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Linear Methods (linear + methods)

Distribution by Scientific Domains

Chemistry	50%

Selected Abstracts

Characterizing instantaneous phase relationships in whole-brain fMRI activation data

HUMAN BRAIN MAPPING, Issue 2 2002
Angela R. Laird
Abstract Typically, fMRI data is processed in the time domain with linear methods such as regression and correlation analysis. We propose that the theory of phase synchronization may be used to more completely understand the dynamics of interacting systems, and can be applied to fMRI data as a novel method of detecting activation. Generalized synchronization is a phenomenon that occurs when there is a nonlinear functional relationship present between two or more coupled, oscillatory systems, whereas phase synchronization is defined as the locking of the phases while the amplitudes may vary. In this study, we developed an application of phase synchronization analysis that is appropriate for fMRI data, in which the phase locking condition is investigated between a voxel time series and the reference function of the task performed. A synchronization index is calculated to quantify the level of phase locking, and a nonparametric permutation test is used to determine the statistical significance of the results. We performed the phase synchronization analysis on the data from five volunteers for an event-related finger-tapping task. Functional maps were created that provide information on the interrelations between the instantaneous phases of the reference function and the voxel time series in a whole-brain fMRI activation data set. We conclude that this method of analysis is useful for revealing additional information on the complex nature of the fMRI time series. Hum. Brain Mapping 16:71,80, 2002. © 2002 Wiley-Liss, Inc. [source]

On the nonlinear isoconversional procedures to evaluate the activation energy of nonisothermal reactions in solids

INTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 2 2004
P. Budrugeac
A general procedure for deriving the equations that underlie various isoconversional nonlinear methods for evaluating the activation energy is presented. A new integral isoconversional nonlinear method with integration over a given range of conversion is suggested. This method was applied to simulated nonisothermal data as well as to data for the nonisothermal decomposition of ammonium perchlorate. The obtained dependencies of the activation energy on the degree of conversion were compared with those resulting from other nonlinear and linear methods of analysis. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 36: 87,93 2004 [source]

All linear methods are equal,and extendible to (some) nonlinearities

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 8 2002
Janos GertlerArticle first published online: 17 JUN 200
Abstract Several linear methods of residual generation for fault detection and diagnosis are reviewed. The parity relation approach is introduced in some detail, for both additive and parametric faults. The Chow,Willsky scheme, various diagnostic observers and principal component analysis are compared to the additive version. The ,local approach' and the least-squares estimation of parameter changes are shown to be related to the parametric variant. Nonlinear extensions are demonstrated for all the techniques under additive faults. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Linear augmented Slater-type orbital method for free standing clusters

JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 8 2009
K. S. Kang
Abstract We have developed a Scalable Linear Augmented Slater-Type Orbital (LASTO) method for electronic-structure calculations on free-standing atomic clusters. As with other linear methods we solve the Schrödinger equation using a mixed basis set consisting of numerical functions inside atom-centered spheres and matched onto tail functions outside. The tail functions are Slater-type orbitals, which are localized, exponentially decaying functions. To solve the Poisson equation between spheres, we use a finite difference method replacing the rapidly varying charge density inside the spheres with a smoothed density with the same multipole moments. We use multigrid techniques on the mesh, which yields the Coulomb potential on the spheres and in turn defines the potential inside via a Dirichlet problem. To solve the linear eigen-problem, we use ScaLAPACK, a well-developed package to solve large eigensystems with dense matrices. We have tested the method on small clusters of palladium. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009 [source]

QSAR of Progestogens: Use of a Priori and Computed Molecular Descriptors and Molecular Graphics

MOLECULAR INFORMATICS, Issue 4 2003
Rudolf Kiralj
Abstract Quantitative Structure-Activity Relationship (QSAR) study of two sets of oral progestogens was carried out by using Principal Component Analysis (PCA), Hierarchical Cluster Analysis (HCA) and Partial Least Squares (PLS). A priori, computed (at DFT 6-31G** level) and molecular graphics and modeling descriptors were employed. Molecular graphics and modeling studies of crystal structures of complexes progesterone receptor (PR)-progesterone, Fab,-progesterone and PR-metribolone have been performed. QSAR of progestogens is a three-dimensional phenomenon (over 96% of information is explained by the first three Principal Components), which can be, although it exhibits significant non-linearity, treated well with linear methods such as PLS. Progestogen activity depends primarily on double bond contents and resonance effects which define the skeletal conformation, and also on substituent characteristics (size, conformational and electronic properties). Sterical relationships between a substituent at C6(sp2) or C6(sp3)-, and sulfur atom from Met 801 residue of PR are important for progesterone binding to the protein and can be quantified. Basically the same was observed for substituents at ,-C10 with respect to residue Met759. [source]