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Linear Scaling (linear + scaling)
Selected AbstractsScaling the structure,function relationship for clinical perimetryACTA OPHTHALMOLOGICA, Issue 4 2005Ronald S. Harwerth Abstract. Purpose:,The full ranges of glaucomatous visual field defects and retinal ganglion cell losses extend over several orders of magnitude and therefore an interpretation of the structure,function relationship for clinical perimetry requires scaling of both variables. However, the most appropriate scale has not been determined. The present study was undertaken to compare linear and logarithmic transformations, which have been proposed for correlating the perimetric defects and neural losses of glaucoma. Methods:,Perimetry, by behavioural testing, and retinal histology data were obtained from rhesus monkeys with significant visual field defects caused by experimental glaucoma. Ganglion cell densities were measured in histologic sections of retina that corresponded to specific perimetry test locations for the treated and control eyes. The linear (percentage) and logarithmic (decibel) relationships for sensitivity loss as a function of ganglion cell loss were analysed. Results:,With decibel scaling, visual sensitivity losses and ganglion cell densities were linearly correlated with high coefficients of determination (r2), although the parameters of the functions varied with eccentricity. The structure,function relationships expressed as linear percentage-loss functions were less systematic in two respects. Firstly, the relationship exhibited considerable scatter in the data for small losses in visual sensitivity and, secondly, visual sensitivity losses became saturated with larger losses in ganglion cell density. The parameters of the percentage-loss functions also varied with eccentricity, but the variation was less than for the decibel-loss functions. Conclusions:,Linear scaling of perimetric defects and ganglion cell losses might potentially improve the structure,function relationship for visual defects associated with small amounts of cell loss, but the usefulness of the relationship is limited because of the high variability in that range. With log,log co-ordinates, the structure,function relationship for clinical perimetry is relatively more accurate and precise for cell losses greater than about 3 dB. The comparatively greater accuracy and precision of decibel loss functions are a likely consequence of the logarithmic scale of stimulus intensities for perimetry measurements and because the relationship between visual sensitivity and the number of neural detectors is a form of probability summation. [source] Extrapolation of the W7-X Magnet System to Reactor SizeCONTRIBUTIONS TO PLASMA PHYSICS, Issue 8 2010F. Schauer Abstract The fusion experiment Wendelstein 7-X (W7-X), presently under construction at the Greifswald branch institute of IPP, shall demonstrate the reactor potential of a HELIAS stellarator. HELIAS reactors with three, four and five periods have been studied at IPP since many years. With a plasma axis induction of 5 T, corresponding to about 10 T maximal induction at the coil, it was shown that such reactors are feasible. Now the possibility is being investigated to increase the conductor induction up to the 12 T , range, corresponding to > 5.5 T at the plasma axis. This improves the stellarator confinement properties but does not change the basic physics with respect to the previously analyzed machines. In particular the 5periodic HELIAS type, HSR5, is considered which evolves from W7-X by linear scaling of the main dimensions by a factor of four. Recent progress in superconductor technology and the extensive development work performed for ITER are taken into account. The latter is particularly relevant since by coincidence the circumferences of the HSR5 and the ITER toroidal field coils are practically the same. For the presented 12 T reactor version, the HSR50a, also the conductor and structural requirements are comparable to the corresponding ITER specifications. Therefore, advantage can be taken of these similarities for the stellarator reactor magnet design. The input was provided by the new code "MODUCO" which was developed for interactive coil layout. It is based on Bézier curve approximations and includes the computation of magnetic surfaces and forces (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A posteriori corrections to multireference limited configuration interaction based on a Brillouin,Wigner perturbative analysisINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4 2002I. Hubac Abstract A new a posteriori correction to the method of limited configuration interaction is described that attempts to restore a linear scaling with particle number. The corrections are based on an analysis of the limited configuration interaction method in terms of the Brillouin,Wigner perturbation theory using a Lippmann,Schwinger-like equation. The new correction procedure is general and, in this work, the application to the limited multireference configuration interaction approximation is considered in some detail. An illustrative application to the rigid rotation of the diimine molecule is presented and the results are compared with those obtained by employing Davidson-like corrections and the corresponding full configuration interaction energies. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002 [source] Estimating WISC-IV indexes: proration versus linear scalingJOURNAL OF CLINICAL PSYCHOLOGY, Issue 10 2008Laura A. Glass Abstract This investigation compared proration and linear scaling for estimating Wechsler Intelligence Scale for Children,Fourth Edition (WISC-IV) verbal comprehension (VCI) and perceptual reasoning (PRI) composites from all relevant two subtest combinations. Using 57 primary school students and 41 clinical referrals, actual VCI and PRI scores were highly correlated with estimated index scores based on proration and linear scaling (all rs,.90). In the school sample, significant mean score differences between the actual and estimated composites were found in two comparisons; however, differences between mean scores were less than three points. No significant differences emerged in the clinical sample. Results indicate that any of the two subtest combinations produced reasonably accurate estimates of actual indexes. There was no advantage of one computational method over the other. © 2008 Wiley Periodicals, Inc. J Clin Psychol 64:1,6, 2008. [source] Energies, structures, and electronic properties of molecules in solution with the C-PCM solvation modelJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 6 2003Maurizio Cossi Abstract The conductor-like solvation model, as developed in the framework of the polarizable continuum model (PCM), has been reformulated and newly implemented in order to compute energies, geometric structures, harmonic frequencies, and electronic properties in solution for any chemical system that can be studied in vacuo. Particular attention is devoted to large systems requiring suitable iterative algorithms to compute the solvation charges: the fast multipole method (FMM) has been extensively used to ensure a linear scaling of the computational times with the size of the solute. A number of test applications are presented to evaluate the performances of the method. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 669,681, 2003 [source] Linear scaling approaches to quantum macromolecular similarity: Evaluating the similarity functionJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 14 2002Pere Constans Abstract The evaluation of the electron density based similarity function scales quadratically with respect to the size of the molecules for simplified, atomic shell densities. Due to the exponential decay of the function's atom-atom terms most interatomic contributions are numerically negligible on large systems. An improved algorithm for the evaluation of the Quantum Molecular Similarity function is presented. This procedure identifies all non-negligible terms without computing unnecessary interatomic squared distances, thus effectively turning to linear scaling the similarity evaluation. Presented also is a minimalist dynamic electron density model. Approximate, single shell densities together with the proposed algorithm facilitate fast electron density based alignments on macromolecules. © 2002 Wiley Periodicals, Inc. J Comput Chem 23: 1305,1313, 2002 [source] Lack of universal conductance features in disordered graphene nanoribbonsPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 3-4 2010Antonino La Magna Abstract Recent experimental characterisation of graphene flakes has demonstrated the existence of local structural alterations of the ideal honeycomb lattice whose influence on the conductance mechanism of this material has not yet been fully evaluated. In this study a numerical statistical analysis of the conductance distribution function in disordered graphene nanoribbons is presented. Calculations are performed in statistically equivalent replica large systems within the Non Equilibrium Green's Function formalism. Different kinds of local scattering centers have been considered. A characteristic general behavior of the conductance variance in these quasi one-dimensional systems is the linear scaling with the average of logarithm of the conductance, in the localization regime. However, in a broad class of realization of the local disorder, the slope is not a constant as the disorder degree varies in any region of the energy spectrum, i.e. the single parameters scaling hypothesis is not verified (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Limitations in predicting dyebath exhaustion using optical spectroscopyCOLORATION TECHNOLOGY, Issue 3 2010Melih Günay There are practical limitations in predicting dyebath concentrations and dyebath exhaustion using absorbance measurements from optical spectroscopy. The purpose of this paper is to examine the common assumptions of prediction models that cause prediction errors, and especially when multiple dye combinations are used. If a linear model is used to map absorbance to concentration, then five assumptions must hold: measurement repeatability, linear scaling, spectral additivity, linear independence of the constituent spectra and the absence of spectral morphing. Violation of one or more of these assumptions will lead to errors in predicting the concentrations of dyes in a dyebath and subsequent exhaustion calculations. [source] | |||||||||||||