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Smooth Curves (smooth + curve)

Distribution by Scientific Domains
Mathematics and Statistics50%

Selected Abstracts

Estimating Trends with Percentage of Smoothness Chosen by the User

INTERNATIONAL STATISTICAL REVIEW, Issue 2 2008
Victor M. Guerrero
Summary This work presents a method for estimating trends of economic time series that allows the user to fix at the outset the desired percentage of smoothness for the trend. The calculations are based on the Hodrick-Prescott (HP) filter usually employed in business cycle analysis. The situation considered here is not related to that kind of analysis, but with describing the dynamic behaviour of the series by way of a smooth curve. To apply the filter, the user has to specify a smoothing constant that determines the dynamic behaviour of the trend. A new method that formalizes the concept of trend smoothness is proposed here to choose that constant. Smoothness of the trend is measured in percentage terms with the aid of an index related to the underlying statistical model of the HP filter. Empirical illustrations are provided using data on Mexico's GDP. Résumé Ce travail présente un méthode pour estimer les tendances des séries de temps économiques qui permet à l'usager fixer dès début le pourcentage désiré de douceur pour la tendance. Les calculs ont fondement en le filtre de Hodrick et Prescott que s'emploie généralement dans l'analyse de cycles économiques. La situation ici considéré n'a pas relation avec ce type d'analyse, mais comment la description du comportement dynamique des séries avec une courbe douce. Pour appliquer le filtre, l'usager a besoin de spécifier une constante de douceur que détermine le comportement dynamique de la tendance. Un nouveau méthode que formalise le concept de douceur de la tendance est ici proposé pour choisir la constante. La douceur de la tendance est mesuré en termes de pourcentage avec l'aide d'un index rapporté avec le modèle statistique après le filtre. Quelques illustrations empiriques sont munies avec données de l'économie mexicaine. [source]

STRANDS: Interactive Simulation of Thin Solids using Cosserat Models

COMPUTER GRAPHICS FORUM, Issue 3 2002
Dinesh K. Pai
Strandsare thin elastic solids that are visually well approximated as smooth curves, and yet possess essential physical behaviors characteristic of solid objects such as twisting. Common examples in computer graphics include: sutures, catheters, and tendons in surgical simulation; hairs, ropes, and vegetation in animation. Physical models based on spring meshes or 3D finite elements for such thin solids are either inaccurate or inefficient for interactive simulation. In this paper we show that models based on the Cosserat theory of elastic rods are very well suited for interactive simulation of these objects. The physical model reduces to a system of spatial ordinary differential equations that can be solved efficiently for typical boundary conditions. The model handles the important geometric non-linearity due to large changes in shape. We introduce Cosserat-type physical models, describe efficient numerical methods for interactive simulation of these models, and implementation results. [source]

Semiparametric approaches to flow normalization and source apportionment of substance transport in rivers

ENVIRONMETRICS, Issue 3 2001
Per Stålnacke
Abstract Statistical analysis of relationships between time series of data exhibiting seasonal variation is often of great interest in environmental monitoring and assessment. The present study focused on regression models with time-varying intercept and slope parameters. In particular, we derived and tested semiparametric models in which rapid interannual and interseasonal variation in the intercept were penalized in the search for a model that combined a good fit to data with smoothly varying parameters. Furthermore, we developed a software package for efficient estimation of the parameters of such models. Test runs on time series of runoff data and riverine loads of nutrients and chloride in the Rhine River showed that the proposed smoothing methods were particularly useful for analysis of time-varying linear relationships between time series of data with both seasonal variation and temporal trends. The predictivity of the semiparametric models was superior to that of conventional parametric models. In addition, normalization of observed annual loads to mean or minimum runoff produced smooth curves that provided convincing evidence of human impact on water quality. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Optimal Velocity Planning of Wheeled Mobile Robots on Specific Paths in Static and Dynamic Environments

JOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 12 2003
María Prado
This paper deals with optimal temporal-planning of wheeled mobile robots (WMRs) when navigating on predefined spatial paths. A method is proposed to generate a time-optimal velocity profile for any spatial path in static environments or when mobile obstacles are present. The method generates a feasible trajectory to be tracked by fully exploiting velocity, acceleration and deceleration boundaries of the WMR, and by ensuring the continuity of the velocity and acceleration functions. As an additional benefit for the tracking process the jerk is also bounded. The algorithm is not time consuming, since it mostly uses closed mathematical expressions, nonetheless iteration strategies are presented to solve specific situations. However, such situations are not expected to occur when the spatial paths are planned as smooth curves. The success of the algorithm was tested by experimental and simulation results on the WMR "RAM." © 2003 Wiley Periodicals, Inc. [source]