scholarly journals Random regression analyses using B-spline functions to model growth of Nellore cattle

animal ◽  
2012 ◽  
Vol 6 (2) ◽  
pp. 212-220 ◽  
Author(s):  
A.A. Boligon ◽  
M.E.Z. Mercadante ◽  
R.B. Lôbo ◽  
F. Baldi ◽  
L.G. Albuquerque
Keyword(s):  
Random Regression ◽  
Spline Functions ◽  
Regression Analyses ◽  
B Spline ◽  
Nellore Cattle

scholarly journals Covariance functions under B-spline polynomials to model Polled Nellore cattle growth

2021 ◽  
Vol 42 (6supl2) ◽  
pp. 3977-3990
Author(s):  
Diego Helcias Cavalcante ◽  
◽  
Carlos Syllas Monteiro Luz ◽  
Marcelo Richelly Alves de Oliveira ◽  
Wéverton José Lima Fonseca ◽  
...  
Keyword(s):  
Random Effects ◽  
Growth Curve ◽  
Fixed Effects ◽  
Random Regression ◽  
Spline Functions ◽  
Average Growth ◽  
B Spline ◽  
Covariance Functions ◽  
Model Animal ◽  
Nellore Cattle

B-spline functions have been used in random regression models (RRM) to model animal weight from birth to adulthood because they are less vulnerable to common difficulties of other methods. However, its application to model growth traits of Polled Nellore cattle has been little studied. Therefore, this study aimed to evaluate polynomial functions of different orders and segment numbers to model effects associated with the Polled Nellore cattle growth curve. For this purpose, we used 15,148 weight records of 3,115 animals aged between 1 and 660 days and reared in northern Brazil and born between 1995 and 2010. Random effects were modeled using B-spline polynomials. As random effects, we considered the direct and maternal genetic additives, as well as direct and maternal permanent environments. As fixed effects were included contemporary group, cow age at calving (linear and quadratic) and fourth-order Legendre polynomials to represent average growth curve. The residue was modeled by considering seven age classes. The bestfitted model was the one that considered cubic B-spline functions with four knots for direct additive genetic effects and three knots for maternal genetic, animal permanent environment, and maternal permanent environment effects (C6555). Therefore, covariance functions under B-spline polynomials are efficient and can be used to model the growth curve of Polled Nellore cattle from birth to 660 days of age.

scholarly journals Genetic evaluation and selection response for growth in meat-type quail through random regression models using B-spline functions and Legendre polynomials

animal ◽  
2018 ◽  
Vol 12 (4) ◽  
pp. 667-674 ◽  
Author(s):  
L.F.M. Mota ◽  
P.G.M.A. Martins ◽  
T.O. Littiere ◽  
L.R.A. Abreu ◽  
M.A. Silva ◽  
...  
Keyword(s):  
Legendre Polynomials ◽  
Regression Models ◽  
Selection Response ◽  
Genetic Evaluation ◽  
Random Regression ◽  
Spline Functions ◽  
B Spline ◽  
Meat Type

scholarly journals A Numerical Solution to Fractional Diffusion Equation for Force-Free Case

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
O. Tasbozan ◽  
A. Esen ◽  
N. M. Yagmurlu ◽  
Y. Ucar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Exact Analytical Solution ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Spline Functions ◽  
B Spline ◽  
Numerical Examples ◽  
Free Case

A collocation finite element method for solving fractional diffusion equation for force-free case is considered. In this paper, we develop an approximation method based on collocation finite elements by cubic B-spline functions to solve fractional diffusion equation for force-free case formulated with Riemann-Liouville operator. Some numerical examples of interest are provided to show the accuracy of the method. A comparison between exact analytical solution and a numerical one has been made.

An efficient Bi-cubic B-spline ADI method for numerical solutions of two-dimensional unsteady advection diffusion equations

2018 ◽  
Vol 28 (11) ◽  
pp. 2620-2649 ◽  
Author(s):  
Rajni Rohila ◽  
R.C. Mittal
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Diffusion Equations ◽  
Spline Functions ◽  
Two Dimensional ◽  
Partial Differential ◽  
Content Type ◽  
B Spline ◽  
Advection Diffusion

Purpose This paper aims to develop a novel numerical method based on bi-cubic B-spline functions and alternating direction (ADI) scheme to study numerical solutions of advection diffusion equation. The method captures important properties in the advection of fluids very efficiently. C.P.U. time has been shown to be very less as compared with other numerical schemes. Problems of great practical importance have been simulated through the proposed numerical scheme to test the efficiency and applicability of method. Design/methodology/approach A bi-cubic B-spline ADI method has been proposed to capture many complex properties in the advection of fluids. Findings Bi-cubic B-spline ADI technique to investigate numerical solutions of partial differential equations has been studied. Presented numerical procedure has been applied to important two-dimensional advection diffusion equations. Computed results are efficient and reliable, have been depicted by graphs and several contour forms and confirm the accuracy of the applied technique. Stability analysis has been performed by von Neumann method and the proposed method is shown to satisfy stability criteria unconditionally. In future, the authors aim to extend this study by applying more complex partial differential equations. Though the structure of the method seems to be little complex, the method has the advantage of using small processing time. Consequently, the method may be used to find solutions at higher time levels also. Originality/value ADI technique has never been applied with bi-cubic B-spline functions for numerical solutions of partial differential equations.

Numerical Solution of a Wave Propagation Problem Along Plate Structures Based on the Isogeometric Approach

2018 ◽  
Vol 26 (01) ◽  
pp. 1750030 ◽  
Author(s):  
V. Hernández ◽  
J. Estrada ◽  
E. Moreno ◽  
S. Rodríguez ◽  
A. Mansur
Keyword(s):  
Degrees Of Freedom ◽  
Eigenvalue Problems ◽  
Computational Cost ◽  
Dispersion Curves ◽  
Wave Number ◽  
Spline Functions ◽  
Shape Functions ◽  
B Spline ◽  
Generalized Eigenvalue ◽  
Generalized Eigenvalue Problems

Ultrasonic guided waves propagating along large structures have great potential as a nondestructive evaluation method. In this context, it is very important to obtain the dispersion curves, which depend on the cross-section of the structure. In this paper, we compute dispersion curves along infinite isotropic plate-like structures using the semi-analytical method (SAFEM) with an isogeometric approach based on B-spline functions. The SAFEM method leads to a family of generalized eigenvalue problems depending on the wave number. For a prescribed wave number, the solution of this problem consists of the nodal displacement vector and the frequency of the guided wave. In this work, the results obtained with B-splines shape functions are compared to the numerical SAFEM solution with quadratic Lagrange shape functions. Advantages of the isogeometric approach are highlighted and include the smoothness of the displacement field components and the computational cost of solving the corresponding generalized eigenvalue problems. Finally, we investigate the convergence of Lagrange and B-spline approaches when the number of degrees of freedom grows. The study shows that cubic B-spline functions provide the best solution with the smallest relative errors for a given number of degrees of freedom.

scholarly journals Genetic evaluation of growth traits in Nellore cattle through multi-trait and random regression models

2018 ◽  
Vol 63 (No. 6) ◽  
pp. 212-221 ◽  
Author(s):  
B.B. Teixeira ◽  
R.R. Mota ◽  
R.B. Lôbo ◽  
L.P. Silva ◽  
A.P. Souza Carneiro ◽  
...  
Keyword(s):  
Random Effects ◽  
Variance Components ◽  
Regression Models ◽  
Growth Traits ◽  
Growth Curves ◽  
Genetic Evaluation ◽  
Information Criteria ◽  
Random Regression ◽  
Nellore Cattle ◽  
Heritability Estimates

We aimed to evaluate different orders of fixed and random effects in random regression models (RRM) based on Legendre orthogonal polynomials as well as to verify the feasibility of these models to describe growth curves in Nellore cattle. The proposed RRM were also compared to multi-trait models (MTM). Variance components and genetic parameters estimates were performed via REML for all models. Twelve RRM were compared through Akaike (AIC) and Bayesian (BIC) information criteria. The model of order three for the fixed curve and four for all random effects (direct genetic, maternal genetic, permanent environment, and maternal permanent environment) fits best. Estimates of direct genetic, maternal genetic, maternal permanent environment, permanent environment, phenotypic and residual variances were similar between MTM and RRM. Heritability estimates were higher via RRM. We presented perspectives for the use of RRM for genetic evaluation of growth traits in Brazilian Nellore cattle. In general, moderate heritability estimates were obtained for the majority of studied traits when using RRM. Additionally, the precision of these estimates was higher when using RRM instead of MTM. However, concerns about the variance components estimates in advanced ages via Legendre polynomial must be taken into account in future studies.

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