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Squares Methods (square + methods)
Selected AbstractsArtemisinin Derivatives with Antimalarial Activity against Plasmodium falciparum Designed with the Aid of Quantum Chemical and Partial Least Squares MethodsMOLECULAR INFORMATICS, Issue 8 2003Abstract Artemisinin derivatives with antimalarial activity against Plasmodium falciparum resistant to mefloquine are designed with the aid of Quantum Chemical and Partial Least Squares Methods. The PLS model with three principal components explaining 89.55% of total variance, Q2=0.83 and R2=0.92 was obtained for 14/5 molecules in the training/external validation set. The most important descriptors for the design of the model were one level above the lowest unoccupied molecular orbital energy (LUMO+1), atomic charges in atoms C9 and C11 (Q9) and (Q11) respectively, the maximum number of hydrogen atoms that might make contact with heme (NH) and RDF030,m (a radial distribution function centered at 3.0,Å interatomic distance and weighted by atomic masses). From a set of ten proposed artemisinin derivatives, a new compound (26), was predicted with antimalarial activity higher than the compounds reported in literature. Molecular graphics and modeling supported the PLS results and revealed heme-ligand and protein-ligand stereoelectronic relationships as important for antimalarial activity. The most active 26 and 29 in the prediction set possess substituents at C9 able to extend to hemoglobin exterior, what determines the high activity of these compounds. [source] Application of Multivariate curve resolution-alternating least square methods on the resolution of overlapping CE peaks from different separation conditionsELECTROPHORESIS, Issue 20 2007Fang Zhang Abstract Discussed in this paper is the development of a new strategy to improve resolution of overlapping CE peaks by using second-order multivariate curve resolution with alternating least square (second-order MCR-ALS) methods. Several kinds of organic reagents are added, respectively, in buffers and sets of overlapping peaks with different separations are obtained. Augmented matrix is formed by the corresponding matrices of the overlapping peaks and is then analyzed by the second-order MCR-ALS method in order to use all data information to improve the precision of the resolution. Similarity between the resolved unit spectrum and the true one is used to assess the quality of the solutions provided by the above method. 3,4-Dihydropyrimidin-2-one derivatives (DHPOs) are used as model components and mixed artificially in order to obtain overlapping peaks. Three different impurity levels, 100, 20, and 10% relative to the main component, are used. With this strategy, the concentration profiles and spectra of impurities, which are no more than 10% of the main component, can be resolved from the overlapping peaks without pure standards participant in the analysis. The effects of the changes in the components spectra in the buffer with different organic reagents on the resolution are also evaluated, which are slight and can thus be ignored in the analysis. Individual data matrices (two-way data) are also analyzed by using MCR-ALS and heuristic evolving latent projections (HELP) methods and their results are compared with those when MCR-ALS is applied to augmented data matrix (three-way data) analysis. [source] Bilinear estimation of pollution source profiles and amounts by using multivariate receptor modelsENVIRONMETRICS, Issue 7 2002Eun Sug Park Abstract Multivariate receptor models aim to identify the pollution sources based on multivariate air pollution data. This article is concerned with estimation of the source profiles (pollution recipes) and their contributions (amounts of pollution). The estimation procedures are based on constrained nonlinear least squares methods with the constraints given by nonnegativity and identifiability conditions of the model parameters. We investigate several identifiability conditions that are appropriate in the context of receptor models, and also present new sets of identifiability conditions, which are often reasonable in practice when the other traditional identifiability conditions fail. The resulting estimators are consistent under appropriate identifiability conditions, and standard errors for the estimators are also provided. Simulation and application to real air pollution data illustrate the results. Copyright © 2002 John Wiley & Sons, Ltd. [source] A note on least squares methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2006G. F. Carey Abstract We examine the relationship of preconditioned L2 residual, Sobolev gradient and H,1 least squares methods. Of particular interest are: (1) a demonstration that the Sobolev gradient approach is simply a form of preconditioning for the standard L2 scheme, and (2) that the Sobolev preconditioner is related to the additional solve step in the H,1 formulation. Copyright © 2005 John Wiley & Sons, Ltd. [source] Monitoring of a second-order reaction by electronic absorption spectroscopy using combined chemometric and kinetic modelsJOURNAL OF CHEMOMETRICS, Issue 6 2003Tom J. Thurston Abstract This paper reports the application of 11 methods for obtaining kinetic constants from a second-order reaction, that between phenylhydrazine and benzophenone. In this type of reaction the number of absorbing species is lower than the number of steps in the reaction minus one, resulting in a rank-deficient response matrix. The methods used include traditional univariate curve fitting, classical least squares using previously recorded pure spectra, alternating least squares methods with both kinetic and non-negativity constraints, and target-testing methods using principal component scores. An additional recently proposed method based on difference spectra is also examined, suitable for any single-step closed reaction. The methods that performed best were difference spectra, kinetically constrained alternating least squares, and target-testing approaches. Limitations of the traditional methods are described. Copyright © 2003 John Wiley & Sons, Ltd. [source] Constrained least squares methods for estimating reaction rate constants from spectroscopic dataJOURNAL OF CHEMOMETRICS, Issue 1 2002Sabina Bijlsma Abstract Model errors, experimental errors and instrumental noise influence the accuracy of reaction rate constant estimates obtained from spectral data recorded in time during a chemical reaction. In order to improve the accuracy, which can be divided into the precision and bias of reaction rate constant estimates, constraints can be used within the estimation procedure. The impact of different constraints on the accuracy of reaction rate constant estimates has been investigated using classical curve resolution (CCR). Different types of constraints can be used in CCR. For example, if pure spectra of reacting absorbing species are known in advance, this knowledge can be used explicitly. Also, the fact that pure spectra of reacting absorbing species are non-negative is a constraint that can be used in CCR. Experimental data have been obtained from UV-vis spectra taken in time of a biochemical reaction. From the experimental data, reaction rate constants and pure spectra were estimated with and without implementation of constraints in CCR. Because only the precision of reaction rate constant estimates could be investigated using the experimental data, simulations were set up that were similar to the experimental data in order to additionally investigate the bias of reaction rate constant estimates. From the results of the simulated data it is concluded that the use of constraints does not result self-evidently in an improvement in the accuracy of rate constant estimates. Guidelines for using constraints are given. Copyright © 2002 John Wiley & Sons, Ltd. [source] Step and pulse response methods for identification of wiener processesAICHE JOURNAL, Issue 2 2006Ho Cheol Park Abstract Lack of simple identification methods for nonlinear processes hinders field applications of nonlinear control systems. For identification methods that are as simple as those for the first order plus time delay models of linear dynamical processes, graphical and least squares methods to identify Wiener-type nonlinear processes from standard responses, such as step, pulse, and square-wave responses, are proposed. Static nonlinear functions are identified independently in Wiener-type nonlinear processes. Graphical methods extract discrete points of the nonlinear static function or a continuous non-parametric model of the nonlinear static function iteratively. The least squares method provides a parametric model of the nonlinear static function. The identified static nonlinear function can be used to design a simple linearizing control system. To illustrate the proposed identification methods, simulation and experimental results are given. © 2005 American Institute of Chemical Engineers AIChE J, 2006 [source] Sure independence screening for ultrahigh dimensional feature spaceJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 5 2008Jianqing Fan Summary., Variable selection plays an important role in high dimensional statistical modelling which nowadays appears in many areas and is key to various scientific discoveries. For problems of large scale or dimensionality p, accuracy of estimation and computational cost are two top concerns. Recently, Candes and Tao have proposed the Dantzig selector using L1 -regularization and showed that it achieves the ideal risk up to a logarithmic factor log (p). Their innovative procedure and remarkable result are challenged when the dimensionality is ultrahigh as the factor log (p) can be large and their uniform uncertainty principle can fail. Motivated by these concerns, we introduce the concept of sure screening and propose a sure screening method that is based on correlation learning, called sure independence screening, to reduce dimensionality from high to a moderate scale that is below the sample size. In a fairly general asymptotic framework, correlation learning is shown to have the sure screening property for even exponentially growing dimensionality. As a methodological extension, iterative sure independence screening is also proposed to enhance its finite sample performance. With dimension reduced accurately from high to below sample size, variable selection can be improved on both speed and accuracy, and can then be accomplished by a well-developed method such as smoothly clipped absolute deviation, the Dantzig selector, lasso or adaptive lasso. The connections between these penalized least squares methods are also elucidated. [source] | |||||||||||||