scholarly journals CONVERGÊNCIA DE RENDA PARA OS MUNICÍPIOS BRASILEIROS: UMA APLICAÇÃO DO MÉTODO CONSTRAINED B-SPLINE SMOOTHING (COBS) – NO PERÍODO DE 2000 A 2010

2013 ◽  
Vol 39 (2) ◽  
Author(s):  
Wilians Santos Silva ◽  
Adriano Nascimento Da Paixão
Keyword(s):  
Spline Smoothing ◽  
B Spline ◽  
B Splines ◽  
Per Capita

P { margin-bottom: 0.21cm; direction: ltr; color: rgb(0, 0, 0); widows: 2; orphans: 2; }A:link { color: rgb(0, 0, 255); } P { margin-bottom: 0.21cm; } P { margin-bottom: 0.21cm; }Este trabalho verifica a formação de clubes de convergência de renda para os municípios brasileiros no período de 2000 a 2010, através dos métodos não paramétricos de: densidade  Kernel, regressão quantílica linear e o doconstrainedsmoothing B-splines (COBS).A análise da densidade Kernel indicou que a distribuição da renda é bimodal. Já o modelo de regressão quantílica linear testou duas hipóteses: P { margin-bottom: 0.21cm; }i) a de β-convergência absoluta, onde somente o quinto e o décimo percentil convergiram; e a ii) a de β-convergência condicional que teve como variáveis explicativas: a renda per capita e os anos de estudos e como resultado, a educação é mais eficiente para mitigar a desigualdade nos municípios mais pobres.Enfim, o método constrained smoothing BsSplines que testou a hipótese de β-convergência e constatou a não linearidade entre os quantis e ratificou a formação de dois polos de convergência.  

Optimization of regularized B-spline smoothing for turbulent Lagrangian trajectories

2021 ◽  
pp. 110376
Author(s):  
Adam Cheminet ◽  
Yasar Ostovan ◽  
Valentina Valori ◽  
Christophe Cuvier ◽  
Fançois Daviaud ◽  
...  
Keyword(s):  
Spline Smoothing ◽  
B Spline

scholarly journals Towards B-Spline Atomic Structure Calculations

Atoms ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 50
Author(s):  
Charlotte Froese Fischer
Keyword(s):  
Atomic Structure ◽  
Bound States ◽  
Virial Theorem ◽  
B Spline ◽  
B Splines ◽  
Self Consistent ◽  
History Of ◽  
Consistent Method ◽  
Atomic Structure Calculations ◽  
Structure Calculations

The paper reviews the history of B-spline methods for atomic structure calculations for bound states. It highlights various aspects of the variational method, particularly with regard to the orthogonality requirements, the iterative self-consistent method, the eigenvalue problem, and the related sphf, dbsr-hf, and spmchf programs. B-splines facilitate the mapping of solutions from one grid to another. The following paper describes a two-stage approach where the goal of the first stage is to determine parameters of the problem, such as the range and approximate values of the orbitals, after which the level of accuracy is raised. Once convergence has been achieved the Virial Theorem, which is evaluated as a check for accuracy. For exact solutions, the V/T ratio for a non-relativistic calculation is −2.

Generation and Modification of Non-Uniform B-Spline Surface Approximations to PDE Surfaces Using the Finite Element Method

1990 ◽  
Author(s):  
Joanna M. Brown ◽  
Malcolm I. G. Bloor ◽  
M. Susan Bloor ◽  
Michael J. Wilson
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Spline Approximation ◽  
The Finite Element Method ◽  
B Spline ◽  
B Splines ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Spline Basis ◽  
Element Method

Abstract A PDE surface is generated by solving partial differential equations subject to boundary conditions. To obtain an approximation of the PDE surface in the form of a B-spline surface the finite element method, with the basis formed from B-spline basis functions, can be used to solve the equations. The procedure is simplest when uniform B-splines are used, but it is also feasible, and in some cases desirable, to use non-uniform B-splines. It will also be shown that it is possible, if required, to modify the non-uniform B-spline approximation in a variety of ways, using the properties of B-spline surfaces.

scholarly journals Hierarchical Genetic Algorithm for B-Spline Surface Approximation of Smooth Explicit Data

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
C. H. Garcia-Capulin ◽  
F. J. Cuevas ◽  
G. Trejo-Caballero ◽  
H. Rostro-Gonzalez
Keyword(s):  
Genetic Algorithm ◽  
Geometric Modeling ◽  
Data Set ◽  
Surface Approximation ◽  
B Spline ◽  
B Splines ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Surface Dimension ◽  
Hierarchical Genetic Algorithm

B-spline surface approximation has been widely used in many applications such as CAD, medical imaging, reverse engineering, and geometric modeling. Given a data set of measures, the surface approximation aims to find a surface that optimally fits the data set. One of the main problems associated with surface approximation by B-splines is the adequate selection of the number and location of the knots, as well as the solution of the system of equations generated by tensor product spline surfaces. In this work, we use a hierarchical genetic algorithm (HGA) to tackle the B-spline surface approximation of smooth explicit data. The proposed approach is based on a novel hierarchical gene structure for the chromosomal representation, which allows us to determine the number and location of the knots for each surface dimension and the B-spline coefficients simultaneously. The method is fully based on genetic algorithms and does not require subjective parameters like smooth factor or knot locations to perform the solution. In order to validate the efficacy of the proposed approach, simulation results from several tests on smooth surfaces and comparison with a successful method have been included.

scholarly journals Maximum Vanishing Moment of Compactly Supported B-spline Wavelets

2019 ◽  
pp. 1-8
Author(s):  
Kanchan Lata Gupta ◽  
B. Kunwar ◽  
V. K. Singh
Keyword(s):  
Scaling Function ◽  
Simple Procedure ◽  
Smoothness Property ◽  
Vanishing Moments ◽  
B Spline ◽  
B Splines ◽  
Compactly Supported ◽  
Spline Wavelets ◽  
Vanishing Moment ◽  
Rule Order

Spline function is of very great interest in field of wavelets due to its compactness and smoothness property. As splines have specific formulae in both time and frequency domain, it greatly facilitates their manipulation. We have given a simple procedure to generate compactly supported orthogonal scaling function for higher order B-splines in our previous work. Here we determine the maximum vanishing moments of the formed spline wavelet as established by the new refinable function using sum rule order method.

scholarly journals B-splines Algorithms for Solving Fredholm Linear Integro-Differential Equations

2004 ◽  
Vol 1 (2) ◽  
pp. 340-346
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equations ◽  
Spline Function ◽  
Cubic Spline ◽  
Second Order ◽  
Third Order ◽  
B Spline ◽  
Numerical Examples ◽  
B Splines ◽  
The Third ◽  
New Procedures

Algorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.

On the Literature of B-Spline Interpolation Functions

2009 ◽  
pp. 214-222
Author(s):  
Carlo Ciulla
Keyword(s):  
Scientific Community ◽  
Polynomial Interpolation ◽  
Spline Interpolation ◽  
Spline Functions ◽  
Great Effort ◽  
Formal Definition ◽  
B Spline ◽  
B Splines ◽  
Scientific Disciplines ◽  
Definition Of

This chapter reviews the extensive and comprehensive literature on B-Splines. In the forthcoming text emphasis is given to hierarchy and formal definition of polynomial interpolation with specific focus to the subclass of functions that are called B-Splines. Also, the literature is reviewed with emphasis on methodologies and applications of B-Splines within a wide array of scientific disciplines. The review is conducted with the intent to inform the reader and also to acknowledge the merit of the scientific community for the great effort devoted to B-Splines. The chapter concludes emphasizing on the proposition that the unifying theory presented throughout this book has for what concerns two specific cases of B-Spline functions: univariate quadratic and cubic models.

scholarly journals Bayesian B-spline mapping for dynamic quantitative traits

2012 ◽  
Vol 94 (2) ◽  
pp. 85-95 ◽  
Author(s):  
JUN XING ◽  
JIAHAN LI ◽  
RUNQING YANG ◽  
XIAOJING ZHOU ◽  
SHIZHONG XU
Keyword(s):  
Legendre Polynomial ◽  
Legendre Polynomials ◽  
Simulated Dataset ◽  
Model Parameters ◽  
B Spline ◽  
B Splines ◽  
Bayesian Mapping ◽  
Bayesian Shrinkage ◽  
Dynamic Traits ◽  
Over Time

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

Choosing the optimal number of B-spline control points (Part 2: Approximation of surfaces and applications)

2017 ◽  
Vol 11 (1) ◽  
Author(s):  
Corinna Harmening ◽  
Hans Neuner
Keyword(s):  
Data Analysis ◽  
Laser Scanner ◽  
Point Clouds ◽  
Optimal Number ◽  
Deformation Analysis ◽  
Control Points ◽  
Trial And Error ◽  
B Spline ◽  
B Splines ◽  
Spline Surfaces

AbstractFreeform surfaces like B-splines have proven to be a suitable tool to model laser scanner point clouds and to form the basis for an areal data analysis, for example an areal deformation analysis.A variety of parameters determine the B-spline's appearance, the B-spline's complexity being mostly determined by the number of control points. Usually, this parameter type is chosen by intuitive trial-and-error-procedures.In [The present paper continues these investigations. If necessary, the methods proposed in [The application of those methods to B-spline surfaces reveals the datum problem of those surfaces, meaning that location and number of control points of two B-splines surfaces are only comparable if they are based on the same parameterization. First investigations to solve this problem are presented.

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