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Nonlinear Transformation (nonlinear + transformation)
Selected AbstractsExtrapolation methods for improving convergence of spherical Bessel integrals for the two-center Coulomb integralsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 11 2006Hassan 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] Scaling and Testing Multiplicative Combinations in the Expectancy,Value Model of AttitudesJOURNAL OF APPLIED SOCIAL PSYCHOLOGY, Issue 9 2008Icek Ajzen This article examines the multiplicative combination of belief strength by outcome evaluation in the expectancy,value model of attitudes. Because linear transformation of a belief strength measure results in a nonlinear transformation of its product with outcome evaluation, use of unipolar or bipolar scoring must be empirically justified. Also, the claim that the Belief × Evaluation product fails to explain significant variance in attitudes is found to be baseless. In regression analyses, the main effect of belief strength takes account of the outcome's valence, and the main effect of outcome evaluation incorporates the outcome's perceived likelihood. Simulated data showed that multiplication adds substantially to the prediction of attitudes only when belief and evaluation measures cover the full range of potential scores. [source] Transformations and seasonal adjustmentJOURNAL OF TIME SERIES ANALYSIS, Issue 1 2009Tommaso Proietti Abstract., We address the problem of seasonal adjustment of a nonlinear transformation of the original time series, measured on a ratio scale, which aims at enforcing two essential features: additivity and orthogonality of the components. The posterior mean and variance of the seasonally adjusted series admit an analytic finite representation only for particular values of the transformation parameter, e.g. for a fractional Box,Cox transformation parameter. Even if available, the analytical derivation can be tedious and difficult. As an alternative we propose to compute the two conditional moments of the seasonally adjusted series by means of numerical and Monte Carlo integration. The former is both fast and reliable in univariate applications. The latter uses the algorithm known as the ,simulation smoother' and it is most useful in multivariate applications. We present two case studies dealing with robust seasonal adjustment under the square root and the fourth root transformation. Our overall conclusion is that robust seasonal adjustment under transformations is feasible from the computational standpoint and that the possibility of transforming the scale ought to be considered as a further option for improving the quality of seasonal adjustment. [source] The S and G transformations for computing three-center nuclear attraction integralsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 8 2009Richard Mikael Slevinsky Abstract It is now well established that nonlinear transformations can be extremely useful in the case of oscillatory integrals. In previous work, we could show that the G transformation, which is not so well known among those interested in the numerical evaluation of highly oscillatory integrals, works very well for the extremely challenging integral called Twisted Tail. In this work, we demonstrate that these techniques also apply to three-center nuclear attraction integrals over exponential type functions. The accurate and rapid evaluation of these integrals is required in ab initio molecular structure calculations and density functional theory. Using a basis set of B functions and profiting from their relatively simple Fourier representation, these integrals are formulated as analytical expressions involving highly oscillatory spherical Bessel integral functions. In the present work, we implement two highly accurate algorithms for three-center nuclear attraction integrals. The first algorithm is based on the G transformation and the second is based on a combination of the S and G transformations. The application of these transformations is largely due to the properties of special functions that allow the computation of higher order derivatives of the integrands with exceptional simplicity. The numerical results illustrate the accuracy of these algorithms applied to three-center nuclear attraction integrals over exponential type functions with a miscellany of different parameters. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] The QSAR Modeling of Cytotoxicity on AnthraquinonesMOLECULAR INFORMATICS, Issue 8 2009Kalev Takkis Abstract A QSAR analysis was carried out on a dataset of 126 anthraquinone-based cytotoxic compounds. A PCA of the molecular descriptors was used to cluster the dataset into smaller subsets according to their structural features and QSAR models were derived for the selected sets. During the modeling, protonated states of molecules and nonlinear transformations of the descriptors were considered. The developed models have been interpreted in the context of cytotoxicity and validated with leave-one-out, and leave-many-out cross-validation. The descriptors in the resulting models describe the size and charge distribution of molecules although in different clusters their proportions vary. [source] | ||||||||||