Cubic Splines (cubic + spline)

Distribution by Scientific Domains

Selected Abstracts

Muscle moment arms of the gibbon hind limb: implications for hylobatid locomotion

Anthony J. Channon
Abstract Muscles facilitate skeletal movement via the production of a torque or moment about a joint. The magnitude of the moment produced depends on both the force of muscular contraction and the size of the moment arm used to rotate the joint. Hence, larger muscle moment arms generate larger joint torques and forces at the point of application. The moment arms of a number of gibbon hind limb muscles were measured on four cadaveric specimens (one Hylobates lar, one H. moloch and two H. syndactylus). The tendon travel technique was used, utilizing an electro-goniometer and a linear voltage displacement transducer. The data were analysed using a technique based on a differentiated cubic spline and normalized to remove the effect of body size. The data demonstrated a functional differentiation between voluminous muscles with short fascicles having small muscle moment arms and muscles with longer fascicles and comparatively smaller physiological cross-sectional area having longer muscle moment arms. The functional implications of these particular configurations were simulated using a simple geometric fascicle strain model that predicts that the rectus femoris and gastrocnemius muscles are more likely to act primarily at their distal joints (knee and ankle, respectively) because they have short fascicles. The data also show that the main hip and knee extensors maintain a very small moment arm throughout the range of joint angles seen in the locomotion of gibbons, which (coupled to voluminous, short-fascicled muscles) might help facilitate rapid joint rotation during powerful movements. [source]

Variable kernel density estimation

Martin L. Hazelton
Summary This paper considers the problem of selecting optimal bandwidths for variable (sample-point adaptive) kernel density estimation. A data-driven variable bandwidth selector is proposed, based on the idea of approximating the log-bandwidth function by a cubic spline. This cubic spline is optimized with respect to a cross-validation criterion. The proposed method can be interpreted as a selector for either integrated squared error (ISE) or mean integrated squared error (MISE) optimal bandwidths. This leads to reflection upon some of the differences between ISE and MISE as error criteria for variable kernel estimation. Results from simulation studies indicate that the proposed method outperforms a fixed kernel estimator (in terms of ISE) when the target density has a combination of sharp modes and regions of smooth undulation. Moreover, some detailed data analyses suggest that the gains in ISE may understate the improvements in visual appeal obtained using the proposed variable kernel estimator. These numerical studies also show that the proposed estimator outperforms existing variable kernel density estimators implemented using piecewise constant bandwidth functions. [source]

Partial regression method to fit a generalized additive model

Shui He
Abstract Generalized additive models (GAMs) have been used as a standard analytic tool in studies of air pollution and health during the last decade. The air pollution measure is usually assumed to be linearly related to the health indicator and the effects of other covariates are modeled through smooth functions. A major statistical concern is the appropriateness of fitting GAMs in the presence of concurvity. Generalized linear models (GLM) with natural cubic splines as smoothers (GLM,+,NS) have been shown to perform better than GAM with smoothing splines (GAM,+,S), in regard to the bias and variance estimates using standard model fitting methods. As nonparametric smoothers are attractive for their flexibility and easy implementation, search for alternative methods to fit GAM,+,S is warranted. In this article, we propose a method using partial residuals to fit GAM,+,S and call it the "partial regression" method. Simulation results indicate better performance of the proposed method compared to gam.exact function in S-plus, the standard tool in air pollution studies, in regard to bias and variance estimates. In addition, the proposed method is less sensitive to the degree of smoothing and accommodates asymmetric smoothers. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Shape optimization of piezoelectric devices using an enriched meshfree method

C. W. Liu
Abstract We present an enriched reproducing kernel particle method for shape sensitivity analysis and shape optimization of two-dimensional electromechanical domains. This meshfree method incorporates enrichment functions for better representation of discontinuous electromechanical fields across internal boundaries. We use cubic splines for delineating the geometry of internal/external domain boundaries; and the nodal coordinates and slopes of these splines at their control points become the design parameters. This approach enables smooth manipulations of bi-material interfaces and external boundaries during the optimization process. It also enables the calculation of displacement and electric-potential field sensitivities with respect to the design parameters through direct differentiation, for which we adopt the classical material derivative approach. We verify this implementation of sensitivity calculations against an exact solution to a variant of Lamé's problem, and also, finite-difference approximations. We follow a sequential quadratic programming approach to minimize the cost function; and demonstrate the utility of the overall technique through a model problem that involves the shape optimization of a piezoelectric fan. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Additive Schwarz-type preconditioners for fourth-order elliptic problems using Hermite cubic splines

Song-Tao Liu
Abstract In this note, we construct the additive Schwarz-type preconditioner for fourth-order elliptic problems with nested subspaces from Hermite cubic splines. We prove that after the preconditioning, the system is well conditioned. The numerical evidence strongly supports our theoretical result. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 [source]

Cubic-spline interpolation on a non-uniform latitude,longitude grid: achieving cross- and circum-polar continuity

Markus Gross
Abstract Although it is straightforward to construct cubic splines in Cartesian geometry, this is not so for latitude-longitude grids over the sphere, because of the polar singularity. Previous work has either introduced ad hoc approximations over the polar caps, to the detriment of both continuity and accuracy, or has been restricted to interpolation of fields defined on uniform grids, with an even number of meridians, and with known polar values. These limitations are addressed herein by reformulating the construction of bicubic splines as the minimisation of an appropriate integral subject to certain constraints. © Crown Copyright 2010. Reproduced with the permission of HMSO. Published by John Wiley & Sons, Ltd. [source]

A ,bottom-up' approach for endo-PK/PD analysis

S. Neelakantan
Abstract A ,bottom-up' PK/PD analysis approach employing system analysis principles of convolution/deconvolution and special nonparametric estimation procedures is presented to resolve the complex ,endo-PK/PD' of the endogenous form of recombinant drugs using erythropoietin (EPO) as an example. A novel cellular deconvolution algorithm is presented that facilitates the identification of the functional relationship between the variables involved in EPO's complex PK/PD. Five sheep each underwent two phlebotomies spaced 4,6 weeks apart when their hemoglobin levels were reduced from 12 g/dl to 3,4 g/dl. EPO levels and reticulocyte counts were frequently sampled. The data were analysed using end-constrained cubic splines. The rate of reticulocyte production was determined using the novel deconvolution methodology. The erythroid progenitor cells activation rate by EPO was estimated from the reticulocyte production rate using a lag-time parameter which determines the delay in the reticulocyte appearance in the blood relative to the activation of erythroid progenitors. Hysteresis minimization combined with cellular deconvolution was employed to determine the population PK/PD transduction function relating the progenitor activation rate to EPO concentrations in a nonparametric manner without assuming a specific structure. The proposed approach provides a rational informative starting point for developing parametric PK/PD models to resolve the complex endo-PK/PD of recombinant drugs. Copyright © 2006 John Wiley & Sons, Ltd. [source]