P.; Lowrey, B.
1976-01-01
The least squares collocation algorithm for estimating gravity anomalies from geodetic data is shown to be an application of the well known regression equations which provide the mean and covariance of a random vector (gravity anomalies) given a realization of a correlated random vector (geodetic data). It is also shown that the collocation solution for gravity anomalies is equivalent to the conventional least-squares-Stokes' function solution when the conventional solution utilizes properly weighted zero a priori estimates. The mathematical and physical assumptions underlying the least squares collocation estimator are described, and its numerical properties are compared with the numerical properties of the conventional least squares estimator.
On the interpretation of least squares collocation. [for geodetic data reduction
NASA Technical Reports Server (NTRS)
Tapley, B. D.
1976-01-01
A demonstration is given of the strict mathematical equivalence between the least squares collocation and the classical minimum variance estimates. It is shown that the least squares collocation algorithms are a special case of the modified minimum variance estimates. The computational efficiency of several forms of the general minimum variance estimation algorithm is discussed. It is pointed out that for certain geodetic applications the least square collocation algorithm may provide a more efficient formulation of the results from the point of view of the computations required.
Evaluation of the spline reconstruction technique for PET
Kastis, George A., E-mail: gkastis@academyofathens.gr; Kyriakopoulou, Dimitra [Research Center of Mathematics, Academy of Athens, Athens 11527 (Greece)] [Research Center of Mathematics, Academy of Athens, Athens 11527 (Greece); Gaitanis, Anastasios [Biomedical Research Foundation of the Academy of Athens (BRFAA), Athens 11527 (Greece)] [Biomedical Research Foundation of the Academy of Athens (BRFAA), Athens 11527 (Greece); Fernández, Yolanda [Centre dImatge Molecular Experimental (CIME), CETIR-ERESA, Barcelona 08950 (Spain)] [Centre dImatge Molecular Experimental (CIME), CETIR-ERESA, Barcelona 08950 (Spain); Hutton, Brian F. [Institute of Nuclear Medicine, University College London, London NW1 2BU (United Kingdom)] [Institute of Nuclear Medicine, University College London, London NW1 2BU (United Kingdom); Fokas, Athanasios S. [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB30WA (United Kingdom)] [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB30WA (United Kingdom)
2014-04-15
Purpose: The spline reconstruction technique (SRT), based on the analytic formula for the inverse Radon transform, has been presented earlier in the literature. In this study, the authors present an improved formulation and numerical implementation of this algorithm and evaluate it in comparison to filtered backprojection (FBP). Methods: The SRT is based on the numerical evaluation of the Hilbert transform of the sinogram via an approximation in terms of custom made cubic splines. By restricting reconstruction only within object pixels and by utilizing certain mathematical symmetries, the authors achieve a reconstruction time comparable to that of FBP. The authors have implemented SRT in STIR and have evaluated this technique using simulated data from a clinical positron emission tomography (PET) system, as well as real data obtained from clinical and preclinical PET scanners. For the simulation studies, the authors have simulated sinograms of a point-source and three digital phantoms. Using these sinograms, the authors have created realizations of Poisson noise at five noise levels. In addition to visual comparisons of the reconstructed images, the authors have determined contrast and bias for different regions of the phantoms as a function of noise level. For the real-data studies, sinograms of an{sup 18}F-FDG injected mouse, a NEMA NU 4-2008 image quality phantom, and a Derenzo phantom have been acquired from a commercial PET system. The authors have determined: (a) coefficient of variations (COV) and contrast from the NEMA phantom, (b) contrast for the various sections of the Derenzo phantom, and (c) line profiles for the Derenzo phantom. Furthermore, the authors have acquired sinograms from a whole-body PET scan of an {sup 18}F-FDG injected cancer patient, using the GE Discovery ST PET/CT system. SRT and FBP reconstructions of the thorax have been visually evaluated. Results: The results indicate an improvement in FWHM and FWTM in both simulated and real point-source studies. In all simulated phantoms, the SRT exhibits higher contrast and lower bias than FBP at all noise levels, by increasing the COV in the reconstructed images. Finally, in real studies, whereas the contrast of the cold chambers are similar for both algorithms, the SRT reconstructed images of the NEMA phantom exhibit slightly higher COV values than those of FBP. In the Derenzo phantom, SRT resolves the 2-mm separated holes slightly better than FBP. The small-animal and human reconstructions via SRT exhibit slightly higher resolution and contrast than the FBP reconstructions. Conclusions: The SRT provides images of higher resolution, higher contrast, and lower bias than FBP, by increasing slightly the noise in the reconstructed images. Furthermore, it eliminates streak artifacts outside the object boundary. Unlike other analytic algorithms, the reconstruction time of SRT is comparable with that of FBP. The source code for SRT will become available in a future release of STIR.
Segmenting echocardiography images using B-Spline snake and active ellipse model.
Marsousi, Mahdi; Alirezaie, Javad; Ahmadian, Alireza; Kocharian, Armen
2010-01-01
In this paper, a fully automated method for segmenting Left Ventricle (LV) in echocardiography images is proposed. A new method named active ellipse model is developed to automatically find the best ellipse inside the LV chamber without intervention of any specialist. A modified B-Spline Snake algorithm is used to segment the LV chamber in which the initial contour is formed by the predefined ellipse. As a result of using active ellipse model, the segmentation is extricated from dealing with gaps within myocardium boundary which are highly problematic in echocardiography image segmentation. Based on the results obtained from different studies, the proposed method is faster and more accurate than previous approaches. Our method is evaluated on 20 sets of echocardiography images of patients; and acquired results (92.30 ą 4.45% dice's coefficient) indicate the proposed method has remarkable performance. PMID:21095747
Change detection of lung cancer using image registration and thin-plate spline warping
NASA Astrophysics Data System (ADS)
Almasslawi, Dawood M. S.; Kabir, Ehsanollah
2011-06-01
Lung cancer has the lowest survival rate comparing to other types of cancer and determination of the patient's cancer stage is the most vital issue regarding the cancer treatment process. In most cases accurate estimation of the cancer stage is not easy to achieve. The changes in the size of the primary tumor can be detected using image registration techniques. The registration method proposed in this paper uses Normalized Mutual Information metric and Thin-Plate Spline transformation function for the accurate determination of the correspondence between series of the lung cancer Computed Tomography images. The Normalized Mutual Information is used as a metric for the rigid registration of the images to better estimate the global motion of the tissues and the Thin Plate Spline is used to deform the image in a locally supported manner. The Control Points needed for the transformation are extracted semiautomatically. This new approach in change detection of the lung cancer is implemented using the Insight Toolkit. The results from implementing this method on the CT images of 8 patients provided a satisfactory quality for change detection of the lung cancer.
Brown, C; Adcock, A; Azevedo, S; Liebman, J; Bond, E
2010-12-28
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, time-varying, 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.
NASA Astrophysics Data System (ADS)
Koch, K.
2011-09-01
To build up a 3D (three-dimensional) model of the surface of an object, the heights of points on the surface are measured, for instance, by a laser scanner. The intensities of the reflected laser beam of the points can be used to visualize the 3D model as range image. It is proposed here to fit a two-dimensional B-spline surface to the measured heights and intensities by the lofting method. To fully use the geometric information of the laser scanning, points on the fitted surface with their intensities are computed with a density higher than that of the measurements. This gives a 3D model of high resolution which is visualized by the intensities of the points on the B-spline surface. For a realistic view of the 3D model, the coordinates of a digital photo of the object are transformed to the coordinate system of the 3D model so that the points get the colors of the digital image. To efficiently compute and store the 3D model, data compression is applied. It is derived from the multi-scale representation of the dense grid of points on the B-spline surface. The proposed method is demonstrated for an example.
NASA Astrophysics Data System (ADS)
Brown, Charles G., Jr.; Adcock, Aaron B.; Azevedo, Stephen G.; Liebman, Judith A.; Bond, Essex J.
2011-03-01
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.
Sun, Weiwei; Huang, Weizhang; Russell, Robert D.
1996-12-01
A technique to construct a low-order finite difference preconditioner for solving orthogonal collocation equations for boundary value problems is presented. It is shown numerically and theoretically that the spectral condition numbers...
High-order compact solution of the one-dimensional heat and advectiondiffusion equations
Akbar Mohebbi; Mehdi Dehghan
2010-01-01
In this work, we propose a high-order accurate method for solving the one-dimensional heat and advectiondiffusion equations. We apply a compact finite difference approximation of fourth-order for discretizing spatial derivatives of these equations and the cubic C1-spline collocation method for the resulting linear system of ordinary differential equations. The cubic C1-spline collocation method is an A-stable method for time integration
Non-rigid surface registration using spherical thin-plate splines.
Zou, Guangyu; Hua, Jing; Muzik, Otto
2007-01-01
Accurate registration of cortical structures plays a fundamental role in statistical analysis of brain images across population. This paper presents a novel framework for the non-rigid intersubject brain surface registration, using conformal structure and spherical thin-plate splines. By resorting to the conformal structure, complete characteristics regarding the intrinsic cortical geometry can be retained as a mean curvature function and a conformal factor function defined on a canonical, spherical domain. In this transformed space, spherical thin-plate splines are firstly used to explicitly match a few prominent homologous landmarks, and in the meanwhile, interpolate a global deformation field. A post-optimization procedure is then employed to further refine the alignment of minor cortical features based on the geometric parameters preserved on the domain. Our experiments demonstrate that the proposed framework is highly competitive with others for brain surface registration and population-based statistical analysis. We have applied our method in the identification of cortical abnormalities in PET imaging of patients with neurological disorders and accurate results are obtained. PMID:18051080
Ahn, W.; Anderson, K.S.; De, S.
2013-01-01
An interpolating spline-based approach is presented for modeling multi-flexible-body systems in the divide-and-conquer (DCA) scheme. This algorithm uses the floating frame of reference formulation and piecewise spline functions to construct and solve the non-linear equations of motion of the multi-flexible-body system undergoing large rotations and translations. The new approach is compared with the flexible DCA (FDCA) that uses the assumed modes method [1]. The FDCA, in many cases, must resort to sub-structuring to accurately model the deformation of the system. We demonstrate, through numerical examples, that the interpolating spline-based approach is comparable in accuracy and superior in efficiency to the FDCA. The present approach is appropriate for modeling flexible mechanisms with thin 1D bodies undergoing large rotations and translations, including those with irregular shapes. As such, the present approach extends the current capability of the DCA to model deformable systems. The algorithm retains the theoretical logarithmic complexity inherent in the DCA when implemented in parallel. PMID:24124265
Optimal aeroassisted orbital transfer with plane change using collocation and nonlinear programming
NASA Technical Reports Server (NTRS)
Shi, Yun. Y.; Nelson, R. L.; Young, D. H.
1990-01-01
The fuel optimal control problem arising in the non-planar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) with orbital plane change. The basic strategy here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the aeroassisted HEO to LEO transfer consists of three phases. In the first phase, the orbital transfer begins with a deorbit impulse at HEO which injects the vehicle into an elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and bank angle modulations to perform the desired orbital plane change and to satisfy heating constraints. Because of the energy loss during the turn, an impulse is required to initiate the third phase to boost the vehicle back to the desired LEO orbital altitude. The third impulse is then used to circularize the orbit at LEO. The problem is solved by a direct optimization technique which uses piecewise polynomial representation for the state and control variables and collocation to satisfy the differential equations. This technique converts the optimal control problem into a nonlinear programming problem which is solved numerically. Solutions were obtained for cases with and without heat constraints and for cases of different orbital inclination changes. The method appears to be more powerful and robust than other optimization methods. In addition, the method can handle complex dynamical constraints.
Cubic spline wavelets with short support adapted to the interval
NASA Astrophysics Data System (ADS)
?erná, Dana; Fin?k, Václav
2013-12-01
Wavelets with the short support and with vanishing moments which form well-conditioned basis are of interest for solving differential equations numerically. The condition number of wavelet bases on the interval depends on the length of the support and it can be further significantly influenced by a proper construction of boundary wavelets. Few years ago, B. Han and Z. Shen constructed Riesz wavelet bases of the space L2(R) with the shortest possible support and with m vanishing moments based on B-spline of order m. In this contribution, we start with their another wavelet with two vanishing moments based on cubic B-splines and propose an adaptation of this basis to the interval.
Cubic spline wavelets with short support adapted to the interval
NASA Astrophysics Data System (ADS)
?erná, Dana; Fin?k, Václav
2013-12-01
Wavelets with the short support and with vanishing moments which form well-conditioned basis are of interest for solving differential equations numerically. The condition number of wavelet bases on the interval depends on the length of the support and it can be further significantly influenced by a proper construction of boundary wavelets. Few years ago, B. Han and Z. Shen constructed Riesz wavelet bases of the space L(R) with the shortest possible support and with m vanishing moments based on B-spline of order m. In this contribution, we start with their another wavelet with two vanishing moments based on cubic B-splines and propose an adaptation of this basis to the interval.
Hybrid physics-based elastic image registration using approximating splines
NASA Astrophysics Data System (ADS)
Wörz, Stefan; Rohr, Karl
2008-03-01
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 well as a regularization based on GEBS. We also include landmark localization uncertainties represented by weight matrices. Since the approach is based on a physical deformation model, cross-effects in elastic deformations can be handled. We demonstrate the applicability of our scheme based on MR images of the human brain. It turns out that the new scheme is superior to a pure landmark-based as well as a pure intensity-based scheme.
Variational Splines and PaleyWiener Spaces on Combinatorial Graphs
Isaac Pesenson
2009-01-01
Notions of interpolating variational splines and PaleyWiener 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 PaleyWiener functions on graphs from their
B-spline snakes: a flexible tool for parametric contour detection
Patrick Brigger; Jeff Hoeg; Michael Unser
2000-01-01
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
Band Decomposition of Voice Signals Using Wavelets Defined from Fractional B-spline Functions
Annamaria Mesaros; Simina Moldovan; E. Lupu
2006-01-01
The B-spline functions constitute a good mathematical background for defining new wavelets. The fractional B-splines provide the only wavelets that have an explicit analytical form, making the mathematical manipulations easier. This paper proposes a decomposition of the voice signal into hierarchical octave bands, by using a fractional B-spline based wavelet decomposition. The proposed decomposition scheme takes into account the location
Gear Geometric Design by B-Spline Curve Fitting and Sweep Surface Modelling
S. Barone
2001-01-01
In this paper, B-spline curve fitting and sweep surface generation are used for the geometric design of involute gears. Tooth\\u000a profiles are described by a B-spline formulation based on interpolating data points with first and second derivative constrains.\\u000a Tooth surfaces are generated by sweeping the B-spline profiles along specified trajectories. This representation scheme enables\\u000a tooth shapes to be inter-actively controlled
Smoothing and interpolation by kriging and with splines
G. S. Watson
1984-01-01
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
Optimization of a Spline-Shaped UWB Antenna by PSO
Leonardo Lizzi; Federico Viani; Renzo Azaro; Andrea Massa
2007-01-01
This letter presents the design of a planar antenna for ultrawideband (UWB) applications with a bandwidth of 5.5 GHz over 3.7 to 9.2 GHz and return loss values lower than -10 dB. The antenna geometry is described in terms of a spline-based representation whose control parameters, together with other geometrical descriptive quantities, are determined through a suitable particle swarm optimizer
A rational trigonometric spline to visualize positive data
NASA Astrophysics Data System (ADS)
Bashir, Uzma; Ali, Jamaludin Md.
2014-07-01
In this paper, we construct a cubic trigonometric Bézier curve with two shape parameters on the basis of cubic trigonometric Bernstein-like blending functions. The proposed curve has all geometric properties of the ordinary cubic Bézier curve. Later, based on these trigonometric blending functions a C1 rational trigonometric spline with four shape parameters to preserve positivity of positive data is generated. Simple data dependent constraints are developed for these shape parameters to get a graphically smooth and visually pleasant curve.
Mining Standard Land Price with Tension Spline Function
Hanning Yuan; Wenzhong Shi; Jiabing Sun
2005-01-01
\\u000a Standard land price is an economical indicator for measuring land value. In this paper, we propose to use the tension spline\\u000a interpolation function to mine standard land price. First, we extend the definition of standard land price, which is based\\u000a on land region composed of several neighboring land parcels with the same or similar features. Second, the regional factors\\u000a that
Control theory and splines, applied to signature storage
NASA Technical Reports Server (NTRS)
Enqvist, Per
1994-01-01
In this report the problem we are going to study is the interpolation of a set of points in the plane with the use of control theory. We will discover how different systems generate different kinds of splines, cubic and exponential, and investigate the effect that the different systems have on the tracking problems. Actually we will see that the important parameters will be the two eigenvalues of the control matrix.
An auroral scintillation observation using precise, collocated GPS receivers
NASA Astrophysics Data System (ADS)
Garner, T. W.; Harris, R. B.; York, J. A.; Herbster, C. S.; Minter, C. F., III; Hampton, D. L.
2011-02-01
On 10 January 2009, an unusual ionospheric scintillation event was observed by a Global Positioning System (GPS) receiver station in Fairbanks, Alaska. The receiver station is part of the National Geospatial-Intelligence Agency's (NGA) Monitoring Station Network (MSN). Each MSN station runs two identical geodetic-grade, dual-frequency, full-code tracking GPS receivers that share a common antenna. At the Fairbanks station, a third separate receiver with a separate antenna is located nearby. During the 10 January event, ionospheric conditions caused two of the receivers to loose lock on a single satellite. The third receiver tracked through the scintillation. The region of scintillation was collocated with an auroral arc and a slant total electron content (TEC) increase of 5.71 TECu (TECu = 1016/m2). The response of the full-code tracking receivers to the scintillation is intriguing. One of these receivers lost lock, but the other receiver did not. This fact argues that a receiver's internal state dictates its reaction to scintillation. Additionally, the scintillation only affected the L2 signal. While this causes the L1 signal to be lost on the semicodelessly receiver, the full-code tracking receiver only lost the L1 signal when the receiver attempted to reacquire the satellite link.
Full-turn symplectic map from a generator in a Fourier-spline basis
NASA Astrophysics Data System (ADS)
Berg, J. S.; Warnock, R. L.; Ruth, R. D.; Forest, É.
1993-12-01
Given an arbitrary symplectic tracking code, one can construct a full-turn symplectic map that approximates the result of the code to high accuracy. The map is defined implicitly by a mixed-variable generating function. The implicit definition is no great drawback in practice, thanks to an efficient use of Newton's method to solve for the explicit map at each iteration. The generator is represented by a Fourier series in angle variables, with coefficients given as B-spline functions of action variables. It is constructed by using results of single-turn tracking from many initial conditions. The method has been applied to a realistic model of the SSC in three degrees of freedom. Orbits can be mapped symplectically for 107 turns on an IBM RS6000 model 320 workstation, in a run of about one day.
A New Fuzzy Vault Method Using Cubic Spline Interpolation
Hailun Liu; Dongmei Sun; Ke Xiong; Zhengding Qiu
2010-01-01
Biometric cryptosystem has emerged as a promising solution in information security. Fuzzy vault is a widely accepted scheme binding biometric data and cryptography effectively. Polynomial projection is often used in the implementation of fuzzy vault. However, the drawback of polynomial projection is that the increase of key length would lead to a higher degree of polynomial, reconstruction of which would
NASA Astrophysics Data System (ADS)
Erdogan, Eren; Dettmering, Denise; Limberger, Marco; Schmidt, Michael; Seitz, Florian; Börger, Klaus; Brandert, Sylvia; Görres, Barbara; Kersten, Wilhelm F.; Bothmer, Volker; Hinrichs, Johannes; Venzmer, Malte
2015-04-01
In May 2014 DGFI-TUM (the former DGFI) and the German Space Situational Awareness Centre (GSSAC) started to develop an OPerational Tool for Ionospheric Mapping And Prediction (OPTIMAP); since November 2014 the Institute of Astrophysics at the University of Göttingen (IAG) joined the group as the third partner. This project aims on the computation and prediction of maps of the vertical total electron content (VTEC) and the electron density distribution of the ionosphere on a global scale from both various space-geodetic observation techniques such as GNSS and satellite altimetry as well as Sun observations. In this contribution we present first results, i.e. a near-real time processing framework for generating VTEC maps by assimilating GNSS (GPS, GLONASS) based ionospheric data into a two-dimensional global B-spline approach. To be more specific, the spatial variations of VTEC are modelled by trigonometric B-spline functions in longitude and by endpoint-interpolating polynomial B-spline functions in latitude, respectively. Since B-spline functions are compactly supported and highly localizing our approach can handle large data gaps appropriately and, thus, provides a better approximation of data with heterogeneous density and quality compared to the commonly used spherical harmonics. The presented method models temporal variations of VTEC inside a Kalman filter. The unknown parameters of the filter state vector are composed of the B-spline coefficients as well as the satellite and receiver DCBs. To approximate the temporal variation of these state vector components as part of the filter the dynamical model has to be set up. The current implementation of the filter allows to select between a random walk process, a Gauss-Markov process and a dynamic process driven by an empirical ionosphere model, e.g. the International Reference Ionosphere (IRI). For running the model ionospheric input data is acquired from terrestrial GNSS networks through online archive systems (such as IGS) with approximately one hour latency. Before feeding the filter with new hourly data, the raw GNSS observations are downloaded and pre-processed via geometry free linear combinations to provide signal delay information including the ionospheric effects and the differential code biases. Next steps will implement further space geodetic techniques and will introduce the Sun observations into the procedure. The final destination is to develop a time dependent model of the electron density based on different geodetic and solar observations.
Fast construction of accurate quaternion splines
Ravi Ramamoorthi; Alan H. Barr
1997-01-01
In 1992, Barr et al. proposed a method for interpolating orien- tations with unit quaternion curves by minimizing covariant ac- celeration. This paper presents a simple improved method which uses cubic basis functions to achieve a speedup of up to three orders of magnitude. A new criterion for automatic refinement based on the Euler-Lagrange error functional is also introduced.
Calculation of laminar flows with second-order schemes and collocated variable arrangement
NASA Astrophysics Data System (ADS)
Biagioli, Fernando
1998-04-01
A numerical study of laminar flows is carried out to examine the performance of two second-order discretization schemes: a total variation diminishing scheme and a second-order upwind scheme. The former has the same form as the standard first-order hybrid central upwind scheme, but with a numerical diffusion reduced by the Van Leer limiter; the latter is based on the linear extrapolation of cell face values using the two upwind neighbors. A collocated grid arrangement is used; oscillations which could be generated by pressure-velocity decoupling are avoided via the Rhie-Chow interpolation. Two iterative solution methods are used: (i) the deferred correction procedure proposed by Khosla and Rubin and (ii) implicit treatment of the second-order upwind contribution. Three two-dimensional laminar test cases are considered for assessment: the plane lid-driven cavity, the plane backward facing step and the axisymmetric pipe with sudden contraction. Experimental data are available for the two last cases. Both the total variation diminishing and the second-order upwind schemes give wiggle-free results and can predict the flowfields more accurately than the standard first-order hybrid central upwind scheme.
TWO-LEVEL TIME MARCHING SCHEME USING SPLINES FOR SOLVING THE ADVECTION EQUATION. (R826371C004)
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...
Grid spacing control with variation diminishing splines
NASA Technical Reports Server (NTRS)
Smith, P. W.
1983-01-01
Methods used to specify and control two and three dimensional grids on which numerical solutions of partial differential equations may be obtained were studied. While initially focusing on grid generation, the research will evolve into a consideration of the interaction of grid generation with the solution of a partial differential equation. The multisurface method of grid generation was used to continuously patch a grid onto an existing grid. In the resulting grid the elements of the Jacobian matrix must be continuous across the boundary between the original grid and the patched grid. Programs were written which accept as input the coordinates of the original grid and the desired new boundary, and then use the three-surface or four-surface version of the multisurface method to extend the original grid out to a new boundary.
Recommended practices for spline usage in CAD/CAM systems: CADCAM-007
Fletcher, S.K.
1984-04-01
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.
Viola, Francesco; Coe, Ryan L.; Owen, Kevin; Guenther, Drake A.; Walker, William F.
2008-01-01
Image registration and motion estimation play central roles in many fields, including RADAR, SONAR, light microscopy, and medical imaging. Because of its central significance, estimator accuracy, precision, and computational cost are of critical importance. We have previously presented a highly accurate, spline-based time delay estimator that directly determines sub-sample time delay estimates from sampled data. The algorithm uses cubic splines to produce a continuous representation of a reference signal and 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 describe the MUlti-dimensional Spline-based Estimator (MUSE) that allows accurate and precise estimation of multidimensional displacements/strain components from multidimensional data sets. We describe the mathematical formulation for two- and three-dimensional motion/strain estimation and present simulation results to assess the intrinsic bias and standard deviation of this algorithm and compare it to currently available multi-dimensional estimators. In 1000 noise-free simulations of ultrasound data we found that 2D MUSE exhibits maximum bias of 2.6 × 10?4 samples in range and 2.2 × 10?3 samples in azimuth (corresponding to 4.8 and 297 nm, respectively). The maximum simulated standard deviation of estimates in both dimensions was comparable at roughly 2.8 × 10?3 samples (corresponding to 54 nm axially and 378 nm laterally). These results are between two and three orders of magnitude better than currently used 2D tracking methods. Simulation of performance in 3D yielded similar results to those observed in 2D. We also present experimental results obtained using 2D MUSE on data acquired by an Ultrasonix Sonix RP imaging system with an L14-5/38 linear array transducer operating at 6.6 MHz. While our validation of the algorithm was performed using ultrasound data, MUSE is broadly applicable across imaging applications. PMID:18807190
Multi-dimensional spline-based non-rigid image registration
NASA Astrophysics Data System (ADS)
Viola, Francesco; Guenther, Drake A.; Coe, Ryan L.; Walker, William F.
2007-03-01
Image registration, or equivalently motion estimation, plays a central role in a broad range of ultrasound applications including elastography, estimation of blood or tissue motion, radiation force imaging, and extended field of view imaging. Because of its central significance, motion estimation accuracy, precision, and computational cost are of critical importance. Furthermore, since motion estimation is typically performed on sampled signals, while estimates are usually desired over a continuous domain, performance should be considered in conjunction with associated interpolation. We have previously presented a highly accurate, spline-based time delay estimator 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 and 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 describe a MUlti-dimensional Spline-based Estimator (MUSE) that allows accurate and precise estimation of multi-dimensional displacements/strain components from multi-dimensional data sets. In this paper we describe the mathematical formulation for three-dimensional (3D) motion/strain estimation and present simulation results to assess the intrinsic bias and standard deviation of this algorithm and compare it to currently available multi-dimensional estimators. In 1,000 noise-free simulations we found that 2D MUSE exhibits maximum bias errors of 4.8nm and 297nm in range and azimuth respectively. The maximum simulated standard deviation of estimates in both dimensions was comparable at 0.0026 samples (corresponding to 54nm axially and 378nm laterally). These results are two to three orders of magnitude lower than currently used 2D tracking methods. Simulation of performance in 3D yielded similar results to those observed in 2D. We also performed experiments using 2D MUSE on an Ultrasonix Sonix RP imaging system with an L14-5/38 linear array transducer operating at 6.6MHz. With this experimental data we found that bias errors were significantly smaller than geometric errors induced by machining of the transducer mount.
ERIC Educational Resources Information Center
Krummes, Cedric; Ensslin, Astrid
2015-01-01
Whereas there exists a plethora of research on collocations and formulaic language in English, this article contributes towards a somewhat less developed area: the understanding and teaching of formulaic language in German as a foreign language. It analyses formulaic sequences and collocations in German writing (corpus-driven) and provides modern
Convergence of spectral methods for hyperbolic initial-boundary value systems
NASA Technical Reports Server (NTRS)
Gottlieb, D.; Lustman, L.; Tadmor, E.
1986-01-01
A convergence proof for spectral approximations is presented for hyperbolic systems with initial and boundary conditions. The Chebyshev collocation is treated in detail, but the final result is readily applicable to other spectral methods, such as Legendre collocation or tau-methods.
COLLINARUS: collection of image-derived non-linear attributes for registration using splines
NASA Astrophysics Data System (ADS)
Chappelow, Jonathan; Bloch, B. Nicolas; Rofsky, Neil; Genega, Elizabeth; Lenkinski, Robert; DeWolf, William; Viswanath, Satish; Madabhushi, Anant
2009-02-01
We present a new method for fully automatic non-rigid registration of multimodal imagery, including structural and functional data, that utilizes multiple texutral feature images to drive an automated spline based non-linear image registration procedure. Multimodal image registration is significantly more complicated than registration of images from the same modality or protocol on account of difficulty in quantifying similarity between different structural and functional information, and also due to possible physical deformations resulting from the data acquisition process. The COFEMI technique for feature ensemble selection and combination has been previously demonstrated to improve rigid registration performance over intensity-based MI for images of dissimilar modalities with visible intensity artifacts. Hence, we present here the natural extension of feature ensembles for driving automated non-rigid image registration in our new technique termed Collection of Image-derived Non-linear Attributes for Registration Using Splines (COLLINARUS). Qualitative and quantitative evaluation of the COLLINARUS scheme is performed on several sets of real multimodal prostate images and synthetic multiprotocol brain images. Multimodal (histology and MRI) prostate image registration is performed for 6 clinical data sets comprising a total of 21 groups of in vivo structural (T2-w) MRI, functional dynamic contrast enhanced (DCE) MRI, and ex vivo WMH images with cancer present. Our method determines a non-linear transformation to align WMH with the high resolution in vivo T2-w MRI, followed by mapping of the histopathologic cancer extent onto the T2-w MRI. The cancer extent is then mapped from T2-w MRI onto DCE-MRI using the combined non-rigid and affine transformations determined by the registration. Evaluation of prostate registration is performed by comparison with the 3 time point (3TP) representation of functional DCE data, which provides an independent estimate of cancer extent. The set of synthetic multiprotocol images, acquired from the BrainWeb Simulated Brain Database, comprises 11 pairs of T1-w and proton density (PD) MRI of the brain. Following the application of a known warping to misalign the images, non-rigid registration was then performed to recover the original, correct alignment of each image pair. Quantitative evaluation of brain registration was performed by direct comparison of (1) the recovered deformation field to the applied field and (2) the original undeformed and recovered PD MRI. For each of the data sets, COLLINARUS is compared with the MI-driven counterpart of the B-spline technique. In each of the quantitative experiments, registration accuracy was found to be significantly (p < 0.05) for COLLINARUS compared with MI-driven B-spline registration. Over 11 slices, the mean absolute error in the deformation field recovered by COLLINARUS was found to be 0.8830 mm.
Koch, M. [Florida State Univ., Tallahasse, FL (United States)
1995-12-31
A new mesh-adaptive 1D collocation technique has been developed to efficiently solve transient advection-dominated transport problems in porous media that are governed by a hyperbolic/parabolic (singularly perturbed) PDE. After spatial discretization a singularly perturbed ODE is obtained which is solved by a modification of the COLNEW ODE-collocation code. The latter also contains an adaptive mesh procedure that has been enhanced here to resolve linear and nonlinear transport flow problems with steep fronts where regular FD and FE methods often fail. An implicit first-order backward Euler and a third-order Taylor-Donea technique are employed for the time integration. Numerical simulations on a variety of high Peclet-number transport phenomena as they occur in realistic porous media flow situations are presented. Examples include classical linear advection-diffusion, nonlinear adsorption, two-phase Buckley-Leverett flow without and with capillary forces (Rapoport-Leas equation) and Burgers` equation for inviscid fluid flow. In most of these examples sharp fronts and/or shocks develop which are resolved in an oscillation-free manner by the present adaptive collocation method. The backward Euler method has some amount of numerical dissipation is observed when the time-steps are too large. The third-order Taylor-Donea technique is less dissipative but is more prone to numerical oscillations. The simulations show that for the efficient solution of nonlinear singularly perturbed PDE`s governing flow transport a careful balance must be struck between the optimal mesh adaptation, the nonlinear iteration method and the time-stepping procedure. More theoretical research is needed with this regard.
Collocated Microstrip Antennas for MIMO Systems With a Low Mutual Coupling Using Mode Confinement
J. Sarrazin; Y. Mahe; S. Avrillon; S. Toutain
2010-01-01
Collocated antennas for mutiple input multiple output (MIMO) systems are presented. The structure is composed of a dual-polarized microstrip square patch combined to a dual-polarized microstrip square ring. Consequently, four different radiation patterns are available simultaneously. With a length of about one guided wavelength, the proposed structure is well suited to reduce the MIMO terminal size. The structure operates in
Greenberg, Saul
find and verify defects along with their associated fixes. Because of the large number and broad rangeCommunication, Collaboration, and Bugs: The Social Nature of Issue Tracking in Small, Collocated.greenberg, walker}@ucalgary.ca ABSTRACT Issue tracking systems help organizations manage issue reporting, assignment
Zender, Charles
aircraft measurements Robert D. Cess,1 Minghua Zhang,1 Francisco P. J. Valero,2 Shelly K. Pope,2 Anthony the interpretations made in two prior studies of the aircraft shortwave radiation measurements that were obtained from two collocated aircraft, an upper aircraft flying above the clouds at an altitude of roughly 14 km
Collocation in Regional Development--The Peel Education and TAFE Response.
ERIC Educational Resources Information Center
Goff, Malcolm H.; Nevard, Jennifer
The collocation of services in regional Western Australia (WA) is an important strand of WA's regional development policy. The initiative is intended to foster working relationships among stakeholder groups with a view toward ensuring that regional WA communities have access to quality services. Clustering compatible services in smaller
EVIDENCE OF THE WEST SAKHALIN CURRENT IN ERS-2 AND ENVISAT COLLOCATED SAR IMAGES
V. A. Dubina; L. M. Mitnik
Collocated ERS-2 SAR and Envisat ASAR images acquired on 4 October 2003 with time difference of about 28 min have trapped the West Sakhalin Current (WSC) during its maximum intensity. The current was observed as a narrow strip the width of about 15 km adjacent to the northwestern Sakhalin coast. Backscatter contrasts in the convergence region between the Tsushima Current
Strategies in Translating Collocations in Religious Texts from Arabic into English
ERIC Educational Resources Information Center
Dweik, Bader S.; Shakra, Mariam M. Abu
2010-01-01
The present study investigated the strategies adopted by students in translating specific lexical and semantic collocations in three religious texts namely, the Holy Quran, the Hadith and the Bible. For this purpose, the researchers selected a purposive sample of 35 MA translation students enrolled in three different public and private Jordanian
Jones, Alan G.
observations: Great Slave Lake shear zone, northern Canada David W. Eaton,1 Alan G. Jones,2,3 and Ian J the Great Slave Lake shear zone, northern Canada, investigated lithospheric anisotropy and tested structure inferred from collocated teleseismic and magnetotelluric observations: Great Slave Lake shear zone
Paris-Sud XI, Université de
Security Awareness in Virtual Communities: The Case of Non-collocated Academic Research the security risk factor linked with virtual collaboration. This study examines the security awareness settings. The paper suggests that a security awareness program aimed at academics should be initiated
EFFICIENT UNCERTAINTY QUANTIFICATION USING A TWO-STEP APPROACH WITH CHAOS COLLOCATION
Alex Loeveny; Jeroen Witteveen; Hester Bijl
2006-01-01
In this paper a Two Step approach with Chaos Collocation for ecient uncer- tainty quantic ation in computational uid-structur e interactions is followed. In Step I, a Sensitivity Analysis is used to eciently narrow the problem down from multiple uncertain parameters to one parameter which has the largest inuenc e on the solution. In Step II, for this most important
Evaluating Remotely-Sensed Surface Soil Moisture Estimates Using Triple Collocation
Technology Transfer Automated Retrieval System (TEKTRAN)
Recent work has demonstrated the potential of enhancing remotely-sensed surface soil moisture validation activities through the application of triple collocation techniques which compare time series of three mutually independent geophysical variable estimates in order to acquire the root-mean-square...
Collocation and inversion for a reentry optimal control problem Tobias NECKEL 1
vector fields and functions are smooth functions. It is desired to find a trajectory of (1) [t0, tfCollocation and inversion for a reentry optimal control problem Tobias NECKEL 1 Christophe TALBOT 2 trajectory optimization as an enabling technology for versatile real-time trajectory gen- eration
Collocational Differences between L1 and L2: Implications for EFL Learners and Teachers
ERIC Educational Resources Information Center
Sadeghi, Karim
2009-01-01
Collocations are one of the areas that produce problems for learners of English as a foreign language. Iranian learners of English are by no means an exception. Teaching experience at schools, private language centers, and universities in Iran suggests that a significant part of EFL learners' problems with producing the language, especially at
ERIC Educational Resources Information Center
Sonbul, Suhad; Schmitt, Norbert
2013-01-01
To date, there has been little empirical research exploring the relationship between implicit and explicit lexical knowledge (of collocations). As a first step in addressing this gap, two laboratory experiments were conducted that evaluate different conditions (enriched, enhanced, and decontextualized) under which both adult native speakers
Shape Control of Plates with Piezo Actuators and Collocated Position/Rate Sensors
NASA Technical Reports Server (NTRS)
Balakrishnan, A. V.
1994-01-01
This paper treats the control problem of shaping the surface deformation of a circular plate using embedded piezo-electric actuator and collocated rate sensors. An explicit Linear Quadratic Gaussian (LQG) optimizer stability augmentation compensator is derived as well as the optimal feed-forward control. Corresponding performance evaluation formulas are also derived.
Shape Control of Plates with Piezo Actuators and Collocated Position/Rate Sensors
NASA Technical Reports Server (NTRS)
Balakrishnan, A. V.
1994-01-01
This paper treats the control problem of shaping the surface deformation of a circular plate using embedded piezo-electric actuators and collocated rate sensors. An explicit Linear Quadratic Gaussian (LQG) optimizer stability augmentation compensator is derived as well as the optimal feed-forward control. Corresponding performance evaluation formulas are also derived.
Utilizing Lexical Data from a Web-Derived Corpus to Expand Productive Collocation Knowledge
ERIC Educational Resources Information Center
Wu, Shaoqun; Witten, Ian H.; Franken, Margaret
2010-01-01
Collocations are of great importance for second language learners, and a learner's knowledge of them plays a key role in producing language fluently (Nation, 2001: 323). In this article we describe and evaluate an innovative system that uses a Web-derived corpus and digital library software to produce a vast concordance and present it in a way
The thirteenth AAAI Mobile Robot Competition and Exhibition was once again collocated with
Maxwell, Bruce
, deployed two robots con- trolled by a single operator to explore the are- nas. The Swarthmore team's human-robot and micro- phones, the PARC team's robots were the only robots to explore the extremely confined spaces The thirteenth AAAI Mobile Robot Competition and Exhibition was once again collocated with AAAI
NASA Technical Reports Server (NTRS)
Phillips, J. R.
1996-01-01
In this paper we derive error bounds for a collocation-grid-projection scheme tuned for use in multilevel methods for solving boundary-element discretizations of potential integral equations. The grid-projection scheme is then combined with a precorrected FFT style multilevel method for solving potential integral equations with 1/r and e(sup ikr)/r kernels. A complexity analysis of this combined method is given to show that for homogeneous problems, the method is order n natural log n nearly independent of the kernel. In addition, it is shown analytically and experimentally that for an inhomogeneity generated by a very finely discretized surface, the combined method slows to order n(sup 4/3). Finally, examples are given to show that the collocation-based grid-projection plus precorrected-FFT scheme is competitive with fast-multipole algorithms when considering realistic problems and 1/r kernels, but can be used over a range of spatial frequencies with only a small performance penalty.
B-splines as a basis for the Rayleigh-Ritz-Galerkin procedure
Snodgrass, Jerry Grant
1975-01-01
($, $) ? 2a(u, g) + a(u, u) = a(&-u, d-u) 2 & Y f / D(u-4) f f ' 2 Q with equality if and only if u = $; therefore, u is the unique solution of the variational problem. Q. E. D. 3. ~Ra leigh-Ritz Procedure To approximate the solution of (1) ? (2.... Normalized quadratic B-spline, N , unequally spaced knots. 1-3 T6 T7 F&G. 9. Normalized quadratic B-spline, N , unequally spaced knots. 1-3 FIG. 10. Normalized quadratic B-spline, N , unequally spaced knots. 2Ci CHAPTER IV COl~d'UTATIONAL ASPECTS l...
NASA Technical Reports Server (NTRS)
Kirkpatrick, J. C.
1976-01-01
A tabulation of selected altitude-correlated values of pressure, density, speed of sound, and coefficient of viscosity for each of six models of the atmosphere is presented in block data format. Interpolation for the desired atmospheric parameters is performed by using cubic spline functions. The recursive relations necessary to compute the cubic spline function coefficients are derived and implemented in subroutine form. Three companion subprograms, which form the preprocessor and processor, are also presented. These subprograms, together with the data element, compose the spline fit atmosphere package. Detailed FLOWGM flow charts and FORTRAN listings of the atmosphere package are presented in the appendix.
Jianning Su; Shutao Zhang
2010-01-01
Based on the characteristics analysis of human and computer during the innovation process, a product shape innovation design method using genetic algorithm is proposed. In this method, the spline is applied to describe the contour of product, which defines the product form. Genetic algorithm is applied to optimize the points that constitute the spline, and then new shapes are created.
A Position Stepping Method for Predicting Performances of Switched Reluctance Motor Drives
X. D. Xue; K. W. E. Cheng; S. L. Ho
2007-01-01
This paper presents a novel numerical method, which will be referred as the position stepping method (PSM), to predict the performances of switched reluctance motor (SRM) drives. The 2D bicubic spline is employed to generate the finite rectangular elements. The 2D bilinear spline is used to model the nonlinear magnetic characteristics in SRMs. Consequently, the conventional nonlinear first-order differential voltage
Time Varying Compensator Design for Reconfigurable Structures Using Non-Collocated Feedback
NASA Technical Reports Server (NTRS)
Scott, Michael A.
1996-01-01
Analysis and synthesis tools are developed to improved the dynamic performance of reconfigurable nonminimum phase, nonstrictly positive real-time variant systems. A novel Spline Varying Optimal (SVO) controller is developed for the kinematic nonlinear system. There are several advantages to using the SVO controller, in which the spline function approximates the system model, observer, and controller gain. They are: The spline function approximation is simply connected, thus the SVO controller is more continuous than traditional gain scheduled controllers when implemented on a time varying plant; ft is easier for real-time implementations in storage and computational effort; where system identification is required, the spline function requires fewer experiments, namely four experiments; and initial startup estimator transients are eliminated. The SVO compensator was evaluated on a high fidelity simulation of the Shuttle Remote Manipulator System. The SVO controller demonstrated significant improvement over the present arm performance: (1) Damping level was improved by a factor of 3; and (2) Peak joint torque was reduced by a factor of 2 following Shuttle thruster firings.
An algorithm for restoring the wafer surface based on B-spline surface reconstruction
NASA Astrophysics Data System (ADS)
Wang, Nan; Jiang, Wei; Yan, Wei; Hu, Song
2013-08-01
Project lithography has experienced the development of contact, stepper, and step and scan lithography machine. Currently lithography machine has entered the age of twinscan lithography machine. The twinscan lithography machine took advantages of high efficiency and good compatibility, but the focal depth of twinscan lithography machine was only in the nanometer range. In order to guarantee the quality of the exposure, the twinscan lithography machine put forward high request for detecting the map of the wafer surface. Usually, the uniform sampling method and the whole map rebuilding method were used to detect the map of the silicon wafer surface, which is a main cause for the data redundancy. On the other hand, the map reconstructed by this means was not smooth which caused the motor of lithography machine can't response. To avoid these disadvantages, an algorithm for restoring the wafer surface based on B-spline surface reconstruction is proposed in this paper. This method is able to satisfy requirements for the local adaptive refinement, which effectively avoid data redundancy. This method is robust, which means the effect of solving nonlinear problems and inhibiting fuzzy noise is remarkable. The surface reconstructed by this new method is very smooth, which is more suitable for the movement of the motor in lithography machine.
Explosion Source Location Study Using Collocated Acoustic and Seismic Networks in Israel
NASA Astrophysics Data System (ADS)
Pinsky, V.; Gitterman, Y.; Arrowsmith, S.; Ben-Horin, Y.
2013-12-01
We explore a joined analysis of seismic and infrasonic signals for improvement in automatic monitoring of small local/regional events, such as construction and quarry blasts, military chemical explosions, sonic booms, etc. using collocated seismic and infrasonic networks recently build in Israel (ISIN) in the frame of the project sponsored by the Bi-national USA-Israel Science Foundation (BSF). The general target is to create an automatic system, which will provide detection, location and identification of explosions in real-time or close-to-real time manner. At the moment the network comprises 15 stations hosting a microphone and seismometer (or accelerometer), operated by the Geophysical Institute of Israel (GII), plus two infrasonic arrays, operated by the National Data Center, Soreq: IOB in the South (Negev desert) and IMA in the North of Israel (Upper Galilee),collocated with the IMS seismic array MMAI. The study utilizes a ground-truth data-base of numerous Rotem phosphate quarry blasts, a number of controlled explosions for demolition of outdated ammunitions and experimental surface explosions for a structure protection research, at the Sayarim Military Range. A special event, comprising four military explosions in a neighboring country, that provided both strong seismic (up to 400 km) and infrasound waves (up to 300 km), is also analyzed. For all of these events the ground-truth coordinates and/or the results of seismic location by the Israel Seismic Network (ISN) have been provided. For automatic event detection and phase picking we tested the new recursive picker, based on Statistically optimal detector. The results were compared to the manual picks. Several location techniques have been tested using the ground-truth event recordings and the preliminary results obtained have been compared to the ground-truth locations: 1) a number of events have been located as intersection of azimuths estimated using the wide-band F-K analysis technique applied to the infrasonic phases of the two distant arrays; 2) a standard robust grid-search location procedure based on phase picks and a constant celerity for a phase (tropospheric or stratospheric) was applied; 3) a joint coordinate grid-search procedure using array waveforms and phase picks was tested, 4) the Bayesian Infrasonic Source Localization (BISL) method, incorporating semi-empirical model-based prior information, was modified for array+network configuration and applied to the ground-truth events. For this purpose we accumulated data of the former observations of the air-to-ground infrasonic phases to compute station specific ground-truth Celerity-Range Histograms (ssgtCRH) and/or model-based CRH (mbCRH), which allow to essentially improve the location results. For building the mbCRH the local meteo-data and the ray-tracing modeling in 3 available azimuth ranges, accounting seasonal variations of winds directivity (quadrants North:315-45, South: 135-225, East 45-135) have been used.
Numerical solution of the linear least squares problem for splines
Vonderhaar, Thomas Jerome
1975-01-01
)+SUM+(G( IX)-BVAL I(DER) ) UE(T~A~NtKiX( IX) ~ NMK=N-K DD 60 I =1 ~ NMK 60 PDERR( I)=-2+PDERR&II RETURN END SUBROUTINE CHOLES(Cr BrArN ~ K) DIMENSION U(40r 20) rC(40 ~ 20) 'DIMENSION A(N) B(N) INTEGER P ~ QrR ~ SrSKP C... the following table: " -k+2" [1] A (t) A () i F(t) is the right most entry of the table. [k-1] ( ) i By specializing to the situation A. = d , all j, we can j evaluate the single B-spline Ni k(t) . F (t) = $ A. N . k(t) = N. k(t) i i, k i, k I is still...
Restoration of noisy blurred images by a smoothing spline filter.
Peyrovian, M J; Sawchuk, A A
1977-12-01
For the restoration of noisy blurred images, a controllable smoothing criterion based on the locally variable statistics and minimization of the second derivative is defined, and the corresponding filter, applicable to both space-variant and space-invariant degradations, is obtained. The output of this filter is a cubic spline function. The parameters of the filter determine the local smoothing window and over-all extent of smoothing, and thus the tradeoff between resolution and smoothing is controllable in a spatially nonstationary manner. The interesting properties of this filter have made it capable of restoring signal-dependent noisy images, and it has been successfully applied for filtering images degraded by film-grain noise. Since the matrices of this filter are banded circulant or Toeplitz, efficient algorithms are used for matrix manipulations. PMID:20174319
NASA Technical Reports Server (NTRS)
Zang, Thomas A.; Mathelin, Lionel; Hussaini, M. Yousuff; Bataille, Francoise
2003-01-01
This paper describes a fully spectral, Polynomial Chaos method for the propagation of uncertainty in numerical simulations of compressible, turbulent flow, as well as a novel stochastic collocation algorithm for the same application. The stochastic collocation method is key to the efficient use of stochastic methods on problems with complex nonlinearities, such as those associated with the turbulence model equations in compressible flow and for CFD schemes requiring solution of a Riemann problem. Both methods are applied to compressible flow in a quasi-one-dimensional nozzle. The stochastic collocation method is roughly an order of magnitude faster than the fully Galerkin Polynomial Chaos method on the inviscid problem.
Biorthogonal Box Spline Wavelet Bases Stephan Dahlke * , Karlheinz Grochenig y , and Vera Latour
Biorthogonal Box Spline Wavelet Bases Stephan Dahlke * , Karlheinz Gr¨ochenig y , and Vera Latour: Stephan Dahlke and Vera Latour Karlheinz Gr¨ochenig Institut f¨ur Geometrie und Department of Mathematics
NASA Astrophysics Data System (ADS)
Ni, Ming-Jiu; Munipalli, Ramakanth; Morley, Neil B.; Huang, Peter; Abdou, Mohamed A.
2007-11-01
A consistent, conservative and accurate scheme has been designed to calculate the current density and the Lorentz force by solving the electrical potential equation for magnetohydrodynamics (MHD) at low magnetic Reynolds numbers and high Hartmann numbers on a finite-volume structured collocated grid. In this collocated grid, velocity ( u), pressure ( p), and electrical potential ( ?) are located in the grid center, while current fluxes are located on the cell faces. The calculation of current fluxes on the cell faces is conducted using a conservative scheme, which is consistent with the discretization scheme for the solution of electrical potential Poisson equation. A conservative interpolation is used to get the current density at the cell center, which is used to conduct the calculation of Lorentz force at the cell center for momentum equations. We will show that both "conservative" and "consistent" are important properties of the scheme to get an accurate result for high Hartmann number MHD flows with a strongly non-uniform mesh employed to resolve the Hartmann layers and side layers of Hunt's conductive walls and Shercliff's insulated walls. A general second-order projection method has been developed for the incompressible Navier-Stokes equations with the Lorentz force included. This projection method can accurately balance the pressure term and the Lorentz force for a fully developed core flow. This method can also simplify the pressure boundary conditions for MHD flows.
High-precision nuclear structure calculations using Spline-Galerkin lattices
NASA Astrophysics Data System (ADS)
Oberacker, V. E.; Kegley, D. R.; Umar, A. S.; Strayer, M. R.
1996-10-01
In connection with new experimental facilities such as HRIBF, we are carrying out high-precision nuclear structure calculations to study nuclei far from stability. Our goal is to use the data obtained by HRIBF to provide a better parametrization of the effective N-N force. This would entail the reproduction of binding energies, charge radii, fission barriers and other observables for several chains of isotopes. The properties of these nuclei are also crucial for various astrophysical nucleosynthesis processes. The main challenge in the theory of exotic nuclei near the proton or neutron drip line is that the outermost nucleons are weakly bound and that these states are close to the particle continuum. Because of the large spatial extent of the weakly bound states, the traditional basis expansion methods fail to converge. We overcome these problems by representing the nuclear Hamiltonian on a coordinate space lattice; very high accuracy is achieved utilizing our recently developed Spline-Galerkin method (D.R. Kegley, Ph.D. thesis, Vanderbilt U. (1996)). First calculations using this method for axially symmetric nuclei will be presented. In particular, we will discuss deformed shell model, HF+BCS and HFB implementations of the method.
Near-best univariate spline discrete quasi-interpolants on non-uniform partitions
D. Barrera; M. J. Ibanez; Paul Sablonniere; D. Sbibih
2004-01-01
Univariate spline discrete quasi-interpolants (abbr. dQIs) are approximation operators using B-spline expansions with coefficients which are linear combinations of discrete values of the function to be approximated. When working with nonuniform partitions, the main challenge is to find dQIs which have both good approximation orders and bounded uniform norms independent of the given partition. Near-best dQIs are obtained by minimizing
Near-Best Univariate Spline Discrete Quasi-Interpolants on Nonuniform Partitions
D. Barrera; M. J. Ibáńez; P. Sablonničre; D. Sbibih
2008-01-01
The univariate spline quasi-interpolants (QIs) studied in this paper are approximation operators using B-spline expansions\\u000a with coefficients that are linear combinations of discrete values of the function to be approximated. When working with nonuniform\\u000a partitions, the main challenge is to find QIs that have both good approximation orders and uniform norms which are bounded\\u000a independently of the given partition. Near-best
Ridge Extraction from Isosurfaces of Volumetric Data Using Implicit B-Splines
Suraj Musuvathy; Tobias Martin; Elaine Cohen
2010-01-01
Ridges are extremal curves of principal curvatures on a surface that indicate salient intrinsic features of its shape. This paper presents a novel approach for extracting ridges of improved quality from isosurfaces of volumetric scalar-valued grids by converting them to implicit trivariate B-spline representations. A robust tracing approach demonstrated to extract ridges accurately from parametric B-spline surfaces is extended to
Free vibration analysis of arbitrary thin shell structures by using spline finite element
S. C. Fan; M. H. Luah
1995-01-01
This paper presents the free vibration analysis of arbitrary thin shell structures by using a newly developed spline finite element. The new element has three salient features in its formulation: (i) the use of B-spline shape functions for the interpolations of both in-plane and out-of-plane displacements of a general thin shell element; (ii) the use of displacement constraints and parameters
Approximation of planar offset curves with globally bounded error for B-spline NC tool paths
Maqsood A. Khan; Z. C. Chen
2011-01-01
The topic of representing the offset of a 2D B-spline curve in the same form has been a topic of research for a long time, and it has many industrial applications, especially in NC tool path generation for pocketing. For B-spline tool paths, it is often required that the tool paths have fewer control points, lower base function degree, and
Nilles, M.A.; Gordon, J.D.; Schroder, L.J.
1994-01-01
A collocated, wet-deposition sampler program has been operated since October 1988 by the U.S. Geological Survey to estimate the overall sampling precision of wet atmospheric deposition data collected at selected sites in the National Atmospheric Deposition Program and National Trends Network (NADP/NTN). A duplicate set of wet-deposition sampling instruments was installed adjacent to existing sampling instruments at four different NADP/NTN sites for each year of the study. Wet-deposition samples from collocated sites were collected and analysed using standard NADP/NTN procedures. Laboratory analyses included determinations of pH, specific conductance, and concentrations of major cations and anions. The estimates of precision included all variability in the data-collection system, from the point of sample collection through storage in the NADP/NTN database. Sampling precision was determined from the absolute value of differences in the analytical results for the paired samples in terms of median relative and absolute difference. The median relative difference for Mg2+, Na+, K+ and NH4+ concentration and deposition was quite variable between sites and exceeded 10% at most sites. Relative error for analytes whose concentrations typically approached laboratory method detection limits were greater than for analytes that did not typically approach detection limits. The median relative difference for SO42- and NO3- concentration, specific conductance, and sample volume at all sites was less than 7%. Precision for H+ concentration and deposition ranged from less than 10% at sites with typically high levels of H+ concentration to greater than 30% at sites with low H+ concentration. Median difference for analyte concentration and deposition was typically 1.5-2-times greater for samples collected during the winter than during other seasons at two northern sites. Likewise, the median relative difference in sample volume for winter samples was more than double the annual median relative difference at the two northern sites. Bias accounted for less than 25% of the collocated variability in analyte concentration and deposition from weekly collocated precipitation samples at most sites.A collocated, wet-deposition sampler program has been operated since OCtober 1988 by the U.S Geological Survey to estimate the overall sampling precision of wet atmospheric deposition data collected at selected sites in the National Atmospheric Deposition Program and National Trends Network (NADP/NTN). A duplicate set of wet-deposition sampling instruments was installed adjacent to existing sampling instruments four different NADP/NTN sites for each year of the study. Wet-deposition samples from collocated sites were collected and analysed using standard NADP/NTN procedures. Laboratory analyses included determinations of pH, specific conductance, and concentrations of major cations and anions. The estimates of precision included all variability in the data-collection system, from the point of sample collection through storage in the NADP/NTN database.
Is the sky pure today? AwkChecker: an assistive tool for detecting and correcting collocation errors
Taehyun Park; Edward Lank; Pascal Poupart; Michael Terry
2008-01-01
Collocation preferences represent the commonly used expressions, idioms, and word pairings of a language. Because collocation preferences arise from consensus usage, rather than a set of well-defined rules, they must be learned on a case-by-case basis, making them particularly challenging for non-native speakers of a language. To assist non-native speakers with these parts of a language, we developed AwkChecker, the
The effects of multimedia communication technology on non-collocated teams: a case study.
Carletta, J; Anderson, A H; McEwan, R
2000-08-01
Collaborative teams are becoming increasingly important for industry, both within and across companies. There is a need for communication technology to support teams because many teams are non-collocated, or 'virtual'. Two automotive supply chain teams were observed while they were experimenting with multimedia conferencing in order to determine what support non-collocated teams need and the potential effects of introducing technologies on their group processes. The observations included meeting recordings and other sources that show the organizational factors affecting teams. Working in teams requires very close collaboration. Communication technology can help teams if it is used to foster close and relatively informal person-to-person interaction. Organizational constraints on how the technology is introduced favour high-technology, special-purpose installations, but teams can best be supported using relatively modest equipment with desktop access. PMID:10975182
NASA Technical Reports Server (NTRS)
Goldsmith, J. E. M.; Bisson, Scott E.; Ferrare, Richard A.; Evans, Keith D.; Whiteman, David N.; Melfi, S. H.
1994-01-01
Raman lidar is a leading candidate for providing the detailed space- and time-resolved measurements of water vapor needed by a variety of atmospheric studies. Simultaneous measurements of atmospheric water vapor are described using two collocated Raman lidar systems. These lidar systems, developed at the NASA/Goddard Space Flight Center and Sandia National Laboratories, acquired approximately 12 hours of simultaneous water vapor data during three nights in November 1992 while the systems were collocated at the Goddard Space Flight Center. Although these lidar systems differ substantially in their design, measured water vapor profiles agreeed within 0.15 g/kg between altitudes of 1 and 5 km. Comparisons with coincident radiosondes showed all instruments agreed within 0.2 g/kg in this same altitude range. Both lidars also clearly showed the advection of water vapor in the middle troposphere and the pronounced increase in water vapor in the nocturnal boundary layer that occurred during one night.
NASA Astrophysics Data System (ADS)
Durmaz, Murat; Karslioglu, Mahmut Onur
2015-04-01
There are various global and regional methods that have been proposed for the modeling of ionospheric vertical total electron content (VTEC). Global distribution of VTEC is usually modeled by spherical harmonic expansions, while tensor products of compactly supported univariate B-splines can be used for regional modeling. In these empirical parametric models, the coefficients of the basis functions as well as differential code biases (DCBs) of satellites and receivers can be treated as unknown parameters which can be estimated from geometry-free linear combinations of global positioning system observables. In this work we propose a new semi-parametric multivariate adaptive regression B-splines (SP-BMARS) method for the regional modeling of VTEC together with satellite and receiver DCBs, where the parametric part of the model is related to the DCBs as fixed parameters and the non-parametric part adaptively models the spatio-temporal distribution of VTEC. The latter is based on multivariate adaptive regression B-splines which is a non-parametric modeling technique making use of compactly supported B-spline basis functions that are generated from the observations automatically. This algorithm takes advantage of an adaptive scale-by-scale model building strategy that searches for best-fitting B-splines to the data at each scale. The VTEC maps generated from the proposed method are compared numerically and visually with the global ionosphere maps (GIMs) which are provided by the Center for Orbit Determination in Europe (CODE). The VTEC values from SP-BMARS and CODE GIMs are also compared with VTEC values obtained through calibration using local ionospheric model. The estimated satellite and receiver DCBs from the SP-BMARS model are compared with the CODE distributed DCBs. The results show that the SP-BMARS algorithm can be used to estimate satellite and receiver DCBs while adaptively and flexibly modeling the daily regional VTEC.
On polynomial collocation for second kind integral equations with fixed singularities of Mellin type
G. Mastroianni; C. Frammartino; A. Rathsfeld
2003-01-01
Summary. ?We consider a polynomial collocation for the numerical solution of a second kind integral equation with an integral kernel\\u000a of Mellin convolution type. Using a stability result by Junghanns and one of the authors, we prove that the error of the approximate\\u000a solution is less than a logarithmic factor times the best approximation and, using the asymptotics of the solution,
NASA Technical Reports Server (NTRS)
Robbins, J. W.
1985-01-01
An autonomous spaceborne gravity gradiometer mission is being considered as a post Geopotential Research Mission project. The introduction of satellite diometry data to geodesy is expected to improve solid earth gravity models. The possibility of utilizing gradiometer data for the determination of pertinent gravimetric quantities on a local basis is explored. The analytical technique of least squares collocation is investigated for its usefulness in local solutions of this type. It is assumed, in the error analysis, that the vertical gravity gradient component of the gradient tensor is used as the raw data signal from which the corresponding reference gradients are removed to create the centered observations required in the collocation solution. The reference gradients are computed from a high degree and order geopotential model. The solution can be made in terms of mean or point gravity anomalies, height anomalies, or other useful gravimetric quantities depending on the choice of covariance types. Selected for this study were 30 x 30 foot mean gravity and height anomalies. Existing software and new software are utilized to implement the collocation technique. It was determined that satellite gradiometry data at an altitude of 200 km can be used successfully for the determination of 30 x 30 foot mean gravity anomalies to an accuracy of 9.2 mgal from this algorithm. It is shown that the resulting accuracy estimates are sensitive to gravity model coefficient uncertainties, data reduction assumptions and satellite mission parameters.
Ma, Chien-Ching; Chuang, Kuo-Chih; Pan, Shan-Ying
2011-12-01
Polyvinylidene fluoride (PVDF) films are light, flexible, and have high piezoelectricity. Because of these advantages, they have been widely used as sensors in applications such as underwater investigation, nondestructive damage detection, robotics, and active vibration suppression. PVDF sensors are especially preferred over conventional strain gauges in active vibration control because the PVDF sensors are easy to cut into different sizes or shapes as piezoelectric actuators and they can then be placed as collocated pairs. In this work, to focus on demonstrating the dynamic sensing performance of the PVDF film sensor, we revisit the active vibration control problem of a cantilever beam using a collocated lead zirconate titanate (PZT) actuator/PVDF film sensor pair. Before applying active vibration control, the measurement characteristics of the PVDF film sensor are studied by simultaneous comparison with a strain gauge. The loading effect of the piezoelectric actuator on the cantilever beam is also investigated in this paper. Finally, four simple, robust active vibration controllers are employed with the collocated PZT/PVDF pair to suppress vibration of the cantilever beam subjected to impact loadings. The four controllers are the velocity feedback controller, the integral resonant controller (IRC), the resonant controller, and the positive position feedback (PPF) controller. Suppression of impact disturbances is especially suitable for the purpose of demonstrating the dynamic sensing performance of the PVDF sensor. The experimental results also provide suggestions for choosing between the previously mentioned controllers, which have been proven to be effective in suppressing impact-induced vibrations. PMID:23443690
NASA Astrophysics Data System (ADS)
Xue, Juntao; Liu, Zhengguang; Zhang, Hongwei; Wang, Shucheng
2007-01-01
Snakes, or active contours, are used extensively in computer vision and image processing application, particularly to locate object boundaries. GVF (Gradient Vector Flow) model has resolved two key problems of the traditional deformable model. However, it still requires both the initial contour being close to the target and a large amount of computation. And it is difficult to process the cupped target edge. This paper analysis the characteristics of deformable model firstly, then proposed a new method based on B-spline lifting wavelet. Experimentations based on GVF model and MRI segmentation show that the proposed method is a good resolution to the initialization sensitivity and the large computation.
Imre, K.
1993-05-01
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.
Spectral methods on arbitrary grids
NASA Technical Reports Server (NTRS)
Carpenter, Mark H.; Gottlieb, David
1995-01-01
Stable and spectrally accurate numerical methods are constructed on arbitrary grids for partial differential equations. These new methods are equivalent to conventional spectral methods but do not rely on specific grid distributions. Specifically, we show how to implement Legendre Galerkin, Legendre collocation, and Laguerre Galerkin methodology on arbitrary grids.
A meshless point collocation treatment of transient bioheat problems.
Bourantas, G C; Loukopoulos, V C; Burganos, V N; Nikiforidis, G C
2014-05-01
A meshless numerical method is proposed for the solution of the transient bioheat equation in two and three dimensions. The Pennes bioheat equation is extended in order to incorporate water evaporation, tissue damage, and temperature-dependent tissue properties during tumor ablation. The conductivity of the tissue is not assumed constant but is treated as a local function to simulate local variability due to the existence of usually unclear interfacing of healthy and pathological segments. In this way, one avoids the need for accurate identification of the boundaries between pathological and healthy regions, which is a typical problem in medical practice, and sidesteps, evidently, the corresponding mathematical treatment of such boundaries, which is usually a tedious procedure with some inevitable degree of approximation. The numerical results of the new method for test applications of the bioheat transfer equation are validated against analytical predictions and predictions of other numerical methods. 3D simulations are presented that involve the modeling of tumor ablation and account for metabolic heat generation, blood perfusion, and heat ablation using realistic values for the various parameters. An evaluation of the effective medium approximation to homogenize conductivity fields for use with the bioheat equation is also provided. PMID:24574248
NASA Astrophysics Data System (ADS)
Delogu, A.; Furini, F.
1991-09-01
Increasing interest in radar cross section (RCS) reduction is placing new demands on theoretical, computation, and graphic techniques for calculating scattering properties of complex targets. In particular, computer codes capable of predicting the RCS of an entire aircraft at high frequency and of achieving RCS control with modest structural changes, are becoming of paramount importance in stealth design. A computer code, evaluating the RCS of arbitrary shaped metallic objects that are computer aided design (CAD) generated, and its validation with measurements carried out using ALENIA RCS test facilities are presented. The code, based on the physical optics method, is characterized by an efficient integration algorithm with error control, in order to contain the computer time within acceptable limits, and by an accurate parametric representation of the target surface in terms of bicubic splines.
Abdalah, Mahmoud; Boutchko, Rostyslav; Mitra, Debasis; Gullberg, Grant T
2015-01-01
In this paper, we propose and validate an algorithm of extracting voxel-by-voxel time activity curves directly from inconsistent projections applied in dynamic cardiac SPECT. The algorithm was derived based on factor analysis of dynamic structures (FADS) approach and imposes prior information by applying several regularization functions with adaptively changing relative weighting. The anatomical information of the imaged subject was used to apply the proposed regularization functions adaptively in the spatial domain. The algorithm performance is validated by reconstructing dynamic datasets simulated using the NCAT phantom with a range of different input tissue time-activity curves. The results are compared to the spline-based and FADS methods. The validated algorithm is then applied to reconstruct pre-clinical cardiac SPECT data from canine and murine subjects. Images, generated from both simulated and experimentally acquired data confirm the ability of the new algorithm to solve the inverse problem of dynamic SPECT with slow gantry rotation. PMID:25167546
NASA Astrophysics Data System (ADS)
Gasso, S.; Torres, O.
2014-12-01
When observing aerosols from space in the UV range , the upwelling radiation is dependent not only on the aerosol intrinsic properties but also on the location of the aerosol layer in the atmospheric column. In the current operational retrieval by the OMI 2-band algorithm (OMAERUV), the aerosol height is assumed and the aerosol optical depth (AOD) and single scattering albedo (SSA) at 388nm are derived. Since the sensitivity to aerosol altitude occurs only at UV wavelengths, it suggests that if the AOD is known a priori, the associated SSA and aerosol height can be derived. The theoretical approach and first applications of this method has been explored previously by combining OMI with MODIS AODs (extrapolated to the OMI's wavelengths) over the ocean. However, no detailed studies have been carried out by comparing with independent measurements such as those from the CALIPSO lidar. This poster will show detailed case studies of collocated and simultaneous observations of aerosol height (from the space borne lidar CALIOP) and AOD (from MODIS-Aqua) with the objective to evaluate the aerosol height assumed and the AOD at 500nm derived by OMAERUV. The cases were selected in areas known for biomass burning (off the coast of South Africa-Madagascar) and for dust and dust mixed with smoke (such as off the coast of Dakar). By comparing with Calipso, this analysis will highlight the sensitivity of OMAERUV retrievals to aerosol layer thickness and location in the atmospheric column, both parameters currently assumed by the retrieval algorithm.
NASA Astrophysics Data System (ADS)
Ginzburg, I.; Wittum, G.
2001-01-01
A two-phase 2D model that combines the volume of fluid (VOF) method with implicit staggered finite volumes discretization of the Navier-Stokes equation is presented. Staggered finite volumes are developed on the basis of nonconforming Crouzeix-Raviart finite elements, where all components of the velocity lie in the middle of the element edges and the pressure degrees of freedom are found in the centers of mass of the elements. Staggered finite Volumes extend marker and cell (MAC) regular staggered grids to unstructured mesh. A linear saddle point problem, resulting from either the discretization or the Newton method, is solved for all unknown pressures and velocities. Interface is represented with spline interpolants which follow the VOF distribution. Adaptive mesh refinement is used to obtain a high level of uniform refining at the domain of dependence of the interface. The aligned grid is obtained by irregular refining of the cells which are intersected by a curve. The boundaries of its elements coincide with the slope segments going through the intersections of the curve with the underlying regular elements boundary. The deformable computational grids are used only to discretize the Navier-Stokes equation. The advection of volume fractions is done on the advection mesh, which corresponds to highest regular refining on the computational grid. Approximation of the surface tension on spline interpolants offers a straightforward way to describe correctly the pressure jumps on interface-fitted staggered grids. This allows deletion of the anomalous currents around a statical bubble and their effective reduction in real simulations. On the aligned grid, the continuity of the viscous stress is modeled exactly due to the finite volume approach. Using the proposed numerical techniques, single bubble rise is analyzed.
3D shape recovery of a newborn skull using thin-plate splines.
Lapeer, R J; Prager, R W
2000-01-01
The objective of this paper is to construct a mesh-model of a newborn skull for finite element analysis to study its deformation when subjected to the forces present during labour. The current state of medical imaging technology has reached a level which allows accurate visualisation and shape recovery of biological organs and body-parts. However, a sufficiently large set of medical images cannot always be obtained, often because of practical or ethical reasons, and the requirement to recover the shape of the biological object of interest has to be met by other means. Such is the case for a newborn skull. A method to recover the three-dimensional (3D) shape from (minimum) two orthogonal atlas images of the object of interest and a homologous object is described. This method is based on matching landmarks and curves on the orthogonal images of the object of interest with corresponding landmarks and curves on the homologous or 'master'-object which is fully defined in 3D space. On the basis of this set of corresponding landmarks, a thin-plate spline function can be derived to warp from the 'master'-object space to the 'slave'-object space. This method is applied to recover the 3D shape of a newborn skull. Images from orthogonal view-planes are obtained from an atlas. The homologous object is an adult skull, obtained from CT-images made available by the Visible Human Project. After shape recovery, a mesh-model of the newborn skull is generated. PMID:10838013
An experiment to determine the relative positions of two collocated laser tracking stations
NASA Technical Reports Server (NTRS)
Dunn, P. J.; Kolenkiewicz, R.; Smith, D. E.
1972-01-01
Two Goddard Space Flight Center laser tracking stations were collocated for a short time towards the end of 1971 for the purposes of comparing their tracking performance and quality. The lasers, only 25 meters apart, obtained simultaneous tracking data on eighteen passes of the Beacon Explorer C spacecraft. These data have now been used to determine the location of one laser with respect to the other with the result that the computed position of the second laser agrees with the surveyed position to 4 centimeters in latitude and height, and 1 centimeter in longitude.
Greenberg, Saul
2009-01-01
. Intergenerational gaming, console games, video games, Wii, Playstation Introduction Since the 1920s, there have been1 Voida, A. & Greenberg, S. (2009). Collocated intergenerational console gaming. Research Report. Collocated Intergenerational Console Gaming Amy Voida & Saul Greenberg Department of Computer Science
Collocated actuator/sensor design for shape control of subregions of structures
NASA Astrophysics Data System (ADS)
Krommer, Michael; Nader, Manfred
2004-07-01
The control of the shape of a sub - region of a structure has many important practical applications; for instance the control of the shape of a conformal antenna that is mounted to the surface of a sub - region of a structure. Given the desired shape of the sub - region one can use self - stress actuators, which only act in the sub - region itself, to implement the required control. However, if the structure is disturbed by external excitations, the actuators have to compensate the additional vibrations too; therefore, also sensors have to be designed. A proper sensor design requires the sensor to be an integrated part of the structure and to be located in the sub - region only. Using self - stress sensors is near at hand; moreover, one may even use the actuators as sensors, resulting in so - called self - sensing actuator / sensor pairs. Clearly, this procedure provides collocation between actuator and sensor automatically, which, from a control point of view, is highly desirable. In the present paper we summarize the design of actuators for the sub - region control of a structure. Then we discuss the design of collocated sensors, their output signal and the application of a PD - control law. We show that the output signal is the natural output of the system and that the closed loop system is stable. Finally, we present numerical results for a beam type structure.
Fortier, Marie-Odile P; Sturm, Belinda S M
2012-10-16
Resource demand analyses indicate that algal biodiesel production would require unsustainable amounts of freshwater and fertilizer supplies. Alternatively, municipal wastewater effluent can be used, but this restricts production of algae to areas near wastewater treatment plants (WWTPs), and to date, there has been no geospatial analysis of the feasibility of collocating large algal ponds with WWTPs. The goals of this analysis were to determine the available areas by land cover type within radial extents (REs) up to 1.5 miles from WWTPs; to determine the limiting factor for algal production using wastewater; and to investigate the potential algal biomass production at urban, near-urban, and rural WWTPs in Kansas. Over 50% and 87% of the land around urban and rural WWTPs, respectively, was found to be potentially available for algal production. The analysis highlights a trade-off between urban WWTPs, which are generally land-limited but have excess wastewater effluent, and rural WWTPs, which are generally water-limited but have 96% of the total available land. Overall, commercial-scale algae production collocated with WWTPs is feasible; 29% of the Kansas liquid fuel demand could be met with implementation of ponds within 1 mile of all WWTPs and supplementation of water and nutrients when these are limited. PMID:22970803
Odum, Jack K.; Stephenson, William J.; Williams, Robert A.; von Hillebrandt-Andrade, Christa
2013-01-01
Shear?wave velocity (VS) and time?averaged shear?wave velocity to 30 m depth (VS30) are the key parameters used in seismic site response modeling and earthquake engineering design. Where VS data are limited, available data are often used to develop and refine map?based proxy models of VS30 for predicting ground?motion intensities. In this paper, we present shallow VS data from 27 sites in Puerto Rico. These data were acquired using a multimethod acquisition approach consisting of noninvasive, collocated, active?source body?wave (refraction/reflection), active?source surface wave at nine sites, and passive?source surface?wave refraction microtremor (ReMi) techniques. VS?versus?depth models are constructed and used to calculate spectral response plots for each site. Factors affecting method reliability are analyzed with respect to site?specific differences in bedrock VS and spectral response. At many but not all sites, body? and surface?wave methods generally determine similar depths to bedrock, and it is the difference in bedrock VS that influences site amplification. The predicted resonant frequencies for the majority of the sites are observed to be within a relatively narrow bandwidth of 13.5 Hz. For a first?order comparison of peak frequency position, predictive spectral response plots from eight sites are plotted along with seismograph instrument spectra derived from the time series of the 16 May 2010 Puerto Rico earthquake. We show how a multimethod acquisition approach using collocated arrays compliments and corroborates VS results, thus adding confidence that reliable site characterization information has been obtained.
A robust false transient method of lines for elliptic partial differential equations
Subramanian, Venkat
, such as finite difference, finite element, finite volume, or collocation methods (Berzins et al., 1989 such as DASKR or DASSL or in a computer algebra system such as Matlab (MathWorks, 2012) Contents lists available
Point-Based Elastic Registration of Medical Image Data Using Approximating Thin-Plate Splines
Karl Rohr; H. Siegfried Stiehl; Rainer Sprengel; Wolfgang Beil; Thorsten M. Buzug; Jürgen Weese; M. H. Kuhn
1996-01-01
. We consider elastic registration of medical image data basedon thin-plate splines using a set of corresponding anatomical point landmarks.Previous work on this topic has concentrated on using interpolationschemes. Such schemes force the corresponding landmarks to exactlymatch each other and assume that the landmark positions are knownexactly. However, in real applications the localization of landmarks isalways prone to some error.
Pi, Archimedes and circular splines P. Sablonni`ere, INSA & IRMAR, Rennes
Boyer, Edmond
Pi, Archimedes and circular splines P. Sablonni`ere, INSA & IRMAR, Rennes June 11, 2013 Abstract by two subdivision algorithms. 1 Introduction: Archimedes and the computation of In his famous treatise On the quadrature of the circle [1], Archimedes (287-212 b.c.) gave the following upper and lower bounds for 3 + 10
GPU-based trimming and tessellation of NURBS and T-Spline surfaces
Michael Guthe; Ákos Balázs; Reinhard Klein
2005-01-01
As there is no hardware support neither for rendering trimmed NURBS -- the standard surface representation in CAD -- nor for T-Spline surfaces the usability of existing rendering APIs like OpenGL, where a run-time tessellation is performed on the CPU, is limited to simple scenes. Due to the irregular mesh data structures required for trimming no algorithms exists that exploit
Hardware-Accelerated High-Quality Box Spline Reconstruction on the BCC Lattice
Zhang, Richard "Hao"
. These lattices are easy to use since indexing, interpolation and representation can be done conveniently lattice. Specif- ically, we present a fast GPU-based implementation of the linear and quin- tic box spline, but it is not interpolating. Therefore, we propose prefiltering as an initialization step to enforce the interpolation
Spline-based frames in the space of periodic signals Amir Averbuch1
Averbuch, Amir
#12;Implicitly, this resilience is utilized in signal/image restoration, which is based on the prior assumption that a frame expansion of a given signal/image is sparse. In principle, only part of the samplesSpline-based frames in the space of periodic signals Amir Averbuch1 Pekka Neittaanm¨aki2 Valery
An Hermitian Approach for Multiresolution Splines Laurent Grisoni, Christophe Schlick, Carole Blanc
Grisoni, Laurent
An Hermitian Approach for Multiresolution Splines Laurent Grisoni, Christophe Schlick, Carole Blanc for multiresolution representation in the field of computer aided design. This new approach involves less computation, is more modular, and is potentially more flexible than the classical approach. This multiresolution scheme
Fusion of 3D B-spline surface patches reconstructed from image sequences
Paris-Sud XI, Université de
. This approach is based on a triangular mesh and surface interpolation through regularized uniform bicubic B-spline surface patches. Experimental results are presented for both synthetic and real data. 1 Introduction One. In the second part, we present experimental results on synthetic and real data. 2 Our approach The parametric
Target curvature driven fairing algorithm for planar cubic B-spline curves
Weishi Li; Shuhong Xu; Jianmin Zheng; Gang Zhao
2004-01-01
This paper presents a new algorithm for fairing planar cubic B-spline curves. Target curvature plots prescribed by designers according to design intent are used to identify bad points and bad curve segments. The corresponding control points are then modified using local constrained optimization. The objective function is a weighed combination of two components, which are associated with the fairness in
Watertight conversion of trimmed CAD surfaces to Clough-Tocher splines
Kosinka, Ji?í; Cashman, Thomas J.
2015-06-10
. These artifacts are caused by the well-known dinosaur back effect, which arises nearly all spline approximations when control meshes are not aligned with features on a model (Farin et al., 2002; gsdörfer et al., 2011). Additionally, once a triangulation has...
Kaan Erkorkmaz; Yusuf Altintas
2001-01-01
Reference trajectory generation plays a key role in the computer control of machine tools. Generated trajectories must not only describe the desired tool path accurately, but must also have smooth kinematic profiles in order to maintain high tracking accuracy, and avoid exciting the natural modes of the mechanical structure or servo control system. Spline trajectory generation techniques have become widely
A WIENER MODEL FOR MEMORY HIGH POWER AMPLIFIERS USING B-SPLINE FUNCTION APPROXIMATION
Chen, Sheng
A WIENER MODEL FOR MEMORY HIGH POWER AMPLIFIERS USING B-SPLINE FUNCTION APPROXIMATION Xia Hong*, Yu modeling approach for memory high power amplifiers in communica- tion systems using observational input industrial/biological systems [9, 10, 11], and the HPA in broadband communi- cation transmitters [8
Periodic learning of B-spline models for output PDF control: application to MWD control
H. Wang; J. F. Zhang; H. Yue
2005-01-01
Periodic learning of B-spline basis functions model for the output probability density function (PDF) control of non-Gaussian systems is studied in this paper using the recursive least square algorithm. Within each control interval, the basis functions are fixed and the control input design is performed that controls the shape of the output PDFs. However, between each control interval, periodic learning
Representation of Spatial Functions in Geodesy Using B-Spline Wavelets with Compact Support
Representation of Spatial Functions in Geodesy Using B-Spline Wavelets with Compact Support Rainer of Astronomical, Physical and Mathematical Geodesy, Technical University of Berlin, Germany 3 German Geodetic product 1 Introduction In geodesy one of the principal research foci is the efficient representation
Technology Transfer Automated Retrieval System (TEKTRAN)
Cubic splines can be used to model fixed and random effects of lactation curves. A total of 64,138 test-day observations for first lactation Holstein cows recorded as treated with bovine somatotropin (bST) and 138,008 test-day observations for untreated cows were obtained from Dairy Records Manageme...
Peters, JĂśrg
polytope is the spline surface. Â convex hull property. The surface lies locally and globally in the convex sets. 1. The convex hull property 2. Tangent continuity 3. Interpolation of the input mesh points 1 #12; not be planar. Â builtÂin smoothness (unless explicitly reduced) and local smoothness preserving editabilÂ ity
Michael F. Hutchinson
1998-01-01
Thin plate smoothing splines incorporating varying degrees of topographic dependence were used to interpolate 100 daily rainfall values, with the degree of data smoothing determined by minimizing the generalised cross validation. Analyses were performed on the square roots of the rainfall values. Model calibration was made difficult by short range correlation and the small size of the data set. Short
A spline-based parameter and state estimation technique for static models of elastic surfaces
NASA Technical Reports Server (NTRS)
Banks, H. T.; Daniel, P. L.; Armstrong, E. S.
1983-01-01
Parameter and state estimation techniques for an elliptic system arising in a developmental model for the antenna surface in the Maypole Hoop/Column antenna are discussed. A computational algorithm based on spline approximations for the state and elastic parameters is given and numerical results obtained using this algorithm are summarized.
Deconvolution of variable rate reservoir performance data using B-splines
Ilk, Dilhan
2007-04-25
in the Laplace domain with the input rate and obtain the sensitivities of the pressure response with respect to individual B-splines after numerical inversion of the Laplace transform. The sensitivity matrix is then used in a regularized least-squares procedure...
A Study of Learners' Usage of a Mobile Learning Application for Learning Idioms and Collocations
ERIC Educational Resources Information Center
Amer, Mahmoud
2014-01-01
This study explored how four groups of language learners used a mobile software application developed by the researcher for learning idiomatic expressions and collocations. A total of 45 participants in the study used the application for a period of one week. Data for this study was collected from the application, a questionnaire, and follow-up
Carl W Myers; Ned Z Elkins
2008-01-01
Underground collocation of nuclear power reactors and the nuclear waste management facilities supporting those reactors, termed an underground nuclear park (UNP), appears to have several advantages compared to the conventional approach to siting reactors and waste management facilities. These advantages include the potential to lower reactor capital and operating cost, lower nuclear waste management cost, and increase margins of physical
ERIC Educational Resources Information Center
Amer, Mahmoud Atiah
2010-01-01
This study explored how four groups of English learners used a mobile software application developed by the researcher for learning idiomatic expressions and collocations. A total of 45 learners in the study used the application for a period of one week. Data for this study was collected from a questionnaire, the application, and follow-up
H. Cho; P. Yang; G. Kattawar; Y. Hu; P. Minnis; D. Winker
2007-01-01
Using the International Satellite Cloud Climatology Project (ISCCP) cloud classification, we investigated the relation of backscatter and backscattering depolarization ratio for nine types of clouds on the basis of the collocated data of the cloud products derived from the measurements made by the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) and the Moderate Resolution Imaging Spectroradiometer (MODIS) aboard Aqua.
ERIC Educational Resources Information Center
Hsu, Jeng-yih
2007-01-01
The present study investigates the use of English lexical collocations and their relation to the online writing of Taiwanese college English majors and non-English majors. Data for the study were collected from 41 English majors and 21 non-English majors at a national university of science and technology in southern Taiwan. Each student was asked
Kiani, M A; Sim, K S; Nia, M E; Tso, C P
2015-05-01
A new technique based on cubic spline interpolation with Savitzky-Golay smoothing using weighted least squares error filter is enhanced for scanning electron microscope (SEM) images. A diversity of sample images is captured and the performance is found to be better when compared with the moving average and the standard median filters, with respect to eliminating noise. This technique can be implemented efficiently on real-time SEM images, with all mandatory data for processing obtained from a single image. Noise in images, and particularly in SEM images, are undesirable. A new noise reduction technique, based on cubic spline interpolation with Savitzky-Golay and weighted least squares error method, is developed. We apply the combined technique to single image signal-to-noise ratio estimation and noise reduction for SEM imaging system. This autocorrelation-based technique requires image details to be correlated over a few pixels, whereas the noise is assumed to be uncorrelated from pixel to pixel. The noise component is derived from the difference between the image autocorrelation at zero offset, and the estimation of the corresponding original autocorrelation. In the few test cases involving different images, the efficiency of the developed noise reduction filter is proved to be significantly better than those obtained from the other methods. Noise can be reduced efficiently with appropriate choice of scan rate from real-time SEM images, without generating corruption or increasing scanning time. PMID:25676007
Nguyen, H.D.; Paik, S. (EG and G Idaho, Inc., Idaho Falls, ID (United States)); Chung, J.N. (Washington State Univ., Pullman, WA (United States). Dept. of Mechanical and Materials Engineering)
1992-01-01
A spectral model, based on the stream function and vorticity, is developed in order to calculate the time-dependent solution of flow past a spherical droplet. Both Chebyshev and Legendre polynomials are used to expand the stream fiinction and vorticity in the radial and angular directions, respectively, along with the backward Euler approximation to advance in time. Consistent treatment of boundary conditions is made to resolve the lack of vorticity boundary conditions by means of the influence matrix technique. The computed flow field, the drag coefficient, and the interfacial velocity are presented for Reynolds numbers in the range from 0.5 to 50 for both continuous and dispersed phases with viscosity ratios of 1 and 3. Comparison of the present results to those found in the literature indicate that the model is capable of predicting the correct nature of the flow associated with a droplet.
Utah, University of
cardiac distress and/or disease. It is widely known that changes in heart position resulting from-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
Particle Tracking and Multispectral Collocation Method for Particle-to-Particle Binding Assays
Santiago, Juan G.
and the transformation matrix generated in this alignment phase are then used to translate and rotate the Ch2 particle of particle monitoring time tch Characteristic minimum evolution time rPMC Particle mask correlation that requires a pair of images, an image- similarity metric, an optimizer, and a transformation type. The metric
Valero, F.P. [Scripps Institution of Oceanography, University of California at San Diego, La Jolla (United States)] [Scripps Institution of Oceanography, University of California at San Diego, La Jolla (United States); Cess, R.D.; Zhang, M. [Marine Sciences Research Center, State University of New York at Stony Brook (United States)] [Marine Sciences Research Center, State University of New York at Stony Brook (United States); Pope, S.K.; Bucholtz, A.; Bush, B. [Scripps Institution of Oceanography, University of California at San Diego, La Jolla (United States)] [Scripps Institution of Oceanography, University of California at San Diego, La Jolla (United States); Vitko, J. Jr. [Sandia National Laboratories, Livermore, California (United States)] [Sandia National Laboratories, Livermore, California (United States)
1997-12-01
As part of the Atmospheric Radiation Measurement (ARM) Enhanced Shortwave Experiment (ARESE), we have obtained and analyzed measurements made from collocated aircraft of the absorption of solar radiation within the atmospheric column between the two aircraft. The measurements were taken during October 1995 at the ARM site in Oklahoma. Relative to a theoretical radiative transfer model, we find no evidence for excess solar absorption in the clear atmosphere and significant evidence for its existence in the cloudy atmosphere. This excess cloud solar absorption appears to occur in both visible (0.224{endash}0.68 {mu}m) and near-infrared (0.68{endash}3.30 {mu}m) spectral regions, although not at 0.5 {mu}m for the visible contribution, and it is shown to be true absorption rather than an artifact of sampling errors caused by measuring three-dimensional clouds. {copyright} 1997 American Geophysical Union
Investigating biases of MODIS AOD from cirrus contamination using collocated CALIOP observations
NASA Astrophysics Data System (ADS)
Oo, M.; Holz, R. E.
2011-12-01
Aerosols have a significant effect on the Earth's radiation balance but aerosol climate forcing is difficult to quantify. The accurate characterization of Aerosol Optical Depth (AOD) is essential in accurately determining the energy balance for climate change studies. The MODIS (Moderate resolution Imaging Spectroradiometer) AOD retrieval uses MODIS to screen for cloud contamination. MODIS can have difficulty detecting optically thin clouds resulting in biases in the AOD retrieval. We present a statistical analysis of MODOS derived AOD with and without the presents of cirrus cloud contamination determined by the collocated CALIPSO (Cloud and Aerosol Lidar and Infrared Pathfinder Spaceborne Observations) retrievals of cirrus optical depth. Global MODIS AOD biases from cirrus contamination will be quantified as a function of geographical region.
NASA Technical Reports Server (NTRS)
Valero, Francisco P. J.; Cess, Robert D.; Zhang, Minghua; Pope, Shelly K.; Bucholtz, Anthony; Bush, Brett; Vitko, John, Jr.
1997-01-01
As part of the Atmospheric Radiation Measurement (ARM) Enhanced Shortwave Experiment (ARESE), we have obtained and analyzed measurements made from collocated aircraft of the absorption of solar radiation within the atmospheric column between the two aircraft. The measurements were taken during October 1995 at the ARM site in Oklahoma. Relative to a theoretical radiative transfer model, we find no evidence for excess solar absorption in the clear atmosphere and significant evidence for its existence in the cloudy atmosphere. This excess cloud solar absorption appears to occur in both visible (0.224-0.68 microns) and near-infrared (0.68-3.30 microns) spectral regions, although not at 0.5 microns for the visible contribution, and it is shown to be true absorption rather than an artifact of sampling errors caused by measuring three-dimensional clouds.
NASA Technical Reports Server (NTRS)
Hastings, E. C., Jr.; Shanks, R. E.; Champine, R. A.; Copeland, W. L.; Young, D. C.
1974-01-01
Flight tests have been conducted to evaluate the effectiveness of a wingtip vortex attenuating device, referred to as a spline. Vortex penetrations were made with a PA-28 behind a C-54 aircraft with and without wingtip splines attached and the resultant rolling acceleration was measured and related to the roll acceleration capability of the PA-28. Tests were conducted over a range of separation distances from about 5 nautical miles (n. mi.) to less than 1 n. mi. Preliminary results indicate that, with the splines installed, there was a significant reduction in the vortex induced roll acceleration experienced by the PA-28 probe aircraft, and the distance at which the PA-28 roll control became ineffective was reduced from 2.5 n. mi. to 0.6 n. mi., or less. There was a slight increase in approach noise (approximately 4 db) with the splines installed due primarily to the higher engine power used during approach. Although splines significantly reduced the C-54 rate of climb, the rates available with four engines were acceptable for this test program. Splines did not introduce any noticeable change in the handling qualities of the C-54.
Improvements on "Fast space-variant elliptical filtering using box splines".
Chaudhury, Kunal Narayan; Sanyal, Sebanti
2012-09-01
It is well-known that box filters can be efficiently computed using pre-integration and local finite-differences. By generalizing this idea and by combining it with a nonstandard variant of the central limit theorem, we had earlier proposed a constant-time or O(1) algorithm that allowed one to perform space-variant filtering using Gaussian-like kernels. The algorithm was based on the observation that both isotropic and anisotropic Gaussians could be approximated using certain bivariate splines called box splines. The attractive feature of the algorithm was that it allowed one to continuously control the shape and size (covariance) of the filter, and that it had a fixed computational cost per pixel, irrespective of the size of the filter. The algorithm, however, offered a limited control on the covariance and accuracy of the Gaussian approximation. In this paper, we propose some improvements of our previous algorithm. PMID:22581135
Pakize Taylan; Gerhard-Wilhelm Weber; Fatma Yerlikaya Özkurt
2010-01-01
This paper introduces a model-based approach to the important data mining tool Multivariate adaptive regression splines (MARS), which has originally been organized in a more model-free way. Indeed, MARS denotes a modern methodology from statistical learning which is important in both classification and regression,\\u000a with an increasing number of applications in many areas of science, economy and technology. It is
Rombado, Gabriel
1989-01-01
. Strain gage orientation on test rotor. 33 test splines, were balanced by Shackelford-Wattner of Houston, Texas. Balancing , of these components was done in accordance with ISO Standard No. 1940: Balance Quality of Rotating Rigid Bodies, 1973. Detailed.... Figure 21. Pneumatic actuator-solenoid arrangement. 48 rotates the hammer-lever arrangement from the horizontal position, about the pivot point, until the hammer tip impacts the balancing land mounted at the test rotor midspan position (refer...
A PSO-Driven Spline-Based Shaping Approach for Ultrawideband (UWB) Antenna Synthesis
Leonardo Lizzi; Federico Viani; Renzo Azaro; Andrea Massa
2008-01-01
Synthesis of ultrawideband (UWB) antennas by means of a particle swarm optimizer (PSO)-driven spline-based shaping approach is described. In order to devise a reliable and effective solution, such a topic is analyzed according to different perspectives: 1) representation of the antenna shape with a simple and efficient description; 2) definition of a suitable description of the UWB Tx\\/Rx system; 3)
IMAGE REGISTRATION BY COMBINING THIN-PLATE SPLINES WITH A 3D MORPHABLE MODEL
Bartoli, Adrien
of parameters, but has the draw- back that the 3D surface is not explicitly reconstructed. We propose an image are typeset using bold fonts, e.g. q, matrices using sans-serif fonts, e.g. E, and scalars in italics, e, drawing on the strengths of both approaches. 2.1. The Image-Based Part: Thin-Plate Splines A TPS
Optimal Knot Selection for Least-squares Fitting of Noisy Data with Spline Functions
Jerome Blair
2008-05-15
An automatic data-smoothing algorithm for data from digital oscilloscopes is described. The algorithm adjusts the bandwidth of the filtering as a function of time to provide minimum mean squared error at each time. It produces an estimate of the root-mean-square error as a function of time and does so without any statistical assumptions about the unknown signal. The algorithm is based on least-squares fitting to the data of cubic spline functions.
Cameron, Andrew; Lui, Dorothy; Boroomand, Ameneh; Glaister, Jeffrey; Wong, Alexander; Bizheva, Kostadinka
2013-01-01
Optical coherence tomography (OCT) allows for non-invasive 3D visualization of biological tissue at cellular level resolution. Often hindered by speckle noise, the visualization of important biological tissue details in OCT that can aid disease diagnosis can be improved by speckle noise compensation. A challenge with handling speckle noise is its inherent non-stationary nature, where the underlying noise characteristics vary with the spatial location. In this study, an innovative speckle noise compensation method is presented for handling the non-stationary traits of speckle noise in OCT imagery. The proposed approach centers on a non-stationary spline-based speckle noise modeling strategy to characterize the speckle noise. The novel method was applied to ultra high-resolution OCT (UHROCT) images of the human retina and corneo-scleral limbus acquired in-vivo that vary in tissue structure and optical properties. Test results showed improved performance of the proposed novel algorithm compared to a number of previously published speckle noise compensation approaches in terms of higher signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR) and better overall visual assessment. PMID:24049697
Berhane, Kiros; Hauptmann, Michael; Langholz, Bryan
2008-11-20
An adequate depiction of exposure-time-response relationships is important in assessing public health implications of an occupational or environmental exposure. Recent advances have focused on flexible modeling of the overall shape of latency. Methods are needed to allow for varying shapes of latency under different exposure profiles. A tensor product spline model is proposed for describing exposure-response relationships for protracted time-dependent occupational exposure histories in epidemiologic studies. The methods use flexible multi-dimensional techniques to jointly model age, latency and exposure-response effects. In analyzing data from the Colorado Plateau Uranium Miners cohort, a model that allows for varying exposure-dependent latency shapes is found to be superior to models that only allowed for an overall latency curve. Specifically, the model suggests that, at low exposure levels risk increased at short latencies followed by a slow decline for longer latency periods. On the other hand, risk was higher but did not change much by latency for higher exposure levels. The proposed methodology has the advantage of allowing for latency functions that vary by exposure levels and, conversely, exposure-response relationships that are influenced by the latency structure. PMID:18613262
Distributed lag and spline modeling for predicting energy expenditure from accelerometry in youth
Chen, Kong Y.; Acra, Sari A.; Buchowski, Maciej S.
2010-01-01
Movement sensing using accelerometers is commonly used for the measurement of physical activity (PA) and estimating energy expenditure (EE) under free-living conditions. The major limitation of this approach is lack of accuracy and precision in estimating EE, especially in low-intensity activities. Thus the objective of this study was to investigate benefits of a distributed lag spline (DLS) modeling approach for the prediction of total daily EE (TEE) and EE in sedentary (1.01.5 metabolic equivalents; MET), light (1.53.0 MET), and moderate/vigorous (?3.0 MET) intensity activities in 10- to 17-year-old youth (n = 76). We also explored feasibility of the DLS modeling approach to predict physical activity EE (PAEE) and METs. Movement was measured by Actigraph accelerometers placed on the hip, wrist, and ankle. With whole-room indirect calorimeter as the reference standard, prediction models (Hip, Wrist, Ankle, Hip+Wrist, Hip+Wrist+Ankle) for TEE, PAEE, and MET were developed and validated using the fivefold cross-validation method. The TEE predictions by these DLS models were not significantly different from the room calorimeter measurements (all P > 0.05). The Hip+Wrist+Ankle predicted TEE better than other models and reduced prediction errors in moderate/vigorous PA for TEE, MET, and PAEE (all P < 0.001). The Hip+Wrist reduced prediction errors for the PAEE and MET at sedentary PA (P = 0.020 and 0.021) compared with the Hip. Models that included Wrist correctly classified time spent at light PA better than other models. The means and standard deviations of the prediction errors for the Hip+Wrist+Ankle and Hip were 0.4 ą 144.0 and 1.5 ą 164.7 kcal for the TEE, 0.0 ą 84.2 and 1.3 ą 104.7 kcal for the PAEE, and ?1.1 ą 97.6 and ?0.1 ą 108.6 MET min for the MET models. We conclude that the DLS approach for accelerometer data improves detailed EE prediction in youth. PMID:19959770
Cell averaging Chebyshev methods for hyperbolic problems. Final report
C. Wei; D. Gottlieb; A. Harten
1990-01-01
A cell averaging method for the Chebyshev approximations of first order hyperbolic equations in conservation form is described. Formulas are presented for transforming between pointwise data at the collocation points and cell averaged quantities, and vice-versa. This step, trivial for the finite difference and Fourier methods, is nontrivial for the global polynomials used in spectral methods. The cell averaging methods
Thorsten Kattelansand; Wilhelm Heinrichs
2008-01-01
We consider a new least-squares spectral collocation scheme for the Stokes and the Navier-Stokes equations. By introducing the Clenshaw-Curtis quadrature rule for imposing the average pressure to be zero we reduce the condition numbers of the over-determined systems. All computations are performed with an explicit scheme and saves a lot of CPU time compared to implicit schemes. We compare two
J. Keder
1999-01-01
Summary A REMTECH PA2 Doppler Sodar is operated regularly at the Czech Hydrometeorological Institute (CHMI) observatory in Prague,\\u000a collocated with a routine rawinsonde sounding system. The Air Pollution Control Division of CHMI utilises the sodar data in\\u000a air pollution studies and as an information support for the smog warning system operated in Prague. Besides of the basic software\\u000a for echo
An E-J Collocated 3-D FDTD Model of Electromagnetic Wave Propagation in Magnetized Cold Plasma
Yaxin Yu; Jamesina J. Simpson
2010-01-01
A new three-dimensional finite-difference time-domain (FDTD) numerical model is proposed herein to simulate electromagnetic wave propagation in an anisotropic magnetized cold plasma medium. Plasma effects contributed by electrons, positive, and negative ions are considered in this model. The current density vectors are collocated at the positions of the electric field vectors, and the complete FDTD algorithm consists of three regular
An Analysis of Peak Wind Speed Data from Collocated Mechanical and Ultrasonic Anemometers
NASA Technical Reports Server (NTRS)
Short, David A.; Wells, Leonard; Merceret, Francis J.; Roeder, William P.
2007-01-01
This study compared peak wind speeds reported by mechanical and ultrasonic anemometers at Cape Canaveral Air Force Station and Kennedy Space Center (CCAFS/KSC) on the east central coast of Florida and Vandenberg Air Force Base (VAFB) on the central coast of California. Launch Weather Officers, forecasters, and Range Safety analysts need to understand the performance of wind sensors at CCAFS/KSC and VAFB for weather warnings, watches, advisories, special ground processing operations, launch pad exposure forecasts, user Launch Commit Criteria (LCC) forecasts and evaluations, and toxic dispersion support. The legacy CCAFS/KSC and VAFB weather tower wind instruments are being changed from propeller-and-vane (CCAFS/KSC) and cup-and-vane (VAFB) sensors to ultrasonic sensors under the Range Standardization and Automation (RSA) program. Mechanical and ultrasonic wind measuring techniques are known to cause differences in the statistics of peak wind speed as shown in previous studies. The 45th Weather Squadron (45 WS) and the 30th Weather Squadron (30 WS) requested the Applied Meteorology Unit (AMU) to compare data between the RSA ultrasonic and legacy mechanical sensors to determine if there are significant differences. Note that the instruments were sited outdoors under naturally varying conditions and that this comparison was not designed to verify either technology. Approximately 3 weeks of mechanical and ultrasonic wind data from each range from May and June 2005 were used in this study. The CCAFS/KSC data spanned the full diurnal cycle, while the VAFB data were confined to 1000-1600 local time. The sample of 1-minute data from numerous levels on five different towers on each range totaled more than 500,000 minutes of data (482,979 minutes of data after quality control). The ten towers were instrumented at several levels, ranging from 12 ft to 492 ft above ground level. The ultrasonic sensors were collocated at the same vertical levels as the mechanical sensors and typically within 15 ft horizontally of each another. Data from a total of 53 RSA ultrasonic sensors, collocated with mechanical sensors were compared. The 1- minute average wind speed/direction and the 1-second peak wind speed/direction were compared.
Assessment of the Suomi NPP/VIIRS aerosol products using the collocated Aqua/MODIS aerosol products
NASA Astrophysics Data System (ADS)
Oo, M. M.; Holz, R.; Cureton, G. P.; Laszlo, I.; Kondragunta, S.; Huang, J.; Remer, L. A.
2012-12-01
Following the successful launch of the Visible Infrared Imaging Radiometer Suite (VIIRS) instrument onboard the Suomi National Polar-orbiting Partnership (NPP) spacecraft, the VIIRS sensor collects daily global aerosol coverage to provide aerosol Intermediate Products (IPs) and Environmental Data Records (EDRs) to the user community. We validate the IPs and EDRs of the VIIRS Aerosol Optical Thickness (AOT) and Angström Exponent (AE) against the collocated well-characterized MODIS aerosol products from the NASA Earth Observing System (EOS) Aqua satellite. Both sensors are on the early afternoon orbit, which provides us an excellent opportunity to cross validate these operational satellite aerosol observations. Qualitative and quantitative assessments are conducted to characterize the VIIRS aerosol products. In the direct comparison, global aerosol maps of the collocated VIIRS-MODIS aerosol products are presented based on various match-up criteria based on quality flags, viewing geometries, AOT and AE data ranges etc. VIIRS AOT appears to match MODIS well over ocean, but is biased high against MODIS over land, except in desert regions. VIIRS AOT appears to correlate best with MODIS for high AE, and less well for coarse particle sizes. These results are based on a very limited analysis period of one month, and could change seasonally. The similarities and differences of the collocated VIIRS and MODIS aerosol products are discussed in details. Statistics of VIIRS vs. MODIS AOT where ?? = ?VIIRS -?MODIS;
NASA Astrophysics Data System (ADS)
Mattes, Julian; Fieres, Johannes; Eils, Roland
2002-05-01
This paper focuses on the problem of ill-posedness of deformable point set registration and we propose a new approach to restrict the solution space using shape information. The basic elements of the investigated kind of registration algorithm are a cost functional, an optimization strategy and a motion model. The motion model determines the kind of motions and deformations that are allowed and how they are restricted. The motion model itself is mainly determined by the kind of parameterized transformation used to express the motion/deformation. Here, we observe that matching with more degrees of freedom (the parameters of the transformation) than necessary can introduce mismatches due to a higher sensitivity to noise or by destroying local shape information. In this paper we propose a cost functional which is robust to noise and we introduce a new method to specify a shape adapted deformation model based on thin-plate splines and initial control point placing using point clustering. We show that these initial positions have a strong impact on the match and we define them as cluster centers where we cluster on one of the point sets (weighting each point of this set with its distance to the other point set). Our experiments with known ground truth show that the shape adapted model recovers constantly very accurately corresponding points. In our evaluation with more than 1200 single experiments we showed that, compared to a conventional octree based scheme, we could save more than 60% of degrees of freedom while preserving matching quality.
Design a LED coupler to collocate with a light guide plate for illumination
NASA Astrophysics Data System (ADS)
Teng, Tun-Chien; Tseng, Li-Wei
2014-09-01
With progress in the LED luminous efficiency, the LED gradually expands the scope of application from the backlight to general lighting. In the application of the backlight, a light guide plate (LGP) is used to guide the LED light and emits the light uniformly from its surface to achieve a uniform planar light source. Except for the merit of slim volume, the LGP can prevent the LED light from directly entering the eyes resulting in glare; thereby the LGP is also used for general lighting applications, especially for the high-directionality lighting with slim volume. For the illumination, the prescribed distribution of the light emitted from the LGP had better modulated by both the microstructure on the LGP surface and a LED lens/coupler. In general, distribution of the light emitted from the LED is partially adjusted by the LED lens/coupler before the light entering the LGP. In this study we designed a LED coupler to collocate with two types of LGPs so that the LGP can uniformly emits the highly-collimated light or the light with the prescribed intensity distribution, which can be used for the backlight or lighting application, respectively.
NASA Astrophysics Data System (ADS)
Huang, Jingfeng; Hsu, N. Christina; Tsay, Si-Chee; Holben, Brent N.; Welton, Ellsworth J.; Smirnov, Alexander; Jeong, Myeong-Jae; Hansell, Richard A.; Berkoff, Timothy A.; Liu, Zhaoyan; Liu, Gin-Rong; Campbell, James R.; Liew, Soo Chin; Barnes, John E.
2012-08-01
Cirrus clouds, particularly subvisual high thin cirrus with low optical thickness, are difficult to screen in operational aerosol retrieval algorithms. Collocated aerosol and cirrus observations from ground measurements, such as the Aerosol Robotic Network (AERONET) and the Micro-Pulse Lidar Network (MPLNET), provide us with an unprecedented opportunity to systematically examine the susceptibility of operational aerosol products to cirrus contamination. Quality assured aerosol optical thickness (AOT) measurements were also tested against the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) vertical feature mask (VFM) and the Moderate Resolution Imaging Spectroradiometer (MODIS) thin cirrus screening parameters for the purpose of evaluating cirrus contamination. Key results of this study include: (1) quantitative evaluations of data uncertainties in AERONET AOT retrievals are conducted; although AERONET cirrus screening schemes are successful in removing most cirrus contamination, strong residuals displaying strong spatial and seasonal variability still exist, particularly over thin cirrus prevalent regions during cirrus peak seasons; (2) challenges in matching up different data for analysis are highlighted and corresponding solutions proposed; and (3) estimates of the relative contributions from cirrus contamination to aerosol retrievals are discussed. The results are valuable for better understanding and further improving ground aerosol measurements that are critical for aerosol-related climate research.
NASA Technical Reports Server (NTRS)
Huang, Jingfeng; Hsu, N. Christina; Tsay, Si-Chee; Holben, Brent N.; Welton, Ellsworth J.; Smirnov, Alexander; Jeong, Myeong-Jae; Hansell, Richard A.; Berkoff, Timothy A.
2012-01-01
Cirrus clouds, particularly sub visual high thin cirrus with low optical thickness, are difficult to be screened in operational aerosol retrieval algorithms. Collocated aerosol and cirrus observations from ground measurements, such as the Aerosol Robotic Network (AERONET) and the Micro-Pulse Lidar Network (MPLNET), provide us with an unprecedented opportunity to examine the susceptibility of operational aerosol products to thin cirrus contamination. Quality assured aerosol optical thickness (AOT) measurements were also tested against the CALIPSO vertical feature mask (VFM) and the MODIS-derived thin cirrus screening parameters for the purpose of evaluating thin cirrus contamination. Key results of this study include: (1) Quantitative evaluations of data uncertainties in AERONET AOT retrievals are conducted. Although AERONET cirrus screening schemes are successful in removing most cirrus contamination, strong residuals displaying strong spatial and seasonal variability still exist, particularly over thin cirrus prevalent regions during cirrus peak seasons, (2) Challenges in matching up different data for analysis are highlighted and corresponding solutions proposed, and (3) Estimation of the relative contributions from cirrus contamination to aerosol retrievals are discussed. The results are valuable for better understanding and further improving ground aerosol measurements that are critical for aerosol-related climate research.
A domain adaptive stochastic collocation approach for analysis of MEMS under uncertainties
Agarwal, Nitin [Department of Mechanical Science and Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, 405 N. Mathews Avenue, Urbana, IL 61801 (United States); Aluru, N.R. [Department of Mechanical Science and Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, 405 N. Mathews Avenue, Urbana, IL 61801 (United States)], E-mail: aluru@uiuc.edu
2009-11-01
This work proposes a domain adaptive stochastic collocation approach for uncertainty quantification, suitable for effective handling of discontinuities or sharp variations in the random domain. The basic idea of the proposed methodology is to adaptively decompose the random domain into subdomains. Within each subdomain, a sparse grid interpolant is constructed using the classical Smolyak construction [S. Smolyak, Quadrature and interpolation formulas for tensor products of certain classes of functions, Soviet Math. Dokl. 4 (1963) 240-243], to approximate the stochastic solution locally. The adaptive strategy is governed by the hierarchical surpluses, which are computed as part of the interpolation procedure. These hierarchical surpluses then serve as an error indicator for each subdomain, and lead to subdivision whenever it becomes greater than a threshold value. The hierarchical surpluses also provide information about the more important dimensions, and accordingly the random elements can be split along those dimensions. The proposed adaptive approach is employed to quantify the effect of uncertainty in input parameters on the performance of micro-electromechanical systems (MEMS). Specifically, we study the effect of uncertain material properties and geometrical parameters on the pull-in behavior and actuation properties of a MEMS switch. Using the adaptive approach, we resolve the pull-in instability in MEMS switches. The results from the proposed approach are verified using Monte Carlo simulations and it is demonstrated that it computes the required statistics effectively.
Keith, Scott W.; Allison, David B.
2014-01-01
This paper details the design, evaluation, and implementation of a framework for detecting and modeling nonlinearity between a binary outcome and a continuous predictor variable adjusted for covariates in complex samples. The framework provides familiar-looking parameterizations of output in terms of linear slope coefficients and odds ratios. Estimation methods focus on maximum likelihood optimization of piecewise linear free-knot splines formulated as B-splines. Correctly specifying the optimal number and positions of the knots improves the model, but is marked by computational intensity and numerical instability. Our inference methods utilize both parametric and nonparametric bootstrapping. Unlike other nonlinear modeling packages, this framework is designed to incorporate multistage survey sample designs common to nationally representative datasets. We illustrate the approach and evaluate its performance in specifying the correct number of knots under various conditions with an example using body mass index (BMI; kg/m2) and the complex multi-stage sampling design from the Third National Health and Nutrition Examination Survey to simulate binary mortality outcomes data having realistic nonlinear sample-weighted risk associations with BMI. BMI and mortality data provide a particularly apt example and area of application since BMI is commonly recorded in large health surveys with complex designs, often categorized for modeling, and nonlinearly related to mortality. When complex sample design considerations were ignored, our method was generally similar to or more accurate than two common model selection procedures, Schwarzs Bayesian Information Criterion (BIC) and Akaikes Information Criterion (AIC), in terms of correctly selecting the correct number of knots. Our approach provided accurate knot selections when complex sampling weights were incorporated, while AIC and BIC were not effective under these conditions. PMID:25610831
A new method of imposing boundary conditions for hyperbolic equations
NASA Technical Reports Server (NTRS)
Funaro, D.; ative.
1987-01-01
A new method to impose boundary conditions for pseudospectral approximations to hyperbolic equations is suggested. This method involves the collocation of the equation at the boundary nodes as well as satisfying boundary conditions. Stability and convergence results are proven for the Chebyshev approximation of linear scalar hyperbolic equations. The eigenvalues of this method applied to parabolic equations are shown to be real and negative.
Fractional-step method for two-dimensional estuarine transport
Bales, Jerad D.; Holley, Edward R.
1988-01-01
The fractional-step method was used in this study to split the longitudinal advective transport term from the other terms in the two-dimensional, laterally-averaged equation for estuarine mass transport. The method of characteristics with spline interpolations was used to approximate the longitudinal advective transport. A general discussion of the fractional-step method, the specific algorithm developed in this investigation, and results of numerical tests are presented. Application of the fractional-step method in conjunction with the characteristic-spline scheme offers the potential for improved simulations of transport for situations in which concentration gradients are steep.
A PSO algorithm for biped gait planning using spline approximation
Zhang Qizhi; Zhou Yali; Ge Xinsheng
2010-01-01
This paper discusses an optimal trajectory planning method for a compass gait biped robot. The biped robot is composed of a stance leg and a swing leg. Each step of walking locomotion is divided into two phases, i.e., the swing phase and toe collision phase. It is assumed that the toe collision is perfect plastic and occurs instantly. The motion
Nagel-Alne, G E; Krontveit, R; Bohlin, J; Valle, P S; Skjerve, E; Sřlverřd, L S
2014-07-01
In 2001, the Norwegian Goat Health Service initiated the Healthier Goats program (HG), with the aim of eradicating caprine arthritis encephalitis, caseous lymphadenitis, and Johne's disease (caprine paratuberculosis) in Norwegian goat herds. The aim of the present study was to explore how control and eradication of the above-mentioned diseases by enrolling in HG affected milk yield by comparison with herds not enrolled in HG. Lactation curves were modeled using a multilevel cubic spline regression model where farm, goat, and lactation were included as random effect parameters. The data material contained 135,446 registrations of daily milk yield from 28,829 lactations in 43 herds. The multilevel cubic spline regression model was applied to 4 categories of data: enrolled early, control early, enrolled late, and control late. For enrolled herds, the early and late notations refer to the situation before and after enrolling in HG; for nonenrolled herds (controls), they refer to development over time, independent of HG. Total milk yield increased in the enrolled herds after eradication: the total milk yields in the fourth lactation were 634.2 and 873.3 kg in enrolled early and enrolled late herds, respectively, and 613.2 and 701.4 kg in the control early and control late herds, respectively. Day of peak yield differed between enrolled and control herds. The day of peak yield came on d 6 of lactation for the control early category for parities 2, 3, and 4, indicating an inability of the goats to further increase their milk yield from the initial level. For enrolled herds, on the other hand, peak yield came between d 49 and 56, indicating a gradual increase in milk yield after kidding. Our results indicate that enrollment in the HG disease eradication program improved the milk yield of dairy goats considerably, and that the multilevel cubic spline regression was a suitable model for exploring effects of disease control and eradication on milk yield. PMID:24819129
Boundary conditions in Chebyshev and Legendre methods
NASA Technical Reports Server (NTRS)
Canuto, C.
1984-01-01
Two different ways of treating non-Dirichlet boundary conditions in Chebyshev and Legendre collocation methods are discussed for second order differential problems. An error analysis is provided. The effect of preconditioning the corresponding spectral operators by finite difference matrices is also investigated.
Computation of eddy current losses induced by magnetic domain walls motion with Ck-spline functions
NASA Astrophysics Data System (ADS)
Lakhdari, Zakaria; Adélaďde, Luca; Makany, Philippe
2008-04-01
This article presents a computation of the nonlinear dynamics of magnetic domain wall motion in ferromagnetic material such as crystalline, like Fe-Si, in formulation H, with interactions between walls, and bulk magnetic induction. These terms have important contributions to ferromagnetic losses in high exciting magnetic fields and are usually neglected. The dynamic trajectories of magnetic domain walls are given as nonlinear coupled ordinary differential time equations. Our simulations use the Ck-spline approach, which allows many algebraic facilities in algorithms and in boundary conditions.
NASA Astrophysics Data System (ADS)
MacCracken, R. F.; Purser, J. J.; Collard, A.
2014-12-01
In the effort to reduce errors, and improve the accuracy of the representation of the vertical profile of temperature, a new "modified cubic spline" interpolation scheme is being tested for use within the Gridded Statistical Interpolation (GSI), within the Global Forecast System. This scheme differs from the existing horizontal and vertical linear interpolation scheme, since it utilizes additional target points to create a smoother profile. Through comparison testing with existing methodologies, it has been determined that better representation at the tropopause has been achieved in several test cases, and in within various zonal global regions. This poster illustrates the implementation of the new interpolation scheme, and the comparison to the existing methodologies.
NASA Technical Reports Server (NTRS)
Anuta, P. E.
1975-01-01
Least squares approximation techniques were developed for use in computer aided correction of spatial image distortions for registration of multitemporal remote sensor imagery. Polynomials were first used to define image distortion over the entire two dimensional image space. Spline functions were then investigated to determine if the combination of lower order polynomials could approximate a higher order distortion with less computational difficulty. Algorithms for generating approximating functions were developed and applied to the description of image distortion in aircraft multispectral scanner imagery. Other applications of the techniques were suggested for earth resources data processing areas other than geometric distortion representation.
NASA Technical Reports Server (NTRS)
Benton, E. R.; Kohl, Benjamin C.
1986-01-01
An optimum truncation level, N, in a spherical-harmonic analysis of the geomagnetic main field at the core-mantle boundary is determined by harmonic-spline analysis. Specifically, that value of N is found at which the two analyses are closest in a well defined sense and, for that value of N, the 'closeness' of two models is determined. Depending slightly on the definition of closeness, optimum N is found to be either 10 or 11. For those values the two analyses give remarkably similar results, showing that the conveniences of spherical harmonics can be retained with little penalty.
NASA Technical Reports Server (NTRS)
Ku, C.-P. Roger; Walton, James F., Jr.; Lund, Jorgen W.
1994-01-01
This paper provided an opportunity to quantify the angular stiffness and equivalent viscous damping coefficients of an axial spline coupling used in high-speed turbomachinery. A unique test methodology and data reduction procedures were developed. The bending moments and angular deflections transmitted across an axial spline coupling were measured while a nonrotating shaft was excited by an external shaker. A rotor dynamics computer program was used to simulate the test conditions and to correlate the angular stiffness and damping coefficients. In addition, sensitivity analyses were performed to show that the accuracy of the dynamic coefficients do not rely on the accuracy of the data reduction procedures.
A high-speed method for eigenvalue problems. II Calculation of the eigenfunction in Milne's method
T. Yano; T. Yokota; K. Kawabata; M. Otsuka; S. Matsushima; Y. Ezawa; S. Tomiyoshi
1992-01-01
A new version of the program MEIGEN is presented for the eigenvalue problem of Sturm-Liouville-type linear equations in Milne's method. Use of the spline function and the WKB approximation provide a high-speed method for calculating eigenvalues and eigenfunctions avoiding divergence problems.
Nakashima, Eiji
2015-07-01
Using the all solid cancer mortality data set of the Life Span Study (LSS) cohort from 1950 to 2003 (LSS Report 14) data among atomic bomb survivors, excess relative risk (ERR) statistical analyses were performed using the second degree polynomial and the threshold and restricted cubic spline (RCS) dose response models. For the RCS models with 3 to 7 knots of equally spaced percentiles with margins in the dose range greater than 50 mGy, the dose response was assumed to be linear at less than 70 to 90 mGy. Due to the skewed dose distribution of atomic bomb survivors, the current knot system for the RCS analysis results in a detailed depiction of the dose response as less than approximately 0.5 Gy. The 6 knot RCS models for the all-solid cancer mortality dose response of the whole dose or less than 2 Gy were selected with the AIC model selection criterion and fit significantly better (p < 0.05) than the linear (L) model. The usual RCS includes the L-global model but not the quadratic (Q) nor linear-quadratic (LQ) global models. The authors extended the RCS to include L or LQ global models by putting L or LQ constraints on the cubic spline in the lower and upper tails, and the best RCS model selected with AIC criterion was the usual RCS with L-constraints in both the lower and upper tails. The selected RCS had a linear dose-response model in the lower dose range (i.e., < 0.2-0.3 Gy) and was compatible with the linear no-threshold (LNT) model in this dose range. The proposed method is also useful in describing the dose response of a specific cancer or non-cancer disease incidence/mortality. PMID:26011495
RGB Color Calibration for Quantitative Image Analysis: The 3D Thin-Plate Spline Warping Approach
Menesatti, Paolo; Angelini, Claudio; Pallottino, Federico; Antonucci, Francesca; Aguzzi, Jacopo; Costa, Corrado
2012-01-01
In the last years the need to numerically define color by its coordinates in n-dimensional space has increased strongly. Colorimetric calibration is fundamental in food processing and other biological disciplines to quantitatively compare samples' color during workflow with many devices. Several software programmes are available to perform standardized colorimetric procedures, but they are often too imprecise for scientific purposes. In this study, we applied the Thin-Plate Spline interpolation algorithm to calibrate colours in sRGB space (the corresponding Matlab code is reported in the Appendix). This was compared with other two approaches. The first is based on a commercial calibration system (ProfileMaker) and the second on a Partial Least Square analysis. Moreover, to explore device variability and resolution two different cameras were adopted and for each sensor, three consecutive pictures were acquired under four different light conditions. According to our results, the Thin-Plate Spline approach reported a very high efficiency of calibration allowing the possibility to create a revolution in the in-field applicative context of colour quantification not only in food sciences, but also in other biological disciplines. These results are of great importance for scientific color evaluation when lighting conditions are not controlled. Moreover, it allows the use of low cost instruments while still returning scientifically sound quantitative data. PMID:22969337
Verhaeghe, Jeroen; D'Asseler, Yves; Vandenberghe, Stefaan; Staelens, Steven; Lemahieu, Ignace [Department of Electronics and Information Systems, Medical Image and Signal Processing Group, Ghent University, Ghent, 9000 (Belgium)
2007-05-15
The use of a temporal B-spline basis for the reconstruction of dynamic positron emission tomography data was investigated. Maximum likelihood (ML) reconstructions using an expectation maximization framework and maximum A-posteriori (MAP) reconstructions using the generalized expectation maximization framework were evaluated. Different parameters of the B-spline basis of such as order, number of basis functions and knot placing were investigated in a reconstruction task using simulated dynamic list-mode data. We found that a higher order basis reduced both the bias and variance. Using a higher number of basis functions in the modeling of the time activity curves (TACs) allowed the algorithm to model faster changes of the TACs, however, the TACs became noisier. We have compared ML, Gaussian postsmoothed ML and MAP reconstructions. The noise level in the ML reconstructions was controlled by varying the number of basis functions. The MAP algorithm penalized the integrated squared curvature of the reconstructed TAC. The postsmoothed ML was always outperformed in terms of bias and variance properties by the MAP and ML reconstructions. A simple adaptive knot placing strategy was also developed and evaluated. It is based on an arc length redistribution scheme during the reconstruction. The free knot reconstruction allowed a more accurate reconstruction while reducing the noise level especially for fast changing TACs such as blood input functions. Limiting the number of temporal basis functions combined with the adaptive knot placing strategy is in this case advantageous for regularization purposes when compared to the other regularization techniques.
Centers, P.W. [Wright Patterson Air Force Base, OH (United States)
1995-05-01
Dependent upon molecular weight and distribution, concentration, temperature, air flow, and test details or field application, polydimethylsiloxane (PDMS) may be neutral, profoamant or antifoamant in polyolesters. This understanding was critical in the solution of a turbine engine lubrication system foaming problem occurring at several military locations. Suspect turbine engine-accessory gearbox assembly materials gathered from several sites were evaluated. One non-specification PDMS-based spline lubricant caused copious foaming of the lubricant at less than ten parts-per-million concentration, while a specification polymethyl-phenylsiloxane (PMPS)-based lubricant required a concentration nearly 2000 times greater to generate equivalent foam. Use of the profoamant PDMS spline lubricant was then prohibited. Since prohibition, foaming of turbine engine lubricants used in the particular application has not been reported. PMPS impact on foaming of ester lubricants is similar to a much more viscous PDMS attributed to the reduced interaction of PMPS in esters due to pendant phenyl structure of PMPS absent in PDMS. These data provide significant additional insight and methodology to investigate foaming tendencies of partially miscible silicone-ester and other fluid systems. 7 refs., 2 figs., 1 tab.
Non-lambertian reflectance modeling and shape recovery of faces using tensor splines.
Kumar, Ritwik; Barmpoutis, Angelos; Banerjee, Arunava; Vemuri, Baba C
2011-03-01
Modeling illumination effects and pose variations of a face is of fundamental importance in the field of facial image analysis. Most of the conventional techniques that simultaneously address both of these problems work with the Lambertian assumption and thus fall short of accurately capturing the complex intensity variation that the facial images exhibit or recovering their 3D shape in the presence of specularities and cast shadows. In this paper, we present a novel Tensor-Spline-based framework for facial image analysis. We show that, using this framework, the facial apparent BRDF field can be accurately estimated while seamlessly accounting for cast shadows and specularities. Further, using local neighborhood information, the same framework can be exploited to recover the 3D shape of the face (to handle pose variation). We quantitatively validate the accuracy of the Tensor Spline model using a more general model based on the mixture of single-lobed spherical functions. We demonstrate the effectiveness of our technique by presenting extensive experimental results for face relighting, 3D shape recovery, and face recognition using the Extended Yale B and CMU PIE benchmark data sets. PMID:21252399
NASA Astrophysics Data System (ADS)
Dvorska, Alice; Milan, Vá?a; Vlastimil, Hanu; Marian, Pavelka
2013-04-01
The collocated station Koetice - K?eín u Pacova, central Czech Republic, is a major research and monitoring infrastructure in the Czech Republic and central Europe. It consists of two basic components: the observatory Koetice run since 1988 by the Czech Hydrometeorological Institute and the atmospheric station (AS) K?eín u Pacova starting operation in 2013. The AS is built and run by CzechGlobe - Global Change Research Centre, Academy of Sciences of the Czech Republic and is situated 100 m far from the observatory. There are three research and monitoring activities at the collocated station providing data necessary for the research on climate and related changes. The AS K?eín u Pacova consists of a 250 m tall tower serving for ground-based and vertical gradient measurements of (i) concentrations of CO2, CO, CH4, total gaseous mercury and tropospheric ozone (continuously), (ii) elemental and organic carbon (semicontinuously), (iii) carbon and oxygen isotopes, radon, N2O, SF6 and other species (episodically), (iv) optical properties of atmospheric aerosols and (v) meteorological parameters and the boundary layer height. Further, eddy covariance measurements in the nearby agroecosystem provide data on CO2 and H2O fluxes between the atmosphere and the ecosystem. Finally, monitoring activities at the nearby small hydrological catchment Anenské povodí run under the GEOMON network enables studying local hydrological and biogeochemical cycles. These measurements are supported by the long-term monitoring of meteorological and air quality parameters at the observatory Koetice, that are representative for the central European background. The collocated station provides a big research opportunity and challenge due to (i) a broad spectra of monitored chemical species, meteorological, hydrological and other parameters, (ii) measurements in various environmental compartments and especially the atmosphere, (iii) provision of data suitable for conducting multidisciplinar research activities and (iv) participation in a number of international programmes and projects, i.e. ICOS (AS K?eín u Pacova), ACTRIS, ACCENT, CLRTAP/EMEP, GAW and ICP-IM (Koetice) and others. Finally, the collocated station has potential for a successful participation in the planned network of European superstations covering both climate and air quality issues, one of the key areas in the European Strategy Forum on Research Infrastructures (ESFRI) process. Acknowledgement: This work is supported by the CzechGlobe (CZ.1.05/1.1.00/02.0073) and CZ.1.07/2.4.00/31.0056 projects.
Arbitrary order Krylov deferred correction methods for differential algebraic equations
Jingfang Huang; Jun Jia; Michael Minion
2007-01-01
In this paper, a new framework for the construction of accurate and efficient numerical methods for differential algebraic equation (DAE) initial value problems is presented. The methods are based on applying spectral deferred correction techniques as preconditioners to a Picard integral collocation formulation for the solution. The resulting preconditioned nonlinear system is solved using NewtonKrylov schemes such as the Newton-GMRES
Methods for local gravity field approximation
NASA Technical Reports Server (NTRS)
Sailor, R. V.; Tait, K. S.; Leschack, A. R.
1989-01-01
The most widely known modern method for estimating gravity field values from observed data is least-squares collocation. Its advantages are that it can make estimates at arbitrary locations based on irregularly spaced observations, and that it makes use of statistical information about errors in the input data while providing corresponding information about the quality of the output estimates. Disadvantages of collocation include the necessity of inverting square matrices of dimension equal to the number of data values and the need to assume covariance models for the gravity field and the data errors. Fourier methods are an important alternative to collocation; having the advantage of greater computational efficiency, but requiring data estimates to be on a regular grid and not using or providing statistical accuracy information. The GEOFAST algorithm is an implementation of collocation that achieves high computational efficiency by transforming the estimation equations into the frequency domain where an accurate approximation may be made to reduce the workload. The forward and inverse Fast Fourier Transforms (FFTs) are utilized. The accuracy and computational efficiency of the GEOFAST algorithm is demonstrated using two sets of synthetic gravity data: marine gravity for an ocean trench region including wavelengths longer than 200 km; and local land gravity containing wavelengths as short as 5 km. These results are discussed along with issues such as the advantages of first removing reference field models before carrying out the estimation algorithm.
Towards a time-dependent description of electron-atom/ion collisions: Two electron systems
Bottcher, C.; Madison, D.H.; Schultz, D.R.
1992-01-01
This report contains the following discussions on a time-dependent description of electron-atom/ion collisions: numerical calculation of correlated wavefunctions for the coulomb three-body problem; the basis-spline collocation method; and time-dependent perturbation theory model.
Towards a time-dependent description of electron-atom/ion collisions: Two electron systems
Bottcher, C.; Madison, D.H.; Schultz, D.R.
1992-12-31
This report contains the following discussions on a time-dependent description of electron-atom/ion collisions: numerical calculation of correlated wavefunctions for the coulomb three-body problem; the basis-spline collocation method; and time-dependent perturbation theory model.
Möller, Torsten
of these reconstruction filters and using the Fourier slice-projection theorem we de- rive their frequency responses lattice. CR Categories: G.1.1 [Numerical Analysis]: Approximation--Box Splines; G.1.2 [Numerical Analy in science and engineering have been dealing with the discrete representations of (assumably) continuous
Optimal trajectory generation for a glider in time-varying 2D ocean flows B-spline model
Weizhong Zhang; Tamer Inane; Sina Ober-blöbaum; Jerrold E. Marsden
2008-01-01
The problem of showing that Lagrangian Coherent Structures (LCS) are useful in determining near optimal trajectories for autonomous underwater vehicles (AUVs) known as gliders is investigated. This paper extends our preliminary results in couple ways. First, the ocean current flows are modeled by 3D B-spline functions in which the input variables are latitude, longitude and time, and the output variable
Optimal Trajectory Generation for a Glider in Time-Varying 2D Ocean Flows B-spline Model
Ober-Blöbaum, Sina
Optimal Trajectory Generation for a Glider in Time-Varying 2D Ocean Flows B-spline Model Weizhong underwater vehicles (AUVs) known as gliders is investigated. This paper extends our preliminary results Generation (NTG) algorithm to find the optimal trajectory of the glider. The trajectories found using the 2D
Baltazar, J. C.; Claridge, D. E.
2002-01-01
The paper presents seventeen approaches that use cubic splines and Fourier series for restoring short term missing data in time series of building energy use and weather data. The study is based on twenty samples of hourly data, each at least one...
Baltazar-Cervantes, J. C.; Claridge, D. E.
2002-01-01
This paper presents seventeen approaches that use cubic splines and Fourier series for restoring short term missing data in time series of building energy use and weather data. The study is based on twenty samples of hourly data, each at least one...
Martin, Fernando; Horner, Daniel A.; Vanroose, Wim; Rescigno,Thomas N.; McCurdy, C. William
2005-11-04
We report a fully ab initio implementation of exterior complex scaling in B-splines to evaluate total, singly and triply differential cross sections in double photoionization problems. Results for He and H{sub 2} double photoionization are presented and compared with experiment.
Technology Transfer Automated Retrieval System (TEKTRAN)
The objective was to estimate genetic parameters for individual test-day milk, fat, and protein yields with a cubic spline model. A total of 196,687 test-day records in the first 305-d of 38,172 first lactation Holstein cows that calved between 1994 and early 1999 were obtained from Dairy Records Ma...
A New Solid Subdivision Scheme based on Box Splines Yu-Sung Chang Kevin T. McDonnell Hong Qin
McDonnell, Kevin
A New Solid Subdivision Scheme based on Box Splines Yu-Sung Chang Kevin T. McDonnell Hong Qin solid modeling tool. In this paper, we propose a novel solid subdivision scheme based on tri-variate box the straightforward implementation of our simple, yet powerful solid subdivision scheme. The subdivision hi- erarchy
Michael F. Hutchinson
1998-01-01
Two dimensional thin plate smoothing splines were used to interpolate 100 daily rainfall values, with the degree of data smoothing determined by minimizing the generalised cross validation. Analyses were performed on the square roots of the rainfall values, permitting robust calibration of spatially distributed standard errors which are correlated with rainfall amount. Initial model calibration was made difficult by apparent
Franke, B. C. [Sandia National Laboratories, Albuquerque, NM 87185 (United States); Prinja, A. K. [Department of Chemical and Nuclear Engineering, University of New Mexico, Albuquerque, NM 87131 (United States)
2013-07-01
The stochastic Galerkin method (SGM) is an intrusive technique for propagating data uncertainty in physical models. The method reduces the random model to a system of coupled deterministic equations for the moments of stochastic spectral expansions of result quantities. We investigate solving these equations using the Monte Carlo technique. We compare the efficiency with brute-force Monte Carlo evaluation of uncertainty, the non-intrusive stochastic collocation method (SCM), and an intrusive Monte Carlo implementation of the stochastic collocation method. We also describe the stability limitations of our SGM implementation. (authors)
Collocated infrasound/airglow observations of eruptive activity at Etna volcano
NASA Astrophysics Data System (ADS)
Marchetti, Emanuele; Ripepe, Maurizio; Wüst, Sabine; Schmidt, Carsten; Kramer, Ricarda; Bittner, Michael
2014-05-01
In the framework of the FP7 ARISE design study project, a collocated infrasound and airglow observation campaign has been organized on Etna volcano. The experiment, carried out during the first 2 years of the project (January 2012-December 2013), consists of simultaneous observations with an infrasound array, operated by UNIFI, and a GRIPS airglow spectrometers, operated by DLR. The infrasound array, deployed on the eastern flank of the volcano at ~2000 m elevation and at a distance of ~5 km from the active craters, allows to detect and analyse infrasound radiated by eruptive activity from Etna volcano and provides the detailed time history of the infrasonic pressure related to the Etna explosive activity. The GRIPS spectrometer is deployed in the city of Catania at a distance of ~ 30 km from the craters and targeting the sky above the summit craters, allowing to measure temperature fluctuations of the airglow layer and thus to retrieve pressure fluctuations in the mesopause region. Given the high efficiency of the Etna volcano to radiate infrasound, the campaign aimed to study the infrasound propagation from the ground to the high atmosphere, as well as to investigate relationship between the eruptive plume and the atmospheric dynamics. Mass injection into a stratified atmosphere results into gravity waves controlled by the Brunt-Vaisala frequency. Here volcanic eruption, able to inject rapidly a large quantity of hot material into a stratified atmosphere is able to excite gravity waves into the atmosphere, that in turn will control the evolution of the eruptive umbrella clouds. Moreover, gravity waves generated by atmospheric dynamics can somehow control the evolution and dispersal of eruptive plume. Gravity waves during the 2012-2013 period are detected from GRIPS measurements, and detailed infrasonic time history is derived from infrasound observation. Here activity from Etna volcano during the experiment was very intense, and was punctuated by 30 lava fountain episodes, often associated with strong ash emissions in the atmosphere affecting local air traffic and nearby communities. The Etna volcano observation campaign represents a key activity within the WP4 of the project that investigates the civil application of the future ARISE infrastructure, with specific attention to the evaluation and reduction of volcanic hazard.
NASA Astrophysics Data System (ADS)
Frey, W.; Eichler, H.; de Reus, M.; Maser, R.; Wendisch, M.; Borrmann, S.
2009-01-01
A new airborne tandem measurement platform for cloud-radiation interaction studies is introduced in this paper. It consists of a Learjet 35A research aircraft and the AIRcraft TOwed Sensor Shuttle (AIRTOSS), which is an instrumented drag-body towed by the Learjet. Currently, the AIRTOSS is instrumented with a Cloud Imaging Probe (CIP) for measuring cloud microphysical properties and an Inertial Navigation System (INS) for measurements of flight attitudes. The cable dragging AIRTOSS can be as long as four kilometres. Thus, truly collocated measurements in two altitudes above, in, and below clouds can be obtained. Results from first test flights with Learjet and AIRTOSS are reported here. The flights were performed from Hohn Airport, Germany. Specific manoeuvres were flown to test the aerodynamic behaviour of the drag-body and to investigate the suitability of AIRTOSS for high-precision irradiance measurements which require a stable flight attitude of AIRTOSS. The flight attitude data show that AIRTOSS is sensitive to several flight manoeuvres such as curves, altitude and airspeed changes, and also to changes of towing cable length. The effects of these manoeuvres on the attitude angles of AIRTOSS have been quantified. Maximum roll angle deviations were observed during curve flight. Even small changes in heading can lead to high roll angles (one degree change in heading causes a change in roll angle of about eight degrees). The pitch angle varies during climb or dive periods, extending or retracting of towing cable, acceleration or deceleration, and even when flying at too low or too high true airspeed depending on altitude. Values of pitch angle between -5° (dive) and 8° (climb and retracting towing cable) have been observed. While change in attitude is not problematic for cloud particle property measurements it is for radiation measurements. Here, the deviation from the horizontal should be no more than 3° to avoid large errors. When keeping the above mentioned flight parameters constant, sufficiently stable flight conditions can be maintained to perform high-quality irradiance measurements with AIRTOSS in future experiments. During this test campaign also observations of cloud microphysical data as for example droplet number concentrations and size distributions with the AIRTOSS in stratocumulus clouds were performed to prove the compliance with scientific needs. Simultaneous radiation measurements of the clouds have been made. The measurements of internal operational data of AIRTOSS as well as the first atmospheric data demonstrate the suitability of this tandem platform for detailed cloud microphysics and radiation interaction studies.
NASA Astrophysics Data System (ADS)
Frey, W.; Eichler, H.; de Reus, M.; Maser, R.; Wendisch, M.; Borrmann, S.
2009-05-01
A new airborne tandem measurement platform for cloud-radiation interaction studies is introduced in this paper. It consists of a Learjet 35A research aircraft and the AIRcraft TOwed Sensor Shuttle (AIRTOSS), which is an instrumented drag-body towed by the Learjet. Currently, the AIRTOSS is instrumented with a Cloud Imaging Probe (CIP) for measuring cloud microphysical properties and an Inertial Navigation System (INS) for measurements of flight attitudes. The cable dragging AIRTOSS can be as long as four kilometres. Thus, truly collocated measurements in two altitudes above, in, and below clouds can be obtained. Results from first test flights with Learjet and AIRTOSS are reported here. The flights were performed from Hohn Airport, Germany. Specific manoeuvres were flown to test the aerodynamic behaviour of the drag-body and to investigate the suitability of AIRTOSS for high-precision irradiance measurements which require a stable flight attitude of AIRTOSS. The flight attitude data show that AIRTOSS is sensitive to several flight manoeuvres such as turns, altitude and airspeed changes, and also to changes of towing cable length. The effects of these manoeuvres on the attitude angles of AIRTOSS have been quantified. Maximum roll angle deviations were observed during turns. Even small changes in heading can lead to high roll angles (one degree change in heading causes a change in roll angle of about eight degrees). The pitch angle varies during climb or dive periods, extending or retracting of towing cable, acceleration or deceleration, and even when flying at too low or too high true airspeed depending on altitude. Values of pitch angle between -5° (dive) and 8° (climb and retracting towing cable) have been observed. While change in attitude is not problematic for cloud particle property measurements it is for radiation measurements. Here, the deviation from the horizontal should be no more than 3° to avoid large errors. When keeping the above mentioned flight parameters constant, sufficiently stable flight conditions can be maintained to perform high-quality irradiance measurements with AIRTOSS in future experiments. During this test campaign also observations of cloud microphysical data as for example droplet number concentrations and size distributions with the AIRTOSS in stratocumulus clouds were performed to prove the compliance with scientific needs. Simultaneous spectral cloud radiation measurements have been made. The measurements of internal operational data of AIRTOSS as well as the first atmospheric data demonstrate the suitability of this tandem platform for detailed cloud microphysics and radiation interaction studies.
An additional branch free algebraic B-spline curve fitting method
Mingxiao Hu; Jieqing Feng; Jianmin Zheng
2010-01-01
Algebraic curve fitting based on the algebraic distance is simple, but it has the disadvantage of inclining to a trivial solution.\\u000a Researchers therefore introduce some constraints into the objective function in order to avoid the trivial solution. However,\\u000a this often causes additional branches. Fitting based on geometric distance can avoid additional branches, but it does not\\u000a offer sufficient fitting precision.
in multidisciplinary applications, ranging from modern medicine using X-ray computerized tomography (CT) and Nuclear, as well as the development of increasingly sensitive detectors and high precision, low cost electronic of medicine, has been used extensively in studies in the field of soil physics [Crestana et al. (1986
Smith, Cherri Imelda
1987-01-01
entity. However, upon construction of the control systems, each unit must be fine tuned to produce optimal results. In the design stage, however, inverse sensitivity analysis could yield information about minor parameter reforms. Bihovski (1958...
A new method for solving fixed geodetic boundary-value problem based on harmonic splines
Abdolreza Safari; Mohammad Ali Sharifi
2010-01-01
Nowadays, the determination of the earth gravity field has various applications in geodesy and geophysics. The gravity field of the earth is determined via solution of a boundary value problem. Gravimetric data with high quality at the earth surface for Earth's gravity field determination are available. These data provide the necessary boundary data to solve our BVP. Because of precise
Modelling of bubble rising by smoothed particle hydrodynamics method
NASA Astrophysics Data System (ADS)
Tofighi, N.; Zainali, A.; Yildiz, M.
2012-09-01
In this paper, an incompressible smoothed particle hydrodynamics (ISPH) method for two-phase flows with an improved surface treatment using continuum surface force (CSF) approach is proposed. A better surface representation is achieved through using a cubic spline weighting function for discretizing the equations related to interfacial forces while a quintic spline function is used for other equations. In order to demonstrate the effectiveness of the aforementioned method, rising of a Newtonian bubble surrounded by a viscous liquid is simulated. Results obtained from current simulations are in agreement with data available in literature and show the same characteristics.
NASA Astrophysics Data System (ADS)
Nieto, Paulino José García; Antón, Juan Carlos Álvarez; Vilán, José Antonio Vilán; García-Gonzalo, Esperanza
2014-10-01
The aim of this research work is to build a regression model of the particulate matter up to 10 micrometers in size (PM10) by using the multivariate adaptive regression splines (MARS) technique in the Oviedo urban area (Northern Spain) at local scale. This research work explores the use of a nonparametric regression algorithm known as multivariate adaptive regression splines (MARS) which has the ability to approximate the relationship between the inputs and outputs, and express the relationship mathematically. In this sense, hazardous air pollutants or toxic air contaminants refer to any substance that may cause or contribute to an increase in mortality or serious illness, or that may pose a present or potential hazard to human health. To accomplish the objective of this study, the experimental dataset of nitrogen oxides (NOx), carbon monoxide (CO), sulfur dioxide (SO2), ozone (O3) and dust (PM10) were collected over 3 years (2006-2008) and they are used to create a highly nonlinear model of the PM10 in the Oviedo urban nucleus (Northern Spain) based on the MARS technique. One main objective of this model is to obtain a preliminary estimate of the dependence between PM10 pollutant in the Oviedo urban area at local scale. A second aim is to determine the factors with the greatest bearing on air quality with a view to proposing health and lifestyle improvements. The United States National Ambient Air Quality Standards (NAAQS) establishes the limit values of the main pollutants in the atmosphere in order to ensure the health of healthy people. Firstly, this MARS regression model captures the main perception of statistical learning theory in order to obtain a good prediction of the dependence among the main pollutants in the Oviedo urban area. Secondly, the main advantages of MARS are its capacity to produce simple, easy-to-interpret models, its ability to estimate the contributions of the input variables, and its computational efficiency. Finally, on the basis of these numerical calculations, using the multivariate adaptive regression splines (MARS) technique, conclusions of this research work are exposed.
Akima splines for minimization of breathing interference in aortic rheography data
NASA Astrophysics Data System (ADS)
Tsoy, Maria O.; Stiukhina, Elena S.; Klochkov, Victor A.; Postnov, Dmitry E.
2015-03-01
The elimination of low-frequency noise of breath and motion artifacts is one of the most difficult challenges of preprocessing rheographic signal. The data filtering is the conventional way to separate useful signal from noise and interferences. Conventionally, linear filtering is used to easy design and implementation. However, in some cases such techniques are difficult, if possible, to apply, since the data frequency range is overlapped with one of interferences. Specifically, it happens in aortic rheography, where some breathing process and pulmonary blood flow contributions are unavoidable. We suggest an alternative approach for breathing interference reduction, based on adaptive reconstruction of baseline deviation. Specifically, the computational scheme based on multiple calculation of Akima splines is suggested, implemented using C# language and validated using surrogate data. The applications of proposed technique to the real data processing deliver the better quality of aortic valve opening detection.