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Extrapolation Methods (extrapolation + methods)

Distribution by Scientific Domains

Life Sciences	28%

Selected Abstracts

A review of vector convergence acceleration methods, with applications to linear algebra problems

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 8 2009
C. Brezinski
Abstract In this article, in a few pages, we will try to give an idea of convergence acceleration methods and extrapolation procedures for vector sequences, and to present some applications to linear algebra problems and to the treatment of the Gibbs phenomenon for Fourier series in order to show their effectiveness. The interested reader is referred to the literature for more details. In the bibliography, due to space limitation, we will only give the more recent items, and, for older ones, we refer to Brezinski and Redivo-Zaglia, Extrapolation methods. (Extrapolation Methods. Theory and Practice, North-Holland, 1991). This book also contains, on a magnetic support, a library (in Fortran 77 language) for convergence acceleration algorithms and extrapolation methods. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source]

Extrapolation methods for improving convergence of spherical Bessel integrals for the two-center Coulomb integrals

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 11 2006
Hassan Safouhi
Abstract Multi-center two-electron Coulomb integrals over Slater-type functions are required for any accurate molecular electronic structure calculations. These integrals, which are numerous, are to be evaluated rapidly and accurately. Slater-type functions are expressed in terms of the so-called B functions, which are best suited to apply the Fourier transform method. The Fourier transform method allowed analytic expressions for these integrals to be developed. Unfortunately, the analytic expressions obtained turned out to be extremely difficult to evaluate accurately due to the presence of highly oscillatory spherical Bessel integrals. In this work, we used techniques based on nonlinear transformation and extrapolation methods for improving convergence of these oscillatory spherical Bessel integrals. These techniques, which led to highly efficient and rapid algorithms for the numerical evaluation of three- and four-center two-electron Coulomb and exchange integrals, are now shown to be applicable to the two-center two-electron Coulomb integrals. The numerical results obtained for the molecular integrals under consideration illustrate the efficiency of the algorithm described in the present work compared with algorithms using the epsilon (,) algorithm of Wynn and Levin's u transform. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source]

Scale dependence of diversity measures in a leaf-litter ant assemblage

ECOGRAPHY, Issue 2 2004
Maurice Leponce
A reliable characterization of community diversity and composition, necessary to allow inter-site comparisons and to monitor changes, is especially difficult to reach in speciose invertebrate communities. Spatial components of the sampling design (sampling interval, extent and grain) as well as temporal variations of species density affect the measures of diversity (species richness S, Buzas and Gibson's evenness E and Shannon's heterogeneity H). Our aim was to document the small-scale spatial distribution of leaf litter ants in a subtropical dry forest of the Argentinian Chaco and analyze how the community characterization was best achieved with a minimal sampling effort. The work was based on the recent standardized protocol for collecting ants of the leaf litter ("A.L.L.": 20 samples at intervals of 10 m). To evaluate the consistency of the sampling method in time and space, the selected site was first subject to a preliminary transect, then submitted after a 9-month interval to an 8-fold oversampling campaign (160 samples at interval of 1.25 m). Leaf litter ants were extracted from elementary 1 m2 quadrats with Winkler apparatus. An increase in the number of samples collected increased S and decreased E but did not affect much H. The sampling interval and extent did not affect S and H beyond a distance of 10 m between samples. An increase of the sampling grain had a similar effect on S than a corresponding increase of the number of samples collected, but caused a proportionaly greater increase of H. The density of species m,2 varied twofold after a 9-month interval; the effect on S could only be partially corrected by rarefaction. The measure of species numerical dominance was little affected by the season. A single standardized A.L.L. transect with Winkler samples collected <45% of the species present in the assemblage. All frequent species were included but their relative frequency was not always representative. A log series distribution of species occurrences was oberved. Fisher's , and Shannon's H were the most appropriate diversity indexes. The former was useful to rarefy or abundify S and the latter was robust against sample size effects. Both parametric and Soberón and Llorente extrapolation methods outperformed non-parametric methods and yielded a fair estimate of total species richness along the transect, a minimum value of S for the habitat sampled. [source]

Methodology for the evaluation of cumulative episodic exposure to chemical stressors in aquatic risk assessment,

ENVIRONMENTAL TOXICOLOGY & CHEMISTRY, Issue 4 2000
Michael G. Morton
Abstract An ecological risk assessment method was developed to evaluate the magnitude, duration, and episodic nature of chemical stressors on aquatic communities. The percent of an ecosystem's species at risk from a designated chemical exposure scenario is generated. In effects assessment, probabilistic extrapolation methods are used to generate estimated safe concentrations (ESCs) for an ecosystem using laboratory toxicity test results. Fate and transport modeling is employed to generate temporal stressor concentration profiles. In risk characterization, area under the curve integration is performed on predicted exposure concentration profiles to calculate a cumulative exposure concentration (CEC) for the exposure event. A correction is made to account for the allowable exposure duration to the stressor ESC. Finally, the CEC is applied to the extrapolation model (curve) of the stressor to predict percent species at risk to the episodic exposure. The method may be used for either prospective or retrospective risk assessments. The results of a retrospective risk assessment performed on the Leadenwah Creek, South Carolina, USA, estuarine community are presented as a case study. The creek experienced periodic episodes of pesticide-contaminated agricultural runoff from 1986 through 1989. Although limited biological data were available for method validation, the risk estimates compared well with the Leadenwah Creek in situ bioassay results. [source]

Extrapolation methods for improving convergence of spherical Bessel integrals for the two-center Coulomb integrals

Prevalence of people with intellectual disability in the Netherlands

JOURNAL OF INTELLECTUAL DISABILITY RESEARCH, Issue 7 2007
M. Wullink
Abstract Background Since the 1990s, people with intellectual disability (ID) in the Netherlands have been moving from institutions to supported accommodation in the community. The Government is in need of recent data on the numbers of these people, to ensure adequate care provision and funding. This paper reports on the prevalence of people with ID in the Netherlands. The research question was: what is the lowest and highest estimation of prevalence of people with ID in the Netherlands? Methods Two extrapolation methods were used, each consisting of a number of stages, using general practice databases and ID care services records. Results The prevalence of people with ID in the Netherlands was 0.7% (111 750 persons). Other assumptions yielded 0.54,0.64%. Arguments for the two extrapolation methods and the lowest and highest estimation of prevalence are discussed. Conclusions Compared with 1988, there has been a slight decrease in the prevalence of people with ID in the Netherlands, even though we included all age groups and even people with ID of who were not included in ID care services records. By using general practitioner databases it was possible to identify these not registered people with ID. [source]

Impact craters on small icy bodies such as icy satellites and comet nuclei

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 2 2005
M. J. Burchell
ABSTRACT Laboratory data and the results of modelling are combined to predict the possible size of craters in icy bodies such as a comet nucleus. This is done in particular for the case of a a 370-kg mass impacting a body the size of the nucleus of comet 9P/Temple-1 at 10 km s,1. This reproduces the Deep Impact comet impact to occur in 2005, when a NASA spacecraft will observe at close range an impact on the comet nucleus of an object deployed from the main spacecraft. The predicted crater size depends not only on uncertainties in extrapolation from laboratory scale and the modelling in general, but also on assumptions made about the nature of the target. In particular, allowance is made for the full range of reasonable target porosities; this can significantly affect the outcome of the Deep Impact event. The range of predicted crater sizes covers some 7,30 m crater depth and some 50,150 m crater diameter. An increasingly porous target (i.e. one with a higher percentage of void space) will increase the depth of the crater but not necessarily the diameter, leading to the possibility of an impact event where much of the crater formation is in the interior of the crater, with work going into compaction of void space and some possible lateral growth of the crater below the surface entrance. Nevertheless, for a wide range of scenarios concerning the nature of the impact, the Deep Impact event should penetrate the surface to depths of a few tens of metres, accessing the immediate subsurface regions. In parallel to this, the same extrapolation methods are used to predict the size of impactors that may have caused the features observed on the surfaces of small bodies, e.g. the Saturnian satellite Phoebe and the nucleus of comet P/Wild-2. [source]