Choosing Smoothness Parameters for Smoothing Splines by Minimizing and Estimate of Risk

Smoothing splines are a popular approach for non-parametric regression problems. We use periodic smoothing splines to fit a periodic signal plus noise model to data for which we assume there are underlying circadian patterns. In the smoothing spline methodology, choosing an appropriate smoothness parameter is an important step in practice. In this paper, we draw a connection between smoothing splines and REACT estimators that provides motivation for the creation of criteria for choosing the smoothness parameter. The new criteria are compared to three existing methods, namely cross-validation, generalized cross-validation, and generalization of maximum likelihood criteria, by a Monte Carlo simulation and by an application to the study of circadian patterns. For most of the situations presented in the simulations, including the practical example, the new criteria out-perform the three existing criteria.

Lower Extremities Magnetic Resonance Angiography With Blood Pressure Cuff Compression: Quantitative Dynamic Analysis

Purpose: To quantitatively evaluate changes induced by the application of a femoral blood-pressure cuff (BPC) on run-off magnetic resonance angiography (MRA). which is a method generally previously proposed to reduce venous contamination in the leg. Materials and Methods: This study was Health Insurance Portability and Accountability Act (HIPAA)- and Institutional Review Board (IRB)-compliant, We used time-resolved gradient-echo gadolinium (Gd)-enhanced MRA to measure BPC effects on arterial, venous, and soft-tissue enhancement. Seven healthy volunteers (six men) were studied with the BPC applied at the mid-femoral level unilaterally using a 1.5T MR system after intravenous injection of Gd-BOPTA. Different statistical tools were used such as the Wilcoxon signed rank test and a cubic smoothing spline fit. Results: We found that BPC application induces delayed venous filling (as previously described), but also induces significant decreases in arterial inflow, arterial enhancement, vascular-soft tissue contrast, and delayed peak enhancement (which have not been previously measured). Conclusion: The potential benefits from using a BPC for run-off MRA must be balanced against the potential pitfalls, elucidated by our findings.

Online bayesian inference in some time-frequency representations of non-stationary processes

The use of Bayesian inference in the inference of time-frequency representations has, thus far, been limited to offline analysis of signals, using a smoothing spline based model of the time-frequency plane. In this paper we introduce a new framework that allows the routine use of Bayesian inference for online estimation of the time-varying spectral density of a locally stationary Gaussian process. The core of our approach is the use of a likelihood inspired by a local Whittle approximation. This choice, along with the use of a recursive algorithm for non-parametric estimation of the local spectral density, permits the use of a particle filter for estimating the time-varying spectral density online. We provide demonstrations of the algorithm through tracking chirps and the analysis of musical data.

Influence diagnostics for elliptical semiparametric mixed models

In this paper we extend semiparametric mixed linear models with normal errors to elliptical errors in order to permit distributions with heavier and lighter tails than the normal ones. Penalized likelihood equations are applied to derive the maximum penalized likelihood estimates (MPLEs) which appear to be robust against outlying observations in the sense of the Mahalanobis distance. A reweighed iterative process based on the back-fitting method is proposed for the parameter estimation and the local influence curvatures are derived under some usual perturbation schemes to study the sensitivity of the MPLEs. Two motivating examples preliminarily analyzed under normal errors are reanalyzed considering some appropriate elliptical errors. The local influence approach is used to compare the sensitivity of the model estimates.

Validated sample ages from 823 EPD sites

The number of well-dated pollen diagrams in Europe has increased considerably over the last 30 years and many of them have been submitted to the European Pollen Database (EPD). This allows for the construction of increasingly precise maps of Holocene vegetation change across the continent. Chronological information in the EPD has been expressed in uncalibrated radiocarbon years, and most chronologies to date are based on this time scale. Here we present new chronologies for most of the datasets stored in the EPD based on calibrated radiocarbon years. Age information associated with pollen diagrams is often derived from the pollen stratigraphy itself or from other sedimentological information. We reviewed these chronological tie points and assigned uncertainties to them. The steps taken to generate the new chronologies are described and the rationale for a new classification system for age uncertainties is introduced. The resulting chronologies are fit for most continental-scale questions. They may not provide the best age model for particular sites, but may be viewed as general purpose chronologies. Taxonomic particularities of the data stored in the EPD are explained. An example is given of how the database can be queried to select samples with appropriate age control as well as the suitable taxonomic level to answer a specific research question.

Intensificação da transferência de calor e otimização de trocadores de calor compactos tipo venezianas com geradores de vórtices tipo delta-winglets.

Esta pesquisa visa a análise da contribuição de cinco variáveis de entrada e a otimização do desempenho termo-hidráulico de trocadores de calor com venezianas combinados com geradores de vórtices delta-winglets. O desempenho termohidráulico de duas geometrias distintas, aqui nomeadas por GEO1 e GEO2, foram avaliadas. Smoothing Spline ANOVA foi usado para avaliar a contribuição dos parâmetros de entrada na transferência de calor e perda de carga. Considerando aplicação automotiva, foram investigados números de Reynolds iguais a 120 e 240, baseados no diâmetro hidráulico. Os resultados indicaram que o ângulo de venezianas é o maior contribuidor para o aumento do fator de atrito para GEO1 e GEO2, para ambos os números de Reynolds. Para o número de Reynolds menor, o parâmetro mais importante em termos de transferência de calor foi o ângulo das venezianas para ambas as geometrias. Para o número de Reynolds maior, o ângulo de ataque dos geradores de vórtices posicionados na primeira fileira é o maior contribuidor para a tranfesferência de calor, no caso da geometria GEO1, enquanto que o ângulo de ataque dos geradores de vórtices na primeira fileira foi tão importante quanto os ângulos das venezianas para a geometria GEO2. Embora as geometrias analisadas possam ser consideradas como técnicas compostas de intensificação da transferência de calor, não foram observadas interações relevantes entre ângulo de venezianas e parâmetros dos geradores de vórtices. O processo de otimização usa NSGA-II (Non-Dominated Sorting Genetic Algorithm) combinado com redes neurais artificiais. Os resultados mostraram que a adição dos geradores de vórtices em GEO1 aumentaram a transferência de calor em 21% e 23% com aumentos na perda de carga iguais a 24,66% e 36,67% para o menor e maior números de Reynolds, respectivamente. Para GEO2, a transferência de calor aumentou 13% e 15% com aumento na perda de carga de 20,33% e 23,70%, para o menor e maior número de Reynolds, respectivamente. As soluções otimizadas para o fator de Colburn mostraram que a transferência de calor atrás da primeira e da segunda fileiras de geradores de vórtices tem a mesma ordem de magnitude para ambos os números de Reynolds. Os padrões de escoamento e as características de transferência de calor das soluções otimizadas apresentaram comportamentos vi particulares, diferentemente daqueles encontrados quando as duas técnicas de intensificação de transferência de calor são aplicadas separadamente.

Measurement of intervertebral cervical motion by means of dynamic X-ray image processing and data interpolation

Accurate measurement of intervertebral kinematics of the cervical spine can support the diagnosis of widespread diseases related to neck pain, such as chronic whiplash dysfunction, arthritis, and segmental degeneration. The natural inaccessibility of the spine, its complex anatomy, and the small range of motion only permit concise measurement in vivo. Low dose X-ray fluoroscopy allows time-continuous screening of cervical spine during patient's spontaneous motion. To obtain accurate motion measurements, each vertebra was tracked by means of image processing along a sequence of radiographic images. To obtain a time-continuous representation of motion and to reduce noise in the experimental data, smoothing spline interpolation was used. Estimation of intervertebral motion for cervical segments was obtained by processing patient's fluoroscopic sequence; intervertebral angle and displacement and the instantaneous centre of rotation were computed. The RMS value of fitting errors resulted in about 0.2 degree for rotation and 0.2 mm for displacements. © 2013 Paolo Bifulco et al.

Adaptive T-spline refinement for isogeometric analysis in planar geometries

[EN]We present a new strategy, based on the meccano method [1, 2, 3], to construct a T-spline parameterization of 2D geometries for the application of isogeometric analysis. The proposed method only demands a boundary representation of the geometry as input data. The algorithm obtains, as a result, high quality parametric transformation between 2D objects and the parametric domain, the unit square. The key of the method lies in defining an isomorphic transformation between the parametric and physical T-mesh finding the optimal position of the interior nodes by applying a new T-mesh untangling and smoothing procedure. Bivariate T-spline representation is calculated by imposing the interpolation conditions on points sited both on the interior and on the boundary of the geometry…

Monotone Constrained Tensor-product B-spline with application to screening studies

When different markers are responsive to different aspects of a disease, combination of multiple markers could provide a better screening test for early detection. It is also resonable to assume that the risk of disease changes smoothly as the biomarker values change and the change in risk is monotone with respect to each biomarker. In this paper, we propose a boundary constrained tensor-product B-spline method to estimate the risk of disease by maximizing a penalized likelihood. To choose the optimal amount of smoothing, two scores are proposed which are extensions of the GCV score (O'Sullivan et al. (1986)) and the GACV score (Ziang and Wahba (1996)) to incorporate linear constraints. Simulation studies are carried out to investigate the performance of the proposed estimator and the selection scores. In addidtion, sensitivities and specificities based ona pproximate leave-one-out estimates are proposed to generate more realisitc ROC curves. Data from a pancreatic cancer study is used for illustration.

Using a causal smoothing to improve the performance of an on-line neural network glucose prediction algorithm

This work evaluates a spline-based smoothing method applied to the output of a glucose predictor. Methods:Our on-line prediction algorithm is based on a neural network model (NNM). We trained/validated the NNM with a prediction horizon of 30 minutes using 39/54 profiles of patients monitored with the Guardian® Real-Time continuous glucose monitoring system The NNM output is smoothed by fitting a causal cubic spline. The assessment parameters are the error (RMSE), mean delay (MD) and the high-frequency noise (HFCrms). The HFCrms is the root-mean-square values of the high-frequency components isolated with a zero-delay non-causal filter. HFCrms is 2.90±1.37 (mg/dl) for the original profiles.

A monolithic smoothing-gap algorithm for contact-impact based on the signed distance function

A new algorithm has been developed for smoothing the surfaces in finite element formulations of contact-impact. A key feature of this method is that the smoothing is done implicitly by constructing smooth signed distance functions for the bodies. These functions are then employed for the computation of the gap and other variables needed for implementation of contact-impact. The smoothed signed distance functions are constructed by a moving least-squares approximation with a polynomial basis. Results show that when nodes are placed on a surface, the surface can be reproduced with an error of about one per cent or less with either a quadratic or a linear basis. With a quadratic basis, the method exactly reproduces a circle or a sphere even for coarse meshes. Results are presented for contact problems involving the contact of circular bodies. Copyright (C) 2002 John Wiley Sons, Ltd.

Real-time 3D interactive segmentation of echocardiographic data through user-based deformation of B-spline explicit active surfaces

Image segmentation is an ubiquitous task in medical image analysis, which is required to estimate morphological or functional properties of given anatomical targets. While automatic processing is highly desirable, image segmentation remains to date a supervised process in daily clinical practice. Indeed, challenging data often requires user interaction to capture the required level of anatomical detail. To optimize the analysis of 3D images, the user should be able to efficiently interact with the result of any segmentation algorithm to correct any possible disagreement. Building on a previously developed real-time 3D segmentation algorithm, we propose in the present work an extension towards an interactive application where user information can be used online to steer the segmentation result. This enables a synergistic collaboration between the operator and the underlying segmentation algorithm, thus contributing to higher segmentation accuracy, while keeping total analysis time competitive. To this end, we formalize the user interaction paradigm using a geometrical approach, where the user input is mapped to a non-cartesian space while this information is used to drive the boundary towards the position provided by the user. Additionally, we propose a shape regularization term which improves the interaction with the segmented surface, thereby making the interactive segmentation process less cumbersome. The resulting algorithm offers competitive performance both in terms of segmentation accuracy, as well as in terms of total analysis time. This contributes to a more efficient use of the existing segmentation tools in daily clinical practice. Furthermore, it compares favorably to state-of-the-art interactive segmentation software based on a 3D livewire-based algorithm.

Optimal design of piezolaminated structures using B-spline strip finite element models

A package of B-spline finite strip models is developed for the linear analysis of piezolaminated plates and shells. This package is associated to a global optimization technique in order to enhance the performance of these types of structures, subjected to various types of objective functions and/or constraints, with discrete and continuous design variables. The models considered are based on a higher-order displacement field and one can apply them to the static, free vibration and buckling analyses of laminated adaptive structures with arbitrary lay-ups, loading and boundary conditions. Genetic algorithms, with either binary or floating point encoding of design variables, were considered to find optimal locations of piezoelectric actuators as well as to determine the best voltages applied to them in order to obtain a desired structure shape. These models provide an overall economy of computing effort for static and vibration problems.

Numerical optimization experiments using the hyperbolic smoothing strategy to solve MPCC

In this work we solve Mathematical Programs with Complementarity Constraints using the hyperbolic smoothing strategy. Under this approach, the complementarity condition is relaxed through the use of the hyperbolic smoothing function, involving a positive parameter that can be decreased to zero. An iterative algorithm is implemented in MATLAB language and a set of AMPL problems from MacMPEC database were tested.