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General Algorithm (general + algorithm)

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Chemistry28%

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A General Algorithm for Univariate Stratification

INTERNATIONAL STATISTICAL REVIEW, Issue 3 2009
Sophie Baillargeon
Summary This paper presents a general algorithm for constructing strata in a population using,X, a univariate stratification variable known for all the units in the population. Stratum,h,consists of all the units with an,X,value in the interval[bh,1,,bh). The stratum boundaries{bh}are obtained by minimizing the anticipated sample size for estimating the population total of a survey variable,Y,with a given level of precision. The stratification criterion allows the presence of a take-none and of a take-all stratum. The sample is allocated to the strata using a general rule that features proportional allocation, Neyman allocation, and power allocation as special cases. The optimization can take into account a stratum-specific anticipated non-response and a model for the relationship between the stratification variable,X,and the survey variable,Y. A loglinear model with stratum-specific mortality for,Y,given,X,is presented in detail. Two numerical algorithms for determining the optimal stratum boundaries, attributable to Sethi and Kozak, are compared in a numerical study. Several examples illustrate the stratified designs that can be constructed with the proposed methodology. All the calculations presented in this paper were carried out with stratification, an R package that will be available on CRAN (Comprehensive R Archive Network). Résumé Cet article présente un algorithme général pour construire des strates dans une population à l'aide de,X, une variable de stratification unidimensionnelle connue pour toutes les unités de la population. La strate,h,contient toutes les unités ayant une valeur de,X,dans l'intervalle [bh,1,,bh). Les frontières des strates {bh} sont obtenues en minimisant la taille d'échantillon anticipée pour l'estimation du total de la variable d'intérêt,Y,avec un niveau de précision prédéterminé. Le critère de stratification permet la présence d'une strate à tirage nul et de strates recensement. L'échantillon est réparti dans les strates à l'aide d'une règle générale qui inclut l'allocation proportionnelle, l'allocation de Neyman et l'allocation de puissance comme des cas particuliers. L'optimisation peut tenir compte d'un taux de non réponse spécifique à la strate et d'un modèle reliant la variable de stratification,X,à la variable d'intérêt,Y. Un modèle loglinéaire avec un taux de mortalité propre à la strate est présenté en détail. Deux algorithmes numériques pour déterminer les frontières de strates optimales, dus à Sethi et Kozak, sont comparés dans une étude numérique. Plusieurs exemples illustrent les plans stratifiés qui peuvent être construits avec la méthodologie proposée. Tous les calculs présentés dans l'article ont été effectués avec stratification, un package R disponible auprès des auteurs. [source]

General algorithm for automated off-center MRI

MAGNETIC RESONANCE IN MEDICINE, Issue 1 2006
J. Magland
Abstract A general formula was derived that automatically modifies any MRI pulse sequence to realize arbitrary field-of-view (FOV) shifts. Unlike conventional techniques for implementing off-center MRI, the new method is completely automatic and can therefore be incorporated into the scanner hardware or software, thereby simplifying the development of MRI pulse sequences. The algorithm was incorporated into a visual pulse sequence programming environment, and several pulse sequences were programmed and tested at various off-center locations using the new technique. Unless there is significant background field inhomogeneity or gradient nonlinearity, research sequences employing the automatic technique need only be programmed and tested at the gradient isocenter, whereas with conventional methods, artifacts can sometimes depend on the position of the FOV. Magn Reson Med, 2006. © 2006 Wiley-Liss, Inc. [source]

Convergence analysis and validation of sequential limit analysis of plane-strain problems of the von Mises model with non-linear isotropic hardening

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2005
S.-Y. Leu
Abstract The paper presents sequential limit analysis of plane-strain problems of the von Mises model with non-linear isotropic hardening by using a general algorithm. The general algorithm is a combined smoothing and successive approximation (CSSA) method. In the paper, emphasis is placed on its convergence analysis and validation applied to sequential limit analysis involving materials with isotropic hardening. By sequential limit analysis, the paper treats deforming problems as a sequence of limit analysis problems stated in the upper bound formulation. Especially, the CSSA algorithm was proved to be unconditionally convergent by utilizing the Cauchy,Schwarz inequality. Finally, rigorous validation was conducted by numerical and analytical studies of a thick-walled cylinder under pressure. It is found that the computed limit loads are rigorous upper bounds and agree very well with the analytical solutions. Copyright © 2005 John Wiley & Sons, Ltd. [source]

A General Algorithm for Univariate Stratification

INTERNATIONAL STATISTICAL REVIEW, Issue 3 2009
Sophie Baillargeon
Summary This paper presents a general algorithm for constructing strata in a population using,X, a univariate stratification variable known for all the units in the population. Stratum,h,consists of all the units with an,X,value in the interval[bh,1,,bh). The stratum boundaries{bh}are obtained by minimizing the anticipated sample size for estimating the population total of a survey variable,Y,with a given level of precision. The stratification criterion allows the presence of a take-none and of a take-all stratum. The sample is allocated to the strata using a general rule that features proportional allocation, Neyman allocation, and power allocation as special cases. The optimization can take into account a stratum-specific anticipated non-response and a model for the relationship between the stratification variable,X,and the survey variable,Y. A loglinear model with stratum-specific mortality for,Y,given,X,is presented in detail. Two numerical algorithms for determining the optimal stratum boundaries, attributable to Sethi and Kozak, are compared in a numerical study. Several examples illustrate the stratified designs that can be constructed with the proposed methodology. All the calculations presented in this paper were carried out with stratification, an R package that will be available on CRAN (Comprehensive R Archive Network). Résumé Cet article présente un algorithme général pour construire des strates dans une population à l'aide de,X, une variable de stratification unidimensionnelle connue pour toutes les unités de la population. La strate,h,contient toutes les unités ayant une valeur de,X,dans l'intervalle [bh,1,,bh). Les frontières des strates {bh} sont obtenues en minimisant la taille d'échantillon anticipée pour l'estimation du total de la variable d'intérêt,Y,avec un niveau de précision prédéterminé. Le critère de stratification permet la présence d'une strate à tirage nul et de strates recensement. L'échantillon est réparti dans les strates à l'aide d'une règle générale qui inclut l'allocation proportionnelle, l'allocation de Neyman et l'allocation de puissance comme des cas particuliers. L'optimisation peut tenir compte d'un taux de non réponse spécifique à la strate et d'un modèle reliant la variable de stratification,X,à la variable d'intérêt,Y. Un modèle loglinéaire avec un taux de mortalité propre à la strate est présenté en détail. Deux algorithmes numériques pour déterminer les frontières de strates optimales, dus à Sethi et Kozak, sont comparés dans une étude numérique. Plusieurs exemples illustrent les plans stratifiés qui peuvent être construits avec la méthodologie proposée. Tous les calculs présentés dans l'article ont été effectués avec stratification, un package R disponible auprès des auteurs. [source]

Maximum likelihood fitting using ordinary least squares algorithms,

JOURNAL OF CHEMOMETRICS, Issue 8-10 2002
Rasmus Bro
Abstract In this paper a general algorithm is provided for maximum likelihood fitting of deterministic models subject to Gaussian-distributed residual variation (including any type of non-singular covariance). By deterministic models is meant models in which no distributional assumptions are valid (or applied) on the parameters. The algorithm may also more generally be used for weighted least squares (WLS) fitting in situations where either distributional assumptions are not available or other than statistical assumptions guide the choice of loss function. The algorithm to solve the associated problem is called MILES (Maximum likelihood via Iterative Least squares EStimation). It is shown that the sought parameters can be estimated using simple least squares (LS) algorithms in an iterative fashion. The algorithm is based on iterative majorization and extends earlier work for WLS fitting of models with heteroscedastic uncorrelated residual variation. The algorithm is shown to include several current algorithms as special cases. For example, maximum likelihood principal component analysis models with and without offsets can be easily fitted with MILES. The MILES algorithm is simple and can be implemented as an outer loop in any least squares algorithm, e.g. for analysis of variance, regression, response surface modeling, etc. Several examples are provided on the use of MILES. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Free Rotational Diffusion of Rigid Particles with Arbitrary Surface Topography: A Brownian Dynamics Study Using Eulerian Angles

MACROMOLECULAR THEORY AND SIMULATIONS, Issue 2-3 2008
Tom Richard Evensen
Abstract Rotational diffusion of rigid bodies is an important topic that has attracted sustained interest for many decades, but most existing studies are limited to particles with simple symmetries. Here, we present a simple Brownian dynamics algorithm that can be used to study the free rotational diffusion of rigid particles with arbitrary surface topography. The main difference between the new algorithm and previous algorithms is how the numerical values of the mobility tensor are calculated. The only parameters in the numerical algorithm that depend on particle shape are the principal values of the particle rotational mobility tensor. These three scalars contain all information about the surface topography that is relevant for the particle rotational diffusion. Because these principal values only need to be pre-calculated once, the resulting general algorithm is highly efficient. The algorithm is valid for arbitrary mass density distribution throughout the rigid body. In this paper, we use Eulerian angles as the generalized coordinates describing the particle angular orientation. [source]

Enantiomorphism of crystallographic groups in higher dimensions with results in dimensions up to 6

ACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2003
Bernd Souvignier
This paper gives classification results for crystallographic groups in dimensions up to 6 which refine earlier enumeration results. Based on the classification data, the asymptotic growth of the number of space-group types is discussed. The classification scheme for crystallographic groups is revisited and a new classification level in between that of geometric and arithmetic crystal classes is introduced and denoted as harmonic crystal classes. Enantiomorphic pairs are determined on all classification levels from space-group types to crystal families and the enantiomorphic pairs of fixed-point-free space groups are given. A general algorithm to compute enantiomorphic pairs is described. [source]