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Value Decomposition (value + decomposition)
Kinds of Value Decomposition Selected AbstractsStrategies for the numerical integration of DAE systems in multibody dynamicsCOMPUTER APPLICATIONS IN ENGINEERING EDUCATION, Issue 2 2004E. Pennestrì Abstract The number of multibody dynamics courses offered in the university is increasing. Often the instructor has the necessity to go through the steps of an algorithm by working out a simple example. This gives the student a better understand of the basic theory. This paper provides a tutorial on the numerical integration of differential-algebraic equations (DAE) arising from the dynamic modeling of multibody mechanical systems. In particular, some algorithms based on the orthogonalization of the Jacobian matrix are herein discussed. All the computational steps involved are explained in detail and by working out a simple example. It is also reported a brief description and an application of the multibody code NumDyn3D which uses the Singular Value Decomposition (SVD) approach. © 2004 Wiley Periodicals, Inc. Comput Appl Eng Educ 12: 106,116, 2004; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae.20005 [source] Unified linear subspace approach to semantic analysisJOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE AND TECHNOLOGY, Issue 1 2010Dandan Li The Basic Vector Space Model (BVSM) is well known in information retrieval. Unfortunately, its retrieval effectiveness is limited because it is based on literal term matching. The Generalized Vector Space Model (GVSM) and Latent Semantic Indexing (LSI) are two prominent semantic retrieval methods, both of which assume there is some underlying latent semantic structure in a dataset that can be used to improve retrieval performance. However, while this structure may be derived from both the term space and the document space, GVSM exploits only the former and LSI the latter. In this article, the latent semantic structure of a dataset is examined from a dual perspective; namely, we consider the term space and the document space simultaneously. This new viewpoint has a natural connection to the notion of kernels. Specifically, a unified kernel function can be derived for a class of vector space models. The dual perspective provides a deeper understanding of the semantic space and makes transparent the geometrical meaning of the unified kernel function. New semantic analysis methods based on the unified kernel function are developed, which combine the advantages of LSI and GVSM. We also prove that the new methods are stable because although the selected rank of the truncated Singular Value Decomposition (SVD) is far from the optimum, the retrieval performance will not be degraded significantly. Experiments performed on standard test collections show that our methods are promising. [source] The three-dimensional power spectrum of dark and luminous matter from the VIRMOS-DESCART cosmic shear surveyMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 3 2003Ue-Li Pen ABSTRACT We present the first optimal power spectrum estimation and three-dimensional deprojections for the dark and luminous matter and their cross-correlations. The results are obtained using a new optimal fast estimator, deprojected using minimum variance and Singular Value Decomposition (SVD) techniques. We show the resulting 3D power spectra for dark matter and galaxies, and their covariance for the VIRMOS-DESCART weak lensing shear and galaxy data. The survey is most sensitive to non-linear scales kNL, 1 h Mpc,1. On these scales, our 3D power spectrum of dark matter is in good agreement with the RCS 3D power spectrum found by Tegmark & Zaldarriaga. Our galaxy power is similar to that found by the 2MASS survey, and larger than that of SDSS, APM and RCS, consistent with the expected difference in galaxy population. We find an average bias b= 1.24 ± 0.18 for the I -selected galaxies, and a cross-correlation coefficient r= 0.75 ± 0.23. Together with the power spectra, these results optimally encode the entire two point information about dark matter and galaxies, including galaxy,galaxy lensing. We address some of the implications regarding galaxy haloes and mass-to-light ratios. The best-fitting ,halo' parameter h,r/b= 0.57 ± 0.16, suggesting that dynamical masses estimated using galaxies systematically underestimate total mass. Ongoing surveys, such as the Canada,France,Hawaii Telescope Legacy Survey, will significantly improve on the dynamic range, and future photometric redshift catalogues will allow tomography along the same principles. [source] Approximation and complexity trade-off by TP model transformation in controller design: A case study of the TORA system,ASIAN JOURNAL OF CONTROL, Issue 5 2010Zoltán Petres Abstract The main objective of the paper is to study the approximation and complexity trade-off capabilities of the recently proposed tensor product distributed compensation (TPDC) based control design framework. The TPDC is the combination of the TP model transformation and the parallel distributed compensation (PDC) framework. The Tensor Product (TP) model transformation includes an Higher Order Singular Value Decomposition (HOSVD)-based technique to solve the approximation and complexity trade-off. In this paper we generate TP models with different complexity and approximation properties, and then we derive controllers for them. We analyze how the trade-off effects the model behavior and control performance. All these properties are studied via the state feedback controller design of the Translational Oscillations with an Eccentric Rotational Proof Mass Actuator (TORA) System. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] The cytochrome cbb3 from Pseudomonas stutzeri displays nitric oxide reductase activityFEBS JOURNAL, Issue 24 2001Elena Forte The cytochrome cbb3 is an isoenzyme in the family of cytochrome c oxidases. This protein purified from Pseudomonas stutzeri displays a cyanide-sensitive nitric oxide reductase activity (Vmax=100±9 mol NO·mol ·min,1 and Km=12±2.5 µm), which is lost upon denaturation. This enzyme is only partially reduced by ascorbate, and readily re-oxidized by NO under anaerobic conditions at a rate consistent with the turnover number for NO consumption. As shown by transient spectroscopy experiments and singular value decomposition (SVD) analysis, these results suggest that the cbb3 -type cytochromes, sharing structural features with bacterial nitric oxide reductases, are the enzymes retaining the highest NO reductase activity within the heme-copper oxidase superfamily. [source] Spatial Analysis of the Factors Contributing to the Relationship between the Transient, Meridional Eddy Sensible, and Latent Heat Flux in the Southern HemisphereGEOGRAPHICAL ANALYSIS, Issue 2 2000Marilyn Raphael In this paper principal component analysis (PCA) and singular value decomposition (SVD) are used to define the importance of the variables contributing to the relationship between the transient latent and sensible heat fluxes and to show their temporal and spatial variation. SVD is offered as an alternative means of isolating spatial and temporal structures in data with the advantage that it can depict simultaneous space-time variations that are aggregates of the results produced by PCA. Both methods of analysis produced two very important uncorrelated modes of variability in January and July, indicating that the transient heat fluxes are influenced by few controlling factors. We suggest that these modes of variability represent the influences of the meridional temperature gradient, atmospheric moisture, and activity within the source and sink regions of the transient heat fluxes. The physical relationships between the heat fluxes that appear to represented by the statistical modes of variability are discussed. [source] A covariance-adaptive approach for regularized inversion in linear modelsGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2007Christopher Kotsakis SUMMARY The optimal inversion of a linear model under the presence of additive random noise in the input data is a typical problem in many geodetic and geophysical applications. Various methods have been developed and applied for the solution of this problem, ranging from the classic principle of least-squares (LS) estimation to other more complex inversion techniques such as the Tikhonov,Philips regularization, truncated singular value decomposition, generalized ridge regression, numerical iterative methods (Landweber, conjugate gradient) and others. In this paper, a new type of optimal parameter estimator for the inversion of a linear model is presented. The proposed methodology is based on a linear transformation of the classic LS estimator and it satisfies two basic criteria. First, it provides a solution for the model parameters that is optimally fitted (in an average quadratic sense) to the classic LS parameter solution. Second, it complies with an external user-dependent constraint that specifies a priori the error covariance (CV) matrix of the estimated model parameters. The formulation of this constrained estimator offers a unified framework for the description of many regularization techniques that are systematically used in geodetic inverse problems, particularly for those methods that correspond to an eigenvalue filtering of the ill-conditioned normal matrix in the underlying linear model. Our study lies on the fact that it adds an alternative perspective on the statistical properties and the regularization mechanism of many inversion techniques commonly used in geodesy and geophysics, by interpreting them as a family of ,CV-adaptive' parameter estimators that obey a common optimal criterion and differ only on the pre-selected form of their error CV matrix under a fixed model design. [source] Shear wave splitting changes associated with the 2001 volcanic eruption on Mt EtnaGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2006Francesca Bianco SUMMARY The time delays and polarizations of shear wave splitting above small earthquakes show variations before the 2001 July 17,August 9 2001 flank eruption on Mt Etna, Sicily. Normalized time delays, measured by singular value decomposition, show a systematic increase starting several days before the onset of the eruption. On several occasions before the eruption, the polarization directions of the shear waves at Station MNT, closest to the eruption, show 90°-flips where the faster and slower split shear waves exchange polarizations. The last 90°-flip being 5 days before the onset of the eruption. The time delays also exhibit a sudden decrease shortly before the start of the eruption suggesting the possible occurrence of a ,relaxation' phenomena, due to crack coalescence. This behaviour has many similarities to that observed before a number of earthquakes elsewhere. [source] Two-dimensional inversion of magnetotelluric data with consecutive use of conjugate gradient and least-squares solution with singular value decomposition algorithmsGEOPHYSICAL PROSPECTING, Issue 1 2008M. Emin Candansayar ABSTRACT I investigated the two-dimensional magnetotelluric data inversion algorithms in studying two significant aspects within a linearized inversion approach. The first one is the method of minimization and second one is the type of stabilizing functional used in parametric functionals. The results of two well-known inversion algorithms, namely conjugate gradient and the least-squares solution with singular value decomposition, were compared in terms of accuracy and CPU time. In addition, magnetotelluric data inversion with various stabilizers, such as L2-norm, smoothing, minimum support, minimum gradient support and first-order minimum entropy, were examined. A new inversion algorithm named least-squares solution with singular value decomposition and conjugate gradient is suggested in seeing the outcomes of the comparisons carried out on least-squares solutions with singular value decomposition and conjugate gradient algorithms subject to a variety of stabilizers. Inversion results of synthetic data showed that the newly suggested algorithm yields better results than those of the individual implementations of conjugate gradient and least-squares solution with singular value decomposition algorithms. The suggested algorithm and the above-mentioned algorithms inversion results for the field data collected along a line crossing the North Anatolian Fault zone were also compared each other and results are discussed. [source] Landweber scheme for compact operator equation in Hilbert space and its applicationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2009Gangrong Qu Abstract We study the Landweber scheme for linear compact operator equation in infinite Hilbert spaces. Using the singular value decomposition for compact operators, we obtain a formula for the Landweber scheme after n iterations and iterative truncated error and consequently establish its convergence conditions. Our results extend known results on convergence conditions. As applications, we apply the Landweber scheme to the X-ray tomography and extrapolation of band-limited functions, and establish accelerated strategies for each application. Copyright © 2008 John Wiley & Sons, Ltd. [source] A fast boundary cloud method for 3D exterior electrostatic analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2004Vaishali Shrivastava Abstract An accelerated boundary cloud method (BCM) for boundary-only analysis of 3D electrostatic problems is presented here. BCM uses scattered points unlike the classical boundary element method (BEM) which uses boundary elements to discretize the surface of the conductors. BCM combines the weighted least-squares approach for the construction of approximation functions with a boundary integral formulation for the governing equations. A linear base interpolating polynomial that can vary from cloud to cloud is employed. The boundary integrals are computed by using a cell structure and different schemes have been used to evaluate the weakly singular and non-singular integrals. A singular value decomposition (SVD) based acceleration technique is employed to solve the dense linear system of equations arising in BCM. The performance of BCM is compared with BEM for several 3D examples. Copyright © 2004 John Wiley & Sons, Ltd. [source] Reduced-order controllers for control of flow past an airfoilINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2006S. S. Ravindran Abstract Reduced-order controller design by means of reduced-order model for control of a wake flow is presented. Reduced-order model is derived by combining the Galerkin projection with proper orthogonal decomposition (POD) or with other related reduced-order approaches such as singular value decomposition or reduced-basis method. In the present investigation, we discuss the applicability of the reduced-order approaches for fast computation of the optimal control for control of vortex shedding behind a thin airfoil through unsteady blowing on the airfoil surface. Accuracy of the reduced-order model is quantified by comparing flow fields obtained from the reduced-order models with those from the full-order simulations under the same free-stream conditions. A control of vortex shedding is demonstrated for Reynolds number 100. It is found that downstream directed blowing on the upper surface of the airfoil near the leading edge is more efficient in mitigating flow separation and suppressing the vortex shedding. Copyright © 2005 John Wiley & Sons, Ltd. [source] Covariabilities of spring soil moisture and summertime United States precipitation in a climate simulationINTERNATIONAL JOURNAL OF CLIMATOLOGY, Issue 4 2007Wanru Wu Abstract This paper explores the space-time connections between springtime soil moisture and summer precipitation over the continental United States by applying a singular value decomposition (SVD) method to a 50-year climate simulation. The first two SVD modes were analyzed. The two leading SVD modes account for 43% of the squared covariance between spring soil moisture and summer precipitation. Their corresponding components explain 14% of the soil moisture variance and 19% of the precipitation variance, respectively, which is larger than that contributed by tropical Pacific sea-surface temperatures (SSTs). The temporal correlations between the two expansion coefficients of each SVD mode are 0.83 and 0.88, respectively, indicating a significant association between spring soil moisture variation and summer precipitation variability. Both positive and negative cross-correlations exist over different regions of the United States in the two modes. Linear regression relates surface relative humidity and surface air temperature to the soil moisture SVD time series. The patterns revealed by the SVD analysis show where the local soil moisture-precipitation coupling contributes to the model's simulation of precipitation. Copyright © 2006 Royal Meteorological Society [source] Multidecadal climate variability of global lands and oceansINTERNATIONAL JOURNAL OF CLIMATOLOGY, Issue 7 2006Gregory J. McCabe Abstract Principal components analysis (PCA) and singular value decomposition (SVD) are used to identify the primary modes of decadal and multidecadal variability in annual global Palmer Drought Severity Index (PDSI) values and sea-surface temperatures (SSTs). The PDSI and SST data for 1925,2003 were detrended and smoothed (with a 10-year moving average) to isolate the decadal and multidecadal variability. The first two principal components (PCs) of the PDSI PCA explained almost 38% of the decadal and multidecadal variance in the detrended and smoothed global annual PDSI data. The first two PCs of detrended and smoothed global annual SSTs explained nearly 56% of the decadal variability in global SSTs. The PDSI PCs and the SST PCs are directly correlated in a pairwise fashion. The first PDSI and SST PCs reflect variability of the detrended and smoothed annual Pacific Decadal Oscillation (PDO), as well as detrended and smoothed annual Indian Ocean SSTs. The second set of PCs is strongly associated with the Atlantic Multidecadal Oscillation (AMO). The SVD analysis of the cross-covariance of the PDSI and SST data confirmed the close link between the PDSI and SST modes of decadal and multidecadal variation and provided a verification of the PCA results. These findings indicate that the major modes of multidecadal variations in SSTs and land-surface climate conditions are highly interrelated through a small number of spatially complex but slowly varying teleconnections. Therefore, these relations may be adaptable to providing improved baseline conditions for seasonal climate forecasting. Copyright © 2006 John Wiley & Sons, Ltd. [source] Trend and variability of China precipitation in spring and summer: linkage to sea-surface temperaturesINTERNATIONAL JOURNAL OF CLIMATOLOGY, Issue 13 2004Fanglin Yang Abstract Observational records in the past 50 years show an upward trend of boreal-summer precipitation over central eastern China and a downward trend over northern China. During boreal spring, the trend is upward over southeastern China and downward over central eastern China. This study explores the forcing mechanism of these trends in association with the global sea-surface temperature (SST) variations on the interannual and interdecadal time scales. Results based on singular value decomposition (SVD) analyses show that the interannual variability of China precipitation in boreal spring and summer can be well defined by two centres of action for each season, which are covarying with two interannual modes of SSTs. The first SVD modes of precipitation in spring and summer, which are centred in southeastern China and northern China respectively, are linked to an El Niño,southern oscillation (ENSO)-like mode of SSTs. The second SVD modes of precipitation in both seasons are confined to central eastern China, and are primarily linked to SST variations over the warm pool and the Indian Ocean. Features of the anomalous 850 hPa winds and 700 hPa geopotential height corresponding to these modes support a physical mechanism that explains the causal links between the modal variations of precipitation and SSTs. On the decadal and longer time scale, similar causal links are found between the same modes of precipitation and SSTs, except for the case of springtime precipitation over central eastern China. For this case, while the interannual mode of precipitation is positively correlated with the interannual variations of SSTs over the warm pool and Indian Ocean, the interdecadal mode is negatively correlated with a different SST mode, i.e. the North Pacific mode. The latter is responsible for the observed downward trend of springtime precipitation over central eastern China. For all other cases, both the interannual and interdecadal variations of precipitation can be explained by the same mode of SSTs. The upward trend of springtime precipitation over southeastern China and downward trend of summertime precipitation over northern China are attributable to the warming trend of the ENSO-like mode. The recent frequent summertime floods over central eastern China are linked to the warming trend of SSTs over the warm pool and Indian Ocean. Copyright © 2004 Royal Meteorological Society [source] An off-line design method of compensation law for constrained linear systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 1 2008Naoyuki Hara Abstract This paper deals with a design method of compensation law for linear constrained systems. By employing singular value decomposition of linear systems, we provide a design method of compensation law which fulfils system constraints. The feature of resulting compensation law is illustrated with numerical examples. Copyright © 2007 John Wiley & Sons, Ltd. [source] PRIMUS: a Windows PC-based system for small-angle scattering data analysisJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 5 2003Petr V. Konarev A program suite for one-dimensional small-angle scattering data processing running on IBM-compatible PCs under Windows 9x/NT/2000/XP is presented. The main program, PRIMUS, has a menu-driven graphical user interface calling computational modules to perform data manipulation and analysis. Experimental data in binary OTOKO format can be reduced by calling the program SAPOKO, which includes statistical analysis of time frames, averaging and scaling. Tools to generate the angular axis and detector response files from diffraction patterns of calibration samples, as well as binary to ASCII transformation programs, are available. Several types of ASCII files can be directly imported into PRIMUS, in particular, sasCIF or ILL-type files are read without modification. PRIMUS provides basic data manipulation functions (averaging, background subtraction, merging of data measured in different angular ranges, extrapolation to zero sample concentration, etc.) and computes invariants from Guinier and Porod plots. Several external modules coupled with PRIMUSvia pop-up menus enable the user to evaluate the characteristic functions by indirect Fourier transformation, to perform peak analysis for partially ordered systems and to find shape approximations in terms of three-parametric geometrical bodies. For the analysis of mixtures, PRIMUS enables model-independent singular value decomposition or linear fitting if the scattering from the components is known. An interface is also provided to the general non-linear fitting program MIXTURE, which is designed for quantitative analysis of multicomponent systems represented by simple geometrical bodies, taking shape and size polydispersity as well as interparticle interference effects into account. [source] Indexing of powder diffraction patterns by iterative use of singular value decompositionJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 1 2003A. A. Coelho A fast method for indexing powder diffraction patterns has been developed for large and small lattices of all symmetries. The method is relatively insensitive to impurity peaks and missing high d -spacings: on simulated data, little effect in terms of successful indexing has been observed when one in three d -spacings are randomly removed. Comparison with three of the most popular indexing programs, namely ITO, DICVOL91 and TREOR90, has shown that the present method as implemented in the program TOPAS is more successful at indexing simulated data. Also significant is that the present method performs well on typically noisy data with large diffractometer zero errors. Critical to its success, the present method uses singular value decomposition in an iterative manner for solving linear equations relating hkl values to d -spacings. [source] QT Dispersion Does Not Represent Electrocardiographic Interlead Heterogeneity of Ventricular RepolarizationJOURNAL OF CARDIOVASCULAR ELECTROPHYSIOLOGY, Issue 8 2000MAREK MALIK Ph.D. QT Dispersion and Repolarization Heterogeneity. Introduction: QT dispersion (QTd, range of QT intervals in 12 ECG leads) is thought to reflect spatial heterogeneity of ventricular refractoriness. However, QTd may be largely due to projections of the repolarization dipole rather than "nondipolar" signals. Methods and Results: Seventy-eight normal subjects (47 ± 16 years, 23 women), 68 hypertrophic cardiomyopathy patients (HCM; 38 ± 15 years. 21 women), 72 dilated cardiomyopathy patients (DCM; 48 ± 15 years, 29 women), and 81 survivors of acute myocardial infarction (AMI; 63 ± 12 years, 20 women) had digital 12-lead resting supine ECGs recorded (10 ECGs recorded in each subject and results averaged). In each ECG lead, QT interval was measured under operator review by QT Guard (GE Marquette) to obtain QTd. QTd was expressed as the range, standard deviation, and highest-to-lowest quartile difference of QT interval in all measurable leads. Singular value decomposition transferred ECGs into a minimum dimensional time orthogonal space. The first three components represented the ECG dipole; other components represented nondipolar signals. The power of the T wave nondipolar within the total components was computed to measure spatial repolarization heterogeneity (relative T wave residuum, TWR). OTd was 33.6 ± 18.3, 47.0 ± 19.3, 34.8 ± 21.2, and 57.5 ± 25.3 msec in normals, HCM, CM, and AMI, respectively (normals vs DCM: NS, other P < 0.009). TWR was 0.029%± 0.031%, 0.067%± 0.067%, 0.112%± 0.154%, and 0.186%± 0.308% in normals, HCM, DCM, and AMI (HCM vs DCM: NS. other P < 0.006), The correlations between QTd and TWR were r = -0.0446, 0.2805, -0.1531, and 0.0771 (P = 0.03 for HCM, other NS) in normals, HCM, DCM, and AMI, respectively. Conclusion: Spatial heterogeneity of ventricular repolarization exists and is measurable in 12-lead resting ECGs. It differs between different clinical groups, but the so-called QT dispersion is unrelated to it. [source] First-order perturbation analysis of the best rank-(R1, R2, R3) approximation in multilinear algebraJOURNAL OF CHEMOMETRICS, Issue 1 2004Lieven De Lathauwer Abstract In this paper we perform a first-order perturbation analysis of the least squares approximation of a given higher-order tensor by a tensor having prespecified n -mode ranks. This work generalizes the classical first-order perturbation analysis of the matrix singular value decomposition. We will show that there are important differences between the matrix and the higher-order tensor case. We subsequently address (1) the best rank-1 approximation of supersymmetric tensors, (2) the best rank-(R1, R2, R3) approximation of arbitrary tensors and (3) the best rank-(R1, R2, R3) approximation of arbitrary tensors. Copyright © 2004 John Wiley & Sons, Ltd. [source] Precision of prediction in second-order calibration, with focus on bilinear regression methodsJOURNAL OF CHEMOMETRICS, Issue 1 2002Marie Linder Abstract We consider calibration of hyphenated instruments with particular focus on determination of the unknown concentrations of new specimens. A hyphenated instrument generates for each specimen a two-way array of data. These are assumed to depend on the concentrations through a bilinear regression model, where each constituent is characterized by a pair of profiles to be determined in the calibration. We discuss the problem of predicting the unknown concentrations in a new specimen, after calibration. We formulate three different predictor construction methods, a ,naive' method, a least squares method, and a refined version of the latter that takes account of the calibration uncertainty. We give formulae for the uncertainty of the predictors under white noise, when calibration can be seen as precise. We refine these formulae to allow for calibration uncertainty, in particular when calibration is carried out by the bilinear least squares (BLLS) method or the singular value decomposition (SVD) method proposed by Linder and Sundberg (Chemometrics Intell. Lab. Syst. 1998; 42: 159,178). By error propagation formulae and previous results on the precision of and we can obtain approximate standard errors for the predicted concentrations, according to each of the two estimation methods. The performance of the predictors and the precision formulae is illustrated on both real (fluorescence) and simulated data. Copyright © 2002 John Wiley & Sons, Ltd. [source] A novel approach for screening discrete variations in organic synthesisJOURNAL OF CHEMOMETRICS, Issue 5 2001Rolf Carlson Abstract In this paper we present a general strategy for screening discrete variations in organic synthesis. The strategy is based upon principal properties, i.e. principal component characterization of the constituents defining the reaction system. The first step is to select subsets of test items from each class of constituents defining the reaction space, i.e. substrates, reagents, solvents, catalysts, etc., so that the selected items from each class cover the properties considered. The second step is to construct a candidate matrix which contains all possible combinations of the items in the subsets. This matrix is a full multilevel factorial design. The third step is to assign a tentative model for the screening experiment and to construct the corresponding candidate model matrix. The fourth step is to select experiments to yield an experimental design that spans the variable space efficiently and that also gives good estimates of the model parameters. We present an algorithm that uses singular value decomposition to select experiments. The proposed strategy is then illustrated with an example of the Fischer indole synthesis. Copyright © 2001 John Wiley & Sons, Ltd. [source] Multivariate chemometric approach to thermal solid-state FT-IR monitoring of pharmaceutical drug compoundJOURNAL OF PHARMACEUTICAL SCIENCES, Issue 8 2008Wei Jian Tan Abstract The study of thermal-related solid-state reaction monitored by spectroscopic method needs the use of advanced multivariate chemometric approach. It is because visual inspection of spectral data on particular functional groups or spectral bands is difficult to reveal the complete physical and chemical information. The spectral contributions from various species involved in the solid-state changes are generally highly overlapping and the spectral differences between reactant and product are usually quite minute. In this article, we demonstrate the use of multivariate chemometric approach to resolve the in situ thermal-dependent Fourier-transform infrared (FT-IR) mixture spectra of lisinopril dihydrate when it was heated from 24 to 170°C. The collected FT-IR mixture spectra were first subjected to singular value decomposition (SVD) to obtain the right singular vectors. The right singular vectors were rotated into a set of pure component spectral estimates based on entropy minimization and spectral dissimilarity objective functions. The resulting pure component spectral estimates were then further refined using alternating least squares (ALS). In current study, four pure component spectra, that is, lisinopril dihydrate, monohydrate, anhydrate, and diketopiperazine (DKP) were all resolved and the relative thermal-dependent contributions of each component were also obtained. These relative contributions revealed the critical temperature for each transformation and degradation. This novel approach provides better interpretation of the pathway of dehydration and intramolecular cyclization of lisinopril dihydrate in the solid state. In addition, it can be used to complement the information obtained from differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA). © 2007 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 97: 3379,3387, 2008 [source] Biplots of compositional dataJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES C (APPLIED STATISTICS), Issue 4 2002John Aitchison Summary. The singular value decomposition and its interpretation as a linear biplot have proved to be a powerful tool for analysing many forms of multivariate data. Here we adapt biplot methodology to the specific case of compositional data consisting of positive vectors each of which is constrained to have unit sum. These relative variation biplots have properties relating to the special features of compositional data: the study of ratios, subcompositions and models of compositional relationships. The methodology is applied to a data set consisting of six-part colour compositions in 22 abstract paintings, showing how the singular value decomposition can achieve an accurate biplot of the colour ratios and how possible models interrelating the colours can be diagnosed. [source] Evaluation of an AIF correction algorithm for dynamic susceptibility contrast-enhanced perfusion MRIMAGNETIC RESONANCE IN MEDICINE, Issue 1 2008Peter Brunecker Abstract For longitudinal studies in patients suffering from cerebrovascular diseases the poor reproducibility of perfusion measurements via dynamic susceptibility-weighted contrast-enhanced MRI (DSC-MRI) is a relevant concern. We evaluate a novel algorithm capable of overcoming limitations in DSC-MRI caused by partial volume and saturation issues in the arterial input function (AIF) by a blood flow stimulation-study. In 21 subjects, perfusion parameters before and after administration of blood flow stimulating L -arginine were calculated utilizing a block-circulant singular value decomposition (cSVD). A total of two different raters and three different rater conditions were employed to select AIFs: Besides 1) an AIF selection by an experienced rater, a beginner rater applied a steady state-oriented strategy, returning; 2) raw; and 3) corrected AIFs. Highly significant changes in regional cerebral blood flow (rCBF) by 9.0% (P < 0.01) could only be found when the AIF correction was performed. To further test for improved reproducibility, in a subgroup of seven subjects the baseline measurement was repeated 6 weeks after the first examination. In this group as well, using the correction algorithm decreased the SD of the difference between the two baseline measurements by 42%. Magn Reson Med 60:102,110, 2008. © 2008 Wiley-Liss, Inc. [source] A twisted factorization method for symmetric SVD of a complex symmetric tridiagonal matrixNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 10 2009Wei Xu Abstract This paper presents an O(n2) method based on the twisted factorization for computing the Takagi vectors of an n -by- n complex symmetric tridiagonal matrix with known singular values. Since the singular values can be obtained in O(n2) flops, the total cost of symmetric singular value decomposition or the Takagi factorization is O(n2) flops. An analysis shows the accuracy and orthogonality of Takagi vectors. Also, techniques for a practical implementation of our method are proposed. Our preliminary numerical experiments have verified our analysis and demonstrated that the twisted factorization method is much more efficient than the implicit QR method, divide-and-conquer method and Matlab singular value decomposition subroutine with comparable accuracy. Copyright © 2009 John Wiley & Sons, Ltd. [source] Comparative analysis of gene expression on mRNA and protein level during development of Streptomyces cultures by using singular value decompositionPROTEINS: STRUCTURE, FUNCTION AND BIOINFORMATICS, Issue 21 2007Jiri Vohradsky Dr. Abstract This paper describes a comparative systems level analysis of the developmental proteome and transcriptome in the model antibiotic-producing eubacterium Streptomyces coelicolor, cultured on different media. The analysis formulates expression as the superposition of effects of regulatory networks and biological processes which can be identified using singular value decomposition (SVD) of a data matrix formed by time series measurements of expression of individual genes throughout the cell cycle of the bacterium. SVD produces linearly orthogonal factors, each of which can represent an independent system behavior defined by a linear combination of the genes/proteins highly correlated with the corresponding factor. By using SVD of the developmental time series of gene expression, as measured by both protein and RNA levels, we show that on the highest level of control (representing the basic kinetic behavior of the population), the results are identical, regardless of the type of experiment or cultivation method. The results show that this approach is capable of identifying basic regulatory processes independent of the environment in which the organism lives. It also shows that these processes are manifested equally on protein and RNA levels. Biological interpretation of the correlation of the genes and proteins with significant eigenprofiles (representing the highest level kinetic behavior of protein and/or RNA synthesis) revealed their association with metabolic processes, stress responses, starvation, and secondary metabolite production. [source] Nondipolar Content of T Wave Derived from a Myocardial Source Simulation with Increased Repolarization InhomogeneityANNALS OF NONINVASIVE ELECTROCARDIOLOGY, Issue 2 2009Milos Kesek M.D., Ph.D. Background: Several conditions with repolarization disturbances are associated with increased level of nondipolar components of the T wave. The nondipolar content has been proposed as a measure of repolarization inhomogeneity. This computer simulation study examines the link between increased nondipolar components and increased repolarization inhomogeneity in an established model. Methods: The simulation was performed with Ecgsim software that uses the equivalent double-layer source model. In the model, the shape of transmembrane potential is derived from biological recordings. Increased repolarization inhomogeneity was simulated globally by increasing the variance in action potential duration and locally by introducing changes mimicking acute myocardial infarction. We synthesized surface ECG recordings with 12, 18, and 300 leads. The T-wave residue was calculated by singular value decomposition. The study examined the effects of the number of ECG leads, changes in definition of end of T wave and random noise added to the signal. Results: Normal myocardial source gave a low level of nondipolar content. Increased nondipolar content was observed in the two types of increased repolarization inhomogeneity. Noise gave a large increase in the nondipolar content. The sensitivity of the result to noise increased when a higher number of principal components were used in the computation. Conclusions: The nondipolar content of the T wave was associated with repolarization inhomogeneity in the computer model. The measure was very sensitive to noise, especially when principal components of high order were included in the computations. Increased number of ECG leads resulted in an increased signal-to-noise ratio. [source] Negative binomial version of the Lee,Carter model for mortality forecastingAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 5 2007Antoine Delwarde Abstract Mortality improvements pose a challenge for the planning of public retirement systems as well as for the private life annuities business. For public policy, as well as for the management of financial institutions, it is important to forecast future mortality rates. Standard models for mortality forecasting assume that the force of mortality at age x in calendar year t is of the form exp(,x + ,x,t). The log of the time series of age-specific death rates is thus expressed as the sum of an age-specific component ,x that is independent of time and another component that is the product of a time-varying parameter ,t reflecting the general level of mortality, and an age-specific component ,x that represents how rapidly or slowly mortality at each age varies when the general level of mortality changes. The parameters are usually estimated via singular value decomposition or via maximum likelihood in a binomial or Poisson regression model. This paper demonstrates that it is possible to take into account the overdispersion present in the mortality data by estimating the parameter in a negative binomial regression model. Copyright © 2007 John Wiley & Sons, Ltd. [source] Analysis of call centre arrival data using singular value decompositionAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2005Haipeng Shen Abstract We consider the general problem of analysing and modelling call centre arrival data. A method is described for analysing such data using singular value decomposition (SVD). We illustrate that the outcome from the SVD can be used for data visualization, detection of anomalies (outliers), and extraction of significant features from noisy data. The SVD can also be employed as a data reduction tool. Its application usually results in a parsimonious representation of the original data without losing much information. We describe how one can use the reduced data for some further, more formal statistical analysis. For example, a short-term forecasting model for call volumes is developed, which is multiplicative with a time series component that depends on day of the week. We report empirical results from applying the proposed method to some real data collected at a call centre of a large-scale U.S. financial organization. Some issues about forecasting call volumes are also discussed. Copyright © 2005 John Wiley & Sons, Ltd. [source] | |||||||||||||||||||||||||