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Least Squares Method (least + square_method)
Selected AbstractsError analysis of proper motions in decination obtained for 807 Hipparcos stars from PZT observations over many decadesASTRONOMISCHE NACHRICHTEN, Issue 8 2010G. Damljanovi Abstract After publication of the Hipparcos catalogue (in 1997), a few new astrometric catalogues have appeared (TYCHO-2, ARIHIP, etc.), as a good combination of the Hipparcos satellite and ground-based data, to get more accurate coordinates and proper motions of stars than the Hipparcos catalogue ones. There are also investigations on improving the Hipparcos coordinates and proper motions by using the astrometric observations of latitude and universal time variations (via observed stars referred to Hipparcos catalogue), together with Hipparcos data, carried out during the last few years. These kind of ground-based data were collected at the end of the last century by J. Vondrák. There are about 4.4 million optical observations made worldwide at 33 observatories and with 47 instruments during 1899.7,1992.0; our Belgrade visual zenith telescope data (for the period 1949.0-1986.0) were included. First of all, these data were used to determine the Earth Orientation Parameters , EOP, but they are also useful for the opposite task , to check the accuracy of coordinates and proper motions of Hipparcos stars which were observed from the ground over many decades. Here, we use the latitude part of ten Photographic Zenith Tubes , PZT data (more than 0.9 million observations made at 6 observatories during the time interval 1915.8,1992.0), and combine them with the Hipparcos catalogue ones, with suitable weights, in order to check the proper motions in declination for 807 common PZT/Hipparcos stars (and to construct the PZT catalogue of ,, for 807 stars). Our standard errors in proper motions in declination of these stars are less than or equal to the Hipparcos ones for 423 stars. The mean value of standard errors of 313 stars observed over more than 20 years by PZT is 0.40 mas/yr. This is 53% of 0.75 mas/yr (the suitable value from the Hipparcos catalogue). We used the Least Squares Method , LSM with the linear model. Our results are in good agreement with the Earth Orientation Catalogue , EOC-2 and the new Hipparcos ones. The main steps of the method and the investigations of systematic errors in determined proper motions (the proper motion differences with respect to the Hipparcos values, the EOC-2 ones and the new Hipparcos ones, as a function of ,, ,, and magnitude) are presented here. A comparison of the four catalogues by pairs shows that there is no significant relationship between the differences of their ,, values and magnitudes and color indices of the common 807 stars. All catalogues have relatively small random and systematic errors which are close to each other. However, the comparison shows that our formal errors are too small. They are underestimated by a factor of nearly 1.7 (for EOC-2, it is 2.0) if we take the new Hipparcos (or Hipparcos) data as reference (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Estimation of backward impedance on low-voltage distribution system using measured resonant currentELECTRICAL ENGINEERING IN JAPAN, Issue 3 2010Toru Miki Abstract Two estimation methods for a backward impedance of a power distribution system are proposed in this paper. According to the first method, the backward impedance is estimated based on information obtained from the frequency response of a transient current flowing into a capacitor connected to a distribution line. The backward impedance is determined from the attenuation constant and the resonant frequency calculated using the capacitance and the impedance of the power distribution system. These parameters can be reliably obtained from a frequency response of the transient current using the least square method. The accuracy of the method strongly depends on the origin on the time axis for Fourier transform. An additional estimate of the time-origin is required for an accurate estimation of the backward impedance. The second method estimates the backward impedance using two transient current waveforms obtained by alternately connecting different capacitors to a distribution line. The backward impedance can be represented as a function of the frequency responses of these currents. Since this method is independent from the time-origin, it is suitable for automatic measurements of the backward impedance. Proposed methods are applicable to the estimation of harmonic currents in distribution systems. In this paper, harmonic currents flowing through a distribution line are calculated based on the estimated backward impedance and on the measured values of voltage harmonics obtained by the instrument developed by the authors. © 2010 Wiley Periodicals, Inc. Electr Eng Jpn, 171(3): 28,40, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20900 [source] Kinetic modeling of esterification of cardanol-based epoxy resin in the presence of triphenylphosphine for producing vinyl ester resin: Mechanistic rate equationJOURNAL OF APPLIED POLYMER SCIENCE, Issue 4 2010Minakshi Sultania Abstract In this study, cardanol-based epoxidized novolac resins and methacrylic acid were used to produce cardanol-based epoxidised novolac vinyl ester resins. The reactions were conducted under nonstoichiometric condition using triphenylphosphine as catalyst in the temperature range of 80,100°C with an interval of 5°C. The first-order rate equation and mechanism based rate equation were examined. Parameters were evaluated by least square method. A comparison of mechnism based rate equation and experimental data showed an excellent agreement. Finally, Arrhenius equation and activation energy were presented. The specific rate constants, based on linear regression analysis, were found to obey Arrhenius equation. The values of activation energy, frequency factor, enthalpy, entropy, and free energy of the reaction revealed that the reaction was spontaneous and irreversible and produced a highly activated complex. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010 [source] Adaptive neuro-fuzzy models for the quasi-static analysis of microstrip lineMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 5 2008Celal Yildiz Abstract This article presents a new method based on adaptive neuro-fuzzy inference system (ANFIS) to calculate the effective permittivities and characteristic impedances of microstrip lines. The ANFIS is a fuzzy inference system (FIS) implemented in the framework of an adaptive fuzzy neural network. It has the advantages of expert knowledge of FISs and learning capability of artificial neural networks. A hybrid learning algorithm, which combines the least square method and the back propagation algorithm, is used to identify the parameters of ANFIS. The results of ANFIS are compared with the results of the experimental works, quasi-static methods, and a commercial electromagnetic simulator IE3D. There is very good agreement among the results of ANFIS models and quasi-static methods, IE3D, and experimental works. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 1191,1196, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23322 [source] Iterative ultrasonic signal and image deconvolution for estimation of the complex medium responseINTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 6 2005Zhiping Mu Abstract The ill-conditioned inverse problem of estimating ultrasonic medium responses by deconvolution of RF signals is investigated. The primary difference between the proposed method and others is that the medium response function is assumed to be complex-valued rather than restricted to being real-valued. Derived from the complex medium model, complex Wiener filtering is presented, and a Hilbert transform related limitation to inverse filtering type methods is discussed. We introduce a nonparametric iterative algorithm, the least squares method with point count regularization (LSPC). The algorithm is successfully applied to simulated and experimental data and demonstrates the capability of recovering both the real and imaginary parts of the medium response. The simulation results indicate that the LSPC method can outperform Wiener filters and improve the resolution of the ultrasound system by factors as high as 3.7. Experimental results using a single element transducer and a conventional medical ultrasound system with a linear array transducer show that despite the errors in pulse estimation and the noise in the RF signals, excellent results can be obtained, demonstrating the stability and robustness of the algorithm. © 2006 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 15, 266,277, 2005 [source] Modelling, identification, and control of a spherical particle trapped in an optical tweezerINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 16 2005A. Ranaweera Abstract We provide an introduction to modelling, identification, and control of a spherical particle trapped in an optical tweezer. The main purpose is to analyse the properties of an optical tweezer from a control systems point of view. By representing the non-inertial dynamics of a trapped particle using a stochastic differential equation, we discuss probability distributions and compute first mean exit times. Within the linear trapping region, experimentally measured mean passage times for a 9.6-µm diameter polystyrene bead show close agreement with theoretical calculations. We apply a recursive least squares method to a trapped 9.6-µm diameter polystyrene bead to study the possibility of obtaining faster calibrations of characteristic frequency. We also compare the performance of proportional control, LQG control, and nonlinear control to reduce fluctuations in particle position due to thermal noise. Assuming a cubic trapping force, we use computer simulations to demonstrate that the nonlinear controller can reduce position variance by a factor of 65 for a 1-µm diameter polystyrene bead under typical conditions. Copyright © 2005 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] Quantitative structure/property relationship analysis of Caco-2 permeability using a genetic algorithm-based partial least squares methodJOURNAL OF PHARMACEUTICAL SCIENCES, Issue 10 2002Fumiyoshi Yamashita Abstract Caco-2 cell monolayers are widely used systems for predicting human intestinal absorption. This study was carried out to develop a quantitative structure,property relationship (QSPR) model of Caco-2 permeability using a novel genetic algorithm-based partial least squares (GA-PLS) method. The Caco-2 permeability data for 73 compounds were taken from the literature. Molconn-Z descriptors of these compounds were calculated as molecular descriptors, and the optimal subset of the descriptors was explored by GA-PLS analysis. A fitness function considering both goodness-of-fit to the training data and predictability of the testing data was adopted throughout the genetic algorithm-driven optimization procedure. The final PLS model consisting of 24 descriptors gave a correlation coefficient (r) of 0.886 for the entire dataset and a predictive correlation coefficient (rpred) of 0.825 that was evaluated by a leave-some-out cross-validation procedure. Thus, the GA-PLS analysis proved to be a reasonable QSPR modeling approach for predicting Caco-2 permeability. © 2002 Wiley-Liss Inc. and the American Pharmaceutical Association J Pharm Sci 91:2230,2239, 2002 [source] Chemiluminescent picture of diphenyleneiodonium-inhibited NADPH oxidase: a bimodal process and its logistic,exponential model-based descriptionLUMINESCENCE: THE JOURNAL OF BIOLOGICAL AND CHEMICAL LUMINESCENCE, Issue 4 2007Bonawentura Kochel Abstract A chemiluminescence (CL) study of diphenyleneiodonium-inhibited NADPH oxidase was performed on a cellular system containing neutrophils stimulated by phorbol myristate acetate, indicating a complex bimodal structure of CL processes corresponding to different stages of the inhibition. The complex structure of these processes was described by a superposition of two logistic,exponential (LE) models, characterizing these processes as bimodal ones. To determine the mechanistic foundation of the LE model-described processes, a generalized form of the second-order dynamic system of CL reactions, the solution to which corresponds to the LE model, was constructed. The diphenyleneiodonium effects on neutrophil NADPH oxidase were separated from the total bimodal CL of the whole measurement system by the use of difference CL processes. These difference processes were also found to be bimodal; thus, inhibitor-induced reduction of CL could be described by a second-order dynamic system. The rate constants and initial concentrations in this dynamic system were determined by the least squares method applied to numerical solutions approximating the difference processes. Using interrelations between the parameters of the dynamic system, cooperative effects in the inhibitor reactions with NADPH oxidase were found and described quantitatively. Other evidences of cooperativity were obtained from integral characteristics of the CL reduction process, i.e. dose,response and progress curves, determined by numerical integration of the LE models constituting the superposition. On this basis, it was also possible to detect a specific binding of the inhibitor to the enzyme. Finally, putative reaction mechanisms suggested by the model obtained were considered and compared with those known at present. Copyright © 2007 John Wiley & Sons, Ltd. [source] An Age-Stratified Poisson Model for Comparing Trends in Cancer Rates Across Overlapping RegionsBIOMETRICAL JOURNAL, Issue 4 2008Yi Li Abstract The annual percent change (APC) has been used as a measure to describe the trend in the age-adjusted cancer incidence or mortality rate over relatively short time intervals. The yearly data on these age-adjusted rates are available from the Surveillance, Epidemiology, and End Results (SEER) Program of the National Cancer Institute. The traditional methods to estimate the APC is to fit a linear regression of logarithm of age-adjusted rates on time using the least squares method or the weighted least squares method, and use the estimate of the slope parameter to define the APC as the percent change in the rates between two consecutive years. For comparing the APC for two regions, one uses a t-test which assumes that the two datasets on the logarithm of the age-adjusted rates are independent and normally distributed with a common variance. Two modifications of this test, when there is an overlap between the two regions or between the time intervals for the two datasets have been recently developed. The first modification relaxes the assumption of the independence of the two datasets but still assumes the common variance. The second modification relaxes the assumption of the common variance also, but assumes that the variances of the age-adjusted rates are obtained using Poisson distributions for the mortality or incidence counts. In this paper, a unified approach to the problem of estimating the APC is undertaken by modeling the counts to follow an age-stratified Poisson regression model, and by deriving a corrected Z -test for testing the equality of two APCs. A simulation study is carried out to assess the performance of the test and an application of the test to compare the trends, for a selected number of cancer sites, for two overlapping regions and with varied degree of overlapping time intervals is presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Application of Residence Time Distribution for Measuring the Fluid Velocity and Dispersion CoefficientCHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 1 2007W. Zhang Abstract Most studies on residence time distribution (RTD) have focused on the tail of the RTD curve, and very little attention has been paid to the effect of white noise on the measured results. The aim of this work is to study the effect of white noise on the calculated parameters with different data processing methods. The anti-disturbance abilities of the moment method and the least squares method are compared. The results show that the anti-disturbance ability of the least squares method was better than that of the moment method. As a result of peak overlapping in the RTD curve of a loop reactor, the moment method cannot be used to calculate the fluid velocity and dispersion coefficient. Experiments show that the least squares method is still applicable in a loop reactor. [source] Relationship between muscle oxygenation and electromyography activity during sustained isometric contractionCLINICAL PHYSIOLOGY AND FUNCTIONAL IMAGING, Issue 4 2008Eiji Yamada Summary The purpose of this study was to clarify the relationship between electromyography (EMG) spectrum changes and muscle oxygenation measured by near-infrared time-resolved spectroscopy (TRS). Each subject performed sustained isometric knee extension at 50% of the maximal voluntary contraction load for 1 min. Surface EMG and TRS were simultaneously recorded from the right vastus lateralis muscle. Mean power frequency (MPF) of the power spectrum was calculated every 5 s during isometric contraction using fast Fourier transform, and decrease in the slope of MPF for 1 min was calculated using the least squares method. The maximal changes in oxygenated haemoglobin and myoglobin (Oxy Hb/Mb) and in deoxygenated haemoglobin and myoglobin (Deoxy Hb/Mb) from pre-contraction values of 1 min were calculated. There were significant relationships between the decrease in the slope of MPF and the maximal changes in Oxy Hb/Mb and Deoxy Hb/Mb (P < 0·05). These findings suggested that changes in Oxy Hb/Mb and Deoxy Hb/Mb indicate muscle fatigue assessed by EMG. [source] On the subdomain-Galerkin/least squares method for 2- and 3-D mixed elliptic problems with reaction termsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2002Suh-Yuh Yang Abstract In this article we apply the subdomain-Galerkin/least squares method, which is first proposed by Chang and Gunzburger for first-order elliptic systems without reaction terms in the plane, to solve second-order non-selfadjoint elliptic problems in two- and three-dimensional bounded domains with triangular or tetrahedral regular triangulations. This method can be viewed as a combination of a direct cell vertex finite volume discretization step and an algebraic least-squares minimization step in which the pressure is approximated by piecewise linear elements and the flux by the lowest order Raviart-Thomas space. This combined approach has the advantages of both finite volume and least-squares methods. Among other things, the combined method is not subject to the Ladyzhenskaya-Babus,ka-Brezzi condition, and the resulting linear system is symmetric and positive definite. An optimal error estimate in the H1(,) × H(div; ,) norm is derived. An equivalent residual-type a posteriori error estimator is also given. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 738,751, 2002; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/num.10030. [source] | |||||||||||||||||||