Weighted Least Squares Fitting Using Ordinary Least Squares Algorithms.

ERIC Educational Resources Information Center

Kiers, Henk A. L.

1997-01-01

A general approach for fitting a model to a data matrix by weighted least squares (WLS) is studied. The approach consists of iteratively performing steps of existing algorithms for ordinary least squares fitting of the same model and is based on maximizing a function that majorizes WLS loss function. (Author/SLD)

Accurate phase extraction algorithm based on Gram–Schmidt orthonormalization and least square ellipse fitting method

NASA Astrophysics Data System (ADS)

Lei, Hebing; Yao, Yong; Liu, Haopeng; Tian, Yiting; Yang, Yanfu; Gu, Yinglong

2018-06-01

An accurate algorithm by combing Gram-Schmidt orthonormalization and least square ellipse fitting technology is proposed, which could be used for phase extraction from two or three interferograms. The DC term of background intensity is suppressed by subtraction operation on three interferograms or by high-pass filter on two interferograms. Performing Gram-Schmidt orthonormalization on pre-processing interferograms, the phase shift error is corrected and a general ellipse form is derived. Then the background intensity error and the corrected error could be compensated by least square ellipse fitting method. Finally, the phase could be extracted rapidly. The algorithm could cope with the two or three interferograms with environmental disturbance, low fringe number or small phase shifts. The accuracy and effectiveness of the proposed algorithm are verified by both of the numerical simulations and experiments.

Method of Characteristics Calculations and Computer Code for Materials with Arbitrary Equations of State and Using Orthogonal Polynomial Least Square Surface Fits

NASA Technical Reports Server (NTRS)

Chang, T. S.

1974-01-01

A numerical scheme using the method of characteristics to calculate the flow properties and pressures behind decaying shock waves for materials under hypervelocity impact is developed. Time-consuming double interpolation subroutines are replaced by a technique based on orthogonal polynomial least square surface fits. Typical calculated results are given and compared with the double interpolation results. The complete computer program is included.

Least Squares Best Fit Method for the Three Parameter Weibull Distribution: Analysis of Tensile and Bend Specimens with Volume or Surface Flaw Failure

NASA Technical Reports Server (NTRS)

Gross, Bernard

1996-01-01

Material characterization parameters obtained from naturally flawed specimens are necessary for reliability evaluation of non-deterministic advanced ceramic structural components. The least squares best fit method is applied to the three parameter uniaxial Weibull model to obtain the material parameters from experimental tests on volume or surface flawed specimens subjected to pure tension, pure bending, four point or three point loading. Several illustrative example problems are provided.

Application of least median of squared orthogonal distance (LMD) and LMD-based reweighted least squares (RLS) methods on the stock-recruitment relationship

NASA Astrophysics Data System (ADS)

Wang, Yan-Jun; Liu, Qun

1999-03-01

Analysis of stock-recruitment (SR) data is most often done by fitting various SR relationship curves to the data. Fish population dynamics data often have stochastic variations and measurement errors, which usually result in a biased regression analysis. This paper presents a robust regression method, least median of squared orthogonal distance (LMD), which is insensitive to abnormal values in the dependent and independent variables in a regression analysis. Outliers that have significantly different variance from the rest of the data can be identified in a residual analysis. Then, the least squares (LS) method is applied to the SR data with defined outliers being down weighted. The application of LMD and LMD-based Reweighted Least Squares (RLS) method to simulated and real fisheries SR data is explored.

Faraday rotation data analysis with least-squares elliptical fitting

DOE Office of Scientific and Technical Information (OSTI.GOV)

White, Adam D.; McHale, G. Brent; Goerz, David A.

2010-10-15

A method of analyzing Faraday rotation data from pulsed magnetic field measurements is described. The method uses direct least-squares elliptical fitting to measured data. The least-squares fit conic parameters are used to rotate, translate, and rescale the measured data. Interpretation of the transformed data provides improved accuracy and time-resolution characteristics compared with many existing methods of analyzing Faraday rotation data. The method is especially useful when linear birefringence is present at the input or output of the sensing medium, or when the relative angle of the polarizers used in analysis is not aligned with precision; under these circumstances the methodmore » is shown to return the analytically correct input signal. The method may be pertinent to other applications where analysis of Lissajous figures is required, such as the velocity interferometer system for any reflector (VISAR) diagnostics. The entire algorithm is fully automated and requires no user interaction. An example of algorithm execution is shown, using data from a fiber-based Faraday rotation sensor on a capacitive discharge experiment.« less

NLINEAR - NONLINEAR CURVE FITTING PROGRAM

NASA Technical Reports Server (NTRS)

Everhart, J. L.

1994-01-01

A common method for fitting data is a least-squares fit. In the least-squares method, a user-specified fitting function is utilized in such a way as to minimize the sum of the squares of distances between the data points and the fitting curve. The Nonlinear Curve Fitting Program, NLINEAR, is an interactive curve fitting routine based on a description of the quadratic expansion of the chi-squared statistic. NLINEAR utilizes a nonlinear optimization algorithm that calculates the best statistically weighted values of the parameters of the fitting function and the chi-square that is to be minimized. The inputs to the program are the mathematical form of the fitting function and the initial values of the parameters to be estimated. This approach provides the user with statistical information such as goodness of fit and estimated values of parameters that produce the highest degree of correlation between the experimental data and the mathematical model. In the mathematical formulation of the algorithm, the Taylor expansion of chi-square is first introduced, and justification for retaining only the first term are presented. From the expansion, a set of n simultaneous linear equations are derived, which are solved by matrix algebra. To achieve convergence, the algorithm requires meaningful initial estimates for the parameters of the fitting function. NLINEAR is written in Fortran 77 for execution on a CDC Cyber 750 under NOS 2.3. It has a central memory requirement of 5K 60 bit words. Optionally, graphical output of the fitting function can be plotted. Tektronix PLOT-10 routines are required for graphics. NLINEAR was developed in 1987.

The derivation of vector magnetic fields from Stokes profiles - Integral versus least squares fitting techniques

NASA Technical Reports Server (NTRS)

Ronan, R. S.; Mickey, D. L.; Orrall, F. Q.

1987-01-01

The results of two methods for deriving photospheric vector magnetic fields from the Zeeman effect, as observed in the Fe I line at 6302.5 A at high spectral resolution (45 mA), are compared. The first method does not take magnetooptical effects into account, but determines the vector magnetic field from the integral properties of the Stokes profiles. The second method is an iterative least-squares fitting technique which fits the observed Stokes profiles to the profiles predicted by the Unno-Rachkovsky solution to the radiative transfer equation. For sunspot fields above about 1500 gauss, the two methods are found to agree in derived azimuthal and inclination angles to within about + or - 20 deg.

Least median of squares and iteratively re-weighted least squares as robust linear regression methods for fluorimetric determination of α-lipoic acid in capsules in ideal and non-ideal cases of linearity.

PubMed

Korany, Mohamed A; Gazy, Azza A; Khamis, Essam F; Ragab, Marwa A A; Kamal, Miranda F

2018-06-01

This study outlines two robust regression approaches, namely least median of squares (LMS) and iteratively re-weighted least squares (IRLS) to investigate their application in instrument analysis of nutraceuticals (that is, fluorescence quenching of merbromin reagent upon lipoic acid addition). These robust regression methods were used to calculate calibration data from the fluorescence quenching reaction (∆F and F-ratio) under ideal or non-ideal linearity conditions. For each condition, data were treated using three regression fittings: Ordinary Least Squares (OLS), LMS and IRLS. Assessment of linearity, limits of detection (LOD) and quantitation (LOQ), accuracy and precision were carefully studied for each condition. LMS and IRLS regression line fittings showed significant improvement in correlation coefficients and all regression parameters for both methods and both conditions. In the ideal linearity condition, the intercept and slope changed insignificantly, but a dramatic change was observed for the non-ideal condition and linearity intercept. Under both linearity conditions, LOD and LOQ values after the robust regression line fitting of data were lower than those obtained before data treatment. The results obtained after statistical treatment indicated that the linearity ranges for drug determination could be expanded to lower limits of quantitation by enhancing the regression equation parameters after data treatment. Analysis results for lipoic acid in capsules, using both fluorimetric methods, treated by parametric OLS and after treatment by robust LMS and IRLS were compared for both linearity conditions. Copyright © 2018 John Wiley & Sons, Ltd.

Respiratory mechanics by least squares fitting in mechanically ventilated patients: application on flow-limited COPD patients.

PubMed

Volta, Carlo A; Marangoni, Elisabetta; Alvisi, Valentina; Capuzzo, Maurizia; Ragazzi, Riccardo; Pavanelli, Lina; Alvisi, Raffaele

2002-01-01

Although computerized methods of analyzing respiratory system mechanics such as the least squares fitting method have been used in various patient populations, no conclusive data are available in patients with chronic obstructive pulmonary disease (COPD), probably because they may develop expiratory flow limitation (EFL). This suggests that respiratory mechanics be determined only during inspiration. Eight-bed multidisciplinary ICU of a teaching hospital. Eight non-flow-limited postvascular surgery patients and eight flow-limited COPD patients. Patients were sedated, paralyzed for diagnostic purposes, and ventilated in volume control ventilation with constant inspiratory flow rate. Data on resistance, compliance, and dynamic intrinsic positive end-expiratory pressure (PEEPi,dyn) obtained by applying the least squares fitting method during inspiration, expiration, and the overall breathing cycle were compared with those obtained by the traditional method (constant flow, end-inspiratory occlusion method). Our results indicate that (a) the presence of EFL markedly decreases the precision of resistance and compliance values measured by the LSF method, (b) the determination of respiratory variables during inspiration allows the calculation of respiratory mechanics in flow limited COPD patients, and (c) the LSF method is able to detect the presence of PEEPi,dyn if only inspiratory data are used.

Application of least-squares fitting of ellipse and hyperbola for two dimensional data

NASA Astrophysics Data System (ADS)

Lawiyuniarti, M. P.; Rahmadiantri, E.; Alamsyah, I. M.; Rachmaputri, G.

2018-01-01

Application of the least-square method of ellipse and hyperbola for two-dimensional data has been applied to analyze the spatial continuity of coal deposits in the mining field, by using the fitting method introduced by Fitzgibbon, Pilu, and Fisher in 1996. This method uses 4{a_0}{a_2} - a_12 = 1 as a constrain function. Meanwhile, in 1994, Gander, Golub and Strebel have introduced ellipse and hyperbola fitting methods using the singular value decomposition approach. This SVD approach can be generalized into a three-dimensional fitting. In this research we, will discuss about those two fitting methods and apply it to four data content of coal that is in the form of ash, calorific value, sulfur and thickness of seam so as to produce form of ellipse or hyperbola. In addition, we compute the error difference resulting from each method and from that calculation, we conclude that although the errors are not much different, the error of the method introduced by Fitzgibbon et al is smaller than the fitting method that introduced by Golub et al.

Exploring the limits of cryospectroscopy: Least-squares based approaches for analyzing the self-association of HCl

NASA Astrophysics Data System (ADS)

De Beuckeleer, Liene I.; Herrebout, Wouter A.

2016-02-01

To rationalize the concentration dependent behavior observed for a large spectral data set of HCl recorded in liquid argon, least-squares based numerical methods are developed and validated. In these methods, for each wavenumber a polynomial is used to mimic the relation between monomer concentrations and measured absorbances. Least-squares fitting of higher degree polynomials tends to overfit and thus leads to compensation effects where a contribution due to one species is compensated for by a negative contribution of another. The compensation effects are corrected for by carefully analyzing, using AIC and BIC information criteria, the differences observed between consecutive fittings when the degree of the polynomial model is systematically increased, and by introducing constraints prohibiting negative absorbances to occur for the monomer or for one of the oligomers. The method developed should allow other, more complicated self-associating systems to be analyzed with a much higher accuracy than before.

A simple method for processing data with least square method

NASA Astrophysics Data System (ADS)

Wang, Chunyan; Qi, Liqun; Chen, Yongxiang; Pang, Guangning

2017-08-01

The least square method is widely used in data processing and error estimation. The mathematical method has become an essential technique for parameter estimation, data processing, regression analysis and experimental data fitting, and has become a criterion tool for statistical inference. In measurement data analysis, the distribution of complex rules is usually based on the least square principle, i.e., the use of matrix to solve the final estimate and to improve its accuracy. In this paper, a new method is presented for the solution of the method which is based on algebraic computation and is relatively straightforward and easy to understand. The practicability of this method is described by a concrete example.

Sensitivity test of derivative matrix isopotential synchronous fluorimetry and least squares fitting methods.

PubMed

Makkai, Géza; Buzády, Andrea; Erostyák, János

2010-01-01

Determination of concentrations of spectrally overlapping compounds has special difficulties. Several methods are available to calculate the constituents' concentrations in moderately complex mixtures. A method which can provide information about spectrally hidden components in mixtures is very useful. Two methods powerful in resolving spectral components are compared in this paper. The first method tested is the Derivative Matrix Isopotential Synchronous Fluorimetry (DMISF). It is based on derivative analysis of MISF spectra, which are constructed using isopotential trajectories in the Excitation-Emission Matrix (EEM) of background solution. For DMISF method, a mathematical routine fitting the 3D data of EEMs was developed. The other method tested uses classical Least Squares Fitting (LSF) algorithm, wherein Rayleigh- and Raman-scattering bands may lead to complications. Both methods give excellent sensitivity and have advantages against each other. Detection limits of DMISF and LSF have been determined at very different concentration and noise levels.

Using Least Squares to Solve Systems of Equations

ERIC Educational Resources Information Center

Tellinghuisen, Joel

2016-01-01

The method of least squares (LS) yields exact solutions for the adjustable parameters when the number of data values n equals the number of parameters "p". This holds also when the fit model consists of "m" different equations and "m = p", which means that LS algorithms can be used to obtain solutions to systems of…

Exploring the limits of cryospectroscopy: Least-squares based approaches for analyzing the self-association of HCl.

PubMed

De Beuckeleer, Liene I; Herrebout, Wouter A

2016-02-05

To rationalize the concentration dependent behavior observed for a large spectral data set of HCl recorded in liquid argon, least-squares based numerical methods are developed and validated. In these methods, for each wavenumber a polynomial is used to mimic the relation between monomer concentrations and measured absorbances. Least-squares fitting of higher degree polynomials tends to overfit and thus leads to compensation effects where a contribution due to one species is compensated for by a negative contribution of another. The compensation effects are corrected for by carefully analyzing, using AIC and BIC information criteria, the differences observed between consecutive fittings when the degree of the polynomial model is systematically increased, and by introducing constraints prohibiting negative absorbances to occur for the monomer or for one of the oligomers. The method developed should allow other, more complicated self-associating systems to be analyzed with a much higher accuracy than before. Copyright © 2015 Elsevier B.V. All rights reserved.

Discrete Tchebycheff orthonormal polynomials and applications

NASA Technical Reports Server (NTRS)

Lear, W. M.

1980-01-01

Discrete Tchebycheff orthonormal polynomials offer a convenient way to make least squares polynomial fits of uniformly spaced discrete data. Computer programs to do so are simple and fast, and appear to be less affected by computer roundoff error, for the higher order fits, than conventional least squares programs. They are useful for any application of polynomial least squares fits: approximation of mathematical functions, noise analysis of radar data, and real time smoothing of noisy data, to name a few.

A Method For Modeling Discontinuities In A Microwave Coaxial Transmission Line

NASA Technical Reports Server (NTRS)

Otoshi, Tom Y.

1994-01-01

A methodology for modeling discountinuities in a coaxial transmission line is presented. The method uses a none-linear least squares fit program to optimize the fit between a theoretical model and experimental data. When the method was applied for modeling discontinuites in a damaged S-band antenna cable, excellent agreement was obtained.

Evaluation of fatty proportion in fatty liver using least squares method with constraints.

PubMed

Li, Xingsong; Deng, Yinhui; Yu, Jinhua; Wang, Yuanyuan; Shamdasani, Vijay

2014-01-01

Backscatter and attenuation parameters are not easily measured in clinical applications due to tissue inhomogeneity in the region of interest (ROI). A least squares method(LSM) that fits the echo signal power spectra from a ROI to a 3-parameter tissue model was used to get attenuation coefficient imaging in fatty liver. Since fat's attenuation value is higher than normal liver parenchyma, a reasonable threshold was chosen to evaluate the fatty proportion in fatty liver. Experimental results using clinical data of fatty liver illustrate that the least squares method can get accurate attenuation estimates. It is proved that the attenuation values have a positive correlation with the fatty proportion, which can be used to evaluate the syndrome of fatty liver.

On the Least-Squares Fitting of Correlated Data: a Priorivs a PosterioriWeighting

NASA Astrophysics Data System (ADS)

Tellinghuisen, Joel

1996-10-01

One of the methods in common use for analyzing large data sets is a two-step procedure, in which subsets of the full data are first least-squares fitted to a preliminary set of parameters, and the latter are subsequently merged to yield the final parameters. The second step of this procedure is properly a correlated least-squares fit and requires the variance-covariance matrices from the first step to construct the weight matrix for the merge. There is, however, an ambiguity concerning the manner in which the first-step variance-covariance matrices are assessed, which leads to different statistical properties for the quantities determined in the merge. The issue is one ofa priorivsa posterioriassessment of weights, which is an application of what was originally calledinternalvsexternal consistencyby Birge [Phys. Rev.40,207-227 (1932)] and Deming ("Statistical Adjustment of Data." Dover, New York, 1964). In the present work the simplest case of a merge fit-that of an average as obtained from a global fit vs a two-step fit of partitioned data-is used to illustrate that only in the case of a priori weighting do the results have the usually expected and desired statistical properties: normal distributions for residuals,tdistributions for parameters assessed a posteriori, and χ2distributions for variances.

Determining a Prony Series for a Viscoelastic Material From Time Varying Strain Data

NASA Technical Reports Server (NTRS)

Tzikang, Chen

2000-01-01

In this study a method of determining the coefficients in a Prony series representation of a viscoelastic modulus from rate dependent data is presented. Load versus time test data for a sequence of different rate loading segments is least-squares fitted to a Prony series hereditary integral model of the material tested. A nonlinear least squares regression algorithm is employed. The measured data includes ramp loading, relaxation, and unloading stress-strain data. The resulting Prony series which captures strain rate loading and unloading effects, produces an excellent fit to the complex loading sequence.

Weighted spline based integration for reconstruction of freeform wavefront.

PubMed

Pant, Kamal K; Burada, Dali R; Bichra, Mohamed; Ghosh, Amitava; Khan, Gufran S; Sinzinger, Stefan; Shakher, Chandra

2018-02-10

In the present work, a spline-based integration technique for the reconstruction of a freeform wavefront from the slope data has been implemented. The slope data of a freeform surface contain noise due to their machining process and that introduces reconstruction error. We have proposed a weighted cubic spline based least square integration method (WCSLI) for the faithful reconstruction of a wavefront from noisy slope data. In the proposed method, the measured slope data are fitted into a piecewise polynomial. The fitted coefficients are determined by using a smoothing cubic spline fitting method. The smoothing parameter locally assigns relative weight to the fitted slope data. The fitted slope data are then integrated using the standard least squares technique to reconstruct the freeform wavefront. Simulation studies show the improved result using the proposed technique as compared to the existing cubic spline-based integration (CSLI) and the Southwell methods. The proposed reconstruction method has been experimentally implemented to a subaperture stitching-based measurement of a freeform wavefront using a scanning Shack-Hartmann sensor. The boundary artifacts are minimal in WCSLI which improves the subaperture stitching accuracy and demonstrates an improved Shack-Hartmann sensor for freeform metrology application.

A Simple Formula to Calculate Shallow-Water Transmission Loss by Means of a Least-Squares Surface Fit Technique.

DTIC Science & Technology

1980-09-01

HASTRUP , T REAL UNCLASSIFIED SACLAATCEN- SM-139 N SACLANTCEN Memorandum SM -139 -LEFW SACLANT ASW RESEARCH CENTRE ~ MEMORANDUM A SIMPLE FORMULA TO...CALCULATE SHALLOW-WATER TRANSMISSION LOSS BY MEANS OF A LEAST- SQUARES SURFACE FIT TECHNIQUE 7-sallby OLE F. HASTRUP and TUNCAY AKAL I SEPTEMBER 1980 NORTH...JRANSi4ISSION LOSS/ BY MEANS OF A LEAST-SQUARES SURFACE fIT TECHNIQUE, C T ~e F./ Hastrup .0TnaAa ()1 Sep 8 This memorandum has been prepared within the

On the log-normality of historical magnetic-storm intensity statistics: implications for extreme-event probabilities

USGS Publications Warehouse

Love, Jeffrey J.; Rigler, E. Joshua; Pulkkinen, Antti; Riley, Pete

2015-01-01

An examination is made of the hypothesis that the statistics of magnetic-storm-maximum intensities are the realization of a log-normal stochastic process. Weighted least-squares and maximum-likelihood methods are used to fit log-normal functions to −Dst storm-time maxima for years 1957-2012; bootstrap analysis is used to established confidence limits on forecasts. Both methods provide fits that are reasonably consistent with the data; both methods also provide fits that are superior to those that can be made with a power-law function. In general, the maximum-likelihood method provides forecasts having tighter confidence intervals than those provided by weighted least-squares. From extrapolation of maximum-likelihood fits: a magnetic storm with intensity exceeding that of the 1859 Carrington event, −Dst≥850 nT, occurs about 1.13 times per century and a wide 95% confidence interval of [0.42,2.41] times per century; a 100-yr magnetic storm is identified as having a −Dst≥880 nT (greater than Carrington) but a wide 95% confidence interval of [490,1187] nT.

Tensor hypercontraction. II. Least-squares renormalization

NASA Astrophysics Data System (ADS)

Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David

2012-12-01

The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)], 10.1063/1.4732310. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1/r12 operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N^5) effort if exact integrals are decomposed, or O(N^4) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N^4) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry.

Tensor hypercontraction. II. Least-squares renormalization.

PubMed

Parrish, Robert M; Hohenstein, Edward G; Martínez, Todd J; Sherrill, C David

2012-12-14

The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)]. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1∕r(12) operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N(5)) effort if exact integrals are decomposed, or O(N(4)) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N(4)) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry.

Order-constrained linear optimization.

PubMed

Tidwell, Joe W; Dougherty, Michael R; Chrabaszcz, Jeffrey S; Thomas, Rick P

2017-11-01

Despite the fact that data and theories in the social, behavioural, and health sciences are often represented on an ordinal scale, there has been relatively little emphasis on modelling ordinal properties. The most common analytic framework used in psychological science is the general linear model, whose variants include ANOVA, MANOVA, and ordinary linear regression. While these methods are designed to provide the best fit to the metric properties of the data, they are not designed to maximally model ordinal properties. In this paper, we develop an order-constrained linear least-squares (OCLO) optimization algorithm that maximizes the linear least-squares fit to the data conditional on maximizing the ordinal fit based on Kendall's τ. The algorithm builds on the maximum rank correlation estimator (Han, 1987, Journal of Econometrics, 35, 303) and the general monotone model (Dougherty & Thomas, 2012, Psychological Review, 119, 321). Analyses of simulated data indicate that when modelling data that adhere to the assumptions of ordinary least squares, OCLO shows minimal bias, little increase in variance, and almost no loss in out-of-sample predictive accuracy. In contrast, under conditions in which data include a small number of extreme scores (fat-tailed distributions), OCLO shows less bias and variance, and substantially better out-of-sample predictive accuracy, even when the outliers are removed. We show that the advantages of OCLO over ordinary least squares in predicting new observations hold across a variety of scenarios in which researchers must decide to retain or eliminate extreme scores when fitting data. © 2017 The British Psychological Society.

A method for cone fitting based on certain sampling strategy in CMM metrology

NASA Astrophysics Data System (ADS)

Zhang, Li; Guo, Chaopeng

2018-04-01

A method of cone fitting in engineering is explored and implemented to overcome shortcomings of current fitting method. In the current method, the calculations of the initial geometric parameters are imprecise which cause poor accuracy in surface fitting. A geometric distance function of cone is constructed firstly, then certain sampling strategy is defined to calculate the initial geometric parameters, afterwards nonlinear least-squares method is used to fit the surface. The experiment is designed to verify accuracy of the method. The experiment data prove that the proposed method can get initial geometric parameters simply and efficiently, also fit the surface precisely, and provide a new accurate way to cone fitting in the coordinate measurement.

Vastly accelerated linear least-squares fitting with numerical optimization for dual-input delay-compensated quantitative liver perfusion mapping.

PubMed

Jafari, Ramin; Chhabra, Shalini; Prince, Martin R; Wang, Yi; Spincemaille, Pascal

2018-04-01

To propose an efficient algorithm to perform dual input compartment modeling for generating perfusion maps in the liver. We implemented whole field-of-view linear least squares (LLS) to fit a delay-compensated dual-input single-compartment model to very high temporal resolution (four frames per second) contrast-enhanced 3D liver data, to calculate kinetic parameter maps. Using simulated data and experimental data in healthy subjects and patients, whole-field LLS was compared with the conventional voxel-wise nonlinear least-squares (NLLS) approach in terms of accuracy, performance, and computation time. Simulations showed good agreement between LLS and NLLS for a range of kinetic parameters. The whole-field LLS method allowed generating liver perfusion maps approximately 160-fold faster than voxel-wise NLLS, while obtaining similar perfusion parameters. Delay-compensated dual-input liver perfusion analysis using whole-field LLS allows generating perfusion maps with a considerable speedup compared with conventional voxel-wise NLLS fitting. Magn Reson Med 79:2415-2421, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Graph-Theoretic Representations for Proximity Matrices through Strongly-Anti-Robinson or Circular Strongly-Anti-Robinson Matrices.

ERIC Educational Resources Information Center

Hubert, Lawrence; Arabie, Phipps; Meulman, Jacqueline

1998-01-01

Introduces a method for fitting order-constrained matrices that satisfy the strongly anti-Robinson restrictions (SAR). The method permits a representation of the fitted values in a (least-squares) SAR approximating matrix as lengths of paths in a graph. The approach is illustrated with a published proximity matrix. (SLD)

Phase aberration compensation of digital holographic microscopy based on least squares surface fitting

NASA Astrophysics Data System (ADS)

Di, Jianglei; Zhao, Jianlin; Sun, Weiwei; Jiang, Hongzhen; Yan, Xiaobo

2009-10-01

Digital holographic microscopy allows the numerical reconstruction of the complex wavefront of samples, especially biological samples such as living cells. In digital holographic microscopy, a microscope objective is introduced to improve the transverse resolution of the sample; however a phase aberration in the object wavefront is also brought along, which will affect the phase distribution of the reconstructed image. We propose here a numerical method to compensate for the phase aberration of thin transparent objects with a single hologram. The least squares surface fitting with points number less than the matrix of the original hologram is performed on the unwrapped phase distribution to remove the unwanted wavefront curvature. The proposed method is demonstrated with the samples of the cicada wings and epidermal cells of garlic, and the experimental results are consistent with that of the double exposure method.

Methods of Fitting a Straight Line to Data: Examples in Water Resources

USGS Publications Warehouse

Hirsch, Robert M.; Gilroy, Edward J.

1984-01-01

Three methods of fitting straight lines to data are described and their purposes are discussed and contrasted in terms of their applicability in various water resources contexts. The three methods are ordinary least squares (OLS), least normal squares (LNS), and the line of organic correlation (OC). In all three methods the parameters are based on moment statistics of the data. When estimation of an individual value is the objective, OLS is the most appropriate. When estimation of many values is the objective and one wants the set of estimates to have the appropriate variance, then OC is most appropriate. When one wishes to describe the relationship between two variables and measurement error is unimportant, then OC is most appropriate. Where the error is important in descriptive problems or in calibration problems, then structural analysis techniques may be most appropriate. Finally, if the problem is one of describing some geographic trajectory, then LNS is most appropriate.

Comparison of beam position calculation methods for application in digital acquisition systems

NASA Astrophysics Data System (ADS)

Reiter, A.; Singh, R.

2018-05-01

Different approaches to the data analysis of beam position monitors in hadron accelerators are compared adopting the perspective of an analog-to-digital converter in a sampling acquisition system. Special emphasis is given to position uncertainty and robustness against bias and interference that may be encountered in an accelerator environment. In a time-domain analysis of data in the presence of statistical noise, the position calculation based on the difference-over-sum method with algorithms like signal integral or power can be interpreted as a least-squares analysis of a corresponding fit function. This link to the least-squares method is exploited in the evaluation of analysis properties and in the calculation of position uncertainty. In an analytical model and experimental evaluations the positions derived from a straight line fit or equivalently the standard deviation are found to be the most robust and to offer the least variance. The measured position uncertainty is consistent with the model prediction in our experiment, and the results of tune measurements improve significantly.

Least Median of Squares Filtering of Locally Optimal Point Matches for Compressible Flow Image Registration

PubMed Central

Castillo, Edward; Castillo, Richard; White, Benjamin; Rojo, Javier; Guerrero, Thomas

2012-01-01

Compressible flow based image registration operates under the assumption that the mass of the imaged material is conserved from one image to the next. Depending on how the mass conservation assumption is modeled, the performance of existing compressible flow methods is limited by factors such as image quality, noise, large magnitude voxel displacements, and computational requirements. The Least Median of Squares Filtered Compressible Flow (LFC) method introduced here is based on a localized, nonlinear least squares, compressible flow model that describes the displacement of a single voxel that lends itself to a simple grid search (block matching) optimization strategy. Spatially inaccurate grid search point matches, corresponding to erroneous local minimizers of the nonlinear compressible flow model, are removed by a novel filtering approach based on least median of squares fitting and the forward search outlier detection method. The spatial accuracy of the method is measured using ten thoracic CT image sets and large samples of expert determined landmarks (available at www.dir-lab.com). The LFC method produces an average error within the intra-observer error on eight of the ten cases, indicating that the method is capable of achieving a high spatial accuracy for thoracic CT registration. PMID:22797602

A calculation and uncertainty evaluation method for the effective area of a piston rod used in quasi-static pressure calibration

NASA Astrophysics Data System (ADS)

Gu, Tingwei; Kong, Deren; Shang, Fei; Chen, Jing

2018-04-01

This paper describes the merits and demerits of different sensors for measuring propellant gas pressure, the applicable range of the frequently used dynamic pressure calibration methods, and the working principle of absolute quasi-static pressure calibration based on the drop-weight device. The main factors affecting the accuracy of pressure calibration are analyzed from two aspects of the force sensor and the piston area. To calculate the effective area of the piston rod and evaluate the uncertainty between the force sensor and the corresponding peak pressure in the absolute quasi-static pressure calibration process, a method for solving these problems based on the least squares principle is proposed. According to the relevant quasi-static pressure calibration experimental data, the least squares fitting model between the peak force and the peak pressure, and the effective area of the piston rod and its measurement uncertainty, are obtained. The fitting model is tested by an additional group of experiments, and the peak pressure obtained by the existing high-precision comparison calibration method is taken as the reference value. The test results show that the peak pressure obtained by the least squares fitting model is closer to the reference value than the one directly calculated by the cross-sectional area of the piston rod. When the peak pressure is higher than 150 MPa, the percentage difference is less than 0.71%, which can meet the requirements of practical application.

Method for exploiting bias in factor analysis using constrained alternating least squares algorithms

DOEpatents

Keenan, Michael R.

2008-12-30

Bias plays an important role in factor analysis and is often implicitly made use of, for example, to constrain solutions to factors that conform to physical reality. However, when components are collinear, a large range of solutions may exist that satisfy the basic constraints and fit the data equally well. In such cases, the introduction of mathematical bias through the application of constraints may select solutions that are less than optimal. The biased alternating least squares algorithm of the present invention can offset mathematical bias introduced by constraints in the standard alternating least squares analysis to achieve factor solutions that are most consistent with physical reality. In addition, these methods can be used to explicitly exploit bias to provide alternative views and provide additional insights into spectral data sets.

Uncertainty propagation in the calibration equations for NTC thermistors

NASA Astrophysics Data System (ADS)

Liu, Guang; Guo, Liang; Liu, Chunlong; Wu, Qingwen

2018-06-01

The uncertainty propagation problem is quite important for temperature measurements, since we rely so much on the sensors and calibration equations. Although uncertainty propagation for platinum resistance or radiation thermometers is well known, there have been few publications concerning negative temperature coefficient (NTC) thermistors. Insight into the propagation characteristics of uncertainty that develop when equations are determined using the Lagrange interpolation or least-squares fitting method is presented here with respect to several of the most common equations used in NTC thermistor calibration. Within this work, analytical expressions of the propagated uncertainties for both fitting methods are derived for the uncertainties in the measured temperature and resistance at each calibration point. High-precision calibration of an NTC thermistor in a precision water bath was performed by means of the comparison method. Results show that, for both fitting methods, the propagated uncertainty is flat in the interpolation region but rises rapidly beyond the calibration range. Also, for temperatures interpolated between calibration points, the propagated uncertainty is generally no greater than that associated with the calibration points. For least-squares fitting, the propagated uncertainty is significantly reduced by increasing the number of calibration points and can be well kept below the uncertainty of the calibration points.

Orthogonal Regression: A Teaching Perspective

ERIC Educational Resources Information Center

Carr, James R.

2012-01-01

A well-known approach to linear least squares regression is that which involves minimizing the sum of squared orthogonal projections of data points onto the best fit line. This form of regression is known as orthogonal regression, and the linear model that it yields is known as the major axis. A similar method, reduced major axis regression, is…

Multistep modeling of protein structure: application towards refinement of tyr-tRNA synthetase

NASA Technical Reports Server (NTRS)

Srinivasan, S.; Shibata, M.; Roychoudhury, M.; Rein, R.

1987-01-01

The scope of multistep modeling (MSM) is expanding by adding a least-squares minimization step in the procedure to fit backbone reconstruction consistent with a set of C-alpha coordinates. The analytical solution of Phi and Psi angles, that fits a C-alpha x-ray coordinate is used for tyr-tRNA synthetase. Phi and Psi angles for the region where the above mentioned method fails, are obtained by minimizing the difference in C-alpha distances between the computed model and the crystal structure in a least-squares sense. We present a stepwise application of this part of MSM to the determination of the complete backbone geometry of the 321 N terminal residues of tyrosine tRNA synthetase to a root mean square deviation of 0.47 angstroms from the crystallographic C-alpha coordinates.

Measuring molecular motions inside single cells with improved analysis of single-particle trajectories

NASA Astrophysics Data System (ADS)

Rowland, David J.; Biteen, Julie S.

2017-04-01

Single-molecule super-resolution imaging and tracking can measure molecular motions inside living cells on the scale of the molecules themselves. Diffusion in biological systems commonly exhibits multiple modes of motion, which can be effectively quantified by fitting the cumulative probability distribution of the squared step sizes in a two-step fitting process. Here we combine this two-step fit into a single least-squares minimization; this new method vastly reduces the total number of fitting parameters and increases the precision with which diffusion may be measured. We demonstrate this Global Fit approach on a simulated two-component system as well as on a mixture of diffusing 80 nm and 200 nm gold spheres to show improvements in fitting robustness and localization precision compared to the traditional Local Fit algorithm.

The recovery of weak impulsive signals based on stochastic resonance and moving least squares fitting.

PubMed

Jiang, Kuosheng; Xu, Guanghua; Liang, Lin; Tao, Tangfei; Gu, Fengshou

2014-07-29

In this paper a stochastic resonance (SR)-based method for recovering weak impulsive signals is developed for quantitative diagnosis of faults in rotating machinery. It was shown in theory that weak impulsive signals follow the mechanism of SR, but the SR produces a nonlinear distortion of the shape of the impulsive signal. To eliminate the distortion a moving least squares fitting method is introduced to reconstruct the signal from the output of the SR process. This proposed method is verified by comparing its detection results with that of a morphological filter based on both simulated and experimental signals. The experimental results show that the background noise is suppressed effectively and the key features of impulsive signals are reconstructed with a good degree of accuracy, which leads to an accurate diagnosis of faults in roller bearings in a run-to failure test.

Application of recursive approaches to differential orbit correction of near Earth asteroids

NASA Astrophysics Data System (ADS)

Dmitriev, Vasily; Lupovka, Valery; Gritsevich, Maria

2016-10-01

Comparison of three approaches to the differential orbit correction of celestial bodies was performed: batch least squares fitting, Kalman filter, and recursive least squares filter. The first two techniques are well known and widely used (Montenbruck, O. & Gill, E., 2000). The most attention is paid to the algorithm and details of program realization of recursive least squares filter. The filter's algorithm was derived based on recursive least squares technique that are widely used in data processing applications (Simon, D, 2006). Usage recursive least squares filter, makes possible to process a new set of observational data, without reprocessing data, which has been processed before. Specific feature of such approach is that number of observation in data set may be variable. This feature makes recursive least squares filter more flexible approach compare to batch least squares (process complete set of observations in each iteration) and Kalman filtering (suppose updating state vector on each epoch with measurements).Advantages of proposed approach are demonstrated by processing of real astrometric observations of near Earth asteroids. The case of 2008 TC3 was studied. 2008 TC3 was discovered just before its impact with Earth. There are a many closely spaced observations of 2008 TC3 on the interval between discovering and impact, which creates favorable conditions for usage of recursive approaches. Each of approaches has very similar precision in case of 2008 TC3. At the same time, recursive least squares approaches have much higher performance. Thus, this approach more favorable for orbit fitting of a celestial body, which was detected shortly before the collision or close approach to the Earth.This work was carried out at MIIGAiK and supported by the Russian Science Foundation, Project no. 14-22-00197.References:O. Montenbruck and E. Gill, "Satellite Orbits, Models, Methods and Applications," Springer-Verlag, 2000, pp. 1-369.D. Simon, "Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches",1 edition. Hoboken, N.J.: Wiley-Interscience, 2006.

Semivariogram modeling by weighted least squares

USGS Publications Warehouse

Jian, X.; Olea, R.A.; Yu, Y.-S.

1996-01-01

Permissible semivariogram models are fundamental for geostatistical estimation and simulation of attributes having a continuous spatiotemporal variation. The usual practice is to fit those models manually to experimental semivariograms. Fitting by weighted least squares produces comparable results to fitting manually in less time, systematically, and provides an Akaike information criterion for the proper comparison of alternative models. We illustrate the application of a computer program with examples showing the fitting of simple and nested models. Copyright ?? 1996 Elsevier Science Ltd.

Fitting Prony Series To Data On Viscoelastic Materials

NASA Technical Reports Server (NTRS)

Hill, S. A.

1995-01-01

Improved method of fitting Prony series to data on viscoelastic materials involves use of least-squares optimization techniques. Based on optimization techniques yields closer correlation with data than traditional method. Involves no assumptions regarding the gamma'(sub i)s and higher-order terms, and provides for as many Prony terms as needed to represent higher-order subtleties in data. Curve-fitting problem treated as design-optimization problem and solved by use of partially-constrained-optimization techniques.

Multi-Gaussian fitting for pulse waveform using Weighted Least Squares and multi-criteria decision making method.

PubMed

Wang, Lu; Xu, Lisheng; Feng, Shuting; Meng, Max Q-H; Wang, Kuanquan

2013-11-01

Analysis of pulse waveform is a low cost, non-invasive method for obtaining vital information related to the conditions of the cardiovascular system. In recent years, different Pulse Decomposition Analysis (PDA) methods have been applied to disclose the pathological mechanisms of the pulse waveform. All these methods decompose single-period pulse waveform into a constant number (such as 3, 4 or 5) of individual waves. Furthermore, those methods do not pay much attention to the estimation error of the key points in the pulse waveform. The estimation of human vascular conditions depends on the key points' positions of pulse wave. In this paper, we propose a Multi-Gaussian (MG) model to fit real pulse waveforms using an adaptive number (4 or 5 in our study) of Gaussian waves. The unknown parameters in the MG model are estimated by the Weighted Least Squares (WLS) method and the optimized weight values corresponding to different sampling points are selected by using the Multi-Criteria Decision Making (MCDM) method. Performance of the MG model and the WLS method has been evaluated by fitting 150 real pulse waveforms of five different types. The resulting Normalized Root Mean Square Error (NRMSE) was less than 2.0% and the estimation accuracy for the key points was satisfactory, demonstrating that our proposed method is effective in compressing, synthesizing and analyzing pulse waveforms. Copyright © 2013 Elsevier Ltd. All rights reserved.

A new family of stable elements for the Stokes problem based on a mixed Galerkin/least-squares finite element formulation

NASA Technical Reports Server (NTRS)

Franca, Leopoldo P.; Loula, Abimael F. D.; Hughes, Thomas J. R.; Miranda, Isidoro

1989-01-01

Adding to the classical Hellinger-Reissner formulation, a residual form of the equilibrium equation, a new Galerkin/least-squares finite element method is derived. It fits within the framework of a mixed finite element method and is stable for rather general combinations of stress and velocity interpolations, including equal-order discontinuous stress and continuous velocity interpolations which are unstable within the Galerkin approach. Error estimates are presented based on a generalization of the Babuska-Brezzi theory. Numerical results (not presented herein) have confirmed these estimates as well as the good accuracy and stability of the method.

On Least Squares Fitting Nonlinear Submodels.

ERIC Educational Resources Information Center

Bechtel, Gordon G.

Three simplifying conditions are given for obtaining least squares (LS) estimates for a nonlinear submodel of a linear model. If these are satisfied, and if the subset of nonlinear parameters may be LS fit to the corresponding LS estimates of the linear model, then one attains the desired LS estimates for the entire submodel. Two illustrative…

Using Weighted Least Squares Regression for Obtaining Langmuir Sorption Constants

USDA-ARS?s Scientific Manuscript database

One of the most commonly used models for describing phosphorus (P) sorption to soils is the Langmuir model. To obtain model parameters, the Langmuir model is fit to measured sorption data using least squares regression. Least squares regression is based on several assumptions including normally dist...

Metafitting: Weight optimization for least-squares fitting of PTTI data

NASA Technical Reports Server (NTRS)

Douglas, Rob J.; Boulanger, J.-S.

1995-01-01

For precise time intercomparisons between a master frequency standard and a slave time scale, we have found it useful to quantitatively compare different fitting strategies by examining the standard uncertainty in time or average frequency. It is particularly useful when designing procedures which use intermittent intercomparisons, with some parameterized fit used to interpolate or extrapolate from the calibrating intercomparisons. We use the term 'metafitting' for the choices that are made before a fitting procedure is operationally adopted. We present methods for calculating the standard uncertainty for general, weighted least-squares fits and a method for optimizing these weights for a general noise model suitable for many PTTI applications. We present the results of the metafitting of procedures for the use of a regular schedule of (hypothetical) high-accuracy frequency calibration of a maser time scale. We have identified a cumulative series of improvements that give a significant reduction of the expected standard uncertainty, compared to the simplest procedure of resetting the maser synthesizer after each calibration. The metafitting improvements presented include the optimum choice of weights for the calibration runs, optimized over a period of a week or 10 days.

Least squares reverse time migration of controlled order multiples

NASA Astrophysics Data System (ADS)

Liu, Y.

2016-12-01

Imaging using the reverse time migration of multiples generates inherent crosstalk artifacts due to the interference among different order multiples. Traditionally, least-square fitting has been used to address this issue by seeking the best objective function to measure the amplitude differences between the predicted and observed data. We have developed an alternative objective function by decomposing multiples into different orders to minimize the difference between Born modeling predicted multiples and specific-order multiples from observational data in order to attenuate the crosstalk. This method is denoted as the least-squares reverse time migration of controlled order multiples (LSRTM-CM). Our numerical examples demonstrated that the LSRTM-CM can significantly improve image quality compared with reverse time migration of multiples and least-square reverse time migration of multiples. Acknowledgments This research was funded by the National Nature Science Foundation of China (Grant Nos. 41430321 and 41374138).

Two-dimensional orthonormal trend surfaces for prospecting

NASA Astrophysics Data System (ADS)

Sarma, D. D.; Selvaraj, J. B.

Orthonormal polynomials have distinct advantages over conventional polynomials: the equations for evaluating trend coefficients are not ill-conditioned and the convergence power of this method is greater compared to the least-squares approximation and therefore the approach by orthonormal functions provides a powerful alternative to the least-squares method. In this paper, orthonormal polynomials in two dimensions are obtained using the Gram-Schmidt method for a polynomial series of the type: Z = 1 + x + y + x2 + xy + y2 + … + yn, where x and y are the locational coordinates and Z is the value of the variable under consideration. Trend-surface analysis, which has wide applications in prospecting, has been carried out using the orthonormal polynomial approach for two sample sets of data from India concerned with gold accumulation from the Kolar Gold Field, and gravity data. A comparison of the orthonormal polynomial trend surfaces with those obtained by the classical least-squares method has been made for the two data sets. In both the situations, the orthonormal polynomial surfaces gave an improved fit to the data. A flowchart and a FORTRAN-IV computer program for deriving orthonormal polynomials of any order and for using them to fit trend surfaces is included. The program has provision for logarithmic transformation of the Z variable. If log-transformation is performed the predicted Z values are reconverted to the original units and the trend-surface map generated for use. The illustration of gold assay data related to the Champion lode system of Kolar Gold Fields, for which a 9th-degree orthonormal trend surface was fit, could be used for further prospecting the area.

Estimation of liver T₂ in transfusion-related iron overload in patients with weighted least squares T₂ IDEAL.

PubMed

Vasanawala, Shreyas S; Yu, Huanzhou; Shimakawa, Ann; Jeng, Michael; Brittain, Jean H

2012-01-01

MRI imaging of hepatic iron overload can be achieved by estimating T(2) values using multiple-echo sequences. The purpose of this work is to develop and clinically evaluate a weighted least squares algorithm based on T(2) Iterative Decomposition of water and fat with Echo Asymmetry and Least-squares estimation (IDEAL) technique for volumetric estimation of hepatic T(2) in the setting of iron overload. The weighted least squares T(2) IDEAL technique improves T(2) estimation by automatically decreasing the impact of later, noise-dominated echoes. The technique was evaluated in 37 patients with iron overload. Each patient underwent (i) a standard 2D multiple-echo gradient echo sequence for T(2) assessment with nonlinear exponential fitting, and (ii) a 3D T(2) IDEAL technique, with and without a weighted least squares fit. Regression and Bland-Altman analysis demonstrated strong correlation between conventional 2D and T(2) IDEAL estimation. In cases of severe iron overload, T(2) IDEAL without weighted least squares reconstruction resulted in a relative overestimation of T(2) compared with weighted least squares. Copyright © 2011 Wiley-Liss, Inc.

Nonlinear filtering properties of detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Kiyono, Ken; Tsujimoto, Yutaka

2016-11-01

Detrended fluctuation analysis (DFA) has been widely used for quantifying long-range correlation and fractal scaling behavior. In DFA, to avoid spurious detection of scaling behavior caused by a nonstationary trend embedded in the analyzed time series, a detrending procedure using piecewise least-squares fitting has been applied. However, it has been pointed out that the nonlinear filtering properties involved with detrending may induce instabilities in the scaling exponent estimation. To understand this issue, we investigate the adverse effects of the DFA detrending procedure on the statistical estimation. We show that the detrending procedure using piecewise least-squares fitting results in the nonuniformly weighted estimation of the root-mean-square deviation and that this property could induce an increase in the estimation error. In addition, for comparison purposes, we investigate the performance of a centered detrending moving average analysis with a linear detrending filter and sliding window DFA and show that these methods have better performance than the standard DFA.

JASMINE -- Japan Astrometry Satellite Mission for INfrared Exploration: Data Analysis and Accuracy Assessment with a Kalman Filter

NASA Astrophysics Data System (ADS)

Yamada, Y.; Shimokawa, T.; Shinomoto, S. Yano, T.; Gouda, N.

2009-09-01

For the purpose of determining the celestial coordinates of stellar positions, consecutive observational images are laid overlapping each other with clues of stars belonging to multiple plates. In the analysis, one has to estimate not only the coordinates of individual plates, but also the possible expansion and distortion of the frame. This problem reduces to a least-squares fit that can in principle be solved by a huge matrix inversion, which is, however, impracticable. Here, we propose using Kalman filtering to perform the least-squares fit and implement a practical iterative algorithm. We also estimate errors associated with this iterative method and suggest a design of overlapping plates to minimize the error.

Inverse models: A necessary next step in ground-water modeling

USGS Publications Warehouse

Poeter, E.P.; Hill, M.C.

1997-01-01

Inverse models using, for example, nonlinear least-squares regression, provide capabilities that help modelers take full advantage of the insight available from ground-water models. However, lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use. This paper presents a simple ground-water flow problem to illustrate the requirements and benefits of the nonlinear least-squares repression method of inverse modeling and discusses how these attributes apply to field problems. The benefits of inverse modeling include: (1) expedited determination of best fit parameter values; (2) quantification of the (a) quality of calibration, (b) data shortcomings and needs, and (c) confidence limits on parameter estimates and predictions; and (3) identification of issues that are easily overlooked during nonautomated calibration.Inverse models using, for example, nonlinear least-squares regression, provide capabilities that help modelers take full advantage of the insight available from ground-water models. However, lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use. This paper presents a simple ground-water flow problem to illustrate the requirements and benefits of the nonlinear least-squares regression method of inverse modeling and discusses how these attributes apply to field problems. The benefits of inverse modeling include: (1) expedited determination of best fit parameter values; (2) quantification of the (a) quality of calibration, (b) data shortcomings and needs, and (c) confidence limits on parameter estimates and predictions; and (3) identification of issues that are easily overlooked during nonautomated calibration.

On the Log-Normality of Historical Magnetic-Storm Intensity Statistics: Implications for Extreme-Event Probabilities

NASA Astrophysics Data System (ADS)

Love, J. J.; Rigler, E. J.; Pulkkinen, A. A.; Riley, P.

2015-12-01

An examination is made of the hypothesis that the statistics of magnetic-storm-maximum intensities are the realization of a log-normal stochastic process. Weighted least-squares and maximum-likelihood methods are used to fit log-normal functions to -Dst storm-time maxima for years 1957-2012; bootstrap analysis is used to established confidence limits on forecasts. Both methods provide fits that are reasonably consistent with the data; both methods also provide fits that are superior to those that can be made with a power-law function. In general, the maximum-likelihood method provides forecasts having tighter confidence intervals than those provided by weighted least-squares. From extrapolation of maximum-likelihood fits: a magnetic storm with intensity exceeding that of the 1859 Carrington event, -Dst > 850 nT, occurs about 1.13 times per century and a wide 95% confidence interval of [0.42, 2.41] times per century; a 100-yr magnetic storm is identified as having a -Dst > 880 nT (greater than Carrington) but a wide 95% confidence interval of [490, 1187] nT. This work is partially motivated by United States National Science and Technology Council and Committee on Space Research and International Living with a Star priorities and strategic plans for the assessment and mitigation of space-weather hazards.

HOLEGAGE 1.0 - Strain-Gauge Drilling Analysis Program

NASA Technical Reports Server (NTRS)

Hampton, Roy V.

1992-01-01

Interior stresses inferred from changes in surface strains as hole is drilled. Computes stresses using strain data from each drilled-hole depth layer. Planar stresses computed in three ways: least-squares fit for linear variation with depth, integral method to give incremental stress data for each layer, and/or linear fit to integral data. Written in FORTRAN 77.

Inter-class sparsity based discriminative least square regression.

PubMed

Wen, Jie; Xu, Yong; Li, Zuoyong; Ma, Zhongli; Xu, Yuanrong

2018-06-01

Least square regression is a very popular supervised classification method. However, two main issues greatly limit its performance. The first one is that it only focuses on fitting the input features to the corresponding output labels while ignoring the correlations among samples. The second one is that the used label matrix, i.e., zero-one label matrix is inappropriate for classification. To solve these problems and improve the performance, this paper presents a novel method, i.e., inter-class sparsity based discriminative least square regression (ICS_DLSR), for multi-class classification. Different from other methods, the proposed method pursues that the transformed samples have a common sparsity structure in each class. For this goal, an inter-class sparsity constraint is introduced to the least square regression model such that the margins of samples from the same class can be greatly reduced while those of samples from different classes can be enlarged. In addition, an error term with row-sparsity constraint is introduced to relax the strict zero-one label matrix, which allows the method to be more flexible in learning the discriminative transformation matrix. These factors encourage the method to learn a more compact and discriminative transformation for regression and thus has the potential to perform better than other methods. Extensive experimental results show that the proposed method achieves the best performance in comparison with other methods for multi-class classification. Copyright © 2018 Elsevier Ltd. All rights reserved.

Precision PEP-II optics measurement with an SVD-enhanced Least-Square fitting

NASA Astrophysics Data System (ADS)

Yan, Y. T.; Cai, Y.

2006-03-01

A singular value decomposition (SVD)-enhanced Least-Square fitting technique is discussed. By automatic identifying, ordering, and selecting dominant SVD modes of the derivative matrix that responds to the variations of the variables, the converging process of the Least-Square fitting is significantly enhanced. Thus the fitting speed can be fast enough for a fairly large system. This technique has been successfully applied to precision PEP-II optics measurement in which we determine all quadrupole strengths (both normal and skew components) and sextupole feed-downs as well as all BPM gains and BPM cross-plane couplings through Least-Square fitting of the phase advances and the Local Green's functions as well as the coupling ellipses among BPMs. The local Green's functions are specified by 4 local transfer matrix components R12, R34, R32, R14. These measurable quantities (the Green's functions, the phase advances and the coupling ellipse tilt angles and axis ratios) are obtained by analyzing turn-by-turn Beam Position Monitor (BPM) data with a high-resolution model-independent analysis (MIA). Once all of the quadrupoles and sextupole feed-downs are determined, we obtain a computer virtual accelerator which matches the real accelerator in linear optics. Thus, beta functions, linear coupling parameters, and interaction point (IP) optics characteristics can be measured and displayed.

Curve Fitting via the Criterion of Least Squares. Applications of Algebra and Elementary Calculus to Curve Fitting. [and] Linear Programming in Two Dimensions: I. Applications of High School Algebra to Operations Research. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 321, 453.

ERIC Educational Resources Information Center

Alexander, John W., Jr.; Rosenberg, Nancy S.

This document consists of two modules. The first of these views applications of algebra and elementary calculus to curve fitting. The user is provided with information on how to: 1) construct scatter diagrams; 2) choose an appropriate function to fit specific data; 3) understand the underlying theory of least squares; 4) use a computer program to…

Prediction Analysis for Measles Epidemics

NASA Astrophysics Data System (ADS)

Sumi, Ayako; Ohtomo, Norio; Tanaka, Yukio; Sawamura, Sadashi; Olsen, Lars Folke; Kobayashi, Nobumichi

2003-12-01

A newly devised procedure of prediction analysis, which is a linearized version of the nonlinear least squares method combined with the maximum entropy spectral analysis method, was proposed. This method was applied to time series data of measles case notification in several communities in the UK, USA and Denmark. The dominant spectral lines observed in each power spectral density (PSD) can be safely assigned as fundamental periods. The optimum least squares fitting (LSF) curve calculated using these fundamental periods can essentially reproduce the underlying variation of the measles data. An extension of the LSF curve can be used to predict measles case notification quantitatively. Some discussions including a predictability of chaotic time series are presented.

Iterative Track Fitting Using Cluster Classification in Multi Wire Proportional Chamber

NASA Astrophysics Data System (ADS)

Primor, David; Mikenberg, Giora; Etzion, Erez; Messer, Hagit

2007-10-01

This paper addresses the problem of track fitting of a charged particle in a multi wire proportional chamber (MWPC) using cathode readout strips. When a charged particle crosses a MWPC, a positive charge is induced on a cluster of adjacent strips. In the presence of high radiation background, the cluster charge measurements may be contaminated due to background particles, leading to less accurate hit position estimation. The least squares method for track fitting assumes the same position error distribution for all hits and thus loses its optimal properties on contaminated data. For this reason, a new robust algorithm is proposed. The algorithm first uses the known spatial charge distribution caused by a single charged particle over the strips, and classifies the clusters into ldquocleanrdquo and ldquodirtyrdquo clusters. Then, using the classification results, it performs an iterative weighted least squares fitting procedure, updating its optimal weights each iteration. The performance of the suggested algorithm is compared to other track fitting techniques using a simulation of tracks with radiation background. It is shown that the algorithm improves the track fitting performance significantly. A practical implementation of the algorithm is presented for muon track fitting in the cathode strip chamber (CSC) of the ATLAS experiment.

The effects of ionic strength and organic matter on virus inactivation at low temperatures: general likelihood uncertainty estimation (GLUE) as an alternative to least-squares parameter optimization for the fitting of virus inactivation models

NASA Astrophysics Data System (ADS)

Mayotte, Jean-Marc; Grabs, Thomas; Sutliff-Johansson, Stacy; Bishop, Kevin

2017-06-01

This study examined how the inactivation of bacteriophage MS2 in water was affected by ionic strength (IS) and dissolved organic carbon (DOC) using static batch inactivation experiments at 4 °C conducted over a period of 2 months. Experimental conditions were characteristic of an operational managed aquifer recharge (MAR) scheme in Uppsala, Sweden. Experimental data were fit with constant and time-dependent inactivation models using two methods: (1) traditional linear and nonlinear least-squares techniques; and (2) a Monte-Carlo based parameter estimation technique called generalized likelihood uncertainty estimation (GLUE). The least-squares and GLUE methodologies gave very similar estimates of the model parameters and their uncertainty. This demonstrates that GLUE can be used as a viable alternative to traditional least-squares parameter estimation techniques for fitting of virus inactivation models. Results showed a slight increase in constant inactivation rates following an increase in the DOC concentrations, suggesting that the presence of organic carbon enhanced the inactivation of MS2. The experiment with a high IS and a low DOC was the only experiment which showed that MS2 inactivation may have been time-dependent. However, results from the GLUE methodology indicated that models of constant inactivation were able to describe all of the experiments. This suggested that inactivation time-series longer than 2 months were needed in order to provide concrete conclusions regarding the time-dependency of MS2 inactivation at 4 °C under these experimental conditions.

Genetic Algorithm for Initial Orbit Determination with Too Short Arc (Continued)

NASA Astrophysics Data System (ADS)

Li, X. R.; Wang, X.

2016-03-01

When using the genetic algorithm to solve the problem of too-short-arc (TSA) determination, due to the difference of computing processes between the genetic algorithm and classical method, the methods for outliers editing are no longer applicable. In the genetic algorithm, the robust estimation is acquired by means of using different loss functions in the fitness function, then the outlier problem of TSAs is solved. Compared with the classical method, the application of loss functions in the genetic algorithm is greatly simplified. Through the comparison of results of different loss functions, it is clear that the methods of least median square and least trimmed square can greatly improve the robustness of TSAs, and have a high breakdown point.

Multivariate qualitative analysis of banned additives in food safety using surface enhanced Raman scattering spectroscopy

NASA Astrophysics Data System (ADS)

He, Shixuan; Xie, Wanyi; Zhang, Wei; Zhang, Liqun; Wang, Yunxia; Liu, Xiaoling; Liu, Yulong; Du, Chunlei

2015-02-01

A novel strategy which combines iteratively cubic spline fitting baseline correction method with discriminant partial least squares qualitative analysis is employed to analyze the surface enhanced Raman scattering (SERS) spectroscopy of banned food additives, such as Sudan I dye and Rhodamine B in food, Malachite green residues in aquaculture fish. Multivariate qualitative analysis methods, using the combination of spectra preprocessing iteratively cubic spline fitting (ICSF) baseline correction with principal component analysis (PCA) and discriminant partial least squares (DPLS) classification respectively, are applied to investigate the effectiveness of SERS spectroscopy for predicting the class assignments of unknown banned food additives. PCA cannot be used to predict the class assignments of unknown samples. However, the DPLS classification can discriminate the class assignment of unknown banned additives using the information of differences in relative intensities. The results demonstrate that SERS spectroscopy combined with ICSF baseline correction method and exploratory analysis methodology DPLS classification can be potentially used for distinguishing the banned food additives in field of food safety.

Robust and efficient pharmacokinetic parameter non-linear least squares estimation for dynamic contrast enhanced MRI of the prostate.

PubMed

Kargar, Soudabeh; Borisch, Eric A; Froemming, Adam T; Kawashima, Akira; Mynderse, Lance A; Stinson, Eric G; Trzasko, Joshua D; Riederer, Stephen J

2018-05-01

To describe an efficient numerical optimization technique using non-linear least squares to estimate perfusion parameters for the Tofts and extended Tofts models from dynamic contrast enhanced (DCE) MRI data and apply the technique to prostate cancer. Parameters were estimated by fitting the two Tofts-based perfusion models to the acquired data via non-linear least squares. We apply Variable Projection (VP) to convert the fitting problem from a multi-dimensional to a one-dimensional line search to improve computational efficiency and robustness. Using simulation and DCE-MRI studies in twenty patients with suspected prostate cancer, the VP-based solver was compared against the traditional Levenberg-Marquardt (LM) strategy for accuracy, noise amplification, robustness to converge, and computation time. The simulation demonstrated that VP and LM were both accurate in that the medians closely matched assumed values across typical signal to noise ratio (SNR) levels for both Tofts models. VP and LM showed similar noise sensitivity. Studies using the patient data showed that the VP method reliably converged and matched results from LM with approximate 3× and 2× reductions in computation time for the standard (two-parameter) and extended (three-parameter) Tofts models. While LM failed to converge in 14% of the patient data, VP converged in the ideal 100%. The VP-based method for non-linear least squares estimation of perfusion parameters for prostate MRI is equivalent in accuracy and robustness to noise, while being more reliably (100%) convergent and computationally about 3× (TM) and 2× (ETM) faster than the LM-based method. Copyright © 2017 Elsevier Inc. All rights reserved.

The long-solved problem of the best-fit straight line: application to isotopic mixing lines

NASA Astrophysics Data System (ADS)

Wehr, Richard; Saleska, Scott R.

2017-01-01

It has been almost 50 years since York published an exact and general solution for the best-fit straight line to independent points with normally distributed errors in both x and y. York's solution is highly cited in the geophysical literature but almost unknown outside of it, so that there has been no ebb in the tide of books and papers wrestling with the problem. Much of the post-1969 literature on straight-line fitting has sown confusion not merely by its content but by its very existence. The optimal least-squares fit is already known; the problem is already solved. Here we introduce the non-specialist reader to York's solution and demonstrate its application in the interesting case of the isotopic mixing line, an analytical tool widely used to determine the isotopic signature of trace gas sources for the study of biogeochemical cycles. The most commonly known linear regression methods - ordinary least-squares regression (OLS), geometric mean regression (GMR), and orthogonal distance regression (ODR) - have each been recommended as the best method for fitting isotopic mixing lines. In fact, OLS, GMR, and ODR are all special cases of York's solution that are valid only under particular measurement conditions, and those conditions do not hold in general for isotopic mixing lines. Using Monte Carlo simulations, we quantify the biases in OLS, GMR, and ODR under various conditions and show that York's general - and convenient - solution is always the least biased.

Comparison of structural and least-squares lines for estimating geologic relations

USGS Publications Warehouse

Williams, G.P.; Troutman, B.M.

1990-01-01

Two different goals in fitting straight lines to data are to estimate a "true" linear relation (physical law) and to predict values of the dependent variable with the smallest possible error. Regarding the first goal, a Monte Carlo study indicated that the structural-analysis (SA) method of fitting straight lines to data is superior to the ordinary least-squares (OLS) method for estimating "true" straight-line relations. Number of data points, slope and intercept of the true relation, and variances of the errors associated with the independent (X) and dependent (Y) variables influence the degree of agreement. For example, differences between the two line-fitting methods decrease as error in X becomes small relative to error in Y. Regarding the second goal-predicting the dependent variable-OLS is better than SA. Again, the difference diminishes as X takes on less error relative to Y. With respect to estimation of slope and intercept and prediction of Y, agreement between Monte Carlo results and large-sample theory was very good for sample sizes of 100, and fair to good for sample sizes of 20. The procedures and error measures are illustrated with two geologic examples. ?? 1990 International Association for Mathematical Geology.

Superpixel Based Factor Analysis and Target Transformation Method for Martian Minerals Detection

NASA Astrophysics Data System (ADS)

Wu, X.; Zhang, X.; Lin, H.

2018-04-01

The Factor analysis and target transformation (FATT) is an effective method to test for the presence of particular mineral on Martian surface. It has been used both in thermal infrared (Thermal Emission Spectrometer, TES) and near-infrared (Compact Reconnaissance Imaging Spectrometer for Mars, CRISM) hyperspectral data. FATT derived a set of orthogonal eigenvectors from a mixed system and typically selected first 10 eigenvectors to least square fit the library mineral spectra. However, minerals present only in a limited pixels will be ignored because its weak spectral features compared with full image signatures. Here, we proposed a superpixel based FATT method to detect the mineral distributions on Mars. The simple linear iterative clustering (SLIC) algorithm was used to partition the CRISM image into multiple connected image regions with spectral homogeneous to enhance the weak signatures by increasing their proportion in a mixed system. A least square fitting was used in target transformation and performed to each region iteratively. Finally, the distribution of the specific minerals in image was obtained, where fitting residual less than a threshold represent presence and otherwise absence. We validate our method by identifying carbonates in a well analysed CRISM image in Nili Fossae on Mars. Our experimental results indicate that the proposed method work well both in simulated and real data sets.

Comparison of baseline removal methods for laser-induced breakdown spectroscopy of geological samples

NASA Astrophysics Data System (ADS)

Dyar, M. Darby; Giguere, Stephen; Carey, CJ; Boucher, Thomas

2016-12-01

This project examines the causes, effects, and optimization of continuum removal in laser-induced breakdown spectroscopy (LIBS) to produce the best possible prediction accuracy of elemental composition in geological samples. We compare prediction accuracy resulting from several different techniques for baseline removal, including asymmetric least squares (ALS), adaptive iteratively reweighted penalized least squares (Air-PLS), fully automatic baseline correction (FABC), continuous wavelet transformation, median filtering, polynomial fitting, the iterative thresholding Dietrich method, convex hull/rubber band techniques, and a newly-developed technique for Custom baseline removal (BLR). We assess the predictive performance of these methods using partial least-squares analysis for 13 elements of geological interest, expressed as the weight percentages of SiO2, Al2O3, TiO2, FeO, MgO, CaO, Na2O, K2O, and the parts per million concentrations of Ni, Cr, Zn, Mn, and Co. We find that previously published methods for baseline subtraction generally produce equivalent prediction accuracies for major elements. When those pre-existing methods are used, automated optimization of their adjustable parameters is always necessary to wring the best predictive accuracy out of a data set; ideally, it should be done for each individual variable. The new technique of Custom BLR produces significant improvements in prediction accuracy over existing methods across varying geological data sets, instruments, and varying analytical conditions. These results also demonstrate the dual objectives of the continuum removal problem: removing a smooth underlying signal to fit individual peaks (univariate analysis) versus using feature selection to select only those channels that contribute to best prediction accuracy for multivariate analyses. Overall, the current practice of using generalized, one-method-fits-all-spectra baseline removal results in poorer predictive performance for all methods. The extra steps needed to optimize baseline removal for each predicted variable and empower multivariate techniques with the best possible input data for optimal prediction accuracy are shown to be well worth the slight increase in necessary computations and complexity.

Analysis method for Thomson scattering diagnostics in GAMMA 10/PDX.

PubMed

Ohta, K; Yoshikawa, M; Yasuhara, R; Chikatsu, M; Shima, Y; Kohagura, J; Sakamoto, M; Nakasima, Y; Imai, T; Ichimura, M; Yamada, I; Funaba, H; Minami, T

2016-11-01

We have developed an analysis method to improve the accuracies of electron temperature measurement by employing a fitting technique for the raw Thomson scattering (TS) signals. Least square fitting of the raw TS signals enabled reduction of the error in the electron temperature measurement. We applied the analysis method to a multi-pass (MP) TS system. Because the interval between the MPTS signals is very short, it is difficult to separately analyze each Thomson scattering signal intensity by using the raw signals. We used the fitting method to obtain the original TS scattering signals from the measured raw MPTS signals to obtain the electron temperatures in each pass.

Weibull Modulus Estimated by the Non-linear Least Squares Method: A Solution to Deviation Occurring in Traditional Weibull Estimation

NASA Astrophysics Data System (ADS)

Li, T.; Griffiths, W. D.; Chen, J.

2017-11-01

The Maximum Likelihood method and the Linear Least Squares (LLS) method have been widely used to estimate Weibull parameters for reliability of brittle and metal materials. In the last 30 years, many researchers focused on the bias of Weibull modulus estimation, and some improvements have been achieved, especially in the case of the LLS method. However, there is a shortcoming in these methods for a specific type of data, where the lower tail deviates dramatically from the well-known linear fit in a classic LLS Weibull analysis. This deviation can be commonly found from the measured properties of materials, and previous applications of the LLS method on this kind of dataset present an unreliable linear regression. This deviation was previously thought to be due to physical flaws ( i.e., defects) contained in materials. However, this paper demonstrates that this deviation can also be caused by the linear transformation of the Weibull function, occurring in the traditional LLS method. Accordingly, it may not be appropriate to carry out a Weibull analysis according to the linearized Weibull function, and the Non-linear Least Squares method (Non-LS) is instead recommended for the Weibull modulus estimation of casting properties.

AVIRIS study of Death Valley evaporite deposits using least-squares band-fitting methods

NASA Technical Reports Server (NTRS)

Crowley, J. K.; Clark, R. N.

1992-01-01

Minerals found in playa evaporite deposits reflect the chemically diverse origins of ground waters in arid regions. Recently, it was discovered that many playa minerals exhibit diagnostic visible and near-infrared (0.4-2.5 micron) absorption bands that provide a remote sensing basis for observing important compositional details of desert ground water systems. The study of such systems is relevant to understanding solute acquisition, transport, and fractionation processes that are active in the subsurface. Observations of playa evaporites may also be useful for monitoring the hydrologic response of desert basins to changing climatic conditions on regional and global scales. Ongoing work using Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data to map evaporite minerals in the Death Valley salt pan is described. The AVIRIS data point to differences in inflow water chemistry in different parts of the Death Valley playa system and have led to the discovery of at least two new North American mineral occurrences. Seven segments of AVIRIS data were acquired over Death Valley on 31 July 1990, and were calibrated to reflectance by using the spectrum of a uniform area of alluvium near the salt pan. The calibrated data were subsequently analyzed by using least-squares spectral band-fitting methods, first described by Clark and others. In the band-fitting procedure, AVIRIS spectra are fit compared over selected wavelength intervals to a series of library reference spectra. Output images showing the degree of fit, band depth, and fit times the band depth are generated for each reference spectrum. The reference spectra used in the study included laboratory data for 35 pure evaporite spectra extracted from the AVIRIS image cube. Additional details of the band-fitting technique are provided by Clark and others elsewhere in this volume.

Meta-Analytic Methods of Pooling Correlation Matrices for Structural Equation Modeling under Different Patterns of Missing Data

ERIC Educational Resources Information Center

Furlow, Carolyn F.; Beretvas, S. Natasha

2005-01-01

Three methods of synthesizing correlations for meta-analytic structural equation modeling (SEM) under different degrees and mechanisms of missingness were compared for the estimation of correlation and SEM parameters and goodness-of-fit indices by using Monte Carlo simulation techniques. A revised generalized least squares (GLS) method for…

Calculation of Hammett Equation parameters for some N,N‧-bis (substituted-phenyl)-1,4-quinonediimines by density functional theory

NASA Astrophysics Data System (ADS)

Sein, Lawrence T.

2011-08-01

Hammett parameters σ' were determined from vertical ionization potentials, vertical electron affinities, adiabatic ionization potentials, adiabatic electron affinities, HOMO, and LUMO energies of a series of N, N' -bis (3',4'-substituted-phenyl)-1,4-quinonediimines computed at the B3LYP/6-311+G(2d,p) level on B3LYP/6-31G ∗ molecular geometries. These parameters were then least squares fit as a function of literature Hammett parameters. For N, N' -bis (4'-substituted-phenyl)-1,4-quinonediimines, the least squares fits demonstrated excellent linearity, with the square of Pearson's correlation coefficient ( r2) greater than 0.98 for all isomers. For N, N' -bis (3'-substituted-3'-aminophenyl)-1,4-quinonediimines, the least squares fits were less nearly linear, with r2 approximately 0.70 for all isomers when derived from calculated vertical ionization potentials, but those from calculated vertical electron affinities usually greater than 0.90.

Interpretation of the Coefficients in the Fit y = at + bx + c

ERIC Educational Resources Information Center

Farnsworth, David L.

2006-01-01

The goals of this note are to derive formulas for the coefficients a and b in the least-squares regression plane y = at + bx + c for observations (t[subscript]i,x[subscript]i,y[subscript]i), i = 1, 2, ..., n, and to present meanings for the coefficients a and b. In this note, formulas for the coefficients a and b in the least-squares fit are…

Open-loop-feedback control of serum drug concentrations: pharmacokinetic approaches to drug therapy.

PubMed

Jelliffe, R W

1983-01-01

Recent developments to optimize open-loop-feedback control of drug dosage regimens, generally applicable to pharmacokinetically oriented therapy with many drugs, involve computation of patient-individualized strategies for obtaining desired serum drug concentrations. Analyses of past therapy are performed by least squares, extended least squares, and maximum a posteriori probability Bayesian methods of fitting pharmacokinetic models to serum level data. Future possibilities for truly optimal open-loop-feedback therapy with full Bayesian methods, and conceivably for optimal closed-loop therapy in such data-poor clinical situations, are also discussed. Implementation of these various therapeutic strategies, using automated, locally controlled infusion devices, has also been achieved in prototype form.

Combining Approach in Stages with Least Squares for fits of data in hyperelasticity

NASA Astrophysics Data System (ADS)

Beda, Tibi

2006-10-01

The present work concerns a method of continuous approximation by block of a continuous function; a method of approximation combining the Approach in Stages with the finite domains Least Squares. An identification procedure by sub-domains: basic generating functions are determined step-by-step permitting their weighting effects to be felt. This procedure allows one to be in control of the signs and to some extent of the optimal values of the parameters estimated, and consequently it provides a unique set of solutions that should represent the real physical parameters. Illustrations and comparisons are developed in rubber hyperelastic modeling. To cite this article: T. Beda, C. R. Mecanique 334 (2006).

Least Squares Approach to the Alignment of the Generic High Precision Tracking System

NASA Astrophysics Data System (ADS)

de Renstrom, Pawel Brückman; Haywood, Stephen

2006-04-01

A least squares method to solve a generic alignment problem of a high granularity tracking system is presented. The algorithm is based on an analytical linear expansion and allows for multiple nested fits, e.g. imposing a common vertex for groups of particle tracks is of particular interest. We present a consistent and complete recipe to impose constraints on either implicit or explicit parameters. The method has been applied to the full simulation of a subset of the ATLAS silicon tracking system. The ultimate goal is to determine ≈35,000 degrees of freedom (DoF's). We present a limited scale exercise exploring various aspects of the solution.

[Locally weighted least squares estimation of DPOAE evoked by continuously sweeping primaries].

PubMed

Han, Xiaoli; Fu, Xinxing; Cui, Jie; Xiao, Ling

2013-12-01

Distortion product otoacoustic emission (DPOAE) signal can be used for diagnosis of hearing loss so that it has an important clinical value. Continuously using sweeping primaries to measure DPOAE provides an efficient tool to record DPOAE data rapidly when DPOAE is measured in a large frequency range. In this paper, locally weighted least squares estimation (LWLSE) of 2f1-f2 DPOAE is presented based on least-squares-fit (LSF) algorithm, in which DPOAE is evoked by continuously sweeping tones. In our study, we used a weighted error function as the loss function and the weighting matrixes in the local sense to obtain a smaller estimated variance. Firstly, ordinary least squares estimation of the DPOAE parameters was obtained. Then the error vectors were grouped and the different local weighting matrixes were calculated in each group. And finally, the parameters of the DPOAE signal were estimated based on least squares estimation principle using the local weighting matrixes. The simulation results showed that the estimate variance and fluctuation errors were reduced, so the method estimates DPOAE and stimuli more accurately and stably, which facilitates extraction of clearer DPOAE fine structure.

Revisiting the Scale-Invariant, Two-Dimensional Linear Regression Method

ERIC Educational Resources Information Center

Patzer, A. Beate C.; Bauer, Hans; Chang, Christian; Bolte, Jan; Su¨lzle, Detlev

2018-01-01

The scale-invariant way to analyze two-dimensional experimental and theoretical data with statistical errors in both the independent and dependent variables is revisited by using what we call the triangular linear regression method. This is compared to the standard least-squares fit approach by applying it to typical simple sets of example data…

From least squares to multilevel modeling: A graphical introduction to Bayesian inference

NASA Astrophysics Data System (ADS)

Loredo, Thomas J.

2016-01-01

This tutorial presentation will introduce some of the key ideas and techniques involved in applying Bayesian methods to problems in astrostatistics. The focus will be on the big picture: understanding the foundations (interpreting probability, Bayes's theorem, the law of total probability and marginalization), making connections to traditional methods (propagation of errors, least squares, chi-squared, maximum likelihood, Monte Carlo simulation), and highlighting problems where a Bayesian approach can be particularly powerful (Poisson processes, density estimation and curve fitting with measurement error). The "graphical" component of the title reflects an emphasis on pictorial representations of some of the math, but also on the use of graphical models (multilevel or hierarchical models) for analyzing complex data. Code for some examples from the talk will be available to participants, in Python and in the Stan probabilistic programming language.

Communication: Acceleration of coupled cluster singles and doubles via orbital-weighted least-squares tensor hypercontraction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Parrish, Robert M.; Sherrill, C. David, E-mail: sherrill@gatech.edu; Hohenstein, Edward G.

2014-05-14

We apply orbital-weighted least-squares tensor hypercontraction decomposition of the electron repulsion integrals to accelerate the coupled cluster singles and doubles (CCSD) method. Using accurate and flexible low-rank factorizations of the electron repulsion integral tensor, we are able to reduce the scaling of the most vexing particle-particle ladder term in CCSD from O(N{sup 6}) to O(N{sup 5}), with remarkably low error. Combined with a T{sub 1}-transformed Hamiltonian, this leads to substantial practical accelerations against an optimized density-fitted CCSD implementation.

Retrieval of the non-depolarizing components of depolarizing Mueller matrices by using symmetry conditions and least squares minimization

NASA Astrophysics Data System (ADS)

Kuntman, Ertan; Canillas, Adolf; Arteaga, Oriol

2017-11-01

Experimental Mueller matrices contain certain amount of uncertainty in their elements and these uncertainties can create difficulties for decomposition methods based on analytic solutions. In an earlier paper [1], we proposed a decomposition method for depolarizing Mueller matrices by using certain symmetry conditions. However, because of the experimental error, that method creates over-determined systems with non-unique solutions. Here we propose to use least squares minimization approach in order to improve the accuracy of our results. In this method, we are taking into account the number of independent parameters of the corresponding symmetry and the rank constraints on the component matrices to decide on our fitting model. This approach is illustrated with experimental Mueller matrices that include material media with different Mueller symmetries.

A method for the selection of a functional form for a thermodynamic equation of state using weighted linear least squares stepwise regression

NASA Technical Reports Server (NTRS)

Jacobsen, R. T.; Stewart, R. B.; Crain, R. W., Jr.; Rose, G. L.; Myers, A. F.

1976-01-01

A method was developed for establishing a rational choice of the terms to be included in an equation of state with a large number of adjustable coefficients. The methods presented were developed for use in the determination of an equation of state for oxygen and nitrogen. However, a general application of the methods is possible in studies involving the determination of an optimum polynomial equation for fitting a large number of data points. The data considered in the least squares problem are experimental thermodynamic pressure-density-temperature data. Attention is given to a description of stepwise multiple regression and the use of stepwise regression in the determination of an equation of state for oxygen and nitrogen.

Separation of detector non-linearity issues and multiple ionization satellites in alpha-particle PIXE

NASA Astrophysics Data System (ADS)

Campbell, John L.; Ganly, Brianna; Heirwegh, Christopher M.; Maxwell, John A.

2018-01-01

Multiple ionization satellites are prominent features in X-ray spectra induced by MeV energy alpha particles. It follows that the accuracy of PIXE analysis using alpha particles can be improved if these features are explicitly incorporated in the peak model description when fitting the spectra with GUPIX or other codes for least-squares fitting PIXE spectra and extracting element concentrations. A method for this incorporation is described and is tested using spectra recorded on Mars by the Curiosity rover's alpha particle X-ray spectrometer. These spectra are induced by both PIXE and X-ray fluorescence, resulting in a spectral energy range from ∼1 to ∼25 keV. This range is valuable in determining the energy-channel calibration, which departs from linearity at low X-ray energies. It makes it possible to separate the effects of the satellites from an instrumental non-linearity component. The quality of least-squares spectrum fits is significantly improved, raising the level of confidence in analytical results from alpha-induced PIXE.

Power spectrum analysis with least-squares fitting: amplitude bias and its elimination, with application to optical tweezers and atomic force microscope cantilevers.

PubMed

Nørrelykke, Simon F; Flyvbjerg, Henrik

2010-07-01

Optical tweezers and atomic force microscope (AFM) cantilevers are often calibrated by fitting their experimental power spectra of Brownian motion. We demonstrate here that if this is done with typical weighted least-squares methods, the result is a bias of relative size between -2/n and +1/n on the value of the fitted diffusion coefficient. Here, n is the number of power spectra averaged over, so typical calibrations contain 10%-20% bias. Both the sign and the size of the bias depend on the weighting scheme applied. Hence, so do length-scale calibrations based on the diffusion coefficient. The fitted value for the characteristic frequency is not affected by this bias. For the AFM then, force measurements are not affected provided an independent length-scale calibration is available. For optical tweezers there is no such luck, since the spring constant is found as the ratio of the characteristic frequency and the diffusion coefficient. We give analytical results for the weight-dependent bias for the wide class of systems whose dynamics is described by a linear (integro)differential equation with additive noise, white or colored. Examples are optical tweezers with hydrodynamic self-interaction and aliasing, calibration of Ornstein-Uhlenbeck models in finance, models for cell migration in biology, etc. Because the bias takes the form of a simple multiplicative factor on the fitted amplitude (e.g. the diffusion coefficient), it is straightforward to remove and the user will need minimal modifications to his or her favorite least-squares fitting programs. Results are demonstrated and illustrated using synthetic data, so we can compare fits with known true values. We also fit some commonly occurring power spectra once-and-for-all in the sense that we give their parameter values and associated error bars as explicit functions of experimental power-spectral values.

Development of Jet Noise Power Spectral Laws Using SHJAR Data

NASA Technical Reports Server (NTRS)

Khavaran, Abbas; Bridges, James

2009-01-01

High quality jet noise spectral data measured at the Aeroacoustic Propulsion Laboratory at the NASA Glenn Research Center is used to examine a number of jet noise scaling laws. Configurations considered in the present study consist of convergent and convergent-divergent axisymmetric nozzles. Following the work of Viswanathan, velocity power factors are estimated using a least squares fit on spectral power density as a function of jet temperature and observer angle. The regression parameters are scrutinized for their uncertainty within the desired confidence margins. As an immediate application of the velocity power laws, spectral density in supersonic jets are decomposed into their respective components attributed to the jet mixing noise and broadband shock associated noise. Subsequent application of the least squares method on the shock power intensity shows that the latter also scales with some power of the shock parameter. A modified shock parameter is defined in order to reduce the dependency of the regression factors on the nozzle design point within the uncertainty margins of the least squares method.

a New Approach for Subway Tunnel Deformation Monitoring: High-Resolution Terrestrial Laser Scanning

NASA Astrophysics Data System (ADS)

Li, J.; Wan, Y.; Gao, X.

2012-07-01

With the improvement of the accuracy and efficiency of laser scanning technology, high-resolution terrestrial laser scanning (TLS) technology can obtain high precise points-cloud and density distribution and can be applied to high-precision deformation monitoring of subway tunnels and high-speed railway bridges and other fields. In this paper, a new approach using a points-cloud segmentation method based on vectors of neighbor points and surface fitting method based on moving least squares was proposed and applied to subway tunnel deformation monitoring in Tianjin combined with a new high-resolution terrestrial laser scanner (Riegl VZ-400). There were three main procedures. Firstly, a points-cloud consisted of several scanning was registered by linearized iterative least squares approach to improve the accuracy of registration, and several control points were acquired by total stations (TS) and then adjusted. Secondly, the registered points-cloud was resampled and segmented based on vectors of neighbor points to select suitable points. Thirdly, the selected points were used to fit the subway tunnel surface with moving least squares algorithm. Then a series of parallel sections obtained from temporal series of fitting tunnel surfaces were compared to analysis the deformation. Finally, the results of the approach in z direction were compared with the fiber optical displacement sensor approach and the results in x, y directions were compared with TS respectively, and comparison results showed the accuracy errors of x, y, z directions were respectively about 1.5 mm, 2 mm, 1 mm. Therefore the new approach using high-resolution TLS can meet the demand of subway tunnel deformation monitoring.

Fast function-on-scalar regression with penalized basis expansions.

PubMed

Reiss, Philip T; Huang, Lei; Mennes, Maarten

2010-01-01

Regression models for functional responses and scalar predictors are often fitted by means of basis functions, with quadratic roughness penalties applied to avoid overfitting. The fitting approach described by Ramsay and Silverman in the 1990 s amounts to a penalized ordinary least squares (P-OLS) estimator of the coefficient functions. We recast this estimator as a generalized ridge regression estimator, and present a penalized generalized least squares (P-GLS) alternative. We describe algorithms by which both estimators can be implemented, with automatic selection of optimal smoothing parameters, in a more computationally efficient manner than has heretofore been available. We discuss pointwise confidence intervals for the coefficient functions, simultaneous inference by permutation tests, and model selection, including a novel notion of pointwise model selection. P-OLS and P-GLS are compared in a simulation study. Our methods are illustrated with an analysis of age effects in a functional magnetic resonance imaging data set, as well as a reanalysis of a now-classic Canadian weather data set. An R package implementing the methods is publicly available.

The long-solved problem of the best-fit straight line: Application to isotopic mixing lines

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wehr, Richard; Saleska, Scott R.

It has been almost 50 years since York published an exact and general solution for the best-fit straight line to independent points with normally distributed errors in both x and y. York's solution is highly cited in the geophysical literature but almost unknown outside of it, so that there has been no ebb in the tide of books and papers wrestling with the problem. Much of the post-1969 literature on straight-line fitting has sown confusion not merely by its content but by its very existence. The optimal least-squares fit is already known; the problem is already solved. Here we introducemore » the non-specialist reader to York's solution and demonstrate its application in the interesting case of the isotopic mixing line, an analytical tool widely used to determine the isotopic signature of trace gas sources for the study of biogeochemical cycles. The most commonly known linear regression methods – ordinary least-squares regression (OLS), geometric mean regression (GMR), and orthogonal distance regression (ODR) – have each been recommended as the best method for fitting isotopic mixing lines. In fact, OLS, GMR, and ODR are all special cases of York's solution that are valid only under particular measurement conditions, and those conditions do not hold in general for isotopic mixing lines. Here, using Monte Carlo simulations, we quantify the biases in OLS, GMR, and ODR under various conditions and show that York's general – and convenient – solution is always the least biased.« less

The long-solved problem of the best-fit straight line: Application to isotopic mixing lines

DOE PAGES

Wehr, Richard; Saleska, Scott R.

2017-01-03

It has been almost 50 years since York published an exact and general solution for the best-fit straight line to independent points with normally distributed errors in both x and y. York's solution is highly cited in the geophysical literature but almost unknown outside of it, so that there has been no ebb in the tide of books and papers wrestling with the problem. Much of the post-1969 literature on straight-line fitting has sown confusion not merely by its content but by its very existence. The optimal least-squares fit is already known; the problem is already solved. Here we introducemore » the non-specialist reader to York's solution and demonstrate its application in the interesting case of the isotopic mixing line, an analytical tool widely used to determine the isotopic signature of trace gas sources for the study of biogeochemical cycles. The most commonly known linear regression methods – ordinary least-squares regression (OLS), geometric mean regression (GMR), and orthogonal distance regression (ODR) – have each been recommended as the best method for fitting isotopic mixing lines. In fact, OLS, GMR, and ODR are all special cases of York's solution that are valid only under particular measurement conditions, and those conditions do not hold in general for isotopic mixing lines. Here, using Monte Carlo simulations, we quantify the biases in OLS, GMR, and ODR under various conditions and show that York's general – and convenient – solution is always the least biased.« less

Interpolating moving least-squares methods for fitting potential energy surfaces: using classical trajectories to explore configuration space.

PubMed

Dawes, Richard; Passalacqua, Alessio; Wagner, Albert F; Sewell, Thomas D; Minkoff, Michael; Thompson, Donald L

2009-04-14

We develop two approaches for growing a fitted potential energy surface (PES) by the interpolating moving least-squares (IMLS) technique using classical trajectories. We illustrate both approaches by calculating nitrous acid (HONO) cis-->trans isomerization trajectories under the control of ab initio forces from low-level HF/cc-pVDZ electronic structure calculations. In this illustrative example, as few as 300 ab initio energy/gradient calculations are required to converge the isomerization rate constant at a fixed energy to approximately 10%. Neither approach requires any preliminary electronic structure calculations or initial approximate representation of the PES (beyond information required for trajectory initial conditions). Hessians are not required. Both approaches rely on the fitting error estimation properties of IMLS fits. The first approach, called IMLS-accelerated direct dynamics, propagates individual trajectories directly with no preliminary exploratory trajectories. The PES is grown "on the fly" with the computation of new ab initio data only when a fitting error estimate exceeds a prescribed tight tolerance. The second approach, called dynamics-driven IMLS fitting, uses relatively inexpensive exploratory trajectories to both determine and fit the dynamically accessible configuration space. Once exploratory trajectories no longer find configurations with fitting error estimates higher than the designated accuracy, the IMLS fit is considered to be complete and usable in classical trajectory calculations or other applications.

Computer program for calculating and fitting thermodynamic functions

NASA Technical Reports Server (NTRS)

Mcbride, Bonnie J.; Gordon, Sanford

1992-01-01

A computer program is described which (1) calculates thermodynamic functions (heat capacity, enthalpy, entropy, and free energy) for several optional forms of the partition function, (2) fits these functions to empirical equations by means of a least-squares fit, and (3) calculates, as a function of temperture, heats of formation and equilibrium constants. The program provides several methods for calculating ideal gas properties. For monatomic gases, three methods are given which differ in the technique used for truncating the partition function. For diatomic and polyatomic molecules, five methods are given which differ in the corrections to the rigid-rotator harmonic-oscillator approximation. A method for estimating thermodynamic functions for some species is also given.

Multivariate qualitative analysis of banned additives in food safety using surface enhanced Raman scattering spectroscopy.

PubMed

He, Shixuan; Xie, Wanyi; Zhang, Wei; Zhang, Liqun; Wang, Yunxia; Liu, Xiaoling; Liu, Yulong; Du, Chunlei

2015-02-25

A novel strategy which combines iteratively cubic spline fitting baseline correction method with discriminant partial least squares qualitative analysis is employed to analyze the surface enhanced Raman scattering (SERS) spectroscopy of banned food additives, such as Sudan I dye and Rhodamine B in food, Malachite green residues in aquaculture fish. Multivariate qualitative analysis methods, using the combination of spectra preprocessing iteratively cubic spline fitting (ICSF) baseline correction with principal component analysis (PCA) and discriminant partial least squares (DPLS) classification respectively, are applied to investigate the effectiveness of SERS spectroscopy for predicting the class assignments of unknown banned food additives. PCA cannot be used to predict the class assignments of unknown samples. However, the DPLS classification can discriminate the class assignment of unknown banned additives using the information of differences in relative intensities. The results demonstrate that SERS spectroscopy combined with ICSF baseline correction method and exploratory analysis methodology DPLS classification can be potentially used for distinguishing the banned food additives in field of food safety. Copyright © 2014 Elsevier B.V. All rights reserved.

Genetic Algorithm for Initial Orbit Determination with Too Short Arc (Continued)

NASA Astrophysics Data System (ADS)

Li, Xin-ran; Wang, Xin

2017-04-01

When the genetic algorithm is used to solve the problem of too short-arc (TSA) orbit determination, due to the difference of computing process between the genetic algorithm and the classical method, the original method for outlier deletion is no longer applicable. In the genetic algorithm, the robust estimation is realized by introducing different loss functions for the fitness function, then the outlier problem of the TSA orbit determination is solved. Compared with the classical method, the genetic algorithm is greatly simplified by introducing in different loss functions. Through the comparison on the calculations of multiple loss functions, it is found that the least median square (LMS) estimation and least trimmed square (LTS) estimation can greatly improve the robustness of the TSA orbit determination, and have a high breakdown point.

Detecting outliers when fitting data with nonlinear regression – a new method based on robust nonlinear regression and the false discovery rate

PubMed Central

Motulsky, Harvey J; Brown, Ronald E

2006-01-01

Background Nonlinear regression, like linear regression, assumes that the scatter of data around the ideal curve follows a Gaussian or normal distribution. This assumption leads to the familiar goal of regression: to minimize the sum of the squares of the vertical or Y-value distances between the points and the curve. Outliers can dominate the sum-of-the-squares calculation, and lead to misleading results. However, we know of no practical method for routinely identifying outliers when fitting curves with nonlinear regression. Results We describe a new method for identifying outliers when fitting data with nonlinear regression. We first fit the data using a robust form of nonlinear regression, based on the assumption that scatter follows a Lorentzian distribution. We devised a new adaptive method that gradually becomes more robust as the method proceeds. To define outliers, we adapted the false discovery rate approach to handling multiple comparisons. We then remove the outliers, and analyze the data using ordinary least-squares regression. Because the method combines robust regression and outlier removal, we call it the ROUT method. When analyzing simulated data, where all scatter is Gaussian, our method detects (falsely) one or more outlier in only about 1–3% of experiments. When analyzing data contaminated with one or several outliers, the ROUT method performs well at outlier identification, with an average False Discovery Rate less than 1%. Conclusion Our method, which combines a new method of robust nonlinear regression with a new method of outlier identification, identifies outliers from nonlinear curve fits with reasonable power and few false positives. PMID:16526949

Spline based least squares integration for two-dimensional shape or wavefront reconstruction

DOE PAGES

Huang, Lei; Xue, Junpeng; Gao, Bo; ...

2016-12-21

In this paper, we present a novel method to handle two-dimensional shape or wavefront reconstruction from its slopes. The proposed integration method employs splines to fit the measured slope data with piecewise polynomials and uses the analytical polynomial functions to represent the height changes in a lateral spacing with the pre-determined spline coefficients. The linear least squares method is applied to estimate the height or wavefront as a final result. Numerical simulations verify that the proposed method has less algorithm errors than two other existing methods used for comparison. Especially at the boundaries, the proposed method has better performance. Themore » noise influence is studied by adding white Gaussian noise to the slope data. Finally, experimental data from phase measuring deflectometry are tested to demonstrate the feasibility of the new method in a practical measurement.« less

Spline based least squares integration for two-dimensional shape or wavefront reconstruction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Lei; Xue, Junpeng; Gao, Bo

In this paper, we present a novel method to handle two-dimensional shape or wavefront reconstruction from its slopes. The proposed integration method employs splines to fit the measured slope data with piecewise polynomials and uses the analytical polynomial functions to represent the height changes in a lateral spacing with the pre-determined spline coefficients. The linear least squares method is applied to estimate the height or wavefront as a final result. Numerical simulations verify that the proposed method has less algorithm errors than two other existing methods used for comparison. Especially at the boundaries, the proposed method has better performance. Themore » noise influence is studied by adding white Gaussian noise to the slope data. Finally, experimental data from phase measuring deflectometry are tested to demonstrate the feasibility of the new method in a practical measurement.« less

Parameter estimation of Monod model by the Least-Squares method for microalgae Botryococcus Braunii sp

NASA Astrophysics Data System (ADS)

See, J. J.; Jamaian, S. S.; Salleh, R. M.; Nor, M. E.; Aman, F.

2018-04-01

This research aims to estimate the parameters of Monod model of microalgae Botryococcus Braunii sp growth by the Least-Squares method. Monod equation is a non-linear equation which can be transformed into a linear equation form and it is solved by implementing the Least-Squares linear regression method. Meanwhile, Gauss-Newton method is an alternative method to solve the non-linear Least-Squares problem with the aim to obtain the parameters value of Monod model by minimizing the sum of square error ( SSE). As the result, the parameters of the Monod model for microalgae Botryococcus Braunii sp can be estimated by the Least-Squares method. However, the estimated parameters value obtained by the non-linear Least-Squares method are more accurate compared to the linear Least-Squares method since the SSE of the non-linear Least-Squares method is less than the linear Least-Squares method.

Graphical and PC-software analysis of volcano eruption precursors according to the Materials Failure Forecast Method (FFM)

NASA Astrophysics Data System (ADS)

Cornelius, Reinold R.; Voight, Barry

1995-03-01

The Materials Failure Forecasting Method for volcanic eruptions (FFM) analyses the rate of precursory phenomena. Time of eruption onset is derived from the time of "failure" implied by accelerating rate of deformation. The approach attempts to fit data, Ω, to the differential relationship Ω¨=AΩ˙, where the dot superscript represents the time derivative, and the data Ω may be any of several parameters describing the accelerating deformation or energy release of the volcanic system. Rate coefficients, A and α, may be derived from appropriate data sets to provide an estimate of time to "failure". As the method is still an experimental technique, it should be used with appropriate judgment during times of volcanic crisis. Limitations of the approach are identified and discussed. Several kinds of eruption precursory phenomena, all simulating accelerating creep during the mechanical deformation of the system, can be used with FFM. Among these are tilt data, slope-distance measurements, crater fault movements and seismicity. The use of seismic coda, seismic amplitude-derived energy release and time-integrated amplitudes or coda lengths are examined. Usage of cumulative coda length directly has some practical advantages to more rigorously derived parameters, and RSAM and SSAM technologies appear to be well suited to real-time applications. One graphical and four numerical techniques of applying FFM are discussed. The graphical technique is based on an inverse representation of rate versus time. For α = 2, the inverse rate plot is linear; it is concave upward for α < 2 and concave downward for α > 2. The eruption time is found by simple extrapolation of the data set toward the time axis. Three numerical techniques are based on linear least-squares fits to linearized data sets. The "linearized least-squares technique" is most robust and is expected to be the most practical numerical technique. This technique is based on an iterative linearization of the given rate-time series. The hindsight technique is disadvantaged by a bias favouring a too early eruption time in foresight applications. The "log rate versus log acceleration technique", utilizing a logarithmic representation of the fundamental differential equation, is disadvantaged by large data scatter after interpolation of accelerations. One further numerical technique, a nonlinear least-squares fit to rate data, requires special and more complex software. PC-oriented computer codes were developed for data manipulation, application of the three linearizing numerical methods, and curve fitting. Separate software is required for graphing purposes. All three linearizing techniques facilitate an eruption window based on a data envelope according to the linear least-squares fit, at a specific level of confidence, and an estimated rate at time of failure.

Quantitative analysis of Ni2+/Ni3+ in Li[NixMnyCoz]O2 cathode materials: Non-linear least-squares fitting of XPS spectra

NASA Astrophysics Data System (ADS)

Fu, Zewei; Hu, Juntao; Hu, Wenlong; Yang, Shiyu; Luo, Yunfeng

2018-05-01

Quantitative analysis of Ni2+/Ni3+ using X-ray photoelectron spectroscopy (XPS) is important for evaluating the crystal structure and electrochemical performance of Lithium-nickel-cobalt-manganese oxide (Li[NixMnyCoz]O2, NMC). However, quantitative analysis based on Gaussian/Lorentzian (G/L) peak fitting suffers from the challenges of reproducibility and effectiveness. In this study, the Ni2+ and Ni3+ standard samples and a series of NMC samples with different Ni doping levels were synthesized. The Ni2+/Ni3+ ratios in NMC were quantitatively analyzed by non-linear least-squares fitting (NLLSF). Two Ni 2p overall spectra of synthesized Li [Ni0.33Mn0.33Co0.33]O2(NMC111) and bulk LiNiO2 were used as the Ni2+ and Ni3+ reference standards. Compared to G/L peak fitting, the fitting parameters required no adjustment, meaning that the spectral fitting process was free from operator dependence and the reproducibility was improved. Comparison of residual standard deviation (STD) showed that the fitting quality of NLLSF was superior to that of G/L peaks fitting. Overall, these findings confirmed the reproducibility and effectiveness of the NLLSF method in XPS quantitative analysis of Ni2+/Ni3+ ratio in Li[NixMnyCoz]O2 cathode materials.

Improved mapping of radio sources from VLBI data by least-square fit

NASA Technical Reports Server (NTRS)

Rodemich, E. R.

1985-01-01

A method is described for producing improved mapping of radio sources from Very Long Base Interferometry (VLBI) data. The method described is more direct than existing Fourier methods, is often more accurate, and runs at least as fast. The visibility data is modeled here, as in existing methods, as a function of the unknown brightness distribution and the unknown antenna gains and phases. These unknowns are chosen so that the resulting function values are as near as possible to the observed values. If researchers use the radio mapping source deviation to measure the closeness of this fit to the observed values, they are led to the problem of minimizing a certain function of all the unknown parameters. This minimization problem cannot be solved directly, but it can be attacked by iterative methods which we show converge automatically to the minimum with no user intervention. The resulting brightness distribution will furnish the best fit to the data among all brightness distributions of given resolution.

Comparing the performance of geostatistical models with additional information from covariates for sewage plume characterization.

PubMed

Del Monego, Maurici; Ribeiro, Paulo Justiniano; Ramos, Patrícia

2015-04-01

In this work, kriging with covariates is used to model and map the spatial distribution of salinity measurements gathered by an autonomous underwater vehicle in a sea outfall monitoring campaign aiming to distinguish the effluent plume from the receiving waters and characterize its spatial variability in the vicinity of the discharge. Four different geostatistical linear models for salinity were assumed, where the distance to diffuser, the west-east positioning, and the south-north positioning were used as covariates. Sample variograms were fitted by the Matèrn models using weighted least squares and maximum likelihood estimation methods as a way to detect eventual discrepancies. Typically, the maximum likelihood method estimated very low ranges which have limited the kriging process. So, at least for these data sets, weighted least squares showed to be the most appropriate estimation method for variogram fitting. The kriged maps show clearly the spatial variation of salinity, and it is possible to identify the effluent plume in the area studied. The results obtained show some guidelines for sewage monitoring if a geostatistical analysis of the data is in mind. It is important to treat properly the existence of anomalous values and to adopt a sampling strategy that includes transects parallel and perpendicular to the effluent dispersion.

A least-squares minimization approach for model parameters estimate by using a new magnetic anomaly formula

NASA Astrophysics Data System (ADS)

Abo-Ezz, E. R.; Essa, K. S.

2016-04-01

A new linear least-squares approach is proposed to interpret magnetic anomalies of the buried structures by using a new magnetic anomaly formula. This approach depends on solving different sets of algebraic linear equations in order to invert the depth ( z), amplitude coefficient ( K), and magnetization angle ( θ) of buried structures using magnetic data. The utility and validity of the new proposed approach has been demonstrated through various reliable synthetic data sets with and without noise. In addition, the method has been applied to field data sets from USA and India. The best-fitted anomaly has been delineated by estimating the root-mean squared (rms). Judging satisfaction of this approach is done by comparing the obtained results with other available geological or geophysical information.

Gompertzian stochastic model with delay effect to cervical cancer growth

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah

2015-02-03

In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.

Modeling Group Differences in OLS and Orthogonal Regression: Implications for Differential Validity Studies

ERIC Educational Resources Information Center

Kane, Michael T.; Mroch, Andrew A.

2010-01-01

In evaluating the relationship between two measures across different groups (i.e., in evaluating "differential validity") it is necessary to examine differences in correlation coefficients and in regression lines. Ordinary least squares (OLS) regression is the standard method for fitting lines to data, but its criterion for optimal fit…

Applying ISO 11929:2010 Standard to detection limit calculation in least-squares based multi-nuclide gamma-ray spectrum evaluation

NASA Astrophysics Data System (ADS)

Kanisch, G.

2017-05-01

The concepts of ISO 11929 (2010) are applied to evaluation of radionuclide activities from more complex multi-nuclide gamma-ray spectra. From net peak areas estimated by peak fitting, activities and their standard uncertainties are calculated by weighted linear least-squares method with an additional step, where uncertainties of the design matrix elements are taken into account. A numerical treatment of the standard's uncertainty function, based on ISO 11929 Annex C.5, leads to a procedure for deriving decision threshold and detection limit values. The methods shown allow resolving interferences between radionuclide activities also in case of calculating detection limits where they can improve the latter by including more than one gamma line per radionuclide. The co"mmon single nuclide weighted mean is extended to an interference-corrected (generalized) weighted mean, which, combined with the least-squares method, allows faster detection limit calculations. In addition, a new grouped uncertainty budget was inferred, which for each radionuclide gives uncertainty budgets from seven main variables, such as net count rates, peak efficiencies, gamma emission intensities and others; grouping refers to summation over lists of peaks per radionuclide.

Comparison of linear and non-linear method in estimating the sorption isotherm parameters for safranin onto activated carbon.

PubMed

Kumar, K Vasanth; Sivanesan, S

2005-08-31

Comparison analysis of linear least square method and non-linear method for estimating the isotherm parameters was made using the experimental equilibrium data of safranin onto activated carbon at two different solution temperatures 305 and 313 K. Equilibrium data were fitted to Freundlich, Langmuir and Redlich-Peterson isotherm equations. All the three isotherm equations showed a better fit to the experimental equilibrium data. The results showed that non-linear method could be a better way to obtain the isotherm parameters. Redlich-Peterson isotherm is a special case of Langmuir isotherm when the Redlich-Peterson isotherm constant g was unity.

Decomposition of mineral absorption bands using nonlinear least squares curve fitting: Application to Martian meteorites and CRISM data

NASA Astrophysics Data System (ADS)

Parente, Mario; Makarewicz, Heather D.; Bishop, Janice L.

2011-04-01

This study advances curve-fitting modeling of absorption bands of reflectance spectra and applies this new model to spectra of Martian meteorites ALH 84001 and EETA 79001 and data from the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM). This study also details a recently introduced automated parameter initialization technique. We assess the performance of this automated procedure by comparing it to the currently available initialization method and perform a sensitivity analysis of the fit results to variation in initial guesses. We explore the issues related to the removal of the continuum, offer guidelines for continuum removal when modeling the absorptions and explore different continuum-removal techniques. We further evaluate the suitability of curve fitting techniques using Gaussians/Modified Gaussians to decompose spectra into individual end-member bands. We show that nonlinear least squares techniques such as the Levenberg-Marquardt algorithm achieve comparable results to the MGM model ( Sunshine and Pieters, 1993; Sunshine et al., 1990) for meteorite spectra. Finally we use Gaussian modeling to fit CRISM spectra of pyroxene and olivine-rich terrains on Mars. Analysis of CRISM spectra of two regions show that the pyroxene-dominated rock spectra measured at Juventae Chasma were modeled well with low Ca pyroxene, while the pyroxene-rich spectra acquired at Libya Montes required both low-Ca and high-Ca pyroxene for a good fit.

Navy Fuel Composition and Screening Tool (FCAST) v2.8

DTIC Science & Technology

2016-05-10

allowed us to develop partial least squares (PLS) models based on gas chromatography–mass spectrometry (GC-MS) data that predict fuel properties. The...Chemometric property modeling Partial least squares PLS Compositional profiler Naval Air Systems Command Air-4.4.5 Patuxent River Naval Air Station Patuxent...Cumulative predicted residual error sum of squares DiEGME Diethylene glycol monomethyl ether FCAST Fuel Composition and Screening Tool FFP Fit for

Least-Squares Approximation of an Improper Correlation Matrix by a Proper One.

ERIC Educational Resources Information Center

Knol, Dirk L.; ten Berge, Jos M. F.

1989-01-01

An algorithm, based on a solution for C. I. Mosier's oblique Procrustes rotation problem, is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. Results are of interest for missing value and tetrachoric correlation, indefinite matrix correlation, and constrained…

Nonlinear least-squares data fitting in Excel spreadsheets.

PubMed

Kemmer, Gerdi; Keller, Sandro

2010-02-01

We describe an intuitive and rapid procedure for analyzing experimental data by nonlinear least-squares fitting (NLSF) in the most widely used spreadsheet program. Experimental data in x/y form and data calculated from a regression equation are inputted and plotted in a Microsoft Excel worksheet, and the sum of squared residuals is computed and minimized using the Solver add-in to obtain the set of parameter values that best describes the experimental data. The confidence of best-fit values is then visualized and assessed in a generally applicable and easily comprehensible way. Every user familiar with the most basic functions of Excel will be able to implement this protocol, without previous experience in data fitting or programming and without additional costs for specialist software. The application of this tool is exemplified using the well-known Michaelis-Menten equation characterizing simple enzyme kinetics. Only slight modifications are required to adapt the protocol to virtually any other kind of dataset or regression equation. The entire protocol takes approximately 1 h.

Maximum-likelihood curve-fitting scheme for experiments with pulsed lasers subject to intensity fluctuations.

PubMed

Metz, Thomas; Walewski, Joachim; Kaminski, Clemens F

2003-03-20

Evaluation schemes, e.g., least-squares fitting, are not generally applicable to any types of experiments. If the evaluation schemes were not derived from a measurement model that properly described the experiment to be evaluated, poorer precision or accuracy than attainable from the measured data could result. We outline ways in which statistical data evaluation schemes should be derived for all types of experiment, and we demonstrate them for laser-spectroscopic experiments, in which pulse-to-pulse fluctuations of the laser power cause correlated variations of laser intensity and generated signal intensity. The method of maximum likelihood is demonstrated in the derivation of an appropriate fitting scheme for this type of experiment. Statistical data evaluation contains the following steps. First, one has to provide a measurement model that considers statistical variation of all enclosed variables. Second, an evaluation scheme applicable to this particular model has to be derived or provided. Third, the scheme has to be characterized in terms of accuracy and precision. A criterion for accepting an evaluation scheme is that it have accuracy and precision as close as possible to the theoretical limit. The fitting scheme derived for experiments with pulsed lasers is compared to well-established schemes in terms of fitting power and rational functions. The precision is found to be as much as three timesbetter than for simple least-squares fitting. Our scheme also suppresses the bias on the estimated model parameters that other methods may exhibit if they are applied in an uncritical fashion. We focus on experiments in nonlinear spectroscopy, but the fitting scheme derived is applicable in many scientific disciplines.

Thermal Property Measurement of Semiconductor Melt using Modified Laser Flash Method

NASA Technical Reports Server (NTRS)

Lin, Bochuan; Zhu, Shen; Ban, Heng; Li, Chao; Scripa, Rosalla N.; Su, Ching-Hua; Lehoczky, Sandor L.

2003-01-01

This study further developed standard laser flash method to measure multiple thermal properties of semiconductor melts. The modified method can determine thermal diffusivity, thermal conductivity, and specific heat capacity of the melt simultaneously. The transient heat transfer process in the melt and its quartz container was numerically studied in detail. A fitting procedure based on numerical simulation results and the least root-mean-square error fitting to the experimental data was used to extract the values of specific heat capacity, thermal conductivity and thermal diffusivity. This modified method is a step forward from the standard laser flash method, which is usually used to measure thermal diffusivity of solids. The result for tellurium (Te) at 873 K: specific heat capacity 300.2 Joules per kilogram K, thermal conductivity 3.50 Watts per meter K, thermal diffusivity 2.04 x 10(exp -6) square meters per second, are within the range reported in literature. The uncertainty analysis showed the quantitative effect of sample geometry, transient temperature measured, and the energy of the laser pulse.

Uncertainty in least-squares fits to the thermal noise spectra of nanomechanical resonators with applications to the atomic force microscope.

PubMed

Sader, John E; Yousefi, Morteza; Friend, James R

2014-02-01

Thermal noise spectra of nanomechanical resonators are used widely to characterize their physical properties. These spectra typically exhibit a Lorentzian response, with additional white noise due to extraneous processes. Least-squares fits of these measurements enable extraction of key parameters of the resonator, including its resonant frequency, quality factor, and stiffness. Here, we present general formulas for the uncertainties in these fit parameters due to sampling noise inherent in all thermal noise spectra. Good agreement with Monte Carlo simulation of synthetic data and measurements of an Atomic Force Microscope (AFM) cantilever is demonstrated. These formulas enable robust interpretation of thermal noise spectra measurements commonly performed in the AFM and adaptive control of fitting procedures with specified tolerances.

Uncertainty in least-squares fits to the thermal noise spectra of nanomechanical resonators with applications to the atomic force microscope

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sader, John E., E-mail: jsader@unimelb.edu.au; Yousefi, Morteza; Friend, James R.

2014-02-15

Thermal noise spectra of nanomechanical resonators are used widely to characterize their physical properties. These spectra typically exhibit a Lorentzian response, with additional white noise due to extraneous processes. Least-squares fits of these measurements enable extraction of key parameters of the resonator, including its resonant frequency, quality factor, and stiffness. Here, we present general formulas for the uncertainties in these fit parameters due to sampling noise inherent in all thermal noise spectra. Good agreement with Monte Carlo simulation of synthetic data and measurements of an Atomic Force Microscope (AFM) cantilever is demonstrated. These formulas enable robust interpretation of thermal noisemore » spectra measurements commonly performed in the AFM and adaptive control of fitting procedures with specified tolerances.« less

Evaluation of fuzzy inference systems using fuzzy least squares

NASA Technical Reports Server (NTRS)

Barone, Joseph M.

1992-01-01

Efforts to develop evaluation methods for fuzzy inference systems which are not based on crisp, quantitative data or processes (i.e., where the phenomenon the system is built to describe or control is inherently fuzzy) are just beginning. This paper suggests that the method of fuzzy least squares can be used to perform such evaluations. Regressing the desired outputs onto the inferred outputs can provide both global and local measures of success. The global measures have some value in an absolute sense, but they are particularly useful when competing solutions (e.g., different numbers of rules, different fuzzy input partitions) are being compared. The local measure described here can be used to identify specific areas of poor fit where special measures (e.g., the use of emphatic or suppressive rules) can be applied. Several examples are discussed which illustrate the applicability of the method as an evaluation tool.

Enhanced data reduction of the velocity data on CETA flight experiment. [Crew and Equipment Translation Aid

NASA Technical Reports Server (NTRS)

Finley, Tom D.; Wong, Douglas T.; Tripp, John S.

1993-01-01

A newly developed technique for enhanced data reduction provides an improved procedure that allows least squares minimization to become possible between data sets with an unequal number of data points. This technique was applied in the Crew and Equipment Translation Aid (CETA) experiment on the STS-37 Shuttle flight in April 1991 to obtain the velocity profile from the acceleration data. The new technique uses a least-squares method to estimate the initial conditions and calibration constants. These initial conditions are estimated by least-squares fitting the displacements indicated by the Hall-effect sensor data to the corresponding displacements obtained from integrating the acceleration data. The velocity and displacement profiles can then be recalculated from the corresponding acceleration data using the estimated parameters. This technique, which enables instantaneous velocities to be obtained from the test data instead of only average velocities at varying discrete times, offers more detailed velocity information, particularly during periods of large acceleration or deceleration.

Non-stationary least-squares complex decomposition for microseismic noise attenuation

NASA Astrophysics Data System (ADS)

Chen, Yangkang

2018-06-01

Microseismic data processing and imaging are crucial for subsurface real-time monitoring during hydraulic fracturing process. Unlike the active-source seismic events or large-scale earthquake events, the microseismic event is usually of very small magnitude, which makes its detection challenging. The biggest trouble of microseismic data is the low signal-to-noise ratio issue. Because of the small energy difference between effective microseismic signal and ambient noise, the effective signals are usually buried in strong random noise. I propose a useful microseismic denoising algorithm that is based on decomposing a microseismic trace into an ensemble of components using least-squares inversion. Based on the predictive property of useful microseismic event along the time direction, the random noise can be filtered out via least-squares fitting of multiple damping exponential components. The method is flexible and almost automated since the only parameter needed to be defined is a decomposition number. I use some synthetic and real data examples to demonstrate the potential of the algorithm in processing complicated microseismic data sets.

A method for modeling discontinuities in a microwave coaxial transmission line

NASA Technical Reports Server (NTRS)

Otoshi, T. Y.

1992-01-01

A method for modeling discontinuities in a coaxial transmission line is presented. The methodology involves the use of a nonlinear least-squares fit program to optimize the fit between theoretical data (from the model) and experimental data. When this method was applied to modeling discontinuities in a slightly damaged Galileo spacecraft S-band (2.295-GHz) antenna cable, excellent agreement between theory and experiment was obtained over a frequency range of 1.70-2.85 GHz. The same technique can be applied for diagnostics and locating unknown discontinuities in other types of microwave transmission lines, such as rectangular, circular, and beam waveguides.

A method for modeling discontinuities in a microwave coaxial transmission line

NASA Astrophysics Data System (ADS)

Otoshi, T. Y.

1992-08-01

A method for modeling discontinuities in a coaxial transmission line is presented. The methodology involves the use of a nonlinear least-squares fit program to optimize the fit between theoretical data (from the model) and experimental data. When this method was applied to modeling discontinuities in a slightly damaged Galileo spacecraft S-band (2.295-GHz) antenna cable, excellent agreement between theory and experiment was obtained over a frequency range of 1.70-2.85 GHz. The same technique can be applied for diagnostics and locating unknown discontinuities in other types of microwave transmission lines, such as rectangular, circular, and beam waveguides.

Additivity and maximum likelihood estimation of nonlinear component biomass models

Treesearch

David L.R. Affleck

2015-01-01

Since Parresol's (2001) seminal paper on the subject, it has become common practice to develop nonlinear tree biomass equations so as to ensure compatibility among total and component predictions and to fit equations jointly using multi-step least squares (MSLS) methods. In particular, many researchers have specified total tree biomass models by aggregating the...

Additive nonlinear biomass equations: A likelihood-based approach

Treesearch

David L. R. Affleck; Ulises Dieguez-Aranda

2016-01-01

Since Parresol’s (Can. J. For. Res. 31:865-878, 2001) seminal article on the topic, it has become standard to develop nonlinear tree biomass equations to ensure compatibility among total and component predictions and to fit these equations using multistep generalized least-squares methods. In particular, many studies have specified equations for total tree...

Radius of Curvature of Off-Axis Paraboloids

NASA Technical Reports Server (NTRS)

Robinson, Brian; Reardon, Patrick; Hadaway, James; Geary, Joseph; Russell, Kevin (Technical Monitor)

2002-01-01

We present several methods for measuring the vertex radius of curvature of off-axis paraboloidal mirrors. One is based on least-squares fitting of interferometer output, one on comparison of sagittal and tangential radii of curvature, and another on measurement of displacement of the nulled test article from the ideal reference wave. Each method defines radius of curvature differently and, as a consequence, produces its own sort of errors.

Monte Carlo calculation of dynamical properties of the two-dimensional Hubbard model

NASA Technical Reports Server (NTRS)

White, S. R.; Scalapino, D. J.; Sugar, R. L.; Bickers, N. E.

1989-01-01

A new method is introduced for analytically continuing imaginary-time data from quantum Monte Carlo calculations to the real-frequency axis. The method is based on a least-squares-fitting procedure with constraints of positivity and smoothness on the real-frequency quantities. Results are shown for the single-particle spectral-weight function and density of states for the half-filled, two-dimensional Hubbard model.

Multivariate curve resolution-alternating least squares and kinetic modeling applied to near-infrared data from curing reactions of epoxy resins: mechanistic approach and estimation of kinetic rate constants.

PubMed

Garrido, M; Larrechi, M S; Rius, F X

2006-02-01

This study describes the combination of multivariate curve resolution-alternating least squares with a kinetic modeling strategy for obtaining the kinetic rate constants of a curing reaction of epoxy resins. The reaction between phenyl glycidyl ether and aniline is monitored by near-infrared spectroscopy under isothermal conditions for several initial molar ratios of the reagents. The data for all experiments, arranged in a column-wise augmented data matrix, are analyzed using multivariate curve resolution-alternating least squares. The concentration profiles recovered are fitted to a chemical model proposed for the reaction. The selection of the kinetic model is assisted by the information contained in the recovered concentration profiles. The nonlinear fitting provides the kinetic rate constants. The optimized rate constants are in agreement with values reported in the literature.

Eliminating the blood-flow confounding effect in intravoxel incoherent motion (IVIM) using the non-negative least square analysis in liver.

PubMed

Gambarota, Giulio; Hitti, Eric; Leporq, Benjamin; Saint-Jalmes, Hervé; Beuf, Olivier

2017-01-01

Tissue perfusion measurements using intravoxel incoherent motion (IVIM) diffusion-MRI are of interest for investigations of liver pathologies. A confounding factor in the perfusion quantification is the partial volume between liver tissue and large blood vessels. The aim of this study was to assess and correct for this partial volume effect in the estimation of the perfusion fraction. MRI experiments were performed at 3 Tesla with a diffusion-MRI sequence at 12 b-values. Diffusion signal decays in liver were analyzed using the non-negative least square (NNLS) method and the biexponential fitting approach. In some voxels, the NNLS analysis yielded a very fast-decaying component that was assigned to partial volume with the blood flowing in large vessels. Partial volume correction was performed by biexponential curve fitting, where the first data point (b = 0 s/mm 2 ) was eliminated in voxels with a very fast-decaying component. Biexponential fitting with partial volume correction yielded parametric maps with perfusion fraction values smaller than biexponential fitting without partial volume correction. The results of the current study indicate that the NNLS analysis in combination with biexponential curve fitting allows to correct for partial volume effects originating from blood flow in IVIM perfusion fraction measurements. Magn Reson Med 77:310-317, 2017. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Simulation and study of small numbers of random events

NASA Technical Reports Server (NTRS)

Shelton, R. D.

1986-01-01

Random events were simulated by computer and subjected to various statistical methods to extract important parameters. Various forms of curve fitting were explored, such as least squares, least distance from a line, maximum likelihood. Problems considered were dead time, exponential decay, and spectrum extraction from cosmic ray data using binned data and data from individual events. Computer programs, mostly of an iterative nature, were developed to do these simulations and extractions and are partially listed as appendices. The mathematical basis for the compuer programs is given.

Identifying model error in metabolic flux analysis - a generalized least squares approach.

PubMed

Sokolenko, Stanislav; Quattrociocchi, Marco; Aucoin, Marc G

2016-09-13

The estimation of intracellular flux through traditional metabolic flux analysis (MFA) using an overdetermined system of equations is a well established practice in metabolic engineering. Despite the continued evolution of the methodology since its introduction, there has been little focus on validation and identification of poor model fit outside of identifying "gross measurement error". The growing complexity of metabolic models, which are increasingly generated from genome-level data, has necessitated robust validation that can directly assess model fit. In this work, MFA calculation is framed as a generalized least squares (GLS) problem, highlighting the applicability of the common t-test for model validation. To differentiate between measurement and model error, we simulate ideal flux profiles directly from the model, perturb them with estimated measurement error, and compare their validation to real data. Application of this strategy to an established Chinese Hamster Ovary (CHO) cell model shows how fluxes validated by traditional means may be largely non-significant due to a lack of model fit. With further simulation, we explore how t-test significance relates to calculation error and show that fluxes found to be non-significant have 2-4 fold larger error (if measurement uncertainty is in the 5-10 % range). The proposed validation method goes beyond traditional detection of "gross measurement error" to identify lack of fit between model and data. Although the focus of this work is on t-test validation and traditional MFA, the presented framework is readily applicable to other regression analysis methods and MFA formulations.

Estimating errors in least-squares fitting

NASA Technical Reports Server (NTRS)

Richter, P. H.

1995-01-01

While least-squares fitting procedures are commonly used in data analysis and are extensively discussed in the literature devoted to this subject, the proper assessment of errors resulting from such fits has received relatively little attention. The present work considers statistical errors in the fitted parameters, as well as in the values of the fitted function itself, resulting from random errors in the data. Expressions are derived for the standard error of the fit, as a function of the independent variable, for the general nonlinear and linear fitting problems. Additionally, closed-form expressions are derived for some examples commonly encountered in the scientific and engineering fields, namely ordinary polynomial and Gaussian fitting functions. These results have direct application to the assessment of the antenna gain and system temperature characteristics, in addition to a broad range of problems in data analysis. The effects of the nature of the data and the choice of fitting function on the ability to accurately model the system under study are discussed, and some general rules are deduced to assist workers intent on maximizing the amount of information obtained form a given set of measurements.

Adaptive channel estimation for soft decision decoding over non-Gaussian optical channel

NASA Astrophysics Data System (ADS)

Xiang, Jing-song; Miao, Tao-tao; Huang, Sheng; Liu, Huan-lin

2016-10-01

An adaptive priori likelihood ratio (LLR) estimation method is proposed over non-Gaussian channel in the intensity modulation/direct detection (IM/DD) optical communication systems. Using the nonparametric histogram and the weighted least square linear fitting in the tail regions, the LLR is estimated and used for the soft decision decoding of the low-density parity-check (LDPC) codes. This method can adapt well to the three main kinds of intensity modulation/direct detection (IM/DD) optical channel, i.e., the chi-square channel, the Webb-Gaussian channel and the additive white Gaussian noise (AWGN) channel. The performance penalty of channel estimation is neglected.

Easy-DHPSF open-source software for three-dimensional localization of single molecules with precision beyond the optical diffraction limit.

PubMed

Lew, Matthew D; von Diezmann, Alexander R S; Moerner, W E

2013-02-25

Automated processing of double-helix (DH) microscope images of single molecules (SMs) streamlines the protocol required to obtain super-resolved three-dimensional (3D) reconstructions of ultrastructures in biological samples by single-molecule active control microscopy. Here, we present a suite of MATLAB subroutines, bundled with an easy-to-use graphical user interface (GUI), that facilitates 3D localization of single emitters (e.g. SMs, fluorescent beads, or quantum dots) with precisions of tens of nanometers in multi-frame movies acquired using a wide-field DH epifluorescence microscope. The algorithmic approach is based upon template matching for SM recognition and least-squares fitting for 3D position measurement, both of which are computationally expedient and precise. Overlapping images of SMs are ignored, and the precision of least-squares fitting is not as high as maximum likelihood-based methods. However, once calibrated, the algorithm can fit 15-30 molecules per second on a 3 GHz Intel Core 2 Duo workstation, thereby producing a 3D super-resolution reconstruction of 100,000 molecules over a 20×20×2 μm field of view (processing 128×128 pixels × 20000 frames) in 75 min.

A direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fitting.

PubMed

Dung, Van Than; Tjahjowidodo, Tegoeh

2017-01-01

B-spline functions are widely used in many industrial applications such as computer graphic representations, computer aided design, computer aided manufacturing, computer numerical control, etc. Recently, there exist some demands, e.g. in reverse engineering (RE) area, to employ B-spline curves for non-trivial cases that include curves with discontinuous points, cusps or turning points from the sampled data. The most challenging task in these cases is in the identification of the number of knots and their respective locations in non-uniform space in the most efficient computational cost. This paper presents a new strategy for fitting any forms of curve by B-spline functions via local algorithm. A new two-step method for fast knot calculation is proposed. In the first step, the data is split using a bisecting method with predetermined allowable error to obtain coarse knots. Secondly, the knots are optimized, for both locations and continuity levels, by employing a non-linear least squares technique. The B-spline function is, therefore, obtained by solving the ordinary least squares problem. The performance of the proposed method is validated by using various numerical experimental data, with and without simulated noise, which were generated by a B-spline function and deterministic parametric functions. This paper also discusses the benchmarking of the proposed method to the existing methods in literature. The proposed method is shown to be able to reconstruct B-spline functions from sampled data within acceptable tolerance. It is also shown that, the proposed method can be applied for fitting any types of curves ranging from smooth ones to discontinuous ones. In addition, the method does not require excessive computational cost, which allows it to be used in automatic reverse engineering applications.

Optimal least-squares finite element method for elliptic problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Povinelli, Louis A.

1991-01-01

An optimal least squares finite element method is proposed for two dimensional and three dimensional elliptic problems and its advantages are discussed over the mixed Galerkin method and the usual least squares finite element method. In the usual least squares finite element method, the second order equation (-Delta x (Delta u) + u = f) is recast as a first order system (-Delta x p + u = f, Delta u - p = 0). The error analysis and numerical experiment show that, in this usual least squares finite element method, the rate of convergence for flux p is one order lower than optimal. In order to get an optimal least squares method, the irrotationality Delta x p = 0 should be included in the first order system.

46 CFR 108.447 - Piping.

Code of Federal Regulations, 2012 CFR

2012-10-01

..., and fitting in a CO2 system must have a bursting pressure of at least 420 kilograms per square centimeter (6,000 pounds per square inch). (b) All piping for a CO2 system of nominal size of 19.05... between 168 and 196 kilograms per square centimeter (2,400 and 2,800 pounds per square inch) in the...

46 CFR 108.447 - Piping.

Code of Federal Regulations, 2013 CFR

2013-10-01

..., and fitting in a CO2 system must have a bursting pressure of at least 420 kilograms per square centimeter (6,000 pounds per square inch). (b) All piping for a CO2 system of nominal size of 19.05... between 168 and 196 kilograms per square centimeter (2,400 and 2,800 pounds per square inch) in the...

46 CFR 108.447 - Piping.

Code of Federal Regulations, 2010 CFR

2010-10-01

..., and fitting in a CO2 system must have a bursting pressure of at least 420 kilograms per square centimeter (6,000 pounds per square inch). (b) All piping for a CO2 system of nominal size of 19.05... between 168 and 196 kilograms per square centimeter (2,400 and 2,800 pounds per square inch) in the...

46 CFR 108.447 - Piping.

Code of Federal Regulations, 2011 CFR

2011-10-01

..., and fitting in a CO2 system must have a bursting pressure of at least 420 kilograms per square centimeter (6,000 pounds per square inch). (b) All piping for a CO2 system of nominal size of 19.05... between 168 and 196 kilograms per square centimeter (2,400 and 2,800 pounds per square inch) in the...

46 CFR 108.447 - Piping.

Code of Federal Regulations, 2014 CFR

2014-10-01

..., and fitting in a CO2 system must have a bursting pressure of at least 420 kilograms per square centimeter (6,000 pounds per square inch). (b) All piping for a CO2 system of nominal size of 19.05... between 168 and 196 kilograms per square centimeter (2,400 and 2,800 pounds per square inch) in the...

Kinetic approach for the enzymatic determination of levodopa and carbidopa assisted by multivariate curve resolution-alternating least squares.

PubMed

Grünhut, Marcos; Garrido, Mariano; Centurión, Maria E; Fernández Band, Beatriz S

2010-07-12

A combination of kinetic spectroscopic monitoring and multivariate curve resolution-alternating least squares (MCR-ALS) was proposed for the enzymatic determination of levodopa (LVD) and carbidopa (CBD) in pharmaceuticals. The enzymatic reaction process was carried out in a reverse stopped-flow injection system and monitored by UV-vis spectroscopy. The spectra (292-600 nm) were recorded throughout the reaction and were analyzed by multivariate curve resolution-alternating least squares. A small calibration matrix containing nine mixtures was used in the model construction. Additionally, to evaluate the prediction ability of the model, a set with six validation mixtures was used. The lack of fit obtained was 4.3%, the explained variance 99.8% and the overall prediction error 5.5%. Tablets of commercial samples were analyzed and the results were validated by pharmacopeia method (high performance liquid chromatography). No significant differences were found (alpha=0.05) between the reference values and the ones obtained with the proposed method. It is important to note that a unique chemometric model made it possible to determine both analytes simultaneously. Copyright 2010 Elsevier B.V. All rights reserved.

Quantitative Modelling of Trace Elements in Hard Coal.

PubMed

Smoliński, Adam; Howaniec, Natalia

2016-01-01

The significance of coal in the world economy remains unquestionable for decades. It is also expected to be the dominant fossil fuel in the foreseeable future. The increased awareness of sustainable development reflected in the relevant regulations implies, however, the need for the development and implementation of clean coal technologies on the one hand, and adequate analytical tools on the other. The paper presents the application of the quantitative Partial Least Squares method in modeling the concentrations of trace elements (As, Ba, Cd, Co, Cr, Cu, Mn, Ni, Pb, Rb, Sr, V and Zn) in hard coal based on the physical and chemical parameters of coal, and coal ash components. The study was focused on trace elements potentially hazardous to the environment when emitted from coal processing systems. The studied data included 24 parameters determined for 132 coal samples provided by 17 coal mines of the Upper Silesian Coal Basin, Poland. Since the data set contained outliers, the construction of robust Partial Least Squares models for contaminated data set and the correct identification of outlying objects based on the robust scales were required. These enabled the development of the correct Partial Least Squares models, characterized by good fit and prediction abilities. The root mean square error was below 10% for all except for one the final Partial Least Squares models constructed, and the prediction error (root mean square error of cross-validation) exceeded 10% only for three models constructed. The study is of both cognitive and applicative importance. It presents the unique application of the chemometric methods of data exploration in modeling the content of trace elements in coal. In this way it contributes to the development of useful tools of coal quality assessment.

Quantitative Modelling of Trace Elements in Hard Coal

PubMed Central

Smoliński, Adam; Howaniec, Natalia

2016-01-01

The significance of coal in the world economy remains unquestionable for decades. It is also expected to be the dominant fossil fuel in the foreseeable future. The increased awareness of sustainable development reflected in the relevant regulations implies, however, the need for the development and implementation of clean coal technologies on the one hand, and adequate analytical tools on the other. The paper presents the application of the quantitative Partial Least Squares method in modeling the concentrations of trace elements (As, Ba, Cd, Co, Cr, Cu, Mn, Ni, Pb, Rb, Sr, V and Zn) in hard coal based on the physical and chemical parameters of coal, and coal ash components. The study was focused on trace elements potentially hazardous to the environment when emitted from coal processing systems. The studied data included 24 parameters determined for 132 coal samples provided by 17 coal mines of the Upper Silesian Coal Basin, Poland. Since the data set contained outliers, the construction of robust Partial Least Squares models for contaminated data set and the correct identification of outlying objects based on the robust scales were required. These enabled the development of the correct Partial Least Squares models, characterized by good fit and prediction abilities. The root mean square error was below 10% for all except for one the final Partial Least Squares models constructed, and the prediction error (root mean square error of cross–validation) exceeded 10% only for three models constructed. The study is of both cognitive and applicative importance. It presents the unique application of the chemometric methods of data exploration in modeling the content of trace elements in coal. In this way it contributes to the development of useful tools of coal quality assessment. PMID:27438794

Geodesic regression on orientation distribution functions with its application to an aging study.

PubMed

Du, Jia; Goh, Alvina; Kushnarev, Sergey; Qiu, Anqi

2014-02-15

In this paper, we treat orientation distribution functions (ODFs) derived from high angular resolution diffusion imaging (HARDI) as elements of a Riemannian manifold and present a method for geodesic regression on this manifold. In order to find the optimal regression model, we pose this as a least-squares problem involving the sum-of-squared geodesic distances between observed ODFs and their model fitted data. We derive the appropriate gradient terms and employ gradient descent to find the minimizer of this least-squares optimization problem. In addition, we show how to perform statistical testing for determining the significance of the relationship between the manifold-valued regressors and the real-valued regressands. Experiments on both synthetic and real human data are presented. In particular, we examine aging effects on HARDI via geodesic regression of ODFs in normal adults aged 22 years old and above. © 2013 Elsevier Inc. All rights reserved.

Beyond maximum entropy: Fractal pixon-based image reconstruction

NASA Technical Reports Server (NTRS)

Puetter, R. C.; Pina, R. K.

1994-01-01

We have developed a new Bayesian image reconstruction method that has been shown to be superior to the best implementations of other methods, including Goodness-of-Fit (e.g. Least-Squares and Lucy-Richardson) and Maximum Entropy (ME). Our new method is based on the concept of the pixon, the fundamental, indivisible unit of picture information. Use of the pixon concept provides an improved image model, resulting in an image prior which is superior to that of standard ME.

Weighted least-square approach for simultaneous measurement of multiple reflective surfaces

NASA Astrophysics Data System (ADS)

Tang, Shouhong; Bills, Richard E.; Freischlad, Klaus

2007-09-01

Phase shifting interferometry (PSI) is a highly accurate method for measuring the nanometer-scale relative surface height of a semi-reflective test surface. PSI is effectively used in conjunction with Fizeau interferometers for optical testing, hard disk inspection, and semiconductor wafer flatness. However, commonly-used PSI algorithms are unable to produce an accurate phase measurement if more than one reflective surface is present in the Fizeau interferometer test cavity. Examples of test parts that fall into this category include lithography mask blanks and their protective pellicles, and plane parallel optical beam splitters. The plane parallel surfaces of these parts generate multiple interferograms that are superimposed in the recording plane of the Fizeau interferometer. When using wavelength shifting in PSI the phase shifting speed of each interferogram is proportional to the optical path difference (OPD) between the two reflective surfaces. The proposed method is able to differentiate each underlying interferogram from each other in an optimal manner. In this paper, we present a method for simultaneously measuring the multiple test surfaces of all underlying interferograms from these superimposed interferograms through the use of a weighted least-square fitting technique. The theoretical analysis of weighted least-square technique and the measurement results will be described in this paper.

Correcting bias in the rational polynomial coefficients of satellite imagery using thin-plate smoothing splines

NASA Astrophysics Data System (ADS)

Shen, Xiang; Liu, Bin; Li, Qing-Quan

2017-03-01

The Rational Function Model (RFM) has proven to be a viable alternative to the rigorous sensor models used for geo-processing of high-resolution satellite imagery. Because of various errors in the satellite ephemeris and instrument calibration, the Rational Polynomial Coefficients (RPCs) supplied by image vendors are often not sufficiently accurate, and there is therefore a clear need to correct the systematic biases in order to meet the requirements of high-precision topographic mapping. In this paper, we propose a new RPC bias-correction method using the thin-plate spline modeling technique. Benefiting from its excellent performance and high flexibility in data fitting, the thin-plate spline model has the potential to remove complex distortions in vendor-provided RPCs, such as the errors caused by short-period orbital perturbations. The performance of the new method was evaluated by using Ziyuan-3 satellite images and was compared against the recently developed least-squares collocation approach, as well as the classical affine-transformation and quadratic-polynomial based methods. The results show that the accuracies of the thin-plate spline and the least-squares collocation approaches were better than the other two methods, which indicates that strong non-rigid deformations exist in the test data because they cannot be adequately modeled by simple polynomial-based methods. The performance of the thin-plate spline method was close to that of the least-squares collocation approach when only a few Ground Control Points (GCPs) were used, and it improved more rapidly with an increase in the number of redundant observations. In the test scenario using 21 GCPs (some of them located at the four corners of the scene), the correction residuals of the thin-plate spline method were about 36%, 37%, and 19% smaller than those of the affine transformation method, the quadratic polynomial method, and the least-squares collocation algorithm, respectively, which demonstrates that the new method can be more effective at removing systematic biases in vendor-supplied RPCs.

The Performance of ML, GLS, and WLS Estimation in Structural Equation Modeling under Conditions of Misspecification and Nonnormality.

ERIC Educational Resources Information Center

Olsson, Ulf Henning; Foss, Tron; Troye, Sigurd V.; Howell, Roy D.

2000-01-01

Used simulation to demonstrate how the choice of estimation method affects indexes of fit and parameter bias for different sample sizes when nested models vary in terms of specification error and the data demonstrate different levels of kurtosis. Discusses results for maximum likelihood (ML), generalized least squares (GLS), and weighted least…

Numerical Technique for Analyzing Rotating Rake Mode Measurements in a Duct With Passive Treatment and Shear Flow

NASA Technical Reports Server (NTRS)

Dahl, Milo D.; Sutliff, Daniel L.

2007-01-01

A technique is presented for the analysis of measured data obtained from a rotating microphone rake system. The system is designed to measure the interaction modes of ducted fans. A Fourier analysis of the data from the rotating system results in a set of circumferential mode levels at each radial location of a microphone inside the duct. Radial basis functions are then least-squares fit to this data to obtain the radial mode amplitudes. For ducts with soft walls and mean flow, the radial basis functions must be numerically computed. The linear companion matrix method is used to obtain both the eigenvalues of interest, without an initial guess, and the radial basis functions. The governing equations allow for the mean flow to have a boundary layer at the wall. In addition, a nonlinear least-squares method is used to adjust the wall impedance to best fit the data in an attempt to use the rotating system as an in-duct wall impedance measurement tool. Simulated and measured data are used to show the effects of wall impedance and mean flow on the computed results.

Single-level resonance parameters fit nuclear cross-sections

NASA Technical Reports Server (NTRS)

Drawbaugh, D. W.; Gibson, G.; Miller, M.; Page, S. L.

1970-01-01

Least squares analyses of experimental differential cross-section data for the U-235 nucleus have yielded single level Breit-Wigner resonance parameters that fit, simultaneously, three nuclear cross sections of capture, fission, and total.

Two smart spectrophotometric methods for the simultaneous estimation of Simvastatin and Ezetimibe in combined dosage form

NASA Astrophysics Data System (ADS)

Magdy, Nancy; Ayad, Miriam F.

2015-02-01

Two simple, accurate, precise, sensitive and economic spectrophotometric methods were developed for the simultaneous determination of Simvastatin and Ezetimibe in fixed dose combination products without prior separation. The first method depends on a new chemometrics-assisted ratio spectra derivative method using moving window polynomial least square fitting method (Savitzky-Golay filters). The second method is based on a simple modification for the ratio subtraction method. The suggested methods were validated according to USP guidelines and can be applied for routine quality control testing.

A Novel Statistical Analysis and Interpretation of Flow Cytometry Data

DTIC Science & Technology

2013-07-05

ing parameters of the mathematical model are determined by using least squares to fit the data in Figures 1 and 2 (see Section 4). The second method is...variance (for all k and j). Then the AIC, which is the expected value of the relative Kullback – Leibler distance for a given model [16], is Kn = n log ( J...emphasized that the fit of the model is quite good for both donors and cell types. As such, we proceed to analyse the dynamic responsiveness of the

A new fitting method for measurement of the curvature radius of a short arc with high precision

NASA Astrophysics Data System (ADS)

Tao, Wei; Zhong, Hong; Chen, Xiao; Selami, Yassine; Zhao, Hui

2018-07-01

The measurement of an object with a short arc is widely encountered in scientific research and industrial production. As the most classic method of arc fitting, the least squares fitting method suffers from low precision when it is used for measurement of arcs with smaller central angles and fewer sampling points. The shorter the arc, the lower is the measurement accuracy. In order to improve the measurement precision of short arcs, a parameter constrained fitting method based on a four-parameter circle equation is proposed in this paper. The generalized Lagrange function was introduced together with the optimization by gradient descent method to reduce the influence from noise. The simulation and experimental results showed that the proposed method has high precision even when the central angle drops below 4° and it has good robustness when the noise standard deviation rises to 0.4 mm. This new fitting method is suitable for the high precision measurement of short arcs with smaller central angles without any prior information.

Kinetic analysis of hyperpolarized data with minimum a priori knowledge: Hybrid maximum entropy and nonlinear least squares method (MEM/NLS).

PubMed

Mariotti, Erika; Veronese, Mattia; Dunn, Joel T; Southworth, Richard; Eykyn, Thomas R

2015-06-01

To assess the feasibility of using a hybrid Maximum-Entropy/Nonlinear Least Squares (MEM/NLS) method for analyzing the kinetics of hyperpolarized dynamic data with minimum a priori knowledge. A continuous distribution of rates obtained through the Laplace inversion of the data is used as a constraint on the NLS fitting to derive a discrete spectrum of rates. Performance of the MEM/NLS algorithm was assessed through Monte Carlo simulations and validated by fitting the longitudinal relaxation time curves of hyperpolarized [1-(13) C] pyruvate acquired at 9.4 Tesla and at three different flip angles. The method was further used to assess the kinetics of hyperpolarized pyruvate-lactate exchange acquired in vitro in whole blood and to re-analyze the previously published in vitro reaction of hyperpolarized (15) N choline with choline kinase. The MEM/NLS method was found to be adequate for the kinetic characterization of hyperpolarized in vitro time-series. Additional insights were obtained from experimental data in blood as well as from previously published (15) N choline experimental data. The proposed method informs on the compartmental model that best approximate the biological system observed using hyperpolarized (13) C MR especially when the metabolic pathway assessed is complex or a new hyperpolarized probe is used. © 2014 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc.

Adaptive optics system performance approximations for atmospheric turbulence correction

NASA Astrophysics Data System (ADS)

Tyson, Robert K.

1990-10-01

Analysis of adaptive optics system behavior often can be reduced to a few approximations and scaling laws. For atmospheric turbulence correction, the deformable mirror (DM) fitting error is most often used to determine a priori the interactuator spacing and the total number of correction zones required. This paper examines the mirror fitting error in terms of its most commonly used exponential form. The explicit constant in the error term is dependent on deformable mirror influence function shape and actuator geometry. The method of least squares fitting of discrete influence functions to the turbulent wavefront is compared to the linear spatial filtering approximation of system performance. It is found that the spatial filtering method overstimates the correctability of the adaptive optics system by a small amount. By evaluating fitting error for a number of DM configurations, actuator geometries, and influence functions, fitting error constants verify some earlier investigations.

MRI quantification of diffusion and perfusion in bone marrow by intravoxel incoherent motion (IVIM) and non-negative least square (NNLS) analysis.

PubMed

Marchand, A J; Hitti, E; Monge, F; Saint-Jalmes, H; Guillin, R; Duvauferrier, R; Gambarota, G

2014-11-01

To assess the feasibility of measuring diffusion and perfusion fraction in vertebral bone marrow using the intravoxel incoherent motion (IVIM) approach and to compare two fitting methods, i.e., the non-negative least squares (NNLS) algorithm and the more commonly used Levenberg-Marquardt (LM) non-linear least squares algorithm, for the analysis of IVIM data. MRI experiments were performed on fifteen healthy volunteers, with a diffusion-weighted echo-planar imaging (EPI) sequence at five different b-values (0, 50, 100, 200, 600 s/mm2), in combination with an STIR module to suppress the lipid signal. Diffusion signal decays in the first lumbar vertebra (L1) were fitted to a bi-exponential function using the LM algorithm and further analyzed with the NNLS algorithm to calculate the values of the apparent diffusion coefficient (ADC), pseudo-diffusion coefficient (D*) and perfusion fraction. The NNLS analysis revealed two diffusion components only in seven out of fifteen volunteers, with ADC=0.60±0.09 (10(-3) mm(2)/s), D*=28±9 (10(-3) mm2/s) and perfusion fraction=14%±6%. The values obtained by the LM bi-exponential fit were: ADC=0.45±0.27 (10(-3) mm2/s), D*=63±145 (10(-3) mm2/s) and perfusion fraction=27%±17%. Furthermore, the LM algorithm yielded values of perfusion fraction in cases where the decay was not bi-exponential, as assessed by NNLS analysis. The IVIM approach allows for measuring diffusion and perfusion fraction in vertebral bone marrow; its reliability can be improved by using the NNLS, which identifies the diffusion decays that display a bi-exponential behavior. Copyright © 2014 Elsevier Inc. All rights reserved.

Paleotemperature reconstruction from mammalian phosphate δ18O records - an alternative view on data processing

NASA Astrophysics Data System (ADS)

Skrzypek, Grzegorz; Sadler, Rohan; Wiśniewski, Andrzej

2017-04-01

The stable oxygen isotope composition of phosphates (δ18O) extracted from mammalian bone and teeth material is commonly used as a proxy for paleotemperature. Historically, several different analytical and statistical procedures for determining air paleotemperatures from the measured δ18O of phosphates have been applied. This inconsistency in both stable isotope data processing and the application of statistical procedures has led to large and unwanted differences between calculated results. This study presents the uncertainty associated with two of the most commonly used regression methods: least squares inverted fit and transposed fit. We assessed the performance of these methods by designing and applying calculation experiments to multiple real-life data sets, calculating in reverse temperatures, and comparing them with true recorded values. Our calculations clearly show that the mean absolute errors are always substantially higher for the inverted fit (a causal model), with the transposed fit (a predictive model) returning mean values closer to the measured values (Skrzypek et al. 2015). The predictive models always performed better than causal models, with 12-65% lower mean absolute errors. Moreover, the least-squares regression (LSM) model is more appropriate than Reduced Major Axis (RMA) regression for calculating the environmental water stable oxygen isotope composition from phosphate signatures, as well as for calculating air temperature from the δ18O value of environmental water. The transposed fit introduces a lower overall error than the inverted fit for both the δ18O of environmental water and Tair calculations; therefore, the predictive models are more statistically efficient than the causal models in this instance. The direct comparison of paleotemperature results from different laboratories and studies may only be achieved if a single method of calculation is applied. Reference Skrzypek G., Sadler R., Wiśniewski A., 2016. Reassessment of recommendations for processing mammal phosphate δ18O data for paleotemperature reconstruction. Palaeogeography, Palaeoclimatology, Palaeoecology 446, 162-167.

Computer-assisted map projection research

USGS Publications Warehouse

Snyder, John Parr

1985-01-01

Computers have opened up areas of map projection research which were previously too complicated to utilize, for example, using a least-squares fit to a very large number of points. One application has been in the efficient transfer of data between maps on different projections. While the transfer of moderate amounts of data is satisfactorily accomplished using the analytical map projection formulas, polynomials are more efficient for massive transfers. Suitable coefficients for the polynomials may be determined more easily for general cases using least squares instead of Taylor series. A second area of research is in the determination of a map projection fitting an unlabeled map, so that accurate data transfer can take place. The computer can test one projection after another, and include iteration where required. A third area is in the use of least squares to fit a map projection with optimum parameters to the region being mapped, so that distortion is minimized. This can be accomplished for standard conformal, equalarea, or other types of projections. Even less distortion can result if complex transformations of conformal projections are utilized. This bulletin describes several recent applications of these principles, as well as historical usage and background.

Efficient generation of sum-of-products representations of high-dimensional potential energy surfaces based on multimode expansions

NASA Astrophysics Data System (ADS)

Ziegler, Benjamin; Rauhut, Guntram

2016-03-01

The transformation of multi-dimensional potential energy surfaces (PESs) from a grid-based multimode representation to an analytical one is a standard procedure in quantum chemical programs. Within the framework of linear least squares fitting, a simple and highly efficient algorithm is presented, which relies on a direct product representation of the PES and a repeated use of Kronecker products. It shows the same scalings in computational cost and memory requirements as the potfit approach. In comparison to customary linear least squares fitting algorithms, this corresponds to a speed-up and memory saving by several orders of magnitude. Different fitting bases are tested, namely, polynomials, B-splines, and distributed Gaussians. Benchmark calculations are provided for the PESs of a set of small molecules.

Efficient generation of sum-of-products representations of high-dimensional potential energy surfaces based on multimode expansions.

PubMed

Ziegler, Benjamin; Rauhut, Guntram

2016-03-21

The transformation of multi-dimensional potential energy surfaces (PESs) from a grid-based multimode representation to an analytical one is a standard procedure in quantum chemical programs. Within the framework of linear least squares fitting, a simple and highly efficient algorithm is presented, which relies on a direct product representation of the PES and a repeated use of Kronecker products. It shows the same scalings in computational cost and memory requirements as the potfit approach. In comparison to customary linear least squares fitting algorithms, this corresponds to a speed-up and memory saving by several orders of magnitude. Different fitting bases are tested, namely, polynomials, B-splines, and distributed Gaussians. Benchmark calculations are provided for the PESs of a set of small molecules.

How many spectral lines are statistically significant?

NASA Astrophysics Data System (ADS)

Freund, J.

When experimental line spectra are fitted with least squares techniques one frequently does not know whether n or n + 1 lines may be fitted safely. This paper shows how an F-test can be applied in order to determine the statistical significance of including an extra line into the fitting routine.

Computation of nonlinear least squares estimator and maximum likelihood using principles in matrix calculus

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Sankar, J. Ravi; Balasiddamuni, P.

2017-11-01

This paper uses matrix calculus techniques to obtain Nonlinear Least Squares Estimator (NLSE), Maximum Likelihood Estimator (MLE) and Linear Pseudo model for nonlinear regression model. David Pollard and Peter Radchenko [1] explained analytic techniques to compute the NLSE. However the present research paper introduces an innovative method to compute the NLSE using principles in multivariate calculus. This study is concerned with very new optimization techniques used to compute MLE and NLSE. Anh [2] derived NLSE and MLE of a heteroscedatistic regression model. Lemcoff [3] discussed a procedure to get linear pseudo model for nonlinear regression model. In this research article a new technique is developed to get the linear pseudo model for nonlinear regression model using multivariate calculus. The linear pseudo model of Edmond Malinvaud [4] has been explained in a very different way in this paper. David Pollard et.al used empirical process techniques to study the asymptotic of the LSE (Least-squares estimation) for the fitting of nonlinear regression function in 2006. In Jae Myung [13] provided a go conceptual for Maximum likelihood estimation in his work “Tutorial on maximum likelihood estimation

Unleashing Empirical Equations with "Nonlinear Fitting" and "GUM Tree Calculator"

NASA Astrophysics Data System (ADS)

Lovell-Smith, J. W.; Saunders, P.; Feistel, R.

2017-10-01

Empirical equations having large numbers of fitted parameters, such as the international standard reference equations published by the International Association for the Properties of Water and Steam (IAPWS), which form the basis of the "Thermodynamic Equation of Seawater—2010" (TEOS-10), provide the means to calculate many quantities very accurately. The parameters of these equations are found by least-squares fitting to large bodies of measurement data. However, the usefulness of these equations is limited since uncertainties are not readily available for most of the quantities able to be calculated, the covariance of the measurement data is not considered, and further propagation of the uncertainty in the calculated result is restricted since the covariance of calculated quantities is unknown. In this paper, we present two tools developed at MSL that are particularly useful in unleashing the full power of such empirical equations. "Nonlinear Fitting" enables propagation of the covariance of the measurement data into the parameters using generalized least-squares methods. The parameter covariance then may be published along with the equations. Then, when using these large, complex equations, "GUM Tree Calculator" enables the simultaneous calculation of any derived quantity and its uncertainty, by automatic propagation of the parameter covariance into the calculated quantity. We demonstrate these tools in exploratory work to determine and propagate uncertainties associated with the IAPWS-95 parameters.

Nonlinear Constitutive Modeling of Piezoelectric Ceramics

NASA Astrophysics Data System (ADS)

Xu, Jia; Li, Chao; Wang, Haibo; Zhu, Zhiwen

2017-12-01

Nonlinear constitutive modeling of piezoelectric ceramics is discussed in this paper. Van der Pol item is introduced to explain the simple hysteretic curve. Improved nonlinear difference items are used to interpret the hysteresis phenomena of piezoelectric ceramics. The fitting effect of the model on experimental data is proved by the partial least-square regression method. The results show that this method can describe the real curve well. The results of this paper are helpful to piezoelectric ceramics constitutive modeling.

Thermal conductivity of particulate materials: A summary of measurements taken at the Marshall Space Flight Center

NASA Technical Reports Server (NTRS)

Fountain, J. A.

1973-01-01

Thermal conductivity measurements of particulate materials in vacuum are presented in summary. Particulate basalt and soda lime glass beads of various size ranges were used as samples. The differentiated line heat source method was used for the measurements. A comprehensive table is shown giving all pertinent experimental conditions. Least-squares curve fits to the data are presented.

Distributed least-squares estimation of a remote chemical source via convex combination in wireless sensor networks.

PubMed

Cao, Meng-Li; Meng, Qing-Hao; Zeng, Ming; Sun, Biao; Li, Wei; Ding, Cheng-Jun

2014-06-27

This paper investigates the problem of locating a continuous chemical source using the concentration measurements provided by a wireless sensor network (WSN). Such a problem exists in various applications: eliminating explosives or drugs, detecting the leakage of noxious chemicals, etc. The limited power and bandwidth of WSNs have motivated collaborative in-network processing which is the focus of this paper. We propose a novel distributed least-squares estimation (DLSE) method to solve the chemical source localization (CSL) problem using a WSN. The DLSE method is realized by iteratively conducting convex combination of the locally estimated chemical source locations in a distributed manner. Performance assessments of our method are conducted using both simulations and real experiments. In the experiments, we propose a fitting method to identify both the release rate and the eddy diffusivity. The results show that the proposed DLSE method can overcome the negative interference of local minima and saddle points of the objective function, which would hinder the convergence of local search methods, especially in the case of locating a remote chemical source.

A novel method for improving the accuracy of coordinate transformation in multiple measurement systems

NASA Astrophysics Data System (ADS)

Liu, W. L.; Li, Y. W.

2017-09-01

Large-scale dimensional metrology usually requires a combination of multiple measurement systems, such as laser tracking, total station, laser scanning, coordinate measuring arm and video photogrammetry, etc. Often, the results from different measurement systems must be combined to provide useful results. The coordinate transformation is used to unify coordinate frames in combination; however, coordinate transformation uncertainties directly affect the accuracy of the final measurement results. In this paper, a novel method is proposed for improving the accuracy of coordinate transformation, combining the advantages of the best-fit least-square and radial basis function (RBF) neural networks. First of all, the configuration of coordinate transformation is introduced and a transformation matrix containing seven variables is obtained. Second, the 3D uncertainty of the transformation model and the residual error variable vector are established based on the best-fit least-square. Finally, in order to optimize the uncertainty of the developed seven-variable transformation model, we used the RBF neural network to identify the uncertainty of the dynamic, and unstructured, owing to its great ability to approximate any nonlinear function to the designed accuracy. Intensive experimental studies were conducted to check the validity of the theoretical results. The results show that the mean error of coordinate transformation decreased from 0.078 mm to 0.054 mm after using this method in contrast with the GUM method.

A fast iterative recursive least squares algorithm for Wiener model identification of highly nonlinear systems.

PubMed

Kazemi, Mahdi; Arefi, Mohammad Mehdi

2017-03-01

In this paper, an online identification algorithm is presented for nonlinear systems in the presence of output colored noise. The proposed method is based on extended recursive least squares (ERLS) algorithm, where the identified system is in polynomial Wiener form. To this end, an unknown intermediate signal is estimated by using an inner iterative algorithm. The iterative recursive algorithm adaptively modifies the vector of parameters of the presented Wiener model when the system parameters vary. In addition, to increase the robustness of the proposed method against variations, a robust RLS algorithm is applied to the model. Simulation results are provided to show the effectiveness of the proposed approach. Results confirm that the proposed method has fast convergence rate with robust characteristics, which increases the efficiency of the proposed model and identification approach. For instance, the FIT criterion will be achieved 92% in CSTR process where about 400 data is used. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Analysis of Learning Curve Fitting Techniques.

DTIC Science & Technology

1987-09-01

1986. 15. Neter, John and others. Applied Linear Regression Models. Homewood IL: Irwin, 19-33. 16. SAS User’s Guide: Basics, Version 5 Edition. SAS... Linear Regression Techniques (15:23-52). Random errors are assumed to be normally distributed when using -# ordinary least-squares, according to Johnston...lot estimated by the improvement curve formula. For a more detailed explanation of the ordinary least-squares technique, see Neter, et. al., Applied

Least-Squares Approximation of an Improper by a Proper Correlation Matrix Using a Semi-Infinite Convex Program. Research Report 87-7.

ERIC Educational Resources Information Center

Knol, Dirk L.; ten Berge, Jos M. F.

An algorithm is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. The proposed algorithm is based on a solution for C. I. Mosier's oblique Procrustes rotation problem offered by J. M. F. ten Berge and K. Nevels (1977). It is shown that the minimization problem…

On the calibration process of film dosimetry: OLS inverse regression versus WLS inverse prediction.

PubMed

Crop, F; Van Rompaye, B; Paelinck, L; Vakaet, L; Thierens, H; De Wagter, C

2008-07-21

The purpose of this study was both putting forward a statistically correct model for film calibration and the optimization of this process. A reliable calibration is needed in order to perform accurate reference dosimetry with radiographic (Gafchromic) film. Sometimes, an ordinary least squares simple linear (in the parameters) regression is applied to the dose-optical-density (OD) curve with the dose as a function of OD (inverse regression) or sometimes OD as a function of dose (inverse prediction). The application of a simple linear regression fit is an invalid method because heteroscedasticity of the data is not taken into account. This could lead to erroneous results originating from the calibration process itself and thus to a lower accuracy. In this work, we compare the ordinary least squares (OLS) inverse regression method with the correct weighted least squares (WLS) inverse prediction method to create calibration curves. We found that the OLS inverse regression method could lead to a prediction bias of up to 7.3 cGy at 300 cGy and total prediction errors of 3% or more for Gafchromic EBT film. Application of the WLS inverse prediction method resulted in a maximum prediction bias of 1.4 cGy and total prediction errors below 2% in a 0-400 cGy range. We developed a Monte-Carlo-based process to optimize calibrations, depending on the needs of the experiment. This type of thorough analysis can lead to a higher accuracy for film dosimetry.

Comparison of Response Surface Construction Methods for Derivative Estimation Using Moving Least Squares, Kriging and Radial Basis Functions

NASA Technical Reports Server (NTRS)

Krishnamurthy, Thiagarajan

2005-01-01

Response construction methods using Moving Least Squares (MLS), Kriging and Radial Basis Functions (RBF) are compared with the Global Least Squares (GLS) method in three numerical examples for derivative generation capability. Also, a new Interpolating Moving Least Squares (IMLS) method adopted from the meshless method is presented. It is found that the response surface construction methods using the Kriging and RBF interpolation yields more accurate results compared with MLS and GLS methods. Several computational aspects of the response surface construction methods also discussed.

Prediction of optimum sorption isotherm: comparison of linear and non-linear method.

PubMed

Kumar, K Vasanth; Sivanesan, S

2005-11-11

Equilibrium parameters for Bismarck brown onto rice husk were estimated by linear least square and a trial and error non-linear method using Freundlich, Langmuir and Redlich-Peterson isotherms. A comparison between linear and non-linear method of estimating the isotherm parameters was reported. The best fitting isotherm was Langmuir isotherm and Redlich-Peterson isotherm equation. The results show that non-linear method could be a better way to obtain the parameters. Redlich-Peterson isotherm is a special case of Langmuir isotherm when the Redlich-Peterson isotherm constant g was unity.

[Evaluation of uncertainty for determination of tin and its compounds in air of workplace by flame atomic absorption spectrometry].

PubMed

Wei, Qiuning; Wei, Yuan; Liu, Fangfang; Ding, Yalei

2015-10-01

To investigate the method for uncertainty evaluation of determination of tin and its compounds in the air of workplace by flame atomic absorption spectrometry. The national occupational health standards, GBZ/T160.28-2004 and JJF1059-1999, were used to build a mathematical model of determination of tin and its compounds in the air of workplace and to calculate the components of uncertainty. In determination of tin and its compounds in the air of workplace using flame atomic absorption spectrometry, the uncertainty for the concentration of the standard solution, atomic absorption spectrophotometer, sample digestion, parallel determination, least square fitting of the calibration curve, and sample collection was 0.436%, 0.13%, 1.07%, 1.65%, 3.05%, and 2.89%, respectively. The combined uncertainty was 9.3%.The concentration of tin in the test sample was 0.132 mg/m³, and the expanded uncertainty for the measurement was 0.012 mg/m³ (K=2). The dominant uncertainty for determination of tin and its compounds in the air of workplace comes from least squares fitting of the calibration curve and sample collection. Quality control should be improved in the process of calibration curve fitting and sample collection.

[Study on the detection of active ingredient contents of Paecilomyces hepiali mycelium via near infrared spectroscopy].

PubMed

Teng, Wei-Zhuo; Song, Jia; Meng, Fan-Xin; Meng, Qing-Fan; Lu, Jia-Hui; Hu, Shuang; Teng, Li-Rong; Wang, Di; Xie, Jing

2014-10-01

Partial least squares (PLS) and radial basis function neural network (RBFNN) combined with near infrared spectros- copy (NIR) were applied to develop models for cordycepic acid, polysaccharide and adenosine analysis in Paecilomyces hepialid fermentation mycelium. The developed models possess well generalization and predictive ability which can be applied for crude drugs and related productions determination. During the experiment, 214 Paecilomyces hepialid mycelium samples were obtained via chemical mutagenesis combined with submerged fermentation. The contents of cordycepic acid, polysaccharide and adenosine were determined via traditional methods and the near infrared spectroscopy data were collected. The outliers were removed and the numbers of calibration set were confirmed via Monte Carlo partial least square (MCPLS) method. Based on the values of degree of approach (Da), both moving window partial least squares (MWPLS) and moving window radial basis function neural network (MWRBFNN) were applied to optimize characteristic wavelength variables, optimum preprocessing methods and other important variables in the models. After comparison, the RBFNN, RBFNN and PLS models were developed successfully for cordycepic acid, polysaccharide and adenosine detection, and the correlation between reference values and predictive values in both calibration set (R2c) and validation set (R2p) of optimum models was 0.9417 and 0.9663, 0.9803 and 0.9850, and 0.9761 and 0.9728, respectively. All the data suggest that these models possess well fitness and predictive ability.

vFitness: a web-based computing tool for improving estimation of in vitro HIV-1 fitness experiments

PubMed Central

2010-01-01

Background The replication rate (or fitness) between viral variants has been investigated in vivo and in vitro for human immunodeficiency virus (HIV). HIV fitness plays an important role in the development and persistence of drug resistance. The accurate estimation of viral fitness relies on complicated computations based on statistical methods. This calls for tools that are easy to access and intuitive to use for various experiments of viral fitness. Results Based on a mathematical model and several statistical methods (least-squares approach and measurement error models), a Web-based computing tool has been developed for improving estimation of virus fitness in growth competition assays of human immunodeficiency virus type 1 (HIV-1). Conclusions Unlike the two-point calculation used in previous studies, the estimation here uses linear regression methods with all observed data in the competition experiment to more accurately estimate relative viral fitness parameters. The dilution factor is introduced for making the computational tool more flexible to accommodate various experimental conditions. This Web-based tool is implemented in C# language with Microsoft ASP.NET, and is publicly available on the Web at http://bis.urmc.rochester.edu/vFitness/. PMID:20482791

vFitness: a web-based computing tool for improving estimation of in vitro HIV-1 fitness experiments.

PubMed

Ma, Jingming; Dykes, Carrie; Wu, Tao; Huang, Yangxin; Demeter, Lisa; Wu, Hulin

2010-05-18

The replication rate (or fitness) between viral variants has been investigated in vivo and in vitro for human immunodeficiency virus (HIV). HIV fitness plays an important role in the development and persistence of drug resistance. The accurate estimation of viral fitness relies on complicated computations based on statistical methods. This calls for tools that are easy to access and intuitive to use for various experiments of viral fitness. Based on a mathematical model and several statistical methods (least-squares approach and measurement error models), a Web-based computing tool has been developed for improving estimation of virus fitness in growth competition assays of human immunodeficiency virus type 1 (HIV-1). Unlike the two-point calculation used in previous studies, the estimation here uses linear regression methods with all observed data in the competition experiment to more accurately estimate relative viral fitness parameters. The dilution factor is introduced for making the computational tool more flexible to accommodate various experimental conditions. This Web-based tool is implemented in C# language with Microsoft ASP.NET, and is publicly available on the Web at http://bis.urmc.rochester.edu/vFitness/.

Uranium, radium and thorium in soils with high-resolution gamma spectroscopy, MCNP-generated efficiencies, and VRF non-linear full-spectrum nuclide shape fitting

NASA Astrophysics Data System (ADS)

Metzger, Robert; Riper, Kenneth Van; Lasche, George

2017-09-01

A new method for analysis of uranium and radium in soils by gamma spectroscopy has been developed using VRF ("Visual RobFit") which, unlike traditional peak-search techniques, fits full-spectrum nuclide shapes with non-linear least-squares minimization of the chi-squared statistic. Gamma efficiency curves were developed for a 500 mL Marinelli beaker geometry as a function of soil density using MCNP. Collected spectra were then analyzed using the MCNP-generated efficiency curves and VRF to deconvolute the 90 keV peak complex of uranium and obtain 238U and 235U activities. 226Ra activity was determined either from the radon daughters if the equilibrium status is known, or directly from the deconvoluted 186 keV line. 228Ra values were determined from the 228Ac daughter activity. The method was validated by analysis of radium, thorium and uranium soil standards and by inter-comparison with other methods for radium in soils. The method allows for a rapid determination of whether a sample has been impacted by a man-made activity by comparison of the uranium and radium concentrations to those that would be expected from a natural equilibrium state.

A smoothing algorithm using cubic spline functions

NASA Technical Reports Server (NTRS)

Smith, R. E., Jr.; Price, J. M.; Howser, L. M.

1974-01-01

Two algorithms are presented for smoothing arbitrary sets of data. They are the explicit variable algorithm and the parametric variable algorithm. The former would be used where large gradients are not encountered because of the smaller amount of calculation required. The latter would be used if the data being smoothed were double valued or experienced large gradients. Both algorithms use a least-squares technique to obtain a cubic spline fit to the data. The advantage of the spline fit is that the first and second derivatives are continuous. This method is best used in an interactive graphics environment so that the junction values for the spline curve can be manipulated to improve the fit.

Modeling and Bayesian parameter estimation for shape memory alloy bending actuators

NASA Astrophysics Data System (ADS)

Crews, John H.; Smith, Ralph C.

2012-04-01

In this paper, we employ a homogenized energy model (HEM) for shape memory alloy (SMA) bending actuators. Additionally, we utilize a Bayesian method for quantifying parameter uncertainty. The system consists of a SMA wire attached to a flexible beam. As the actuator is heated, the beam bends, providing endoscopic motion. The model parameters are fit to experimental data using an ordinary least-squares approach. The uncertainty in the fit model parameters is then quantified using Markov Chain Monte Carlo (MCMC) methods. The MCMC algorithm provides bounds on the parameters, which will ultimately be used in robust control algorithms. One purpose of the paper is to test the feasibility of the Random Walk Metropolis algorithm, the MCMC method used here.

Objective scatterometer wind ambiguity removal using smoothness and dynamical constraints

NASA Technical Reports Server (NTRS)

Hoffman, R. N.

1984-01-01

In the present investigation, a variational analysis method (VAM) is used to remove the ambiguity of the Seasat-A Satellite Scatterometer (SASS) winds. At each SASS data point, two, three, or four wind vectors (termed ambiguities) are retrieved. It is pointed out that the VAM is basically a least squares method for fitting data. The problem may be nonlinear. The best fit to the data and constraints is obtained on the basis of a minimization of the objective function. The VAM was tested and tuned at 12 h GMT Sept. 10, 1978. Attention is given to a case study involving an intense cyclone centered south of Japan at 138 deg E.

The thermodynamic properties of nitrogen from 65 to 2000 K with pressures to 10,000 atmospheres. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Jacobsen, R. T.

1972-01-01

An equation of state is presented for liquid and gaseous nitrogen for temperatures from 65 degrees K to 2000 degrees K and pressures to 10,000 atmospheres. All the pressure-density-temperature data available from published literature have been corrected and applied to bring experimental temperatures into accord with the International Practical Temperature Scale of 1968. The coefficients of the equation of state were determined by a weighted least squares fit to selected published pressure-density-temperature data. The methods of weighting the various data for simultaneous fitting are presented and discussed.

Some applications of categorical data analysis to epidemiological studies.

PubMed Central

Grizzle, J E; Koch, G G

1979-01-01

Several examples of categorized data from epidemiological studies are analyzed to illustrate that more informative analysis than tests of independence can be performed by fitting models. All of the analyses fit into a unified conceptual framework that can be performed by weighted least squares. The methods presented show how to calculate point estimate of parameters, asymptotic variances, and asymptotically valid chi 2 tests. The examples presented are analysis of relative risks estimated from several 2 x 2 tables, analysis of selected features of life tables, construction of synthetic life tables from cross-sectional studies, and analysis of dose-response curves. PMID:540590

Determination of the neutron activation profile of core drill samples by gamma-ray spectrometry.

PubMed

Gurau, D; Boden, S; Sima, O; Stanga, D

2018-04-01

This paper provides guidance for determining the neutron activation profile of core drill samples taken from the biological shield of nuclear reactors using gamma spectrometry measurements. Thus, it provides guidance for selecting a model of the right form to fit data and using least squares methods for model fitting. The activity profiles of two core samples taken from the biological shield of a nuclear reactor were determined. The effective activation depth and the total activity of core samples along with their uncertainties were computed by Monte Carlo simulation. Copyright © 2017 Elsevier Ltd. All rights reserved.

Precise calibration of spatial phase response nonuniformity arising in liquid crystal on silicon.

PubMed

Xu, Jingquan; Qin, SiYi; Liu, Chen; Fu, Songnian; Liu, Deming

2018-06-15

In order to calibrate the spatial phase response nonuniformity of liquid crystal on silicon (LCoS), we propose to use a Twyman-Green interferometer to characterize the wavefront distortion, due to the inherent curvature of the device. During the characterization, both the residual carrier frequency introduced by the Fourier transform evaluation method and the lens aberration are error sources. For the tilted phase error introduced by residual carrier frequency, the least mean square fitting method is used to obtain the tilted phase error. Meanwhile, we use Zernike polynomials fitting based on plane mirror calibration to mitigate the lens aberration. For a typical LCoS with 1×12,288 pixels after calibration, the peak-to-valley value of the inherent wavefront distortion is approximately 0.25λ at 1550 nm, leading to a half-suppression of wavefront distortion. All efforts can suppress the root mean squares value of the inherent wavefront distortion to approximately λ/34.

A high order compact least-squares reconstructed discontinuous Galerkin method for the steady-state compressible flows on hybrid grids

NASA Astrophysics Data System (ADS)

Cheng, Jian; Zhang, Fan; Liu, Tiegang

2018-06-01

In this paper, a class of new high order reconstructed DG (rDG) methods based on the compact least-squares (CLS) reconstruction [23,24] is developed for simulating the two dimensional steady-state compressible flows on hybrid grids. The proposed method combines the advantages of the DG discretization with the flexibility of the compact least-squares reconstruction, which exhibits its superior potential in enhancing the level of accuracy and reducing the computational cost compared to the underlying DG methods with respect to the same number of degrees of freedom. To be specific, a third-order compact least-squares rDG(p1p2) method and a fourth-order compact least-squares rDG(p2p3) method are developed and investigated in this work. In this compact least-squares rDG method, the low order degrees of freedom are evolved through the underlying DG(p1) method and DG(p2) method, respectively, while the high order degrees of freedom are reconstructed through the compact least-squares reconstruction, in which the constitutive relations are built by requiring the reconstructed polynomial and its spatial derivatives on the target cell to conserve the cell averages and the corresponding spatial derivatives on the face-neighboring cells. The large sparse linear system resulted by the compact least-squares reconstruction can be solved relatively efficient when it is coupled with the temporal discretization in the steady-state simulations. A number of test cases are presented to assess the performance of the high order compact least-squares rDG methods, which demonstrates their potential to be an alternative approach for the high order numerical simulations of steady-state compressible flows.

Developing an Optical Lunar Occultation Measurement Reduction System for Observations at Kaau Observatory

NASA Astrophysics Data System (ADS)

Malawi, Abdulrahman A.

2013-06-01

We present here a detailed explanation of the reduction method that we use to determine the angular diameters of the stars occulted by the dark limb of the moon. This is a main part of the lunar occultation observation program running at King Abdul Aziz University observatory since late 1993. The process is based on the least square model fitting method of analyzing occultation data, first introduced by Nather et al. (Astron. J. 75:963, 1970).

A program for identification of linear systems

NASA Technical Reports Server (NTRS)

Buell, J.; Kalaba, R.; Ruspini, E.; Yakush, A.

1971-01-01

A program has been written for the identification of parameters in certain linear systems. These systems appear in biomedical problems, particularly in compartmental models of pharmacokinetics. The method presented here assumes that some of the state variables are regularly modified by jump conditions. This simulates administration of drugs following some prescribed drug regime. Parameters are identified by a least-square fit of the linear differential system to a set of experimental observations. The method is especially suited when the interval of observation of the system is very long.

Detection of Tetracycline in Milk using NIR Spectroscopy and Partial Least Squares

NASA Astrophysics Data System (ADS)

Wu, Nan; Xu, Chenshan; Yang, Renjie; Ji, Xinning; Liu, Xinyuan; Yang, Fan; Zeng, Ming

2018-02-01

The feasibility of measuring tetracycline in milk was investigated by near infrared (NIR) spectroscopic technique combined with partial least squares (PLS) method. The NIR transmittance spectra of 40 pure milk samples and 40 tetracycline adulterated milk samples with different concentrations (from 0.005 to 40 mg/L) were obtained. The pure milk and tetracycline adulterated milk samples were properly assigned to the categories with 100% accuracy in the calibration set, and the rate of correct classification of 96.3% was obtained in the prediction set. For the quantitation of tetracycline in adulterated milk, the root mean squares errors for calibration and prediction models were 0.61 mg/L and 4.22 mg/L, respectively. The PLS model had good fitting effect in calibration set, however its predictive ability was limited, especially for low tetracycline concentration samples. Totally, this approach can be considered as a promising tool for discrimination of tetracycline adulterated milk, as a supplement to high performance liquid chromatography.

Visual recognition system of cherry picking robot based on Lab color model

NASA Astrophysics Data System (ADS)

Zhang, Qirong; Zuo, Jianjun; Yu, Tingzhong; Wang, Yan

2017-12-01

This paper designs a visual recognition system suitable for cherry picking. First, the system deals with the image using the vector median filter. And then it extracts a channel of Lab color model to divide the cherries and the background. The cherry contour was successfully fitted by the least square method, and the centroid and radius of the cherry were extracted. Finally, the cherry was successfully extracted.

Least-Squares Self-Calibration of Imaging Array Data

NASA Technical Reports Server (NTRS)

Arendt, R. G.; Moseley, S. H.; Fixsen, D. J.

2004-01-01

When arrays are used to collect multiple appropriately-dithered images of the same region of sky, the resulting data set can be calibrated using a least-squares minimization procedure that determines the optimal fit between the data and a model of that data. The model parameters include the desired sky intensities as well as instrument parameters such as pixel-to-pixel gains and offsets. The least-squares solution simultaneously provides the formal error estimates for the model parameters. With a suitable observing strategy, the need for separate calibration observations is reduced or eliminated. We show examples of this calibration technique applied to HST NICMOS observations of the Hubble Deep Fields and simulated SIRTF IRAC observations.

Fitting aerodynamic forces in the Laplace domain: An application of a nonlinear nongradient technique to multilevel constrained optimization

NASA Technical Reports Server (NTRS)

Tiffany, S. H.; Adams, W. M., Jr.

1984-01-01

A technique which employs both linear and nonlinear methods in a multilevel optimization structure to best approximate generalized unsteady aerodynamic forces for arbitrary motion is described. Optimum selection of free parameters is made in a rational function approximation of the aerodynamic forces in the Laplace domain such that a best fit is obtained, in a least squares sense, to tabular data for purely oscillatory motion. The multilevel structure and the corresponding formulation of the objective models are presented which separate the reduction of the fit error into linear and nonlinear problems, thus enabling the use of linear methods where practical. Certain equality and inequality constraints that may be imposed are identified; a brief description of the nongradient, nonlinear optimizer which is used is given; and results which illustrate application of the method are presented.

Analytic solutions to modelling exponential and harmonic functions using Chebyshev polynomials: fitting frequency-domain lifetime images with photobleaching.

PubMed

Malachowski, George C; Clegg, Robert M; Redford, Glen I

2007-12-01

A novel approach is introduced for modelling linear dynamic systems composed of exponentials and harmonics. The method improves the speed of current numerical techniques up to 1000-fold for problems that have solutions of multiple exponentials plus harmonics and decaying components. Such signals are common in fluorescence microscopy experiments. Selective constraints of the parameters being fitted are allowed. This method, using discrete Chebyshev transforms, will correctly fit large volumes of data using a noniterative, single-pass routine that is fast enough to analyse images in real time. The method is applied to fluorescence lifetime imaging data in the frequency domain with varying degrees of photobleaching over the time of total data acquisition. The accuracy of the Chebyshev method is compared to a simple rapid discrete Fourier transform (equivalent to least-squares fitting) that does not take the photobleaching into account. The method can be extended to other linear systems composed of different functions. Simulations are performed and applications are described showing the utility of the method, in particular in the area of fluorescence microscopy.

General Methods for Analysis of Sequential “n-step” Kinetic Mechanisms: Application to Single Turnover Kinetics of Helicase-Catalyzed DNA Unwinding

PubMed Central

Lucius, Aaron L.; Maluf, Nasib K.; Fischer, Christopher J.; Lohman, Timothy M.

2003-01-01

Helicase-catalyzed DNA unwinding is often studied using “all or none” assays that detect only the final product of fully unwound DNA. Even using these assays, quantitative analysis of DNA unwinding time courses for DNA duplexes of different lengths, L, using “n-step” sequential mechanisms, can reveal information about the number of intermediates in the unwinding reaction and the “kinetic step size”, m, defined as the average number of basepairs unwound between two successive rate limiting steps in the unwinding cycle. Simultaneous nonlinear least-squares analysis using “n-step” sequential mechanisms has previously been limited by an inability to float the number of “unwinding steps”, n, and m, in the fitting algorithm. Here we discuss the behavior of single turnover DNA unwinding time courses and describe novel methods for nonlinear least-squares analysis that overcome these problems. Analytic expressions for the time courses, fss(t), when obtainable, can be written using gamma and incomplete gamma functions. When analytic expressions are not obtainable, the numerical solution of the inverse Laplace transform can be used to obtain fss(t). Both methods allow n and m to be continuous fitting parameters. These approaches are generally applicable to enzymes that translocate along a lattice or require repetition of a series of steps before product formation. PMID:14507688

General methods for analysis of sequential "n-step" kinetic mechanisms: application to single turnover kinetics of helicase-catalyzed DNA unwinding.

PubMed

Lucius, Aaron L; Maluf, Nasib K; Fischer, Christopher J; Lohman, Timothy M

2003-10-01

Helicase-catalyzed DNA unwinding is often studied using "all or none" assays that detect only the final product of fully unwound DNA. Even using these assays, quantitative analysis of DNA unwinding time courses for DNA duplexes of different lengths, L, using "n-step" sequential mechanisms, can reveal information about the number of intermediates in the unwinding reaction and the "kinetic step size", m, defined as the average number of basepairs unwound between two successive rate limiting steps in the unwinding cycle. Simultaneous nonlinear least-squares analysis using "n-step" sequential mechanisms has previously been limited by an inability to float the number of "unwinding steps", n, and m, in the fitting algorithm. Here we discuss the behavior of single turnover DNA unwinding time courses and describe novel methods for nonlinear least-squares analysis that overcome these problems. Analytic expressions for the time courses, f(ss)(t), when obtainable, can be written using gamma and incomplete gamma functions. When analytic expressions are not obtainable, the numerical solution of the inverse Laplace transform can be used to obtain f(ss)(t). Both methods allow n and m to be continuous fitting parameters. These approaches are generally applicable to enzymes that translocate along a lattice or require repetition of a series of steps before product formation.

The influence of a time-varying least squares parametric model when estimating SFOAEs evoked with swept-frequency tones

NASA Astrophysics Data System (ADS)

Hajicek, Joshua J.; Selesnick, Ivan W.; Henin, Simon; Talmadge, Carrick L.; Long, Glenis R.

2018-05-01

Stimulus frequency otoacoustic emissions (SFOAEs) were evoked and estimated using swept-frequency tones with and without the use of swept suppressor tones. SFOAEs were estimated using a least-squares fitting procedure. The estimated SFOAEs for the two paradigms (with- and without-suppression) were similar in amplitude and phase. The fitting procedure minimizes the square error between a parametric model of total ear-canal pressure (with unknown amplitudes and phases) and ear-canal pressure acquired during each paradigm. Modifying the parametric model to allow SFOAE amplitude and phase to vary over time revealed additional amplitude and phase fine structure in the without-suppressor, but not the with-suppressor paradigm. The use of a time-varying parametric model to estimate SFOAEs without-suppression may provide additional information about cochlear mechanics not available when using a with-suppressor paradigm.

Optimal measurement of ice-sheet deformation from surface-marker arrays

NASA Astrophysics Data System (ADS)

Macayeal, D. R.

Surface strain rate is best observed by fitting a strain-rate ellipsoid to the measured movement of a stake network or other collection of surface features, using a least squares procedure. Error of the resulting fit varies as 1/(L delta t square root of N), where L is the stake separation, delta is the time period between initial and final stake survey, and n is the number of stakes in the network. This relation suggests that if n is sufficiently high, the traditional practice of revisiting stake-network sites on successive field seasons may be replaced by a less costly single year operation. A demonstration using Ross Ice Shelf data shows that reasonably accurate measurements are obtained from 12 stakes after only 4 days of deformation. It is possible for the least squares procedure to aid airborne photogrammetric surveys because reducing the time interval between survey and re-survey permits better surface feature recognition.

Three-Dimensional Surface Parameters and Multi-Fractal Spectrum of Corroded Steel

PubMed Central

Shanhua, Xu; Songbo, Ren; Youde, Wang

2015-01-01

To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the multi-fractal spectrum of corroded steel surface, the least squares method was applied to the quadratic fitting of the multi-fractal spectrum of corroded surface. The fitting function was quantitatively analyzed to simplify the calculation of multi-fractal characteristics of corroded surface. The results showed that the multi-fractal spectrum of corroded surface was fitted well with the method using quadratic curve fitting, and the evolution rules and trends were forecasted accurately. The findings can be applied to research on the mechanisms of corroded surface formation of steel and provide a new approach for the establishment of corrosion damage constitutive models of steel. PMID:26121468

A step-by-step guide to non-linear regression analysis of experimental data using a Microsoft Excel spreadsheet.

PubMed

Brown, A M

2001-06-01

The objective of this present study was to introduce a simple, easily understood method for carrying out non-linear regression analysis based on user input functions. While it is relatively straightforward to fit data with simple functions such as linear or logarithmic functions, fitting data with more complicated non-linear functions is more difficult. Commercial specialist programmes are available that will carry out this analysis, but these programmes are expensive and are not intuitive to learn. An alternative method described here is to use the SOLVER function of the ubiquitous spreadsheet programme Microsoft Excel, which employs an iterative least squares fitting routine to produce the optimal goodness of fit between data and function. The intent of this paper is to lead the reader through an easily understood step-by-step guide to implementing this method, which can be applied to any function in the form y=f(x), and is well suited to fast, reliable analysis of data in all fields of biology.

Three-Dimensional Surface Parameters and Multi-Fractal Spectrum of Corroded Steel.

PubMed

Shanhua, Xu; Songbo, Ren; Youde, Wang

2015-01-01

To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the multi-fractal spectrum of corroded steel surface, the least squares method was applied to the quadratic fitting of the multi-fractal spectrum of corroded surface. The fitting function was quantitatively analyzed to simplify the calculation of multi-fractal characteristics of corroded surface. The results showed that the multi-fractal spectrum of corroded surface was fitted well with the method using quadratic curve fitting, and the evolution rules and trends were forecasted accurately. The findings can be applied to research on the mechanisms of corroded surface formation of steel and provide a new approach for the establishment of corrosion damage constitutive models of steel.

On the analytical determination of relaxation modulus of viscoelastic materials by Prony's interpolation method

NASA Technical Reports Server (NTRS)

Rodriguez, Pedro I.

1986-01-01

A computer implementation to Prony's curve fitting by exponential functions is presented. The method, although more than one hundred years old, has not been utilized to its fullest capabilities due to the restriction that the time range must be given in equal increments in order to obtain the best curve fit for a given set of data. The procedure used in this paper utilizes the 3-dimensional capabilities of the Interactive Graphics Design System (I.G.D.S.) in order to obtain the equal time increments. The resultant information is then input into a computer program that solves directly for the exponential constants yielding the best curve fit. Once the exponential constants are known, a simple least squares solution can be applied to obtain the final form of the equation.

Prediction of Therapy Tumor-Absorbed Dose Estimates in I-131 Radioimmunotherapy Using Tracer Data Via a Mixed-Model Fit to Time Activity

PubMed Central

Koral, Kenneth F.; Avram, Anca M.; Kaminski, Mark S.; Dewaraja, Yuni K.

2012-01-01

Abstract Background For individualized treatment planning in radioimmunotherapy (RIT), correlations must be established between tracer-predicted and therapy-delivered absorbed doses. The focus of this work was to investigate this correlation for tumors. Methods The study analyzed 57 tumors in 19 follicular lymphoma patients treated with I-131 tositumomab and imaged with SPECT/CT multiple times after tracer and therapy administrations. Instead of the typical least-squares fit to a single tumor's measured time-activity data, estimation was accomplished via a biexponential mixed model in which the curves from multiple subjects were jointly estimated. The tumor-absorbed dose estimates were determined by patient-specific Monte Carlo calculation. Results The mixed model gave realistic tumor time-activity fits that showed the expected uptake and clearance phases even with noisy data or missing time points. Correlation between tracer and therapy tumor-residence times (r=0.98; p<0.0001) and correlation between tracer-predicted and therapy-delivered mean tumor-absorbed doses (r=0.86; p<0.0001) were very high. The predicted and delivered absorbed doses were within±25% (or within±75 cGy) for 80% of tumors. Conclusions The mixed-model approach is feasible for fitting tumor time-activity data in RIT treatment planning when individual least-squares fitting is not possible due to inadequate sampling points. The good correlation between predicted and delivered tumor doses demonstrates the potential of using a pretherapy tracer study for tumor dosimetry-based treatment planning in RIT. PMID:22947086

Stochastic growth logistic model with aftereffect for batch fermentation process

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah

2014-06-19

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

Stochastic growth logistic model with aftereffect for batch fermentation process

NASA Astrophysics Data System (ADS)

Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md

2014-06-01

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

Bootstrapping Least Squares Estimates in Biochemical Reaction Networks

PubMed Central

Linder, Daniel F.

2015-01-01

The paper proposes new computational methods of computing confidence bounds for the least squares estimates (LSEs) of rate constants in mass-action biochemical reaction network and stochastic epidemic models. Such LSEs are obtained by fitting the set of deterministic ordinary differential equations (ODEs), corresponding to the large volume limit of a reaction network, to network’s partially observed trajectory treated as a continuous-time, pure jump Markov process. In the large volume limit the LSEs are asymptotically Gaussian, but their limiting covariance structure is complicated since it is described by a set of nonlinear ODEs which are often ill-conditioned and numerically unstable. The current paper considers two bootstrap Monte-Carlo procedures, based on the diffusion and linear noise approximations for pure jump processes, which allow one to avoid solving the limiting covariance ODEs. The results are illustrated with both in-silico and real data examples from the LINE 1 gene retrotranscription model and compared with those obtained using other methods. PMID:25898769

A method to estimate statistical errors of properties derived from charge-density modelling

PubMed Central

Lecomte, Claude

2018-01-01

Estimating uncertainties of property values derived from a charge-density model is not straightforward. A methodology, based on calculation of sample standard deviations (SSD) of properties using randomly deviating charge-density models, is proposed with the MoPro software. The parameter shifts applied in the deviating models are generated in order to respect the variance–covariance matrix issued from the least-squares refinement. This ‘SSD methodology’ procedure can be applied to estimate uncertainties of any property related to a charge-density model obtained by least-squares fitting. This includes topological properties such as critical point coordinates, electron density, Laplacian and ellipticity at critical points and charges integrated over atomic basins. Errors on electrostatic potentials and interaction energies are also available now through this procedure. The method is exemplified with the charge density of compound (E)-5-phenylpent-1-enylboronic acid, refined at 0.45 Å resolution. The procedure is implemented in the freely available MoPro program dedicated to charge-density refinement and modelling. PMID:29724964

A Simulated Annealing based Optimization Algorithm for Automatic Variogram Model Fitting

NASA Astrophysics Data System (ADS)

Soltani-Mohammadi, Saeed; Safa, Mohammad

2016-09-01

Fitting a theoretical model to an experimental variogram is an important issue in geostatistical studies because if the variogram model parameters are tainted with uncertainty, the latter will spread in the results of estimations and simulations. Although the most popular fitting method is fitting by eye, in some cases use is made of the automatic fitting method on the basis of putting together the geostatistical principles and optimization techniques to: 1) provide a basic model to improve fitting by eye, 2) fit a model to a large number of experimental variograms in a short time, and 3) incorporate the variogram related uncertainty in the model fitting. Effort has been made in this paper to improve the quality of the fitted model by improving the popular objective function (weighted least squares) in the automatic fitting. Also, since the variogram model function (£) and number of structures (m) too affect the model quality, a program has been provided in the MATLAB software that can present optimum nested variogram models using the simulated annealing method. Finally, to select the most desirable model from among the single/multi-structured fitted models, use has been made of the cross-validation method, and the best model has been introduced to the user as the output. In order to check the capability of the proposed objective function and the procedure, 3 case studies have been presented.

A high resolution spectroscopic study of the oxygen molecule. Ph.D. Thesis Final Report

NASA Technical Reports Server (NTRS)

Ritter, K. J.

1984-01-01

A high resolution spectrometer which incorporates a narrow line width tunable dye laser was used to make absorption profiles of 57 spectral lines in the Oxygen A-Band at pressures up to one atmosphere in pure O2. The observed line profiles are compared to the Voigt, and a collisionally narrowed, profile using a least squares fitting procedure. The collisionally narrowed profile compares more favorable to the observed profiles. Values of the line strengths and self broadening coeffiencients, determined from the least square fitting process, are presented in tabular form. It is found that the experssion by Watson are in closest agreement with the experimentally determined strengths. The self broadening coefficients are compared with the measurements of several other investigators.

The covariance matrix for the solution vector of an equality-constrained least-squares problem

NASA Technical Reports Server (NTRS)

Lawson, C. L.

1976-01-01

Methods are given for computing the covariance matrix for the solution vector of an equality-constrained least squares problem. The methods are matched to the solution algorithms given in the book, 'Solving Least Squares Problems.'

Artificial neural network and classical least-squares methods for neurotransmitter mixture analysis.

PubMed

Schulze, H G; Greek, L S; Gorzalka, B B; Bree, A V; Blades, M W; Turner, R F

1995-02-01

Identification of individual components in biological mixtures can be a difficult problem regardless of the analytical method employed. In this work, Raman spectroscopy was chosen as a prototype analytical method due to its inherent versatility and applicability to aqueous media, making it useful for the study of biological samples. Artificial neural networks (ANNs) and the classical least-squares (CLS) method were used to identify and quantify the Raman spectra of the small-molecule neurotransmitters and mixtures of such molecules. The transfer functions used by a network, as well as the architecture of a network, played an important role in the ability of the network to identify the Raman spectra of individual neurotransmitters and the Raman spectra of neurotransmitter mixtures. Specifically, networks using sigmoid and hyperbolic tangent transfer functions generalized better from the mixtures in the training data set to those in the testing data sets than networks using sine functions. Networks with connections that permit the local processing of inputs generally performed better than other networks on all the testing data sets. and better than the CLS method of curve fitting, on novel spectra of some neurotransmitters. The CLS method was found to perform well on noisy, shifted, and difference spectra.

Wing Shape Sensing from Measured Strain

NASA Technical Reports Server (NTRS)

Pak, Chan-Gi

2015-01-01

A new two step theory is investigated for predicting the deflection and slope of an entire structure using strain measurements at discrete locations. In the first step, a measured strain is fitted using a piecewise least squares curve fitting method together with the cubic spline technique. These fitted strains are integrated twice to obtain deflection data along the fibers. In the second step, computed deflection along the fibers are combined with a finite element model of the structure in order to extrapolate the deflection and slope of the entire structure through the use of System Equivalent Reduction and Expansion Process. The theory is first validated on a computational model, a cantilevered rectangular wing. It is then applied to test data from a cantilevered swept wing model.

MIA analysis of FPGA BPMs and beam optics at APS

NASA Astrophysics Data System (ADS)

Ji, Da-Heng; Wang, Chun-Xi; Qin, Qing

2012-11-01

Model independent analysis, which was developed for high precision and fast beam dynamics analysis, is a promising diagnostic tool for modern accelerators. We implemented a series of methods to analyze the turn-by-turn BPM data. Green's functions corresponding to the local transfer matrix elements R12 or R34 are extracted from BPM data and fitted with the model lattice using least-square fitting. Here, we report experimental results obtained from analyzing the transverse motion of a beam in the storage ring at the Advanced Photon Source. BPM gains and uncoupled optics parameters are successfully determined. Quadrupole strengths are adjusted for fitting but can not be uniquely determined in general due to an insufficient number of BPMs.

40 CFR 1051.243 - How do I determine deterioration factors from exhaust durability testing?

Code of Federal Regulations, 2011 CFR

2011-07-01

... measure emissions at three or more points, use a linear least-squares fit of your test data for each... points. (2) Operate the vehicle or engine over a representative duty cycle for a period at least as long...

40 CFR 1051.243 - How do I determine deterioration factors from exhaust durability testing?

Code of Federal Regulations, 2014 CFR

2014-07-01

... measure emissions at three or more points, use a linear least-squares fit of your test data for each... points. (2) Operate the vehicle or engine over a representative duty cycle for a period at least as long...

40 CFR 1051.243 - How do I determine deterioration factors from exhaust durability testing?

Code of Federal Regulations, 2012 CFR

2012-07-01

... measure emissions at three or more points, use a linear least-squares fit of your test data for each... points. (2) Operate the vehicle or engine over a representative duty cycle for a period at least as long...

40 CFR 1051.243 - How do I determine deterioration factors from exhaust durability testing?

Code of Federal Regulations, 2013 CFR

2013-07-01

... measure emissions at three or more points, use a linear least-squares fit of your test data for each... points. (2) Operate the vehicle or engine over a representative duty cycle for a period at least as long...

nmrfit

DOE Office of Scientific and Technical Information (OSTI.GOV)

2017-09-01

Nmrfit reads the output from a nuclear magnetic resonance (NMR) experiment and, through a number of intuitive API calls, produces a least-squares fit of Voigt-function approximations via particle swarm optimization.

40 CFR 89.319 - Hydrocarbon analyzer calibration.

Code of Federal Regulations, 2013 CFR

2013-07-01

... each range calibrated, if the deviation from a least-squares best-fit straight line is 2 percent or... ±0.3 percent of full scale on the zero, the best-fit non-linear equation which represents the data to within these limits shall be used to determine concentration. (d) Oxygen interference optimization...

40 CFR 89.319 - Hydrocarbon analyzer calibration.

Code of Federal Regulations, 2014 CFR

2014-07-01

... each range calibrated, if the deviation from a least-squares best-fit straight line is 2 percent or... ±0.3 percent of full scale on the zero, the best-fit non-linear equation which represents the data to within these limits shall be used to determine concentration. (d) Oxygen interference optimization...

40 CFR 89.319 - Hydrocarbon analyzer calibration.

Code of Federal Regulations, 2012 CFR

2012-07-01

... each range calibrated, if the deviation from a least-squares best-fit straight line is 2 percent or... ±0.3 percent of full scale on the zero, the best-fit non-linear equation which represents the data to within these limits shall be used to determine concentration. (d) Oxygen interference optimization...

40 CFR 89.320 - Carbon monoxide analyzer calibration.

Code of Federal Regulations, 2014 CFR

2014-07-01

... monoxide as described in this section. (b) Initial and periodic interference check. Prior to its... engineering practice. For each range calibrated, if the deviation from a least-squares best-fit straight line... range. If the deviation exceeds these limits, the best-fit non-linear equation which represents the data...

40 CFR 89.320 - Carbon monoxide analyzer calibration.

Code of Federal Regulations, 2013 CFR

2013-07-01

... monoxide as described in this section. (b) Initial and periodic interference check. Prior to its... engineering practice. For each range calibrated, if the deviation from a least-squares best-fit straight line... range. If the deviation exceeds these limits, the best-fit non-linear equation which represents the data...

40 CFR 89.320 - Carbon monoxide analyzer calibration.

Code of Federal Regulations, 2012 CFR

2012-07-01

... monoxide as described in this section. (b) Initial and periodic interference check. Prior to its... engineering practice. For each range calibrated, if the deviation from a least-squares best-fit straight line... range. If the deviation exceeds these limits, the best-fit non-linear equation which represents the data...

40 CFR 89.320 - Carbon monoxide analyzer calibration.

Code of Federal Regulations, 2011 CFR

2011-07-01

... monoxide as described in this section. (b) Initial and periodic interference check. Prior to its... engineering practice. For each range calibrated, if the deviation from a least-squares best-fit straight line... range. If the deviation exceeds these limits, the best-fit non-linear equation which represents the data...

A method for generating reduced-order combustion mechanisms that satisfy the differential entropy inequality

NASA Astrophysics Data System (ADS)

Ream, Allen E.; Slattery, John C.; Cizmas, Paul G. A.

2018-04-01

This paper presents a new method for determining the Arrhenius parameters of a reduced chemical mechanism such that it satisfies the second law of thermodynamics. The strategy is to approximate the progress of each reaction in the reduced mechanism from the species production rates of a detailed mechanism by using a linear least squares method. A series of non-linear least squares curve fittings are then carried out to find the optimal Arrhenius parameters for each reaction. At this step, the molar rates of production are written such that they comply with a theorem that provides the sufficient conditions for satisfying the second law of thermodynamics. This methodology was used to modify the Arrhenius parameters for the Westbrook and Dryer two-step mechanism and the Peters and Williams three-step mechanism for methane combustion. Both optimized mechanisms showed good agreement with the detailed mechanism for species mole fractions and production rates of most major species. Both optimized mechanisms showed significant improvement over previous mechanisms in minor species production rate prediction. Both optimized mechanisms produced no violations of the second law of thermodynamics.

An optimization approach for fitting canonical tensor decompositions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dunlavy, Daniel M.; Acar, Evrim; Kolda, Tamara Gibson

Tensor decompositions are higher-order analogues of matrix decompositions and have proven to be powerful tools for data analysis. In particular, we are interested in the canonical tensor decomposition, otherwise known as the CANDECOMP/PARAFAC decomposition (CPD), which expresses a tensor as the sum of component rank-one tensors and is used in a multitude of applications such as chemometrics, signal processing, neuroscience, and web analysis. The task of computing the CPD, however, can be difficult. The typical approach is based on alternating least squares (ALS) optimization, which can be remarkably fast but is not very accurate. Previously, nonlinear least squares (NLS) methodsmore » have also been recommended; existing NLS methods are accurate but slow. In this paper, we propose the use of gradient-based optimization methods. We discuss the mathematical calculation of the derivatives and further show that they can be computed efficiently, at the same cost as one iteration of ALS. Computational experiments demonstrate that the gradient-based optimization methods are much more accurate than ALS and orders of magnitude faster than NLS.« less

Adaptive Modal Identification for Flutter Suppression Control

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Drew, Michael; Swei, Sean S.

2016-01-01

In this paper, we will develop an adaptive modal identification method for identifying the frequencies and damping of a flutter mode based on model-reference adaptive control (MRAC) and least-squares methods. The least-squares parameter estimation will achieve parameter convergence in the presence of persistent excitation whereas the MRAC parameter estimation does not guarantee parameter convergence. Two adaptive flutter suppression control approaches are developed: one based on MRAC and the other based on the least-squares method. The MRAC flutter suppression control is designed as an integral part of the parameter estimation where the feedback signal is used to estimate the modal information. On the other hand, the separation principle of control and estimation is applied to the least-squares method. The least-squares modal identification is used to perform parameter estimation.

Determining the refractive index and thickness of thin films from prism coupler measurements

NASA Technical Reports Server (NTRS)

Kirsch, S. T.

1981-01-01

A simple method of determining thin film parameters from mode indices measured using a prism coupler is described. The problem is reduced to doing two least squares straight line fits through measured mode indices vs effective mode number. The slope and y intercept of the line are simply related to the thickness and refractive index of film, respectively. The approach takes into account the correlation between as well as the uncertainty in the individual measurements from all sources of error to give precise error tolerances on the best fit values. Due to the precision of the tolerances, anisotropic films can be identified and characterized.

Least-squares collocation meshless approach for radiative heat transfer in absorbing and scattering media

NASA Astrophysics Data System (ADS)

Liu, L. H.; Tan, J. Y.

2007-02-01

A least-squares collocation meshless method is employed for solving the radiative heat transfer in absorbing, emitting and scattering media. The least-squares collocation meshless method for radiative transfer is based on the discrete ordinates equation. A moving least-squares approximation is applied to construct the trial functions. Except for the collocation points which are used to construct the trial functions, a number of auxiliary points are also adopted to form the total residuals of the problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of residuals of all collocation and auxiliary points. Three numerical examples are studied to illustrate the performance of this new solution method. The numerical results are compared with the other benchmark approximate solutions. By comparison, the results show that the least-squares collocation meshless method is efficient, accurate and stable, and can be used for solving the radiative heat transfer in absorbing, emitting and scattering media.

Spatial Prediction and Optimized Sampling Design for Sodium Concentration in Groundwater

PubMed Central

Shabbir, Javid; M. AbdEl-Salam, Nasser; Hussain, Tajammal

2016-01-01

Sodium is an integral part of water, and its excessive amount in drinking water causes high blood pressure and hypertension. In the present paper, spatial distribution of sodium concentration in drinking water is modeled and optimized sampling designs for selecting sampling locations is calculated for three divisions in Punjab, Pakistan. Universal kriging and Bayesian universal kriging are used to predict the sodium concentrations. Spatial simulated annealing is used to generate optimized sampling designs. Different estimation methods (i.e., maximum likelihood, restricted maximum likelihood, ordinary least squares, and weighted least squares) are used to estimate the parameters of the variogram model (i.e, exponential, Gaussian, spherical and cubic). It is concluded that Bayesian universal kriging fits better than universal kriging. It is also observed that the universal kriging predictor provides minimum mean universal kriging variance for both adding and deleting locations during sampling design. PMID:27683016

Prediction of clinical depression scores and detection of changes in whole-brain using resting-state functional MRI data with partial least squares regression

PubMed Central

Shimizu, Yu; Yoshimoto, Junichiro; Takamura, Masahiro; Okada, Go; Okamoto, Yasumasa; Yamawaki, Shigeto; Doya, Kenji

2017-01-01

In diagnostic applications of statistical machine learning methods to brain imaging data, common problems include data high-dimensionality and co-linearity, which often cause over-fitting and instability. To overcome these problems, we applied partial least squares (PLS) regression to resting-state functional magnetic resonance imaging (rs-fMRI) data, creating a low-dimensional representation that relates symptoms to brain activity and that predicts clinical measures. Our experimental results, based upon data from clinically depressed patients and healthy controls, demonstrated that PLS and its kernel variants provided significantly better prediction of clinical measures than ordinary linear regression. Subsequent classification using predicted clinical scores distinguished depressed patients from healthy controls with 80% accuracy. Moreover, loading vectors for latent variables enabled us to identify brain regions relevant to depression, including the default mode network, the right superior frontal gyrus, and the superior motor area. PMID:28700672

The comparison of robust partial least squares regression with robust principal component regression on a real

NASA Astrophysics Data System (ADS)

Polat, Esra; Gunay, Suleyman

2013-10-01

One of the problems encountered in Multiple Linear Regression (MLR) is multicollinearity, which causes the overestimation of the regression parameters and increase of the variance of these parameters. Hence, in case of multicollinearity presents, biased estimation procedures such as classical Principal Component Regression (CPCR) and Partial Least Squares Regression (PLSR) are then performed. SIMPLS algorithm is the leading PLSR algorithm because of its speed, efficiency and results are easier to interpret. However, both of the CPCR and SIMPLS yield very unreliable results when the data set contains outlying observations. Therefore, Hubert and Vanden Branden (2003) have been presented a robust PCR (RPCR) method and a robust PLSR (RPLSR) method called RSIMPLS. In RPCR, firstly, a robust Principal Component Analysis (PCA) method for high-dimensional data on the independent variables is applied, then, the dependent variables are regressed on the scores using a robust regression method. RSIMPLS has been constructed from a robust covariance matrix for high-dimensional data and robust linear regression. The purpose of this study is to show the usage of RPCR and RSIMPLS methods on an econometric data set, hence, making a comparison of two methods on an inflation model of Turkey. The considered methods have been compared in terms of predictive ability and goodness of fit by using a robust Root Mean Squared Error of Cross-validation (R-RMSECV), a robust R2 value and Robust Component Selection (RCS) statistic.

On the Least-Squares Fitting of Slater-Type Orbitals with Gaussians: Reproduction of the STO-NG Fits Using Microsoft Excel and Maple

ERIC Educational Resources Information Center

Pye, Cory C.; Mercer, Colin J.

2012-01-01

The symbolic algebra program Maple and the spreadsheet Microsoft Excel were used in an attempt to reproduce the Gaussian fits to a Slater-type orbital, required to construct the popular STO-NG basis sets. The successes and pitfalls encountered in such an approach are chronicled. (Contains 1 table and 3 figures.)

Study on creep behavior of Grade 91 heat-resistant steel using theta projection method

NASA Astrophysics Data System (ADS)

Ren, Facai; Tang, Xiaoying

2017-10-01

Creep behavior of Grade 91 heat-resistant steel used for steam cooler was characterized using the theta projection method. Creep tests were conducted at the temperature of 923K under the stress ranging from 100-150MPa. Based on the creep curve results, four theta parameters were established using a nonlinear least square fitting method. Four theta parameters showed a good linearity as a function of stress. The predicted curves coincided well with the experimental data and creep curves were also modeled to the low stress level of 60MPa.

A simple algorithm to estimate the effective regional atmospheric parameters for thermal-inertia mapping

USGS Publications Warehouse

Watson, K.; Hummer-Miller, S.

1981-01-01

A method based solely on remote sensing data has been developed to estimate those meteorological effects which are required for thermal-inertia mapping. It assumes that the atmospheric fluxes are spatially invariant and that the solar, sky, and sensible heat fluxes can be approximated by a simple mathematical form. Coefficients are determined from least-squares method by fitting observational data to our thermal model. A comparison between field measurements and the model-derived flux shows the type of agreement which can be achieved. An analysis of the limitations of the method is also provided. ?? 1981.

Effects of sample size on KERNEL home range estimates

USGS Publications Warehouse

Seaman, D.E.; Millspaugh, J.J.; Kernohan, Brian J.; Brundige, Gary C.; Raedeke, Kenneth J.; Gitzen, Robert A.

1999-01-01

Kernel methods for estimating home range are being used increasingly in wildlife research, but the effect of sample size on their accuracy is not known. We used computer simulations of 10-200 points/home range and compared accuracy of home range estimates produced by fixed and adaptive kernels with the reference (REF) and least-squares cross-validation (LSCV) methods for determining the amount of smoothing. Simulated home ranges varied from simple to complex shapes created by mixing bivariate normal distributions. We used the size of the 95% home range area and the relative mean squared error of the surface fit to assess the accuracy of the kernel home range estimates. For both measures, the bias and variance approached an asymptote at about 50 observations/home range. The fixed kernel with smoothing selected by LSCV provided the least-biased estimates of the 95% home range area. All kernel methods produced similar surface fit for most simulations, but the fixed kernel with LSCV had the lowest frequency and magnitude of very poor estimates. We reviewed 101 papers published in The Journal of Wildlife Management (JWM) between 1980 and 1997 that estimated animal home ranges. A minority of these papers used nonparametric utilization distribution (UD) estimators, and most did not adequately report sample sizes. We recommend that home range studies using kernel estimates use LSCV to determine the amount of smoothing, obtain a minimum of 30 observations per animal (but preferably a?Y50), and report sample sizes in published results.

Radioecological modelling of Polonium-210 and Caesium-137 in lichen-reindeer-man and top predators.

PubMed

Persson, Bertil R R; Gjelsvik, Runhild; Holm, Elis

2018-06-01

This work deals with analysis and modelling of the radionuclides 210 Pb and 210 Po in the food-chain lichen-reindeer-man in addition to 210 Po and 137 Cs in top predators. By using the methods of Partial Least Square Regression (PLSR) the atmospheric deposition of 210 Pb and 210 Po is predicted at the sample locations. Dynamic modelling of the activity concentration with differential equations is fitted to the sample data. Reindeer lichen consumption, gastrointestinal absorption, organ distribution and elimination is derived from information in the literature. Dynamic modelling of transfer of 210 Pb and 210 Po to reindeer meat, liver and bone from lichen consumption, fitted well with data from Sweden and Finland from 1966 to 1971. The activity concentration of 210 Pb in the skeleton in man is modelled by using the results of studying the kinetics of lead in skeleton and blood in lead-workers after end of occupational exposure. The result of modelling 210 Pb and 210 Po activity in skeleton matched well with concentrations of 210 Pb and 210 Po in teeth from reindeer-breeders and autopsy bone samples in Finland. The results of 210 Po and 137 Cs in different tissues of wolf, wolverine and lynx previously published, are analysed with multivariate data processing methods such as Principal Component Analysis PCA, and modelled with the method of Projection to Latent Structures, PLS, or Partial Least Square Regression PLSR. Copyright © 2017 Elsevier Ltd. All rights reserved.

Robust fitting for neuroreceptor mapping.

PubMed

Chang, Chung; Ogden, R Todd

2009-03-15

Among many other uses, positron emission tomography (PET) can be used in studies to estimate the density of a neuroreceptor at each location throughout the brain by measuring the concentration of a radiotracer over time and modeling its kinetics. There are a variety of kinetic models in common usage and these typically rely on nonlinear least-squares (LS) algorithms for parameter estimation. However, PET data often contain artifacts (such as uncorrected head motion) and so the assumptions on which the LS methods are based may be violated. Quantile regression (QR) provides a robust alternative to LS methods and has been used successfully in many applications. We consider fitting various kinetic models to PET data using QR and study the relative performance of the methods via simulation. A data adaptive method for choosing between LS and QR is proposed and the performance of this method is also studied.

Domain Decomposition Algorithms for First-Order System Least Squares Methods

NASA Technical Reports Server (NTRS)

Pavarino, Luca F.

1996-01-01

Least squares methods based on first-order systems have been recently proposed and analyzed for second-order elliptic equations and systems. They produce symmetric and positive definite discrete systems by using standard finite element spaces, which are not required to satisfy the inf-sup condition. In this paper, several domain decomposition algorithms for these first-order least squares methods are studied. Some representative overlapping and substructuring algorithms are considered in their additive and multiplicative variants. The theoretical and numerical results obtained show that the classical convergence bounds (on the iteration operator) for standard Galerkin discretizations are also valid for least squares methods.

Tip-tilt disturbance model identification based on non-linear least squares fitting for Linear Quadratic Gaussian control

NASA Astrophysics Data System (ADS)

Yang, Kangjian; Yang, Ping; Wang, Shuai; Dong, Lizhi; Xu, Bing

2018-05-01

We propose a method to identify tip-tilt disturbance model for Linear Quadratic Gaussian control. This identification method based on Levenberg-Marquardt method conducts with a little prior information and no auxiliary system and it is convenient to identify the tip-tilt disturbance model on-line for real-time control. This identification method makes it easy that Linear Quadratic Gaussian control runs efficiently in different adaptive optics systems for vibration mitigation. The validity of the Linear Quadratic Gaussian control associated with this tip-tilt disturbance model identification method is verified by experimental data, which is conducted in replay mode by simulation.

40 CFR 86.1324-84 - Carbon dioxide analyzer calibration.

Code of Federal Regulations, 2013 CFR

2013-07-01

... calibrated, if the deviation from a least-squares best-fit straight line is within ±2 percent or less of the... exceeds these limits, then the best-fit non-linear equation which represents the data within these limits shall be used to determine concentration values. (d) The initial and periodic interference, system check...

40 CFR 91.316 - Hydrocarbon analyzer calibration.

Code of Federal Regulations, 2014 CFR

2014-07-01

... deviation from a least-squares best-fit straight line is two percent or less of the value at each data point... exceeds two percent at any point, use the best-fit non-linear equation which represents the data to within two percent of each test point to determine concentration. (d) Oxygen interference optimization...

40 CFR 89.322 - Carbon dioxide analyzer calibration.

Code of Federal Regulations, 2011 CFR

2011-07-01

... engineering practice. For each range calibrated, if the deviation from a least-squares best-fit straight line... range. If the deviation exceeds these limits, the best-fit non-linear equation which represents the data... interference, system check, and calibration test procedures specified in 40 CFR part 1065 may be used in lieu...

40 CFR 90.316 - Hydrocarbon analyzer calibration.

Code of Federal Regulations, 2012 CFR

2012-07-01

... from a least-squares best-fit straight line is two percent or less of the value at each data point... exceeds two percent at any point, use the best-fit non-linear equation which represents the data to within two percent of each test point to determine concentration. (d) Oxygen interference optimization. Prior...

40 CFR 86.1324-84 - Carbon dioxide analyzer calibration.

Code of Federal Regulations, 2012 CFR

2012-07-01

... calibrated, if the deviation from a least-squares best-fit straight line is within ±2 percent or less of the... exceeds these limits, then the best-fit non-linear equation which represents the data within these limits shall be used to determine concentration values. (d) The initial and periodic interference, system check...

40 CFR 90.316 - Hydrocarbon analyzer calibration.

Code of Federal Regulations, 2013 CFR

2013-07-01

... from a least-squares best-fit straight line is two percent or less of the value at each data point... exceeds two percent at any point, use the best-fit non-linear equation which represents the data to within two percent of each test point to determine concentration. (d) Oxygen interference optimization. Prior...

40 CFR 90.316 - Hydrocarbon analyzer calibration.

Code of Federal Regulations, 2014 CFR

2014-07-01

... from a least-squares best-fit straight line is two percent or less of the value at each data point... exceeds two percent at any point, use the best-fit non-linear equation which represents the data to within two percent of each test point to determine concentration. (d) Oxygen interference optimization. Prior...

40 CFR 86.1324-84 - Carbon dioxide analyzer calibration.

Code of Federal Regulations, 2011 CFR

2011-07-01

... calibrated, if the deviation from a least-squares best-fit straight line is within ±2 percent or less of the... exceeds these limits, then the best-fit non-linear equation which represents the data within these limits shall be used to determine concentration values. (d) The initial and periodic interference, system check...

40 CFR 89.322 - Carbon dioxide analyzer calibration.

Code of Federal Regulations, 2013 CFR

2013-07-01

... engineering practice. For each range calibrated, if the deviation from a least-squares best-fit straight line... range. If the deviation exceeds these limits, the best-fit non-linear equation which represents the data... interference, system check, and calibration test procedures specified in 40 CFR part 1065 may be used in lieu...

40 CFR 91.316 - Hydrocarbon analyzer calibration.

Code of Federal Regulations, 2012 CFR

2012-07-01

... deviation from a least-squares best-fit straight line is two percent or less of the value at each data point... exceeds two percent at any point, use the best-fit non-linear equation which represents the data to within two percent of each test point to determine concentration. (d) Oxygen interference optimization...

40 CFR 86.1323-84 - Oxides of nitrogen analyzer calibration.

Code of Federal Regulations, 2012 CFR

2012-07-01

... calibrated, if the deviation from a least-squares best-fit straight line is within ±2 percent of the value at... exceeds these limits, then the best-fit non-linear equation which represents the data within these limits shall be used to determine concentration values. (c) The initial and periodic interference, system check...

40 CFR 86.1323-84 - Oxides of nitrogen analyzer calibration.

Code of Federal Regulations, 2013 CFR

2013-07-01

... calibrated, if the deviation from a least-squares best-fit straight line is within ±2 percent of the value at... exceeds these limits, then the best-fit non-linear equation which represents the data within these limits shall be used to determine concentration values. (c) The initial and periodic interference, system check...

40 CFR 89.322 - Carbon dioxide analyzer calibration.

Code of Federal Regulations, 2014 CFR

2014-07-01

... engineering practice. For each range calibrated, if the deviation from a least-squares best-fit straight line... range. If the deviation exceeds these limits, the best-fit non-linear equation which represents the data... interference, system check, and calibration test procedures specified in 40 CFR part 1065 may be used in lieu...

40 CFR 91.316 - Hydrocarbon analyzer calibration.

Code of Federal Regulations, 2013 CFR

2013-07-01

... deviation from a least-squares best-fit straight line is two percent or less of the value at each data point... exceeds two percent at any point, use the best-fit non-linear equation which represents the data to within two percent of each test point to determine concentration. (d) Oxygen interference optimization...

40 CFR 89.322 - Carbon dioxide analyzer calibration.

Code of Federal Regulations, 2012 CFR

2012-07-01

... engineering practice. For each range calibrated, if the deviation from a least-squares best-fit straight line... range. If the deviation exceeds these limits, the best-fit non-linear equation which represents the data... interference, system check, and calibration test procedures specified in 40 CFR part 1065 may be used in lieu...

The Routine Fitting of Kinetic Data to Models

PubMed Central

Berman, Mones; Shahn, Ezra; Weiss, Marjory F.

1962-01-01

A mathematical formalism is presented for use with digital computers to permit the routine fitting of data to physical and mathematical models. Given a set of data, the mathematical equations describing a model, initial conditions for an experiment, and initial estimates for the values of model parameters, the computer program automatically proceeds to obtain a least squares fit of the data by an iterative adjustment of the values of the parameters. When the experimental measures are linear combinations of functions, the linear coefficients for a least squares fit may also be calculated. The values of both the parameters of the model and the coefficients for the sum of functions may be unknown independent variables, unknown dependent variables, or known constants. In the case of dependence, only linear dependencies are provided for in routine use. The computer program includes a number of subroutines, each one of which performs a special task. This permits flexibility in choosing various types of solutions and procedures. One subroutine, for example, handles linear differential equations, another, special non-linear functions, etc. The use of analytic or numerical solutions of equations is possible. PMID:13867975

A study of data analysis techniques for the multi-needle Langmuir probe

NASA Astrophysics Data System (ADS)

Hoang, H.; Røed, K.; Bekkeng, T. A.; Moen, J. I.; Spicher, A.; Clausen, L. B. N.; Miloch, W. J.; Trondsen, E.; Pedersen, A.

2018-06-01

In this paper we evaluate two data analysis techniques for the multi-needle Langmuir probe (m-NLP). The instrument uses several cylindrical Langmuir probes, which are positively biased with respect to the plasma potential in order to operate in the electron saturation region. Since the currents collected by these probes can be sampled at kilohertz rates, the instrument is capable of resolving the ionospheric plasma structure down to the meter scale. The two data analysis techniques, a linear fit and a non-linear least squares fit, are discussed in detail using data from the Investigation of Cusp Irregularities 2 sounding rocket. It is shown that each technique has pros and cons with respect to the m-NLP implementation. Even though the linear fitting technique seems to be better than measurements from incoherent scatter radar and in situ instruments, m-NLPs can be longer and can be cleaned during operation to improve instrument performance. The non-linear least squares fitting technique would be more reliable provided that a higher number of probes are deployed.

Fast and exact Newton and Bidirectional fitting of Active Appearance Models.

PubMed

Kossaifi, Jean; Tzimiropoulos, Yorgos; Pantic, Maja

2016-12-21

Active Appearance Models (AAMs) are generative models of shape and appearance that have proven very attractive for their ability to handle wide changes in illumination, pose and occlusion when trained in the wild, while not requiring large training dataset like regression-based or deep learning methods. The problem of fitting an AAM is usually formulated as a non-linear least squares one and the main way of solving it is a standard Gauss-Newton algorithm. In this paper we extend Active Appearance Models in two ways: we first extend the Gauss-Newton framework by formulating a bidirectional fitting method that deforms both the image and the template to fit a new instance. We then formulate a second order method by deriving an efficient Newton method for AAMs fitting. We derive both methods in a unified framework for two types of Active Appearance Models, holistic and part-based, and additionally show how to exploit the structure in the problem to derive fast yet exact solutions. We perform a thorough evaluation of all algorithms on three challenging and recently annotated inthe- wild datasets, and investigate fitting accuracy, convergence properties and the influence of noise in the initialisation. We compare our proposed methods to other algorithms and show that they yield state-of-the-art results, out-performing other methods while having superior convergence properties.

Isotope pattern deconvolution for peptide mass spectrometry by non-negative least squares/least absolute deviation template matching

PubMed Central

2012-01-01

Background The robust identification of isotope patterns originating from peptides being analyzed through mass spectrometry (MS) is often significantly hampered by noise artifacts and the interference of overlapping patterns arising e.g. from post-translational modifications. As the classification of the recorded data points into either ‘noise’ or ‘signal’ lies at the very root of essentially every proteomic application, the quality of the automated processing of mass spectra can significantly influence the way the data might be interpreted within a given biological context. Results We propose non-negative least squares/non-negative least absolute deviation regression to fit a raw spectrum by templates imitating isotope patterns. In a carefully designed validation scheme, we show that the method exhibits excellent performance in pattern picking. It is demonstrated that the method is able to disentangle complicated overlaps of patterns. Conclusions We find that regularization is not necessary to prevent overfitting and that thresholding is an effective and user-friendly way to perform feature selection. The proposed method avoids problems inherent in regularization-based approaches, comes with a set of well-interpretable parameters whose default configuration is shown to generalize well without the need for fine-tuning, and is applicable to spectra of different platforms. The R package IPPD implements the method and is available from the Bioconductor platform (http://bioconductor.fhcrc.org/help/bioc-views/devel/bioc/html/IPPD.html). PMID:23137144

Statistical assessment of bi-exponential diffusion weighted imaging signal characteristics induced by intravoxel incoherent motion in malignant breast tumors

PubMed Central

Wong, Oi Lei; Lo, Gladys G.; Chan, Helen H. L.; Wong, Ting Ting; Cheung, Polly S. Y.

2016-01-01

Background The purpose of this study is to statistically assess whether bi-exponential intravoxel incoherent motion (IVIM) model better characterizes diffusion weighted imaging (DWI) signal of malignant breast tumor than mono-exponential Gaussian diffusion model. Methods 3 T DWI data of 29 malignant breast tumors were retrospectively included. Linear least-square mono-exponential fitting and segmented least-square bi-exponential fitting were used for apparent diffusion coefficient (ADC) and IVIM parameter quantification, respectively. F-test and Akaike Information Criterion (AIC) were used to statistically assess the preference of mono-exponential and bi-exponential model using region-of-interests (ROI)-averaged and voxel-wise analysis. Results For ROI-averaged analysis, 15 tumors were significantly better fitted by bi-exponential function and 14 tumors exhibited mono-exponential behavior. The calculated ADC, D (true diffusion coefficient) and f (pseudo-diffusion fraction) showed no significant differences between mono-exponential and bi-exponential preferable tumors. Voxel-wise analysis revealed that 27 tumors contained more voxels exhibiting mono-exponential DWI decay while only 2 tumors presented more bi-exponential decay voxels. ADC was consistently and significantly larger than D for both ROI-averaged and voxel-wise analysis. Conclusions Although the presence of IVIM effect in malignant breast tumors could be suggested, statistical assessment shows that bi-exponential fitting does not necessarily better represent the DWI signal decay in breast cancer under clinically typical acquisition protocol and signal-to-noise ratio (SNR). Our study indicates the importance to statistically examine the breast cancer DWI signal characteristics in practice. PMID:27709078

A Numerical Method for Calculating Stellar Occultation Light Curves from an Arbitrary Atmospheric Model

NASA Technical Reports Server (NTRS)

Chamberlain, D. M.; Elliot, J. L.

1997-01-01

We present a method for speeding up numerical calculations of a light curve for a stellar occultation by a planetary atmosphere with an arbitrary atmospheric model that has spherical symmetry. This improved speed makes least-squares fitting for model parameters practical. Our method takes as input several sets of values for the first two radial derivatives of the refractivity at different values of model parameters, and interpolates to obtain the light curve at intermediate values of one or more model parameters. It was developed for small occulting bodies such as Pluto and Triton, but is applicable to planets of all sizes. We also present the results of a series of tests showing that our method calculates light curves that are correct to an accuracy of 10(exp -4) of the unocculted stellar flux. The test benchmarks are (i) an atmosphere with a l/r dependence of temperature, which yields an analytic solution for the light curve, (ii) an atmosphere that produces an exponential refraction angle, and (iii) a small-planet isothermal model. With our method, least-squares fits to noiseless data also converge to values of parameters with fractional errors of no more than 10(exp -4), with the largest errors occurring in small planets. These errors are well below the precision of the best stellar occultation data available. Fits to noisy data had formal errors consistent with the level of synthetic noise added to the light curve. We conclude: (i) one should interpolate refractivity derivatives and then form light curves from the interpolated values, rather than interpolating the light curves themselves; (ii) for the most accuracy, one must specify the atmospheric model for radii many scale heights above half light; and (iii) for atmospheres with smoothly varying refractivity with altitude, light curves can be sampled as coarsely as two points per scale height.

Data Series Subtraction with Unknown and Unmodeled Background Noise

NASA Technical Reports Server (NTRS)

Vitale, Stefano; Congedo, Giuseppe; Dolesi, Rita; Ferroni, Valerio; Hueller, Mauro; Vetrugno, Daniele; Weber, William Joseph; Audley, Heather; Danzmann, Karsten; Diepholz, Ingo;

Ordinary Least Squares and Quantile Regression: An Inquiry-Based Learning Approach to a Comparison of Regression Methods

ERIC Educational Resources Information Center

Helmreich, James E.; Krog, K. Peter

2018-01-01

We present a short, inquiry-based learning course on concepts and methods underlying ordinary least squares (OLS), least absolute deviation (LAD), and quantile regression (QR). Students investigate squared, absolute, and weighted absolute distance functions (metrics) as location measures. Using differential calculus and properties of convex…

A compact and accurate semi-global potential energy surface for malonaldehyde from constrained least squares regression

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mizukami, Wataru, E-mail: wataru.mizukami@bristol.ac.uk; Tew, David P., E-mail: david.tew@bristol.ac.uk; Habershon, Scott, E-mail: S.Habershon@warwick.ac.uk

2014-10-14

We present a new approach to semi-global potential energy surface fitting that uses the least absolute shrinkage and selection operator (LASSO) constrained least squares procedure to exploit an extremely flexible form for the potential function, while at the same time controlling the risk of overfitting and avoiding the introduction of unphysical features such as divergences or high-frequency oscillations. Drawing from a massively redundant set of overlapping distributed multi-dimensional Gaussian functions of inter-atomic separations we build a compact full-dimensional surface for malonaldehyde, fit to explicitly correlated coupled cluster CCSD(T)(F12*) energies with a root mean square deviations accuracy of 0.3%–0.5% up tomore » 25 000 cm{sup −1} above equilibrium. Importance-sampled diffusion Monte Carlo calculations predict zero point energies for malonaldehyde and its deuterated isotopologue of 14 715.4(2) and 13 997.9(2) cm{sup −1} and hydrogen transfer tunnelling splittings of 21.0(4) and 3.2(4) cm{sup −1}, respectively, which are in excellent agreement with the experimental values of 21.583 and 2.915(4) cm{sup −1}.« less

A spectral mimetic least-squares method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bochev, Pavel; Gerritsma, Marc

We present a spectral mimetic least-squares method for a model diffusion–reaction problem, which preserves key conservation properties of the continuum problem. Casting the model problem into a first-order system for two scalar and two vector variables shifts material properties from the differential equations to a pair of constitutive relations. We also use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are alsomore » satisfied exactly. Additionally, the latter are reduced to purely topological relationships for the degrees of freedom that can be satisfied without reference to basis functions. Furthermore, numerical experiments confirm the spectral accuracy of the method and its local conservation.« less

A spectral mimetic least-squares method

DOE PAGES

Bochev, Pavel; Gerritsma, Marc

2014-09-01

We present a spectral mimetic least-squares method for a model diffusion–reaction problem, which preserves key conservation properties of the continuum problem. Casting the model problem into a first-order system for two scalar and two vector variables shifts material properties from the differential equations to a pair of constitutive relations. We also use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are alsomore » satisfied exactly. Additionally, the latter are reduced to purely topological relationships for the degrees of freedom that can be satisfied without reference to basis functions. Furthermore, numerical experiments confirm the spectral accuracy of the method and its local conservation.« less

Adaptive slab laser beam quality improvement using a weighted least-squares reconstruction algorithm.

PubMed

Chen, Shanqiu; Dong, LiZhi; Chen, XiaoJun; Tan, Yi; Liu, Wenjin; Wang, Shuai; Yang, Ping; Xu, Bing; Ye, YuTang

2016-04-10

Adaptive optics is an important technology for improving beam quality in solid-state slab lasers. However, there are uncorrectable aberrations in partial areas of the beam. In the criterion of the conventional least-squares reconstruction method, it makes the zones with small aberrations nonsensitive and hinders this zone from being further corrected. In this paper, a weighted least-squares reconstruction method is proposed to improve the relative sensitivity of zones with small aberrations and to further improve beam quality. Relatively small weights are applied to the zones with large residual aberrations. Comparisons of results show that peak intensity in the far field improved from 1242 analog digital units (ADU) to 2248 ADU, and beam quality β improved from 2.5 to 2.0. This indicates the weighted least-squares method has better performance than the least-squares reconstruction method when there are large zonal uncorrectable aberrations in the slab laser system.

A point cloud modeling method based on geometric constraints mixing the robust least squares method

NASA Astrophysics Data System (ADS)

Yue, JIanping; Pan, Yi; Yue, Shun; Liu, Dapeng; Liu, Bin; Huang, Nan

2016-10-01

The appearance of 3D laser scanning technology has provided a new method for the acquisition of spatial 3D information. It has been widely used in the field of Surveying and Mapping Engineering with the characteristics of automatic and high precision. 3D laser scanning data processing process mainly includes the external laser data acquisition, the internal industry laser data splicing, the late 3D modeling and data integration system. For the point cloud modeling, domestic and foreign researchers have done a lot of research. Surface reconstruction technology mainly include the point shape, the triangle model, the triangle Bezier surface model, the rectangular surface model and so on, and the neural network and the Alfa shape are also used in the curved surface reconstruction. But in these methods, it is often focused on single surface fitting, automatic or manual block fitting, which ignores the model's integrity. It leads to a serious problems in the model after stitching, that is, the surfaces fitting separately is often not satisfied with the well-known geometric constraints, such as parallel, vertical, a fixed angle, or a fixed distance. However, the research on the special modeling theory such as the dimension constraint and the position constraint is not used widely. One of the traditional modeling methods adding geometric constraints is a method combing the penalty function method and the Levenberg-Marquardt algorithm (L-M algorithm), whose stability is pretty good. But in the research process, it is found that the method is greatly influenced by the initial value. In this paper, we propose an improved method of point cloud model taking into account the geometric constraint. We first apply robust least-squares to enhance the initial value's accuracy, and then use penalty function method to transform constrained optimization problems into unconstrained optimization problems, and finally solve the problems using the L-M algorithm. The experimental results show that the internal accuracy is improved, and it is shown that the improved method for point clouds modeling proposed by this paper outperforms the traditional point clouds modeling methods.

Modelling local GPS/levelling geoid undulations using artificial neural networks

NASA Astrophysics Data System (ADS)

Kavzoglu, T.; Saka, M. H.

2005-04-01

The use of GPS for establishing height control in an area where levelling data are available can involve the so-called GPS/levelling technique. Modelling of the GPS/levelling geoid undulations has usually been carried out using polynomial surface fitting, least-squares collocation (LSC) and finite-element methods. Artificial neural networks (ANNs) have recently been used for many investigations, and proven to be effective in solving complex problems represented by noisy and missing data. In this study, a feed-forward ANN structure, learning the characteristics of the training data through the back-propagation algorithm, is employed to model the local GPS/levelling geoid surface. The GPS/levelling geoid undulations for Istanbul, Turkey, were estimated from GPS and precise levelling measurements obtained during a field study in the period 1998-99. The results are compared to those produced by two well-known conventional methods, namely polynomial fitting and LSC, in terms of root mean square error (RMSE) that ranged from 3.97 to 5.73 cm. The results show that ANNs can produce results that are comparable to polynomial fitting and LSC. The main advantage of the ANN-based surfaces seems to be the low deviations from the GPS/levelling data surface, which is particularly important for distorted levelling networks.

Least squares regression methods for clustered ROC data with discrete covariates.

PubMed

Tang, Liansheng Larry; Zhang, Wei; Li, Qizhai; Ye, Xuan; Chan, Leighton

2016-07-01

The receiver operating characteristic (ROC) curve is a popular tool to evaluate and compare the accuracy of diagnostic tests to distinguish the diseased group from the nondiseased group when test results from tests are continuous or ordinal. A complicated data setting occurs when multiple tests are measured on abnormal and normal locations from the same subject and the measurements are clustered within the subject. Although least squares regression methods can be used for the estimation of ROC curve from correlated data, how to develop the least squares methods to estimate the ROC curve from the clustered data has not been studied. Also, the statistical properties of the least squares methods under the clustering setting are unknown. In this article, we develop the least squares ROC methods to allow the baseline and link functions to differ, and more importantly, to accommodate clustered data with discrete covariates. The methods can generate smooth ROC curves that satisfy the inherent continuous property of the true underlying curve. The least squares methods are shown to be more efficient than the existing nonparametric ROC methods under appropriate model assumptions in simulation studies. We apply the methods to a real example in the detection of glaucomatous deterioration. We also derive the asymptotic properties of the proposed methods. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

LOGISTIC FUNCTION PROFILE FIT: A least-squares program for fitting interface profiles to an extended logistic function

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kirchhoff, William H.

2012-09-15

The extended logistic function provides a physically reasonable description of interfaces such as depth profiles or line scans of surface topological or compositional features. It describes these interfaces with the minimum number of parameters, namely, position, width, and asymmetry. Logistic Function Profile Fit (LFPF) is a robust, least-squares fitting program in which the nonlinear extended logistic function is linearized by a Taylor series expansion (equivalent to a Newton-Raphson approach) with no apparent introduction of bias in the analysis. The program provides reliable confidence limits for the parameters when systematic errors are minimal and provides a display of the residuals frommore » the fit for the detection of systematic errors. The program will aid researchers in applying ASTM E1636-10, 'Standard practice for analytically describing sputter-depth-profile and linescan-profile data by an extended logistic function,' and may also prove useful in applying ISO 18516: 2006, 'Surface chemical analysis-Auger electron spectroscopy and x-ray photoelectron spectroscopy-determination of lateral resolution.' Examples are given of LFPF fits to a secondary ion mass spectrometry depth profile, an Auger surface line scan, and synthetic data generated to exhibit known systematic errors for examining the significance of such errors to the extrapolation of partial profiles.« less

Optimal methods for fitting probability distributions to propagule retention time in studies of zoochorous dispersal.

PubMed

Viana, Duarte S; Santamaría, Luis; Figuerola, Jordi

2016-02-01

Propagule retention time is a key factor in determining propagule dispersal distance and the shape of "seed shadows". Propagules dispersed by animal vectors are either ingested and retained in the gut until defecation or attached externally to the body until detachment. Retention time is a continuous variable, but it is commonly measured at discrete time points, according to pre-established sampling time-intervals. Although parametric continuous distributions have been widely fitted to these interval-censored data, the performance of different fitting methods has not been evaluated. To investigate the performance of five different fitting methods, we fitted parametric probability distributions to typical discretized retention-time data with known distribution using as data-points either the lower, mid or upper bounds of sampling intervals, as well as the cumulative distribution of observed values (using either maximum likelihood or non-linear least squares for parameter estimation); then compared the estimated and original distributions to assess the accuracy of each method. We also assessed the robustness of these methods to variations in the sampling procedure (sample size and length of sampling time-intervals). Fittings to the cumulative distribution performed better for all types of parametric distributions (lognormal, gamma and Weibull distributions) and were more robust to variations in sample size and sampling time-intervals. These estimated distributions had negligible deviations of up to 0.045 in cumulative probability of retention times (according to the Kolmogorov-Smirnov statistic) in relation to original distributions from which propagule retention time was simulated, supporting the overall accuracy of this fitting method. In contrast, fitting the sampling-interval bounds resulted in greater deviations that ranged from 0.058 to 0.273 in cumulative probability of retention times, which may introduce considerable biases in parameter estimates. We recommend the use of cumulative probability to fit parametric probability distributions to propagule retention time, specifically using maximum likelihood for parameter estimation. Furthermore, the experimental design for an optimal characterization of unimodal propagule retention time should contemplate at least 500 recovered propagules and sampling time-intervals not larger than the time peak of propagule retrieval, except in the tail of the distribution where broader sampling time-intervals may also produce accurate fits.

Estimating locations and total magnetization vectors of compact magnetic sources from scalar, vector, or tensor magnetic measurements through combined Helbig and Euler analysis

USGS Publications Warehouse

Phillips, J.D.; Nabighian, M.N.; Smith, D.V.; Li, Y.

2007-01-01

The Helbig method for estimating total magnetization directions of compact sources from magnetic vector components is extended so that tensor magnetic gradient components can be used instead. Depths of the compact sources can be estimated using the Euler equation, and their dipole moment magnitudes can be estimated using a least squares fit to the vector component or tensor gradient component data. ?? 2007 Society of Exploration Geophysicists.

Nocturnal heart rate variability in 1-year-old infants analyzed by using the Least Square Cosine Spectrum Method.

PubMed

Kochiya, Yuko; Hirabayashi, Akari; Ichimaru, Yuhei

2017-09-16

To evaluate the dynamic nature of nocturnal heart rate variability, RR intervals recorded with a wearable heart rate sensor were analyzed using the Least Square Cosine Spectrum Method. Six 1-year-old infants participated in the study. A wearable heart rate sensor was placed on their chest to measure RR intervals and 3-axis acceleration. Heartbeat time series were analyzed for every 30 s using the Least Square Cosine Spectrum Method, and an original parameter to quantify the regularity of respiratory-related heart rate rhythm was extracted and referred to as "RA (RA-COSPEC: Respiratory Area obtained by COSPEC)." The RA value is higher when a cosine curve is fitted to the original data series. The time sequential changes of RA showed cyclic changes with significant rhythm during the night. The mean cycle length of RA was 70 ± 15 min, which is shorter than young adult's cycle in our previous study. At the threshold level of RA greater than 3, the HR was significantly decreased compared with the RA value less than 3. The regularity of heart rate rhythm showed dynamic changes during the night in 1-year-old infants. Significant decrease of HR at the time of higher RA suggests the increase of parasympathetic activity. We suspect that the higher RA reflects the regular respiratory pattern during the night. This analysis system may be useful for quantitative assessment of regularity and dynamic changes of nocturnal heart rate variability in infants.

An information geometric approach to least squares minimization

NASA Astrophysics Data System (ADS)

Transtrum, Mark; Machta, Benjamin; Sethna, James

2009-03-01

Parameter estimation by nonlinear least squares minimization is a ubiquitous problem that has an elegant geometric interpretation: all possible parameter values induce a manifold embedded within the space of data. The minimization problem is then to find the point on the manifold closest to the origin. The standard algorithm for minimizing sums of squares, the Levenberg-Marquardt algorithm, also has geometric meaning. When the standard algorithm fails to efficiently find accurate fits to the data, geometric considerations suggest improvements. Problems involving large numbers of parameters, such as often arise in biological contexts, are notoriously difficult. We suggest an algorithm based on geodesic motion that may offer improvements over the standard algorithm for a certain class of problems.

Scatter of X-rays on polished surfaces

NASA Technical Reports Server (NTRS)

Hasinger, G.

1981-01-01

In investigating the dispersion properties of telescope mirrors used in X-ray astronomy, the slight scattering characteristics of X-ray radiation by statistically rough surfaces were examined. The mathematics and geometry of scattering theory are described. The measurement test assembly is described and results of measurements on samples of plane mirrors are given. Measurement results are evaluated. The direct beam, the convolution of the direct beam and the scattering halo, curve fitting by the method of least squares, various autocorrelation functions, results of the fitting procedure for small scattering, and deviations in the kernel of the scattering distribution are presented. A procedure for quality testing of mirror systems through diagnosis of rough surfaces is described.

Deriving the Regression Equation without Using Calculus

ERIC Educational Resources Information Center

Gordon, Sheldon P.; Gordon, Florence S.

2004-01-01

Probably the one "new" mathematical topic that is most responsible for modernizing courses in college algebra and precalculus over the last few years is the idea of fitting a function to a set of data in the sense of a least squares fit. Whether it be simple linear regression or nonlinear regression, this topic opens the door to applying the…

46 CFR 116.435 - Doors.

Code of Federal Regulations, 2010 CFR

2010-10-01

... boundary in which the doors are fitted; (5) Door frames must be of rigid construction and provide at least... inches) square. A self-closing hinged or pivoted steel or equivalent material cover must be fitted in the...) A door in a bulkhead required to be A-60, A-30, or A-15 Class must be of hollow steel or equivalent...

46 CFR 116.435 - Doors.

Code of Federal Regulations, 2011 CFR

2011-10-01

... boundary in which the doors are fitted; (5) Door frames must be of rigid construction and provide at least... inches) square. A self-closing hinged or pivoted steel or equivalent material cover must be fitted in the...) A door in a bulkhead required to be A-60, A-30, or A-15 Class must be of hollow steel or equivalent...

New fast least-squares algorithm for estimating the best-fitting parameters due to simple geometric-structures from gravity anomalies.

PubMed

Essa, Khalid S

2014-01-01

A new fast least-squares method is developed to estimate the shape factor (q-parameter) of a buried structure using normalized residual anomalies obtained from gravity data. The problem of shape factor estimation is transformed into a problem of finding a solution of a non-linear equation of the form f(q) = 0 by defining the anomaly value at the origin and at different points on the profile (N-value). Procedures are also formulated to estimate the depth (z-parameter) and the amplitude coefficient (A-parameter) of the buried structure. The method is simple and rapid for estimating parameters that produced gravity anomalies. This technique is used for a class of geometrically simple anomalous bodies, including the semi-infinite vertical cylinder, the infinitely long horizontal cylinder, and the sphere. The technique is tested and verified on theoretical models with and without random errors. It is also successfully applied to real data sets from Senegal and India, and the inverted-parameters are in good agreement with the known actual values.

[Research on partial least squares for determination of impurities in the presence of high concentration of matrix by ICP-AES].

PubMed

Wang, Yan-peng; Gong, Qi; Yu, Sheng-rong; Liu, You-yan

2012-04-01

A method for detecting trace impurities in high concentration matrix by ICP-AES based on partial least squares (PLS) was established. The research showed that PLS could effectively correct the interference caused by high level of matrix concentration error and could withstand higher concentrations of matrix than multicomponent spectral fitting (MSF). When the mass ratios of matrix to impurities were from 1 000 : 1 to 20 000 : 1, the recoveries of standard addition were between 95% and 105% by PLS. For the system in which interference effect has nonlinear correlation with the matrix concentrations, the prediction accuracy of normal PLS method was poor, but it can be improved greatly by using LIN-PPLS, which was based on matrix transformation of sample concentration. The contents of Co, Pb and Ga in stream sediment (GBW07312) were detected by MSF, PLS and LIN-PPLS respectively. The results showed that the prediction accuracy of LIN-PPLS was better than PLS, and the prediction accuracy of PLS was better than MSF.

New fast least-squares algorithm for estimating the best-fitting parameters due to simple geometric-structures from gravity anomalies

PubMed Central

Essa, Khalid S.

2013-01-01

A new fast least-squares method is developed to estimate the shape factor (q-parameter) of a buried structure using normalized residual anomalies obtained from gravity data. The problem of shape factor estimation is transformed into a problem of finding a solution of a non-linear equation of the form f(q) = 0 by defining the anomaly value at the origin and at different points on the profile (N-value). Procedures are also formulated to estimate the depth (z-parameter) and the amplitude coefficient (A-parameter) of the buried structure. The method is simple and rapid for estimating parameters that produced gravity anomalies. This technique is used for a class of geometrically simple anomalous bodies, including the semi-infinite vertical cylinder, the infinitely long horizontal cylinder, and the sphere. The technique is tested and verified on theoretical models with and without random errors. It is also successfully applied to real data sets from Senegal and India, and the inverted-parameters are in good agreement with the known actual values. PMID:25685472

Rapid and Simultaneous Prediction of Eight Diesel Quality Parameters through ATR-FTIR Analysis.

PubMed

Nespeca, Maurilio Gustavo; Hatanaka, Rafael Rodrigues; Flumignan, Danilo Luiz; de Oliveira, José Eduardo

2018-01-01

Quality assessment of diesel fuel is highly necessary for society, but the costs and time spent are very high while using standard methods. Therefore, this study aimed to develop an analytical method capable of simultaneously determining eight diesel quality parameters (density; flash point; total sulfur content; distillation temperatures at 10% (T10), 50% (T50), and 85% (T85) recovery; cetane index; and biodiesel content) through attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopy and the multivariate regression method, partial least square (PLS). For this purpose, the quality parameters of 409 samples were determined using standard methods, and their spectra were acquired in ranges of 4000-650 cm -1 . The use of the multivariate filters, generalized least squares weighting (GLSW) and orthogonal signal correction (OSC), was evaluated to improve the signal-to-noise ratio of the models. Likewise, four variable selection approaches were tested: manual exclusion, forward interval PLS (FiPLS), backward interval PLS (BiPLS), and genetic algorithm (GA). The multivariate filters and variables selection algorithms generated more fitted and accurate PLS models. According to the validation, the FTIR/PLS models presented accuracy comparable to the reference methods and, therefore, the proposed method can be applied in the diesel routine monitoring to significantly reduce costs and analysis time.

Rapid and Simultaneous Prediction of Eight Diesel Quality Parameters through ATR-FTIR Analysis

PubMed Central

Hatanaka, Rafael Rodrigues; Flumignan, Danilo Luiz; de Oliveira, José Eduardo

2018-01-01

Quality assessment of diesel fuel is highly necessary for society, but the costs and time spent are very high while using standard methods. Therefore, this study aimed to develop an analytical method capable of simultaneously determining eight diesel quality parameters (density; flash point; total sulfur content; distillation temperatures at 10% (T10), 50% (T50), and 85% (T85) recovery; cetane index; and biodiesel content) through attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopy and the multivariate regression method, partial least square (PLS). For this purpose, the quality parameters of 409 samples were determined using standard methods, and their spectra were acquired in ranges of 4000–650 cm−1. The use of the multivariate filters, generalized least squares weighting (GLSW) and orthogonal signal correction (OSC), was evaluated to improve the signal-to-noise ratio of the models. Likewise, four variable selection approaches were tested: manual exclusion, forward interval PLS (FiPLS), backward interval PLS (BiPLS), and genetic algorithm (GA). The multivariate filters and variables selection algorithms generated more fitted and accurate PLS models. According to the validation, the FTIR/PLS models presented accuracy comparable to the reference methods and, therefore, the proposed method can be applied in the diesel routine monitoring to significantly reduce costs and analysis time. PMID:29629209

Understanding Least Squares through Monte Carlo Calculations

ERIC Educational Resources Information Center

Tellinghuisen, Joel

2005-01-01

The method of least squares (LS) is considered as an important data analysis tool available to physical scientists. The mathematics of linear least squares(LLS) is summarized in a very compact matrix rotation that renders it practically "formulaic".

The rotational elements of Mars and its satellites

NASA Astrophysics Data System (ADS)

Jacobson, R. A.; Konopliv, A. S.; Park, R. S.; Folkner, W. M.

2018-03-01

The International Astronomical Union (IAU) defines planet and satellite coordinate systems relative to their axis of rotation and the angle about that axis. The rotational elements of the bodies are the right ascension and declination of the rotation axis in the International Celestial Reference Frame and the rotation angle, W, measured easterly along the body's equator. The IAU specifies the location of the body's prime meridian by providing a value for W at epoch J2000. We provide new trigonometric series representations of the rotational elements of Mars and its satellites, Phobos and Deimos. The series for Mars are from a least squares fit to the rotation model used to orient the Martian gravity field. The series for the satellites are from a least squares fit to rotation models developed in accordance with IAU conventions from recent ephemerides.

Mapping Quantitative Trait Loci in Crosses between Outbred Lines Using Least Squares

PubMed Central

Haley, C. S.; Knott, S. A.; Elsen, J. M.

1994-01-01

The use of genetic maps based upon molecular markers has allowed the dissection of some of the factors underlying quantitative variation in crosses between inbred lines. For many species crossing inbred lines is not a practical proposition, although crosses between genetically very different outbred lines are possible. Here we develop a least squares method for the analysis of crosses between outbred lines which simultaneously uses information from multiple linked markers. The method is suitable for crosses where the lines may be segregating at marker loci but can be assumed to be fixed for alternative alleles at the major quantitative trait loci (QTLs) affecting the traits under analysis (e.g., crosses between divergent selection lines or breeds with different selection histories). The simultaneous use of multiple markers from a linkage group increases the sensitivity of the test statistic, and thus the power for the detection of QTLs, compared to the use of single markers or markers flanking an interval. The gain is greater for more closely spaced markers and for markers of lower information content. Use of multiple markers can also remove the bias in the estimated position and effect of a QTL which may result when different markers in a linkage group vary in their heterozygosity in the F(1) (and thus in their information content) and are considered only singly or a pair at a time. The method is relatively simple to apply so that more complex models can be fitted than is currently possible by maximum likelihood. Thus fixed effects and effects of background genotype can be fitted simultaneously with the exploration of a single linkage group which will increase the power to detect QTLs by reducing the residual variance. More complex models with several QTLs in the same linkage group and two-locus interactions between QTLs can similarly be examined. Thus least squares provides a powerful tool to extend the range of crosses from which QTLs can be dissected whilst at the same time allowing flexible and realistic models to be explored. PMID:8005424

[Near infrared spectroscopy study on water content in turbine oil].

PubMed

Chen, Bin; Liu, Ge; Zhang, Xian-Ming

2013-11-01

Near infrared (NIR) spectroscopy combined with successive projections algorithm (SPA) was investigated for determination of water content in turbine oil. Through the 57 samples of different water content in turbine oil scanned applying near infrared (NIR) spectroscopy, with the water content in the turbine oil of 0-0.156%, different pretreatment methods such as the original spectra, first derivative spectra and differential polynomial least squares fitting algorithm Savitzky-Golay (SG), and successive projections algorithm (SPA) were applied for the extraction of effective wavelengths, the correlation coefficient (R) and root mean square error (RMSE) were used as the model evaluation indices, accordingly water content in turbine oil was investigated. The results indicated that the original spectra with different water content in turbine oil were pretreated by the performance of first derivative + SG pretreatments, then the selected effective wavelengths were used as the inputs of least square support vector machine (LS-SVM). A total of 16 variables selected by SPA were employed to construct the model of SPA and least square support vector machine (SPA-LS-SVM). There is 9 as The correlation coefficient was 0.975 9 and the root of mean square error of validation set was 2.655 8 x 10(-3) using the model, and it is feasible to determine the water content in oil using near infrared spectroscopy and SPA-LS-SVM, and an excellent prediction precision was obtained. This study supplied a new and alternative approach to the further application of near infrared spectroscopy in on-line monitoring of contamination such as water content in oil.

Sci—Fri PM: Topics — 06: The influence of regional dose sensitivity on salivary loss and recovery in the parotid gland

DOE Office of Scientific and Technical Information (OSTI.GOV)

Clark, H; BC Cancer Agency, Surrey, B.C.; BC Cancer Agency, Vancouver, B.C.

Purpose: The Quantitative Analyses of Normal Tissue Effects in the Clinic (QUANTEC 2010) survey of radiation dose-volume effects on salivary gland function has called for improved understanding of intragland dose sensitivity and the effectiveness of partial sparing in salivary glands. Regional dose susceptibility of sagittally- and coronally-sub-segmented parotid gland has been studied. Specifically, we examine whether individual consideration of sub-segments leads to improved prediction of xerostomia compared with whole parotid mean dose. Methods: Data from 102 patients treated for head-and-neck cancers at the BC Cancer Agency were used in this study. Whole mouth stimulated saliva was collected before (baseline), threemore » months, and one year after cessation of radiotherapy. Organ volumes were contoured using treatment planning CT images and sub-segmented into regional portions. Both non-parametric (local regression) and parametric (mean dose exponential fitting) methods were employed. A bootstrap technique was used for reliability estimation and cross-comparison. Results: Salivary loss is described well using non-parametric and mean dose models. Parametric fits suggest a significant distinction in dose response between medial-lateral and anterior-posterior aspects of the parotid (p<0.01). Least-squares and least-median squares estimates differ significantly (p<0.00001), indicating fits may be skewed by noise or outliers. Salivary recovery exhibits a weakly arched dose response: the highest recovery is seen at intermediate doses. Conclusions: Salivary function loss is strongly dose dependent. In contrast no useful dose dependence was observed for function recovery. Regional dose dependence was observed, but may have resulted from a bias in dose distributions.« less

A Bayesian model averaging method for the derivation of reservoir operating rules

NASA Astrophysics Data System (ADS)

Zhang, Jingwen; Liu, Pan; Wang, Hao; Lei, Xiaohui; Zhou, Yanlai

2015-09-01

Because the intrinsic dynamics among optimal decision making, inflow processes and reservoir characteristics are complex, functional forms of reservoir operating rules are always determined subjectively. As a result, the uncertainty of selecting form and/or model involved in reservoir operating rules must be analyzed and evaluated. In this study, we analyze the uncertainty of reservoir operating rules using the Bayesian model averaging (BMA) model. Three popular operating rules, namely piecewise linear regression, surface fitting and a least-squares support vector machine, are established based on the optimal deterministic reservoir operation. These individual models provide three-member decisions for the BMA combination, enabling the 90% release interval to be estimated by the Markov Chain Monte Carlo simulation. A case study of China's the Baise reservoir shows that: (1) the optimal deterministic reservoir operation, superior to any reservoir operating rules, is used as the samples to derive the rules; (2) the least-squares support vector machine model is more effective than both piecewise linear regression and surface fitting; (3) BMA outperforms any individual model of operating rules based on the optimal trajectories. It is revealed that the proposed model can reduce the uncertainty of operating rules, which is of great potential benefit in evaluating the confidence interval of decisions.

Sediment data sources and estimated annual suspended-sediment loads of rivers and streams in Colorado

USGS Publications Warehouse

Elliott, J.G.; DeFeyter, K.L.

1986-01-01

Sources of sediment data collected by several government agencies through water year 1984 are summarized for Colorado. The U.S. Geological Survey has collected suspended-sediment data at 243 sites; these data are stored in the U.S. Geological Survey 's water data storage and retrieval system. The U.S. Forest Service has collected suspended-sediment and bedload data at an additional 225 sites, and most of these data are stored in the U.S. Environmental Protection Agency 's water-quality-control information system. Additional unpublished sediment data are in the possession of the collecting entities. Annual suspended-sediment loads were computed for 133 U.S. Geological Survey sediment-data-collection sites using the daily mean water-discharge/sediment-transport-curve method. Sediment-transport curves were derived for each site by one of three techniques: (1) Least-squares linear regression of all pairs of suspended-sediment and corresponding water-discharge data, (2) least-squares linear regression of data sets subdivided on the basis of hydrograph season; and (3) graphical fit to a logarithm-logarithm plot of data. The curve-fitting technique used for each site depended on site-specific characteristics. Sediment-data sources and estimates of annual loads of suspended, bed, and total sediment from several other reports also are summarized. (USGS)

SPECIFIC HEAT DATA ANALYSIS PROGRAM FOR THE IBM 704 DIGITAL COMPUTER

DOE Office of Scientific and Technical Information (OSTI.GOV)

Roach, P.R.

1962-01-01

A computer program was developed to calculate the specific heat of a substance in the temperature range from 0.3 to 4.2 deg K, given temperature calibration data for a carbon resistance thermometer, experimental temperature drift, and heating period data. The speciftc heats calculated from these data are then fitted by a curve by the methods of least squares and the specific heats are corrected for the effect of the curvature of the data. The method, operation, program details, and program stops are discussed. A program listing is included. (M.C.G.)

A fast least-squares algorithm for population inference

PubMed Central

2013-01-01

Background Population inference is an important problem in genetics used to remove population stratification in genome-wide association studies and to detect migration patterns or shared ancestry. An individual’s genotype can be modeled as a probabilistic function of ancestral population memberships, Q, and the allele frequencies in those populations, P. The parameters, P and Q, of this binomial likelihood model can be inferred using slow sampling methods such as Markov Chain Monte Carlo methods or faster gradient based approaches such as sequential quadratic programming. This paper proposes a least-squares simplification of the binomial likelihood model motivated by a Euclidean interpretation of the genotype feature space. This results in a faster algorithm that easily incorporates the degree of admixture within the sample of individuals and improves estimates without requiring trial-and-error tuning. Results We show that the expected value of the least-squares solution across all possible genotype datasets is equal to the true solution when part of the problem has been solved, and that the variance of the solution approaches zero as its size increases. The Least-squares algorithm performs nearly as well as Admixture for these theoretical scenarios. We compare least-squares, Admixture, and FRAPPE for a variety of problem sizes and difficulties. For particularly hard problems with a large number of populations, small number of samples, or greater degree of admixture, least-squares performs better than the other methods. On simulated mixtures of real population allele frequencies from the HapMap project, Admixture estimates sparsely mixed individuals better than Least-squares. The least-squares approach, however, performs within 1.5% of the Admixture error. On individual genotypes from the HapMap project, Admixture and least-squares perform qualitatively similarly and within 1.2% of each other. Significantly, the least-squares approach nearly always converges 1.5- to 6-times faster. Conclusions The computational advantage of the least-squares approach along with its good estimation performance warrants further research, especially for very large datasets. As problem sizes increase, the difference in estimation performance between all algorithms decreases. In addition, when prior information is known, the least-squares approach easily incorporates the expected degree of admixture to improve the estimate. PMID:23343408

A fast least-squares algorithm for population inference.

PubMed

Parry, R Mitchell; Wang, May D

2013-01-23

Population inference is an important problem in genetics used to remove population stratification in genome-wide association studies and to detect migration patterns or shared ancestry. An individual's genotype can be modeled as a probabilistic function of ancestral population memberships, Q, and the allele frequencies in those populations, P. The parameters, P and Q, of this binomial likelihood model can be inferred using slow sampling methods such as Markov Chain Monte Carlo methods or faster gradient based approaches such as sequential quadratic programming. This paper proposes a least-squares simplification of the binomial likelihood model motivated by a Euclidean interpretation of the genotype feature space. This results in a faster algorithm that easily incorporates the degree of admixture within the sample of individuals and improves estimates without requiring trial-and-error tuning. We show that the expected value of the least-squares solution across all possible genotype datasets is equal to the true solution when part of the problem has been solved, and that the variance of the solution approaches zero as its size increases. The Least-squares algorithm performs nearly as well as Admixture for these theoretical scenarios. We compare least-squares, Admixture, and FRAPPE for a variety of problem sizes and difficulties. For particularly hard problems with a large number of populations, small number of samples, or greater degree of admixture, least-squares performs better than the other methods. On simulated mixtures of real population allele frequencies from the HapMap project, Admixture estimates sparsely mixed individuals better than Least-squares. The least-squares approach, however, performs within 1.5% of the Admixture error. On individual genotypes from the HapMap project, Admixture and least-squares perform qualitatively similarly and within 1.2% of each other. Significantly, the least-squares approach nearly always converges 1.5- to 6-times faster. The computational advantage of the least-squares approach along with its good estimation performance warrants further research, especially for very large datasets. As problem sizes increase, the difference in estimation performance between all algorithms decreases. In addition, when prior information is known, the least-squares approach easily incorporates the expected degree of admixture to improve the estimate.

Computer programs of information processing of nuclear physical methods as a demonstration material in studying nuclear physics and numerical methods

NASA Astrophysics Data System (ADS)

Bateev, A. B.; Filippov, V. P.

2017-01-01

The principle possibility of using computer program Univem MS for Mössbauer spectra fitting as a demonstration material at studying such disciplines as atomic and nuclear physics and numerical methods by students is shown in the article. This program is associated with nuclear-physical parameters such as isomer (or chemical) shift of nuclear energy level, interaction of nuclear quadrupole moment with electric field and of magnetic moment with surrounded magnetic field. The basic processing algorithm in such programs is the Least Square Method. The deviation of values of experimental points on spectra from the value of theoretical dependence is defined on concrete examples. This value is characterized in numerical methods as mean square deviation. The shape of theoretical lines in the program is defined by Gaussian and Lorentzian distributions. The visualization of the studied material on atomic and nuclear physics can be improved by similar programs of the Mössbauer spectroscopy, X-ray Fluorescence Analyzer or X-ray diffraction analysis.

Orthogonalizing EM: A design-based least squares algorithm.

PubMed

Xiong, Shifeng; Dai, Bin; Huling, Jared; Qian, Peter Z G

We introduce an efficient iterative algorithm, intended for various least squares problems, based on a design of experiments perspective. The algorithm, called orthogonalizing EM (OEM), works for ordinary least squares and can be easily extended to penalized least squares. The main idea of the procedure is to orthogonalize a design matrix by adding new rows and then solve the original problem by embedding the augmented design in a missing data framework. We establish several attractive theoretical properties concerning OEM. For the ordinary least squares with a singular regression matrix, an OEM sequence converges to the Moore-Penrose generalized inverse-based least squares estimator. For ordinary and penalized least squares with various penalties, it converges to a point having grouping coherence for fully aliased regression matrices. Convergence and the convergence rate of the algorithm are examined. Finally, we demonstrate that OEM is highly efficient for large-scale least squares and penalized least squares problems, and is considerably faster than competing methods when n is much larger than p . Supplementary materials for this article are available online.

The Co-simulation of Humanoid Robot Based on Solidworks, ADAMS and Simulink

NASA Astrophysics Data System (ADS)

Song, Dalei; Zheng, Lidan; Wang, Li; Qi, Weiwei; Li, Yanli

A simulation method of adaptive controller is proposed for the humanoid robot system based on co-simulation of Solidworks, ADAMS and Simulink. A complex mathematical modeling process is avoided by this method, and the real time dynamic simulating function of Simulink would be exerted adequately. This method could be generalized to other complicated control system. This method is adopted to build and analyse the model of humanoid robot. The trajectory tracking and adaptive controller design also proceed based on it. The effect of trajectory tracking is evaluated by fitting-curve theory of least squares method. The anti-interference capability of the robot is improved a lot through comparative analysis.

Video-based noncooperative iris image segmentation.

PubMed

Du, Yingzi; Arslanturk, Emrah; Zhou, Zhi; Belcher, Craig

2011-02-01

In this paper, we propose a video-based noncooperative iris image segmentation scheme that incorporates a quality filter to quickly eliminate images without an eye, employs a coarse-to-fine segmentation scheme to improve the overall efficiency, uses a direct least squares fitting of ellipses method to model the deformed pupil and limbic boundaries, and develops a window gradient-based method to remove noise in the iris region. A remote iris acquisition system is set up to collect noncooperative iris video images. An objective method is used to quantitatively evaluate the accuracy of the segmentation results. The experimental results demonstrate the effectiveness of this method. The proposed method would make noncooperative iris recognition or iris surveillance possible.

40 CFR 86.125-94 - Methane analyzer calibration.

Code of Federal Regulations, 2012 CFR

2012-07-01

.... Additional calibration points may be generated. For each range calibrated, if the deviation from a least-squares best-fit straight line is 2 percent or less of the value at each data point, concentration values...

40 CFR 86.125-94 - Methane analyzer calibration.

Code of Federal Regulations, 2014 CFR

2014-07-01

.... Additional calibration points may be generated. For each range calibrated, if the deviation from a least-squares best-fit straight line is 2 percent or less of the value at each data point, concentration values...

40 CFR 86.125-94 - Methane analyzer calibration.

Code of Federal Regulations, 2013 CFR

2013-07-01

.... Additional calibration points may be generated. For each range calibrated, if the deviation from a least-squares best-fit straight line is 2 percent or less of the value at each data point, concentration values...

A Two-Layer Least Squares Support Vector Machine Approach to Credit Risk Assessment

NASA Astrophysics Data System (ADS)

Liu, Jingli; Li, Jianping; Xu, Weixuan; Shi, Yong

Least squares support vector machine (LS-SVM) is a revised version of support vector machine (SVM) and has been proved to be a useful tool for pattern recognition. LS-SVM had excellent generalization performance and low computational cost. In this paper, we propose a new method called two-layer least squares support vector machine which combines kernel principle component analysis (KPCA) and linear programming form of least square support vector machine. With this method sparseness and robustness is obtained while solving large dimensional and large scale database. A U.S. commercial credit card database is used to test the efficiency of our method and the result proved to be a satisfactory one.

The Local Minima Problem in Hierarchical Classes Analysis: An Evaluation of a Simulated Annealing Algorithm and Various Multistart Procedures

ERIC Educational Resources Information Center

Ceulemans, Eva; Van Mechelen, Iven; Leenen, Iwin

2007-01-01

Hierarchical classes models are quasi-order retaining Boolean decomposition models for N-way N-mode binary data. To fit these models to data, rationally started alternating least squares (or, equivalently, alternating least absolute deviations) algorithms have been proposed. Extensive simulation studies showed that these algorithms succeed quite…

A deconvolution extraction method for 2D multi-object fibre spectroscopy based on the regularized least-squares QR-factorization algorithm

NASA Astrophysics Data System (ADS)

Yu, Jian; Yin, Qian; Guo, Ping; Luo, A.-li

2014-09-01

This paper presents an efficient method for the extraction of astronomical spectra from two-dimensional (2D) multifibre spectrographs based on the regularized least-squares QR-factorization (LSQR) algorithm. We address two issues: we propose a modified Gaussian point spread function (PSF) for modelling the 2D PSF from multi-emission-line gas-discharge lamp images (arc images), and we develop an efficient deconvolution method to extract spectra in real circumstances. The proposed modified 2D Gaussian PSF model can fit various types of 2D PSFs, including different radial distortion angles and ellipticities. We adopt the regularized LSQR algorithm to solve the sparse linear equations constructed from the sparse convolution matrix, which we designate the deconvolution spectrum extraction method. Furthermore, we implement a parallelized LSQR algorithm based on graphics processing unit programming in the Compute Unified Device Architecture to accelerate the computational processing. Experimental results illustrate that the proposed extraction method can greatly reduce the computational cost and memory use of the deconvolution method and, consequently, increase its efficiency and practicability. In addition, the proposed extraction method has a stronger noise tolerance than other methods, such as the boxcar (aperture) extraction and profile extraction methods. Finally, we present an analysis of the sensitivity of the extraction results to the radius and full width at half-maximum of the 2D PSF.

The Use of Alternative Regression Methods in Social Sciences and the Comparison of Least Squares and M Estimation Methods in Terms of the Determination of Coefficient

ERIC Educational Resources Information Center

Coskuntuncel, Orkun

2013-01-01

The purpose of this study is two-fold; the first aim being to show the effect of outliers on the widely used least squares regression estimator in social sciences. The second aim is to compare the classical method of least squares with the robust M-estimator using the "determination of coefficient" (R[superscript 2]). For this purpose,…

Simplified Least Squares Shadowing sensitivity analysis for chaotic ODEs and PDEs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chater, Mario, E-mail: chaterm@mit.edu; Ni, Angxiu, E-mail: niangxiu@mit.edu; Wang, Qiqi, E-mail: qiqi@mit.edu

This paper develops a variant of the Least Squares Shadowing (LSS) method, which has successfully computed the derivative for several chaotic ODEs and PDEs. The development in this paper aims to simplify Least Squares Shadowing method by improving how time dilation is treated. Instead of adding an explicit time dilation term as in the original method, the new variant uses windowing, which can be more efficient and simpler to implement, especially for PDEs.

Comparing least-squares and quantile regression approaches to analyzing median hospital charges.

PubMed

Olsen, Cody S; Clark, Amy E; Thomas, Andrea M; Cook, Lawrence J

2012-07-01

Emergency department (ED) and hospital charges obtained from administrative data sets are useful descriptors of injury severity and the burden to EDs and the health care system. However, charges are typically positively skewed due to costly procedures, long hospital stays, and complicated or prolonged treatment for few patients. The median is not affected by extreme observations and is useful in describing and comparing distributions of hospital charges. A least-squares analysis employing a log transformation is one approach for estimating median hospital charges, corresponding confidence intervals (CIs), and differences between groups; however, this method requires certain distributional properties. An alternate method is quantile regression, which allows estimation and inference related to the median without making distributional assumptions. The objective was to compare the log-transformation least-squares method to the quantile regression approach for estimating median hospital charges, differences in median charges between groups, and associated CIs. The authors performed simulations using repeated sampling of observed statewide ED and hospital charges and charges randomly generated from a hypothetical lognormal distribution. The median and 95% CI and the multiplicative difference between the median charges of two groups were estimated using both least-squares and quantile regression methods. Performance of the two methods was evaluated. In contrast to least squares, quantile regression produced estimates that were unbiased and had smaller mean square errors in simulations of observed ED and hospital charges. Both methods performed well in simulations of hypothetical charges that met least-squares method assumptions. When the data did not follow the assumed distribution, least-squares estimates were often biased, and the associated CIs had lower than expected coverage as sample size increased. Quantile regression analyses of hospital charges provide unbiased estimates even when lognormal and equal variance assumptions are violated. These methods may be particularly useful in describing and analyzing hospital charges from administrative data sets. © 2012 by the Society for Academic Emergency Medicine.

Quantum algorithm for linear regression

NASA Astrophysics Data System (ADS)

Wang, Guoming

2017-07-01

We present a quantum algorithm for fitting a linear regression model to a given data set using the least-squares approach. Differently from previous algorithms which yield a quantum state encoding the optimal parameters, our algorithm outputs these numbers in the classical form. So by running it once, one completely determines the fitted model and then can use it to make predictions on new data at little cost. Moreover, our algorithm works in the standard oracle model, and can handle data sets with nonsparse design matrices. It runs in time poly( log2(N ) ,d ,κ ,1 /ɛ ) , where N is the size of the data set, d is the number of adjustable parameters, κ is the condition number of the design matrix, and ɛ is the desired precision in the output. We also show that the polynomial dependence on d and κ is necessary. Thus, our algorithm cannot be significantly improved. Furthermore, we also give a quantum algorithm that estimates the quality of the least-squares fit (without computing its parameters explicitly). This algorithm runs faster than the one for finding this fit, and can be used to check whether the given data set qualifies for linear regression in the first place.

New method to incorporate Type B uncertainty into least-squares procedures in radionuclide metrology.

PubMed

Han, Jubong; Lee, K B; Lee, Jong-Man; Park, Tae Soon; Oh, J S; Oh, Pil-Jei

2016-03-01

We discuss a new method to incorporate Type B uncertainty into least-squares procedures. The new method is based on an extension of the likelihood function from which a conventional least-squares function is derived. The extended likelihood function is the product of the original likelihood function with additional PDFs (Probability Density Functions) that characterize the Type B uncertainties. The PDFs are considered to describe one's incomplete knowledge on correction factors being called nuisance parameters. We use the extended likelihood function to make point and interval estimations of parameters in the basically same way as the least-squares function used in the conventional least-squares method is derived. Since the nuisance parameters are not of interest and should be prevented from appearing in the final result, we eliminate such nuisance parameters by using the profile likelihood. As an example, we present a case study for a linear regression analysis with a common component of Type B uncertainty. In this example we compare the analysis results obtained from using our procedure with those from conventional methods. Copyright © 2015. Published by Elsevier Ltd.

Local polynomial estimation of heteroscedasticity in a multivariate linear regression model and its applications in economics.

PubMed

Su, Liyun; Zhao, Yanyong; Yan, Tianshun; Li, Fenglan

2012-01-01

Multivariate local polynomial fitting is applied to the multivariate linear heteroscedastic regression model. Firstly, the local polynomial fitting is applied to estimate heteroscedastic function, then the coefficients of regression model are obtained by using generalized least squares method. One noteworthy feature of our approach is that we avoid the testing for heteroscedasticity by improving the traditional two-stage method. Due to non-parametric technique of local polynomial estimation, it is unnecessary to know the form of heteroscedastic function. Therefore, we can improve the estimation precision, when the heteroscedastic function is unknown. Furthermore, we verify that the regression coefficients is asymptotic normal based on numerical simulations and normal Q-Q plots of residuals. Finally, the simulation results and the local polynomial estimation of real data indicate that our approach is surely effective in finite-sample situations.

Size distribution of Portuguese firms between 2006 and 2012

NASA Astrophysics Data System (ADS)

Pascoal, Rui; Augusto, Mário; Monteiro, A. M.

2016-09-01

This study aims to describe the size distribution of Portuguese firms, as measured by annual sales and total assets, between 2006 and 2012, giving an economic interpretation for the evolution of the distribution along the time. Three distributions are fitted to data: the lognormal, the Pareto (and as a particular case Zipf) and the Simplified Canonical Law (SCL). We present the main arguments found in literature to justify the use of distributions and emphasize the interpretation of SCL coefficients. Methods of estimation include Maximum Likelihood, modified Ordinary Least Squares in log-log scale and Nonlinear Least Squares considering the Levenberg-Marquardt algorithm. When applying these approaches to Portuguese's firms data, we analyze if the evolution of estimated parameters in both lognormal power and SCL is in accordance with the known existence of a recession period after 2008. This is confirmed for sales but not for assets, leading to the conclusion that the first variable is a best proxy for firm size.

The program LOPT for least-squares optimization of energy levels

NASA Astrophysics Data System (ADS)

Kramida, A. E.

2011-02-01

The article describes a program that solves the least-squares optimization problem for finding the energy levels of a quantum-mechanical system based on a set of measured energy separations or wavelengths of transitions between those energy levels, as well as determining the Ritz wavelengths of transitions and their uncertainties. The energy levels are determined by solving the matrix equation of the problem, and the uncertainties of the Ritz wavenumbers are determined from the covariance matrix of the problem. Program summaryProgram title: LOPT Catalogue identifier: AEHM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHM_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 19 254 No. of bytes in distributed program, including test data, etc.: 427 839 Distribution format: tar.gz Programming language: Perl v.5 Computer: PC, Mac, Unix workstations Operating system: MS Windows (XP, Vista, 7), Mac OS X, Linux, Unix (AIX) RAM: 3 Mwords or more Word size: 32 or 64 Classification: 2.2 Nature of problem: The least-squares energy-level optimization problem, i.e., finding a set of energy level values that best fits the given set of transition intervals. Solution method: The solution of the least-squares problem is found by solving the corresponding linear matrix equation, where the matrix is constructed using a new method with variable substitution. Restrictions: A practical limitation on the size of the problem N is imposed by the execution time, which scales as N and depends on the computer. Unusual features: Properly rounds the resulting data and formats the output in a format suitable for viewing with spreadsheet editing software. Estimates numerical errors resulting from the limited machine precision. Running time: 1 s for N=100, or 60 s for N=400 on a typical PC.

Multi-element least square HDMR methods and their applications for stochastic multiscale model reduction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiang, Lijian, E-mail: ljjiang@hnu.edu.cn; Li, Xinping, E-mail: exping@126.com

Stochastic multiscale modeling has become a necessary approach to quantify uncertainty and characterize multiscale phenomena for many practical problems such as flows in stochastic porous media. The numerical treatment of the stochastic multiscale models can be very challengeable as the existence of complex uncertainty and multiple physical scales in the models. To efficiently take care of the difficulty, we construct a computational reduced model. To this end, we propose a multi-element least square high-dimensional model representation (HDMR) method, through which the random domain is adaptively decomposed into a few subdomains, and a local least square HDMR is constructed in eachmore » subdomain. These local HDMRs are represented by a finite number of orthogonal basis functions defined in low-dimensional random spaces. The coefficients in the local HDMRs are determined using least square methods. We paste all the local HDMR approximations together to form a global HDMR approximation. To further reduce computational cost, we present a multi-element reduced least-square HDMR, which improves both efficiency and approximation accuracy in certain conditions. To effectively treat heterogeneity properties and multiscale features in the models, we integrate multiscale finite element methods with multi-element least-square HDMR for stochastic multiscale model reduction. This approach significantly reduces the original model's complexity in both the resolution of the physical space and the high-dimensional stochastic space. We analyze the proposed approach, and provide a set of numerical experiments to demonstrate the performance of the presented model reduction techniques. - Highlights: • Multi-element least square HDMR is proposed to treat stochastic models. • Random domain is adaptively decomposed into some subdomains to obtain adaptive multi-element HDMR. • Least-square reduced HDMR is proposed to enhance computation efficiency and approximation accuracy in certain conditions. • Integrating MsFEM and multi-element least square HDMR can significantly reduce computation complexity.« less

An interactive graphics program to retrieve, display, compare, manipulate, curve fit, difference and cross plot wind tunnel data

NASA Technical Reports Server (NTRS)

Elliott, R. D.; Werner, N. M.; Baker, W. M.

1975-01-01

The Aerodynamic Data Analysis and Integration System (ADAIS), developed as a highly interactive computer graphics program capable of manipulating large quantities of data such that addressable elements of a data base can be called up for graphic display, compared, curve fit, stored, retrieved, differenced, etc., was described. The general nature of the system is evidenced by the fact that limited usage has already occurred with data bases consisting of thermodynamic, basic loads, and flight dynamics data. Productivity using ADAIS of five times that for conventional manual methods of wind tunnel data analysis is routinely achieved. In wind tunnel data analysis, data from one or more runs of a particular test may be called up and displayed along with data from one or more runs of a different test. Curves may be faired through the data points by any of four methods, including cubic spline and least squares polynomial fit up to seventh order.

Simultaneous estimation of plasma parameters from spectroscopic data of neutral helium using least square fitting of CR-model

NASA Astrophysics Data System (ADS)

Jain, Jalaj; Prakash, Ram; Vyas, Gheesa Lal; Pal, Udit Narayan; Chowdhuri, Malay Bikas; Manchanda, Ranjana; Halder, Nilanjan; Choyal, Yaduvendra

2015-12-01

In the present work an effort has been made to estimate the plasma parameters simultaneously like—electron density, electron temperature, ground state atom density, ground state ion density and metastable state density from the observed visible spectra of penning plasma discharge (PPD) source using least square fitting. The analysis is performed for the prominently observed neutral helium lines. The atomic data and analysis structure (ADAS) database is used to provide the required collisional-radiative (CR) photon emissivity coefficients (PECs) values under the optical thin plasma condition in the analysis. With this condition the estimated plasma temperature from the PPD is found rather high. It is seen that the inclusion of opacity in the observed spectral lines through PECs and addition of diffusion of neutrals and metastable state species in the CR-model code analysis improves the electron temperature estimation in the simultaneous measurement.

Simultaneous quantitative analysis of olmesartan, amlodipine and hydrochlorothiazide in their combined dosage form utilizing classical and alternating least squares based chemometric methods.

PubMed

Darwish, Hany W; Bakheit, Ahmed H; Abdelhameed, Ali S

2016-03-01

Simultaneous spectrophotometric analysis of a multi-component dosage form of olmesartan, amlodipine and hydrochlorothiazide used for the treatment of hypertension has been carried out using various chemometric methods. Multivariate calibration methods include classical least squares (CLS) executed by net analyte processing (NAP-CLS), orthogonal signal correction (OSC-CLS) and direct orthogonal signal correction (DOSC-CLS) in addition to multivariate curve resolution-alternating least squares (MCR-ALS). Results demonstrated the efficiency of the proposed methods as quantitative tools of analysis as well as their qualitative capability. The three analytes were determined precisely using the aforementioned methods in an external data set and in a dosage form after optimization of experimental conditions. Finally, the efficiency of the models was validated via comparison with the partial least squares (PLS) method in terms of accuracy and precision.

Multiparameter linear least-squares fitting to Poisson data one count at a time

NASA Technical Reports Server (NTRS)

Wheaton, Wm. A.; Dunklee, Alfred L.; Jacobsen, Allan S.; Ling, James C.; Mahoney, William A.; Radocinski, Robert G.

1995-01-01

A standard problem in gamma-ray astronomy data analysis is the decomposition of a set of observed counts, described by Poisson statistics, according to a given multicomponent linear model, with underlying physical count rates or fluxes which are to be estimated from the data. Despite its conceptual simplicity, the linear least-squares (LLSQ) method for solving this problem has generally been limited to situations in which the number n(sub i) of counts in each bin i is not too small, conventionally more than 5-30. It seems to be widely believed that the failure of the LLSQ method for small counts is due to the failure of the Poisson distribution to be even approximately normal for small numbers. The cause is more accurately the strong anticorrelation between the data and the wieghts w(sub i) in the weighted LLSQ method when square root of n(sub i) instead of square root of bar-n(sub i) is used to approximate the uncertainties, sigma(sub i), in the data, where bar-n(sub i) = E(n(sub i)), the expected value of N(sub i). We show in an appendix that, avoiding this approximation, the correct equations for the Poisson LLSQ (PLLSQ) problems are actually identical to those for the maximum likelihood estimate using the exact Poisson distribution. We apply the method to solve a problem in high-resolution gamma-ray spectroscopy for the JPL High-Resolution Gamma-Ray Spectrometer flown on HEAO 3. Systematic error in subtracting the strong, highly variable background encountered in the low-energy gamma-ray region can be significantly reduced by closely pairing source and background data in short segments. Significant results can be built up by weighted averaging of the net fluxes obtained from the subtraction of many individual source/background pairs. Extension of the approach to complex situations, with multiple cosmic sources and realistic background parameterizations, requires a means of efficiently fitting to data from single scans in the narrow (approximately = 1.2 keV, HEAO 3) energy channels of a Ge spectrometer, where the expected number of counts obtained per scan may be very low. Such an analysis system is discussed and compared to the method previously used.

An error analysis of least-squares finite element method of velocity-pressure-vorticity formulation for Stokes problem

NASA Technical Reports Server (NTRS)

Chang, Ching L.; Jiang, Bo-Nan

1990-01-01

A theoretical proof of the optimal rate of convergence for the least-squares method is developed for the Stokes problem based on the velocity-pressure-vorticity formula. The 2D Stokes problem is analyzed to define the product space and its inner product, and the a priori estimates are derived to give the finite-element approximation. The least-squares method is found to converge at the optimal rate for equal-order interpolation.

MEM spectral analysis for predicting influenza epidemics in Japan.

PubMed

Sumi, Ayako; Kamo, Ken-ichi

2012-03-01

The prediction of influenza epidemics has long been the focus of attention in epidemiology and mathematical biology. In this study, we tested whether time series analysis was useful for predicting the incidence of influenza in Japan. The method of time series analysis we used consists of spectral analysis based on the maximum entropy method (MEM) in the frequency domain and the nonlinear least squares method in the time domain. Using this time series analysis, we analyzed the incidence data of influenza in Japan from January 1948 to December 1998; these data are unique in that they covered the periods of pandemics in Japan in 1957, 1968, and 1977. On the basis of the MEM spectral analysis, we identified the periodic modes explaining the underlying variations of the incidence data. The optimum least squares fitting (LSF) curve calculated with the periodic modes reproduced the underlying variation of the incidence data. An extension of the LSF curve could be used to predict the incidence of influenza quantitatively. Our study suggested that MEM spectral analysis would allow us to model temporal variations of influenza epidemics with multiple periodic modes much more effectively than by using the method of conventional time series analysis, which has been used previously to investigate the behavior of temporal variations in influenza data.

2-D weighted least-squares phase unwrapping

DOEpatents

Ghiglia, Dennis C.; Romero, Louis A.

1995-01-01

Weighted values of interferometric signals are unwrapped by determining the least squares solution of phase unwrapping for unweighted values of the interferometric signals; and then determining the least squares solution of phase unwrapping for weighted values of the interferometric signals by preconditioned conjugate gradient methods using the unweighted solutions as preconditioning values. An output is provided that is representative of the least squares solution of phase unwrapping for weighted values of the interferometric signals.

2-D weighted least-squares phase unwrapping

DOEpatents

Ghiglia, D.C.; Romero, L.A.

1995-06-13

Weighted values of interferometric signals are unwrapped by determining the least squares solution of phase unwrapping for unweighted values of the interferometric signals; and then determining the least squares solution of phase unwrapping for weighted values of the interferometric signals by preconditioned conjugate gradient methods using the unweighted solutions as preconditioning values. An output is provided that is representative of the least squares solution of phase unwrapping for weighted values of the interferometric signals. 6 figs.

Lunar-edge based on-orbit modulation transfer function (MTF) measurement

NASA Astrophysics Data System (ADS)

Cheng, Ying; Yi, Hongwei; Liu, Xinlong

2017-10-01

Modulation transfer function (MTF) is an important parameter for image quality evaluation of on-orbit optical image systems. Various methods have been proposed to determine the MTF of an imaging system which are based on images containing point, pulse and edge features. In this paper, the edge of the moon can be used as a high contrast target to measure on-orbit MTF of image systems based on knife-edge methods. The proposed method is an extension of the ISO 12233 Slanted-edge Spatial Frequency Response test, except that the shape of the edge is a circular arc instead of a straight line. In order to get more accurate edge locations and then obtain a more authentic edge spread function (ESF), we choose circular fitting method based on least square to fit lunar edge in sub-pixel edge detection process. At last, simulation results show that the MTF value at Nyquist frequency calculated using our lunar edge method is reliable and accurate with error less than 2% comparing with theoretical MTF value.

Tensile stress-strain behavior of graphite/epoxy laminates

NASA Technical Reports Server (NTRS)

Garber, D. P.

1982-01-01

The tensile stress-strain behavior of a variety of graphite/epoxy laminates was examined. Longitudinal and transverse specimens from eleven different layups were monotonically loaded in tension to failure. Ultimate strength, ultimate strain, and strss-strain curves wee obtained from four replicate tests in each case. Polynominal equations were fitted by the method of least squares to the stress-strain data to determine average curves. Values of Young's modulus and Poisson's ratio, derived from polynomial coefficients, were compared with laminate analysis results. While the polynomials appeared to accurately fit the stress-strain data in most cases, the use of polynomial coefficients to calculate elastic moduli appeared to be of questionable value in cases involving sharp changes in the slope of the stress-strain data or extensive scatter.

Relation between the Surface Friction of Plates and their Statistical Microgeometry

DTIC Science & Technology

1980-01-01

3-6 and 𔃽-7. Calibration-- are taken for each of the Uicr~r unit exponent values and best fit li;nes by least squares fitted through each"n set of...parameter, [ = 1.de (2-43) (Clauser 1954, 1956). Data from near equilibrium flows (Coles & Hurst 1968) was plotted along with some typical non-equilibrium...too bad a fit even for the non equilibrium flows. Coles and Hurst (1968) recommended that the fit of the law of the wake to velocity profiles should be

Spacecraft inertia estimation via constrained least squares

NASA Technical Reports Server (NTRS)

Keim, Jason A.; Acikmese, Behcet A.; Shields, Joel F.

2006-01-01

This paper presents a new formulation for spacecraft inertia estimation from test data. Specifically, the inertia estimation problem is formulated as a constrained least squares minimization problem with explicit bounds on the inertia matrix incorporated as LMIs [linear matrix inequalities). The resulting minimization problem is a semidefinite optimization that can be solved efficiently with guaranteed convergence to the global optimum by readily available algorithms. This method is applied to data collected from a robotic testbed consisting of a freely rotating body. The results show that the constrained least squares approach produces more accurate estimates of the inertia matrix than standard unconstrained least squares estimation methods.

Orthogonalizing EM: A design-based least squares algorithm

PubMed Central

Xiong, Shifeng; Dai, Bin; Huling, Jared; Qian, Peter Z. G.

2016-01-01

We introduce an efficient iterative algorithm, intended for various least squares problems, based on a design of experiments perspective. The algorithm, called orthogonalizing EM (OEM), works for ordinary least squares and can be easily extended to penalized least squares. The main idea of the procedure is to orthogonalize a design matrix by adding new rows and then solve the original problem by embedding the augmented design in a missing data framework. We establish several attractive theoretical properties concerning OEM. For the ordinary least squares with a singular regression matrix, an OEM sequence converges to the Moore-Penrose generalized inverse-based least squares estimator. For ordinary and penalized least squares with various penalties, it converges to a point having grouping coherence for fully aliased regression matrices. Convergence and the convergence rate of the algorithm are examined. Finally, we demonstrate that OEM is highly efficient for large-scale least squares and penalized least squares problems, and is considerably faster than competing methods when n is much larger than p. Supplementary materials for this article are available online. PMID:27499558

Cylinder surface test with Chebyshev polynomial fitting method

NASA Astrophysics Data System (ADS)

Yu, Kui-bang; Guo, Pei-ji; Chen, Xi

2017-10-01

Zernike polynomials fitting method is often applied in the test of optical components and systems, used to represent the wavefront and surface error in circular domain. Zernike polynomials are not orthogonal in rectangular region which results in its unsuitable for the test of optical element with rectangular aperture such as cylinder surface. Applying the Chebyshev polynomials which are orthogonal among the rectangular area as an substitution to the fitting method, can solve the problem. Corresponding to a cylinder surface with diameter of 50 mm and F number of 1/7, a measuring system has been designed in Zemax based on Fizeau Interferometry. The expressions of the two-dimensional Chebyshev polynomials has been given and its relationship with the aberration has been presented. Furthermore, Chebyshev polynomials are used as base items to analyze the rectangular aperture test data. The coefficient of different items are obtained from the test data through the method of least squares. Comparing the Chebyshev spectrum in different misalignment, it show that each misalignment is independence and has a certain relationship with the certain Chebyshev terms. The simulation results show that, through the Legendre polynomials fitting method, it will be a great improvement in the efficient of the detection and adjustment of the cylinder surface test.

Spreadsheet for designing valid least-squares calibrations: A tutorial.

PubMed

Bettencourt da Silva, Ricardo J N

2016-02-01

Instrumental methods of analysis are used to define the price of goods, the compliance of products with a regulation, or the outcome of fundamental or applied research. These methods can only play their role properly if reported information is objective and their quality is fit for the intended use. If measurement results are reported with an adequately small measurement uncertainty both of these goals are achieved. The evaluation of the measurement uncertainty can be performed by the bottom-up approach, that involves a detailed description of the measurement process, or using a pragmatic top-down approach that quantify major uncertainty components from global performance data. The bottom-up approach is not so frequently used due to the need to master the quantification of individual components responsible for random and systematic effects that affect measurement results. This work presents a tutorial that can be easily used by non-experts in the accurate evaluation of the measurement uncertainty of instrumental methods of analysis calibrated using least-squares regressions. The tutorial includes the definition of the calibration interval, the assessments of instrumental response homoscedasticity, the definition of calibrators preparation procedure required for least-squares regression model application, the assessment of instrumental response linearity and the evaluation of measurement uncertainty. The developed measurement model is only applicable in calibration ranges where signal precision is constant. A MS-Excel file is made available to allow the easy application of the tutorial. This tool can be useful for cases where top-down approaches cannot produce results with adequately low measurement uncertainty. An example of the application of this tool to the determination of nitrate in water by ion chromatography is presented. Copyright © 2015 Elsevier B.V. All rights reserved.

Mathcad in the Chemistry Curriculum Symbolic Software in the Chemistry Curriculum

NASA Astrophysics Data System (ADS)

Zielinski, Theresa Julia

2000-05-01

Physical chemistry is such a broad discipline that the topics we expect average students to complete in two semesters usually exceed their ability for meaningful learning. Consequently, the number and kind of topics and the efficiency with which students can learn them are important concerns. What topics are essential and what can we do to provide efficient and effective access to those topics? How do we accommodate the fact that students come to upper-division chemistry courses with a variety of nonuniformly distributed skills, a bit of calculus, and some physics studied one or more years before physical chemistry? The critical balance between depth and breadth of learning in courses and curricula may be achieved through appropriate use of technology and especially through the use of symbolic mathematics software. Software programs such as Mathcad, Mathematica, and Maple, however, have learning curves that diminish their effectiveness for novices. There are several ways to address the learning curve conundrum. First, basic instruction in the software provided during laboratory sessions should be followed by requiring laboratory reports that use the software. Second, one should assign weekly homework that requires the software and builds student skills within the discipline and with the software. Third, a complementary method, supported by this column, is to provide students with Mathcad worksheets or templates that focus on one set of related concepts and incorporate a variety of features of the software that they are to use to learn chemistry. In this column we focus on two significant topics for young chemists. The first is curve-fitting and the statistical analysis of the fitting parameters. The second is the analysis of the rotation/vibration spectrum of a diatomic molecule, HCl. A broad spectrum of Mathcad documents exists for teaching chemistry. One collection of 50 documents can be found at http://www.monmouth.edu/~tzielins/mathcad/Lists/index.htm. Another collection of peer-reviewed documents is developing through this column at the JCE Internet Web site, http://jchemed.chem.wisc.edu/JCEWWW/Features/ McadInChem/index.html. With this column we add three peer-reviewed and tested Mathcad documents to the JCE site. In Linear Least-Squares Regression, Sidney H. Young and Andrzej Wierzbicki demonstrate various implicit and explicit methods for determining the slope and intercept of the regression line for experimental data. The document shows how to determine the standard deviation for the slope, the intercept, and the standard deviation of the overall fit. Students are next given the opportunity to examine the confidence level for the fit through the Student's t-test. Examination of the residuals of the fit leads students to explore the possibility of rejecting points in a set of data. The document concludes with a discussion of and practice with adding a quadratic term to create a polynomial fit to a set of data and how to determine if the quadratic term is statistically significant. There is full documentation of the various steps used throughout the exposition of the statistical concepts. Although the statistical methods presented in this worksheet are generally accessible to average physical chemistry students, an instructor would be needed to explain the finer points of the matrix methods used in some sections of the worksheet. The worksheet is accompanied by a set of data for students to use to practice the techniques presented. It would be worthwhile for students to spend one or two laboratory periods learning to use the concepts presented and then to apply them to experimental data they have collected for themselves. Any linear or linearizable data set would be appropriate for use with this Mathcad worksheet. Alternatively, instructors may select sections of the document suited to the skill level of their students and the laboratory tasks at hand. In a second Mathcad document, Non-Linear Least-Squares Regression, Young and Wierzbicki introduce the basic concepts of nonlinear curve-fitting and develop the techniques needed to fit a variety of mathematical functions to experimental data. This approach is especially important when mathematical models for chemical processes cannot be linearized. In Mathcad the Levenberg-Marquardt algorithm is used to determine the best fitting parameters for a particular mathematical model. As in linear least-squares, the goal of the fitting process is to find the values for the fitting parameters that minimize the sum of the squares of the deviations between the data and the mathematical model. Students are asked to determine the fitting parameters, use the Hessian matrix to compute the standard deviation of the fitting parameters, test for the significance of the parameters using Student's t-test, use residual analysis to test for data points to remove, and repeat the calculations for another set of data. The nonlinear least-squares procedure follows closely on the pattern set up for linear least-squares by the same authors (see above). If students master the linear least-squares worksheet content they will be able to master the nonlinear least-squares technique (see also refs 1, 2). In the third document, The Analysis of the Vibrational Spectrum of a Linear Molecule by Richard Schwenz, William Polik, and Sidney Young, the authors build on the concepts presented in the curve fitting worksheets described above. This vibrational analysis document, which supports a classic experiment performed in the physical chemistry laboratory, shows how a Mathcad worksheet can increase the efficiency by which a set of complicated manipulations for data reduction can be made more accessible for students. The increase in efficiency frees up time for students to develop a fuller understanding of the physical chemistry concepts important to the interpretation of spectra and understanding of bond vibrations in general. The analysis of the vibration/rotation spectrum for a linear molecule worksheet builds on the rich literature for this topic (3). Before analyzing their own spectral data, students practice and learn the concepts and methods of the HCl spectral analysis by using the fundamental and first harmonic vibrational frequencies provided by the authors. This approach has a fundamental pedagogical advantage. Most explanations in laboratory texts are very concise and lack mathematical details required by average students. This Mathcad worksheet acts as a tutor; it guides students through the essential concepts for data reduction and lets them focus on learning important spectroscopic concepts. The Mathcad worksheet is amply annotated. Students who have moderate skill with the software and have learned about regression analysis from the curve-fitting worksheets described in this column will be able to complete and understand their analysis of the IR spectrum of HCl. The three Mathcad worksheets described here stretch the physical chemistry curriculum by presenting important topics in forms that students can use with only moderate Mathcad skills. The documents facilitate learning by giving students opportunities to interact with the material in meaningful ways in addition to using the documents as sources of techniques for building their own data-reduction worksheets. However, working through these Mathcad worksheets is not a trivial task for the average student. Support needs to be provided by the instructor to ease students through more advanced mathematical and Mathcad processes. These worksheets raise the question of how much we can ask diligent students to do in one course and how much time they need to spend to master the essential concepts of that course. The Mathcad documents and associated PDF versions are available at the JCE Internet WWW site. The Mathcad documents require Mathcad version 6.0 or higher and the PDF files require Adobe Acrobat. Every effort has been made to make the documents fully compatible across the various Mathcad versions. Users may need to refer to Mathcad manuals for functions that vary with the Mathcad version number. Literature Cited 1. Bevington, P. R. Data Reduction and Error Analysis for the Physical Sciences; McGraw-Hill: New York, 1969. 2. Zielinski, T. J.; Allendoerfer, R. D. J. Chem. Educ. 1997, 74, 1001. 3. Schwenz, R. W.; Polik, W. F. J. Chem. Educ. 1999, 76, 1302.

Numerical inverse method predicting acoustic spinning modes radiated by a ducted fan from free-field test data.

PubMed

Lewy, Serge

2008-07-01

Spinning modes generated by a ducted turbofan at a given frequency determine the acoustic free-field directivity. An inverse method starting from measured directivity patterns is interesting in providing information on the noise sources without requiring tedious spinning-mode experimental analyses. According to a previous article, equations are based on analytical modal splitting inside a cylindrical duct and on a Rayleigh or a Kirchhoff integral on the duct exit cross section to get far-field directivity. Equations are equal in number to free-field measurement locations and the unknowns are the propagating mode amplitudes (there are generally more unknowns than equations). A MATLAB procedure has been implemented by using either the pseudoinverse function or the backslash operator. A constraint comes from the fact that squared modal amplitudes must be positive which involves an iterative least squares fitting. Numerical simulations are discussed along with several examples based on tests performed by Rolls-Royce in the framework of a European project. It is assessed that computation is very fast and it well fits the measured directivities, but the solution depends on the method and is not unique. This means that the initial set of modes should be chosen according to any known physical property of the acoustic sources.

Application of several methods for determining transfer functions and frequency response of aircraft from flight data

NASA Technical Reports Server (NTRS)

Eggleston, John M; Mathews, Charles W

1954-01-01

In the process of analyzing the longitudinal frequency-response characteristics of aircraft, information on some of the methods of analysis has been obtained by the Langley Aeronautical Laboratory of the National Advisory Committee for Aeronautics. In the investigation of these methods, the practical applications and limitations were stressed. In general, the methods considered may be classed as: (1) analysis of sinusoidal response, (2) analysis of transient response as to harmonic content through determination of the Fourier integral by manual or machine methods, and (3) analysis of the transient through the use of least-squares solutions of the coefficients of an assumed equation for either the transient time response or frequency response (sometimes referred to as curve-fitting methods). (author)

Uncertainty based pressure reconstruction from velocity measurement with generalized least squares

NASA Astrophysics Data System (ADS)

Zhang, Jiacheng; Scalo, Carlo; Vlachos, Pavlos

2017-11-01

A method using generalized least squares reconstruction of instantaneous pressure field from velocity measurement and velocity uncertainty is introduced and applied to both planar and volumetric flow data. Pressure gradients are computed on a staggered grid from flow acceleration. The variance-covariance matrix of the pressure gradients is evaluated from the velocity uncertainty by approximating the pressure gradient error to a linear combination of velocity errors. An overdetermined system of linear equations which relates the pressure and the computed pressure gradients is formulated and then solved using generalized least squares with the variance-covariance matrix of the pressure gradients. By comparing the reconstructed pressure field against other methods such as solving the pressure Poisson equation, the omni-directional integration, and the ordinary least squares reconstruction, generalized least squares method is found to be more robust to the noise in velocity measurement. The improvement on pressure result becomes more remarkable when the velocity measurement becomes less accurate and more heteroscedastic. The uncertainty of the reconstructed pressure field is also quantified and compared across the different methods.

Simultaneous Intrinsic and Extrinsic Parameter Identification of a Hand-Mounted Laser-Vision Sensor

PubMed Central

Lee, Jong Kwang; Kim, Kiho; Lee, Yongseok; Jeong, Taikyeong

2011-01-01

In this paper, we propose a simultaneous intrinsic and extrinsic parameter identification of a hand-mounted laser-vision sensor (HMLVS). A laser-vision sensor (LVS), consisting of a camera and a laser stripe projector, is used as a sensor component of the robotic measurement system, and it measures the range data with respect to the robot base frame using the robot forward kinematics and the optical triangulation principle. For the optimal estimation of the model parameters, we applied two optimization techniques: a nonlinear least square optimizer and a particle swarm optimizer. Best-fit parameters, including both the intrinsic and extrinsic parameters of the HMLVS, are simultaneously obtained based on the least-squares criterion. From the simulation and experimental results, it is shown that the parameter identification problem considered was characterized by a highly multimodal landscape; thus, the global optimization technique such as a particle swarm optimization can be a promising tool to identify the model parameters for a HMLVS, while the nonlinear least square optimizer often failed to find an optimal solution even when the initial candidate solutions were selected close to the true optimum. The proposed optimization method does not require good initial guesses of the system parameters to converge at a very stable solution and it could be applied to a kinematically dissimilar robot system without loss of generality. PMID:22164104

Unsteady Aerodynamic Force Sensing from Strain Data

NASA Technical Reports Server (NTRS)

Pak, Chan-Gi

2017-01-01

A simple approach for computing unsteady aerodynamic forces from simulated measured strain data is proposed in this study. First, the deflection and slope of the structure are computed from the unsteady strain using the two-step approach. Velocities and accelerations of the structure are computed using the autoregressive moving average model, on-line parameter estimator, low-pass filter, and a least-squares curve fitting method together with analytical derivatives with respect to time. Finally, aerodynamic forces over the wing are computed using modal aerodynamic influence coefficient matrices, a rational function approximation, and a time-marching algorithm.

A method for nonlinear exponential regression analysis

NASA Technical Reports Server (NTRS)

Junkin, B. G.

1971-01-01

A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.

Level Energies, Oscillator Strengths and Lifetimes for Transitions in Pb IV

DOE Office of Scientific and Technical Information (OSTI.GOV)

Colon, C.; Alonso-Medina, A.; Zanon, A.

2008-10-22

Oscillator strengths for several lines of astrophysical interest arising from some configurations and some levels radiative lifetimes of Pb IV have been calculated. These values were obtained in intermediate coupling (IC) and using ab initio relativistic Hartree-Fock calculations. We use for the IC calculations the standard method of least square fitting of experimental energy levels by means of computer codes from Cowan. Transition Probabilities and oscillator strengths obtained, although in general agreement with the rare experimental data, do present some noticeable discrepancies that are studied in the text.

Effects of vegetation canopy on the radar backscattering coefficient

NASA Technical Reports Server (NTRS)

Mo, T.; Blanchard, B. J.; Schmugge, T. J.

1983-01-01

Airborne L- and C-band scatterometer data, taken over both vegetation-covered and bare fields, were systematically analyzed and theoretically reproduced, using a recently developed model for calculating radar backscattering coefficients of rough soil surfaces. The results show that the model can reproduce the observed angular variations of radar backscattering coefficient quite well via a least-squares fit method. Best fits to the data provide estimates of the statistical properties of the surface roughness, which is characterized by two parameters: the standard deviation of surface height, and the surface correlation length. In addition, the processes of vegetation attenuation and volume scattering require two canopy parameters, the canopy optical thickness and a volume scattering factor. Canopy parameter values for individual vegetation types, including alfalfa, milo and corn, were also determined from the best-fit results. The uncertainties in the scatterometer data were also explored.

Estimation of time- and state-dependent delays and other parameters in functional differential equations

NASA Technical Reports Server (NTRS)

Murphy, K. A.

1988-01-01

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Measurement and fitting techniques for the assessment of material nonlinearity using nonlinear Rayleigh waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Torello, David; Kim, Jin-Yeon; Qu, Jianmin

2015-03-31

This research considers the effects of diffraction, attenuation, and the nonlinearity of generating sources on measurements of nonlinear ultrasonic Rayleigh wave propagation. A new theoretical framework for correcting measurements made with air-coupled and contact piezoelectric receivers for the aforementioned effects is provided based on analytical models and experimental considerations. A method for extracting the nonlinearity parameter β{sub 11} is proposed based on a nonlinear least squares curve-fitting algorithm that is tailored for Rayleigh wave measurements. Quantitative experiments are conducted to confirm the predictions for the nonlinearity of the piezoelectric source and to demonstrate the effectiveness of the curve-fitting procedure. Thesemore » experiments are conducted on aluminum 2024 and 7075 specimens and a β{sub 11}{sup 7075}/β{sub 11}{sup 2024} measure of 1.363 agrees well with previous literature and earlier work.« less

Estimation of time- and state-dependent delays and other parameters in functional differential equations

NASA Technical Reports Server (NTRS)

Murphy, K. A.

1990-01-01

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

A synthetic method of solar spectrum based on LED

NASA Astrophysics Data System (ADS)

Wang, Ji-qiang; Su, Shi; Zhang, Guo-yu; Zhang, Jian

2017-10-01

A synthetic method of solar spectrum which based on the spectral characteristics of the solar spectrum and LED, and the principle of arbitrary spectral synthesis was studied by using 14 kinds of LED with different central wavelengths.The LED and solar spectrum data were selected by Origin Software firstly, then calculated the total number of LED for each center band by the transformation relation between brightness and illumination and Least Squares Curve Fit in Matlab.Finally, the spectrum curve of AM1.5 standard solar spectrum was obtained. The results met the technical indexes of the solar spectrum matching with ±20% and the solar constant with >0.5.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Hao; Zhang, Guifu; Zhao, Kun

A hybrid method of combining linear programming (LP) and physical constraints is developed to estimate specific differential phase (K DP) and to improve rain estimation. Moreover, the hybrid K DP estimator and the existing estimators of LP, least squares fitting, and a self-consistent relation of polarimetric radar variables are evaluated and compared using simulated data. Our simulation results indicate the new estimator's superiority, particularly in regions where backscattering phase (δ hv) dominates. Further, a quantitative comparison between auto-weather-station rain-gauge observations and K DP-based radar rain estimates for a Meiyu event also demonstrate the superiority of the hybrid K DP estimatormore » over existing methods.« less

Generalizations of Tikhonov's regularized method of least squares to non-Euclidean vector norms

NASA Astrophysics Data System (ADS)

Volkov, V. V.; Erokhin, V. I.; Kakaev, V. V.; Onufrei, A. Yu.

2017-09-01

Tikhonov's regularized method of least squares and its generalizations to non-Euclidean norms, including polyhedral, are considered. The regularized method of least squares is reduced to mathematical programming problems obtained by "instrumental" generalizations of the Tikhonov lemma on the minimal (in a certain norm) solution of a system of linear algebraic equations with respect to an unknown matrix. Further studies are needed for problems concerning the development of methods and algorithms for solving reduced mathematical programming problems in which the objective functions and admissible domains are constructed using polyhedral vector norms.

Field determination of the three-dimensional hydraulic conductivity tensor of anisotropic media: 2. Methodology and application to fractured rocks

USGS Publications Warehouse

Hsieh, Paul A.; Neuman, Shlomo P.; Stiles, Gary K.; Simpson, Eugene S.

1985-01-01

The analytical solutions developed in the first paper can be used to interpret the results of cross-hole tests conducted in anisotropic porous or fractured media. In the particular case where the injection and monitoring intervals are short relative to the distance between them, the test results can be analyzed graphically. From the transient variation of hydraulic head in a given monitoring interval, one can determine the directional hydraulic diffusivity, Kd(e)/Ss, and the quantity D/Ss, by curve matching. (Here Kd(e) is directional hydraulic conductivity parallel to the unit vector, e, pointing from the injection to the monitoring interval, Ss is specific storage, and D is the determinant of the hydraulic conductivity tensor, K.) The principal values and directions of K, together with Ss, can then be evaluated by fitting an ellipsoid to the square roots of the directional diffusivities. Ideally, six directional measurements are required. In practice, a larger number of measurements is often necessary to enable fitting an ellipsoid to the data by least squares. If the computed [Kd(e)/ss]½ values fluctuate so severely that a meaningful least squares fit is not possible, one has a direct indication that the subsurface does not behave as a uniform anisotropic medium on the scale of the test. Test results from a granitic rock near Oracle in southern Arizona are presented to illustrate how the method works for fractured rocks. At the site, the Oracle granite is shown to respond as a near-uniform, anisotropic medium, the hydraulic conductivity of which is strongly controlled by the orientations of major fracture sets. The cross-hole test results are shown to be consistent with the results of more than 100 single-hole packer tests conducted at the site.

A component prediction method for flue gas of natural gas combustion based on nonlinear partial least squares method.

PubMed

Cao, Hui; Yan, Xingyu; Li, Yaojiang; Wang, Yanxia; Zhou, Yan; Yang, Sanchun

2014-01-01

Quantitative analysis for the flue gas of natural gas-fired generator is significant for energy conservation and emission reduction. The traditional partial least squares method may not deal with the nonlinear problems effectively. In the paper, a nonlinear partial least squares method with extended input based on radial basis function neural network (RBFNN) is used for components prediction of flue gas. For the proposed method, the original independent input matrix is the input of RBFNN and the outputs of hidden layer nodes of RBFNN are the extension term of the original independent input matrix. Then, the partial least squares regression is performed on the extended input matrix and the output matrix to establish the components prediction model of flue gas. A near-infrared spectral dataset of flue gas of natural gas combustion is used for estimating the effectiveness of the proposed method compared with PLS. The experiments results show that the root-mean-square errors of prediction values of the proposed method for methane, carbon monoxide, and carbon dioxide are, respectively, reduced by 4.74%, 21.76%, and 5.32% compared to those of PLS. Hence, the proposed method has higher predictive capabilities and better robustness.

Triangulation of multistation camera data to locate a curved line in space

NASA Technical Reports Server (NTRS)

Fricke, C. L.

1974-01-01

A method is described for finding the location of a curved line in space from local azimuth as a function of elevation data obtained at several observation sites. A least-squares criterion is used to insure the best fit to the data. The method is applicable to the triangulation of an object having no identifiable structural features, provided its width is very small compared with its length so as to approximate a line in space. The method was implemented with a digital computer program and was successfully applied to data obtained from photographs of a barium ion cloud which traced out the earth's magnetic field line at very high altitudes.

Autonomous celestial navigation based on Earth ultraviolet radiance and fast gradient statistic feature extraction

NASA Astrophysics Data System (ADS)

Lu, Shan; Zhang, Hanmo

2016-01-01

To meet the requirement of autonomous orbit determination, this paper proposes a fast curve fitting method based on earth ultraviolet features to obtain accurate earth vector direction, in order to achieve the high precision autonomous navigation. Firstly, combining the stable characters of earth ultraviolet radiance and the use of transmission model software of atmospheric radiation, the paper simulates earth ultraviolet radiation model on different time and chooses the proper observation band. Then the fast improved edge extracting method combined Sobel operator and local binary pattern (LBP) is utilized, which can both eliminate noises efficiently and extract earth ultraviolet limb features accurately. And earth's centroid locations on simulated images are estimated via the least square fitting method using part of the limb edges. Taken advantage of the estimated earth vector direction and earth distance, Extended Kalman Filter (EKF) is applied to realize the autonomous navigation finally. Experiment results indicate the proposed method can achieve a sub-pixel earth centroid location estimation and extremely enhance autonomous celestial navigation precision.

The role of temperature in reported chickenpox cases from 2000 to 2011 in Japan.

PubMed

Harigane, K; Sumi, A; Mise, K; Kobayashi, N

2015-09-01

Annual periodicities of reported chickenpox cases have been observed in several countries. Of these, Japan has reported a two-peaked, bimodal annual cycle of reported chickenpox cases. This study investigated the possible underlying association of the bimodal cycle observed in the surveillance data of reported chickenpox cases with the meteorological factors of temperature, relative humidity and rainfall. A time-series analysis consisting of the maximum entropy method spectral analysis and the least squares method was applied to the chickenpox data and meteorological data of 47 prefectures in Japan. In all of the power spectral densities for the 47 prefectures, the spectral lines were observed at the frequency positions corresponding to the 1-year and 6-month cycles. The optimum least squares fitting (LSF) curves calculated with the 1-year and 6-month cycles explained the underlying variation of the chickenpox data. The LSF curves reproduced the bimodal and unimodal cycles that were clearly observed in northern and southern Japan, respectively. The data suggest that the second peaks in the bimodal cycles in the reported chickenpox cases in Japan occurred at a temperature of approximately 8·5 °C.

A method of discriminating transuranic radionuclides from radon progeny using low-resolution alpha spectroscopy and curve-fitting techniques.

PubMed

Konzen, Kevin; Brey, Richard

2012-05-01

²²²Rn (radon) and ²²⁰Rn (thoron) progeny are known to interfere with determining the presence of long-lived transuranic radionuclides, such as plutonium and americium, and require from several hours up to several days for conclusive results. Methods are proposed that should expedite the analysis of air samples for determining the amount of transuranic radionuclides present using low-resolution alpha spectroscopy systems available from typical alpha continuous air monitors (CAMs) with multi-channel analyzer (MCA) capabilities. An alpha spectra simulation program was developed in Microsoft Excel visual basic that employed the use of Monte Carlo numerical methods and serial-decay differential equations that resembled actual spectra. Transuranic radionuclides were able to be quantified with statistical certainty by applying peak fitting equations using the method of least squares. Initial favorable results were achieved when samples containing radon progeny were decayed 15 to 30 min, and samples containing both radon and thoron progeny were decayed at least 60 min. The effort indicates that timely decisions can be made when determining transuranic activity using available alpha CAMs with alpha spectroscopy capabilities for counting retrospective air samples if accompanied by analyses that consider the characteristics of serial decay.

Notes and Discussion

ERIC Educational Resources Information Center

American Journal of Physics, 1978

1978-01-01

Includes eleven short notes, comments and responses to comments on a variety of topics such as uncertainty in a least-squares fit, display of diffraction patterns, the dark night sky paradox, error in the dynamics of deformable bodies and relative velocities and the runner. (GA)

SPSS macros to compare any two fitted values from a regression model.

PubMed

Weaver, Bruce; Dubois, Sacha

2012-12-01

In regression models with first-order terms only, the coefficient for a given variable is typically interpreted as the change in the fitted value of Y for a one-unit increase in that variable, with all other variables held constant. Therefore, each regression coefficient represents the difference between two fitted values of Y. But the coefficients represent only a fraction of the possible fitted value comparisons that might be of interest to researchers. For many fitted value comparisons that are not captured by any of the regression coefficients, common statistical software packages do not provide the standard errors needed to compute confidence intervals or carry out statistical tests-particularly in more complex models that include interactions, polynomial terms, or regression splines. We describe two SPSS macros that implement a matrix algebra method for comparing any two fitted values from a regression model. The !OLScomp and !MLEcomp macros are for use with models fitted via ordinary least squares and maximum likelihood estimation, respectively. The output from the macros includes the standard error of the difference between the two fitted values, a 95% confidence interval for the difference, and a corresponding statistical test with its p-value.

Surface fitting three-dimensional bodies

NASA Technical Reports Server (NTRS)

Dejarnette, F. R.

1974-01-01

The geometry of general three-dimensional bodies is generated from coordinates of points in several cross sections. Since these points may not be smooth, they are divided into segments and general conic sections are curve fit in a least-squares sense to each segment of a cross section. The conic sections are then blended in the longitudinal direction by fitting parametric cubic-spline curves through coordinate points which define the conic sections in the cross-sectional planes. Both the cross-sectional and longitudinal curves may be modified by specifying particular segments as straight lines and slopes at selected points. Slopes may be continuous or discontinuous and finite or infinite. After a satisfactory surface fit has been obtained, cards may be punched with the data necessary to form a geometry subroutine package for use in other computer programs. At any position on the body, coordinates, slopes and second partial derivatives are calculated. The method is applied to a blunted 70 deg delta wing, and it was found to generate the geometry very well.

Least Squares Moving-Window Spectral Analysis.

PubMed

Lee, Young Jong

2017-08-01

Least squares regression is proposed as a moving-windows method for analysis of a series of spectra acquired as a function of external perturbation. The least squares moving-window (LSMW) method can be considered an extended form of the Savitzky-Golay differentiation for nonuniform perturbation spacing. LSMW is characterized in terms of moving-window size, perturbation spacing type, and intensity noise. Simulation results from LSMW are compared with results from other numerical differentiation methods, such as single-interval differentiation, autocorrelation moving-window, and perturbation correlation moving-window methods. It is demonstrated that this simple LSMW method can be useful for quantitative analysis of nonuniformly spaced spectral data with high frequency noise.

A curve fitting method for extrinsic camera calibration from a single image of a cylindrical object

NASA Astrophysics Data System (ADS)

Winkler, A. W.; Zagar, B. G.

2013-08-01

An important step in the process of optical steel coil quality assurance is to measure the proportions of width and radius of steel coils as well as the relative position and orientation of the camera. This work attempts to estimate these extrinsic parameters from single images by using the cylindrical coil itself as the calibration target. Therefore, an adaptive least-squares algorithm is applied to fit parametrized curves to the detected true coil outline in the acquisition. The employed model allows for strictly separating the intrinsic and the extrinsic parameters. Thus, the intrinsic camera parameters can be calibrated beforehand using available calibration software. Furthermore, a way to segment the true coil outline in the acquired images is motivated. The proposed optimization method yields highly accurate results and can be generalized even to measure other solids which cannot be characterized by the identification of simple geometric primitives.

Monte Carlo based approach to the LS-NaI 4πβ-γ anticoincidence extrapolation and uncertainty

PubMed Central

Fitzgerald, R.

2016-01-01

The 4πβ-γ anticoincidence method is used for the primary standardization of β−, β+, electron capture (EC), α, and mixed-mode radionuclides. Efficiency extrapolation using one or more γ ray coincidence gates is typically carried out by a low-order polynomial fit. The approach presented here is to use a Geant4-based Monte Carlo simulation of the detector system to analyze the efficiency extrapolation. New code was developed to account for detector resolution, direct γ ray interaction with the PMT, and implementation of experimental β-decay shape factors. The simulation was tuned to 57Co and 60Co data, then tested with 99mTc data, and used in measurements of 18F, 129I, and 124I. The analysis method described here offers a more realistic activity value and uncertainty than those indicated from a least-squares fit alone. PMID:27358944

a Unified Matrix Polynomial Approach to Modal Identification

NASA Astrophysics Data System (ADS)

Allemang, R. J.; Brown, D. L.

1998-04-01

One important current focus of modal identification is a reformulation of modal parameter estimation algorithms into a single, consistent mathematical formulation with a corresponding set of definitions and unifying concepts. Particularly, a matrix polynomial approach is used to unify the presentation with respect to current algorithms such as the least-squares complex exponential (LSCE), the polyreference time domain (PTD), Ibrahim time domain (ITD), eigensystem realization algorithm (ERA), rational fraction polynomial (RFP), polyreference frequency domain (PFD) and the complex mode indication function (CMIF) methods. Using this unified matrix polynomial approach (UMPA) allows a discussion of the similarities and differences of the commonly used methods. the use of least squares (LS), total least squares (TLS), double least squares (DLS) and singular value decomposition (SVD) methods is discussed in order to take advantage of redundant measurement data. Eigenvalue and SVD transformation methods are utilized to reduce the effective size of the resulting eigenvalue-eigenvector problem as well.

Optimized volume models of earthquake-triggered landslides

PubMed Central

Xu, Chong; Xu, Xiwei; Shen, Lingling; Yao, Qi; Tan, Xibin; Kang, Wenjun; Ma, Siyuan; Wu, Xiyan; Cai, Juntao; Gao, Mingxing; Li, Kang

2016-01-01

In this study, we proposed three optimized models for calculating the total volume of landslides triggered by the 2008 Wenchuan, China Mw 7.9 earthquake. First, we calculated the volume of each deposit of 1,415 landslides triggered by the quake based on pre- and post-quake DEMs in 20 m resolution. The samples were used to fit the conventional landslide “volume-area” power law relationship and the 3 optimized models we proposed, respectively. Two data fitting methods, i.e. log-transformed-based linear and original data-based nonlinear least square, were employed to the 4 models. Results show that original data-based nonlinear least square combining with an optimized model considering length, width, height, lithology, slope, peak ground acceleration, and slope aspect shows the best performance. This model was subsequently applied to the database of landslides triggered by the quake except for two largest ones with known volumes. It indicates that the total volume of the 196,007 landslides is about 1.2 × 1010 m3 in deposit materials and 1 × 1010 m3 in source areas, respectively. The result from the relationship of quake magnitude and entire landslide volume related to individual earthquake is much less than that from this study, which reminds us the necessity to update the power-law relationship. PMID:27404212

Optimized volume models of earthquake-triggered landslides.

PubMed

Xu, Chong; Xu, Xiwei; Shen, Lingling; Yao, Qi; Tan, Xibin; Kang, Wenjun; Ma, Siyuan; Wu, Xiyan; Cai, Juntao; Gao, Mingxing; Li, Kang

2016-07-12

In this study, we proposed three optimized models for calculating the total volume of landslides triggered by the 2008 Wenchuan, China Mw 7.9 earthquake. First, we calculated the volume of each deposit of 1,415 landslides triggered by the quake based on pre- and post-quake DEMs in 20 m resolution. The samples were used to fit the conventional landslide "volume-area" power law relationship and the 3 optimized models we proposed, respectively. Two data fitting methods, i.e. log-transformed-based linear and original data-based nonlinear least square, were employed to the 4 models. Results show that original data-based nonlinear least square combining with an optimized model considering length, width, height, lithology, slope, peak ground acceleration, and slope aspect shows the best performance. This model was subsequently applied to the database of landslides triggered by the quake except for two largest ones with known volumes. It indicates that the total volume of the 196,007 landslides is about 1.2 × 10(10) m(3) in deposit materials and 1 × 10(10) m(3) in source areas, respectively. The result from the relationship of quake magnitude and entire landslide volume related to individual earthquake is much less than that from this study, which reminds us the necessity to update the power-law relationship.

Ordinary least squares regression is indicated for studies of allometry.

PubMed

Kilmer, J T; Rodríguez, R L

2017-01-01

When it comes to fitting simple allometric slopes through measurement data, evolutionary biologists have been torn between regression methods. On the one hand, there is the ordinary least squares (OLS) regression, which is commonly used across many disciplines of biology to fit lines through data, but which has a reputation for underestimating slopes when measurement error is present. On the other hand, there is the reduced major axis (RMA) regression, which is often recommended as a substitute for OLS regression in studies of allometry, but which has several weaknesses of its own. Here, we review statistical theory as it applies to evolutionary biology and studies of allometry. We point out that the concerns that arise from measurement error for OLS regression are small and straightforward to deal with, whereas RMA has several key properties that make it unfit for use in the field of allometry. The recommended approach for researchers interested in allometry is to use OLS regression on measurements taken with low (but realistically achievable) measurement error. If measurement error is unavoidable and relatively large, it is preferable to correct for slope attenuation rather than to turn to RMA regression, or to take the expected amount of attenuation into account when interpreting the data. © 2016 European Society For Evolutionary Biology. Journal of Evolutionary Biology © 2016 European Society For Evolutionary Biology.

The mechanism of ΔT variation in coupled heat transfer and phase transformation for elastocaloric materials and its application in materials characterization

NASA Astrophysics Data System (ADS)

Qian, Suxin; Yuan, Lifen; Yu, Jianlin; Yan, Gang

2017-11-01

Elastocaloric cooling serves as a promising environmental friendly candidate with substantial energy saving potential as the next generation cooling technology for air-conditioning, refrigeration, and electronic cooling applications. The temperature change (ΔT) of elastocaloric materials is a direct measure of their elastocaloric effect, which scales proportionally with the device cooling performance based on this phenomenon. Here, the underlying physics between the measured ΔT and the adiabatic temperature span ΔTad is revealed by theoretical investigation of the simplified energy equation describing the coupled simultaneous heat transfer and phase transformation processes. The revealed relation of ΔT depends on a simple and symmetric non-linear function, which requires the introduction of an important dimensionless number Φ, defined as the ratio between convective heat transfer energy and variation of internal energy of the material. The theory was supported by more than 100 data points from the open literature for four different material compositions. Based on the theory, a data sampling and reduction technique was proposed to assist future material characterization studies. Instead of approaching ΔTad by applying an ultrafast strain rate in the old way, the proposed prediction of ΔTad is based on the non-linear least squares fitting method with the measured ΔT dataset at different strain rates within the moderate range. Numerical case studies indicated that the uncertainty associated with the proposed method is within ±1 K if the sampled data satisfied two conditions. In addition, the heat transfer coefficient can be estimated as a by-product of the least squares fitting method proposed in this study.

Methods of automatic nucleotide-sequence analysis. Multicomponent spectrophotometric analysis of mixtures of nucleic acid components by a least-squares procedure

PubMed Central

Lee, Sheila; McMullen, D.; Brown, G. L.; Stokes, A. R.

1965-01-01

1. A theoretical analysis of the errors in multicomponent spectrophotometric analysis of nucleoside mixtures, by a least-squares procedure, has been made to obtain an expression for the error coefficient, relating the error in calculated concentration to the error in extinction measurements. 2. The error coefficients, which depend only on the `library' of spectra used to fit the experimental curves, have been computed for a number of `libraries' containing the following nucleosides found in s-RNA: adenosine, guanosine, cytidine, uridine, 5-ribosyluracil, 7-methylguanosine, 6-dimethylaminopurine riboside, 6-methylaminopurine riboside and thymine riboside. 3. The error coefficients have been used to determine the best conditions for maximum accuracy in the determination of the compositions of nucleoside mixtures. 4. Experimental determinations of the compositions of nucleoside mixtures have been made and the errors found to be consistent with those predicted by the theoretical analysis. 5. It has been demonstrated that, with certain precautions, the multicomponent spectrophotometric method described is suitable as a basis for automatic nucleotide-composition analysis of oligonucleotides containing nine nucleotides. Used in conjunction with continuous chromatography and flow chemical techniques, this method can be applied to the study of the sequence of s-RNA. PMID:14346087

A User’s Manual for Fiber Diffraction: The Automated Picker and Huber Diffractometers

DTIC Science & Technology

1990-07-01

17 3. Layer line scan of degummed silk ( Bombyx mori ) ................................. 18...index (arbitrary units) Figure 3. Layer line scan of degummed silk ( Bombyx mori ) showing layers 0 through 6. If the fit is rejected, new values for... originally made at intervals larger than 0.010. The smoothing and interpolation is done by a least-squares polynomial fit to segments of the data. The number

A Modified LS+AR Model to Improve the Accuracy of the Short-term Polar Motion Prediction

NASA Astrophysics Data System (ADS)

Wang, Z. W.; Wang, Q. X.; Ding, Y. Q.; Zhang, J. J.; Liu, S. S.

2017-03-01

There are two problems of the LS (Least Squares)+AR (AutoRegressive) model in polar motion forecast: the inner residual value of LS fitting is reasonable, but the residual value of LS extrapolation is poor; and the LS fitting residual sequence is non-linear. It is unsuitable to establish an AR model for the residual sequence to be forecasted, based on the residual sequence before forecast epoch. In this paper, we make solution to those two problems with two steps. First, restrictions are added to the two endpoints of LS fitting data to fix them on the LS fitting curve. Therefore, the fitting values next to the two endpoints are very close to the observation values. Secondly, we select the interpolation residual sequence of an inward LS fitting curve, which has a similar variation trend as the LS extrapolation residual sequence, as the modeling object of AR for the residual forecast. Calculation examples show that this solution can effectively improve the short-term polar motion prediction accuracy by the LS+AR model. In addition, the comparison results of the forecast models of RLS (Robustified Least Squares)+AR, RLS+ARIMA (AutoRegressive Integrated Moving Average), and LS+ANN (Artificial Neural Network) confirm the feasibility and effectiveness of the solution for the polar motion forecast. The results, especially for the polar motion forecast in the 1-10 days, show that the forecast accuracy of the proposed model can reach the world level.

An analysis of the least-squares problem for the DSN systematic pointing error model

NASA Technical Reports Server (NTRS)

Alvarez, L. S.

1991-01-01

A systematic pointing error model is used to calibrate antennas in the Deep Space Network. The least squares problem is described and analyzed along with the solution methods used to determine the model's parameters. Specifically studied are the rank degeneracy problems resulting from beam pointing error measurement sets that incorporate inadequate sky coverage. A least squares parameter subset selection method is described and its applicability to the systematic error modeling process is demonstrated on Voyager 2 measurement distribution.

Polynomial dual energy inverse functions for bone Calcium/Phosphorus ratio determination and experimental evaluation.

PubMed

Sotiropoulou, P; Fountos, G; Martini, N; Koukou, V; Michail, C; Kandarakis, I; Nikiforidis, G

2016-12-01

An X-ray dual energy (XRDE) method was examined, using polynomial nonlinear approximation of inverse functions for the determination of the bone Calcium-to-Phosphorus (Ca/P) mass ratio. Inverse fitting functions with the least-squares estimation were used, to determine calcium and phosphate thicknesses. The method was verified by measuring test bone phantoms with a dedicated dual energy system and compared with previously published dual energy data. The accuracy in the determination of the calcium and phosphate thicknesses improved with the polynomial nonlinear inverse function method, introduced in this work, (ranged from 1.4% to 6.2%), compared to the corresponding linear inverse function method (ranged from 1.4% to 19.5%). Copyright © 2016 Elsevier Ltd. All rights reserved.

Solution of a Complex Least Squares Problem with Constrained Phase.

PubMed

Bydder, Mark

2010-12-30

The least squares solution of a complex linear equation is in general a complex vector with independent real and imaginary parts. In certain applications in magnetic resonance imaging, a solution is desired such that each element has the same phase. A direct method for obtaining the least squares solution to the phase constrained problem is described.

Use of partial least squares regression to impute SNP genotypes in Italian cattle breeds.

PubMed

Dimauro, Corrado; Cellesi, Massimo; Gaspa, Giustino; Ajmone-Marsan, Paolo; Steri, Roberto; Marras, Gabriele; Macciotta, Nicolò P P

2013-06-05

The objective of the present study was to test the ability of the partial least squares regression technique to impute genotypes from low density single nucleotide polymorphisms (SNP) panels i.e. 3K or 7K to a high density panel with 50K SNP. No pedigree information was used. Data consisted of 2093 Holstein, 749 Brown Swiss and 479 Simmental bulls genotyped with the Illumina 50K Beadchip. First, a single-breed approach was applied by using only data from Holstein animals. Then, to enlarge the training population, data from the three breeds were combined and a multi-breed analysis was performed. Accuracies of genotypes imputed using the partial least squares regression method were compared with those obtained by using the Beagle software. The impact of genotype imputation on breeding value prediction was evaluated for milk yield, fat content and protein content. In the single-breed approach, the accuracy of imputation using partial least squares regression was around 90 and 94% for the 3K and 7K platforms, respectively; corresponding accuracies obtained with Beagle were around 85% and 90%. Moreover, computing time required by the partial least squares regression method was on average around 10 times lower than computing time required by Beagle. Using the partial least squares regression method in the multi-breed resulted in lower imputation accuracies than using single-breed data. The impact of the SNP-genotype imputation on the accuracy of direct genomic breeding values was small. The correlation between estimates of genetic merit obtained by using imputed versus actual genotypes was around 0.96 for the 7K chip. Results of the present work suggested that the partial least squares regression imputation method could be useful to impute SNP genotypes when pedigree information is not available.

FIT: Computer Program that Interactively Determines Polynomial Equations for Data which are a Function of Two Independent Variables

NASA Technical Reports Server (NTRS)

Arbuckle, P. D.; Sliwa, S. M.; Roy, M. L.; Tiffany, S. H.

1985-01-01

A computer program for interactively developing least-squares polynomial equations to fit user-supplied data is described. The program is characterized by the ability to compute the polynomial equations of a surface fit through data that are a function of two independent variables. The program utilizes the Langley Research Center graphics packages to display polynomial equation curves and data points, facilitating a qualitative evaluation of the effectiveness of the fit. An explanation of the fundamental principles and features of the program, as well as sample input and corresponding output, are included.

Nuclear Matter Properties with the Re-evaluated Coefficients of Liquid Drop Model

NASA Astrophysics Data System (ADS)

Chowdhury, P. Roy; Basu, D. N.

2006-06-01

The coefficients of the volume, surface, Coulomb, asymmetry and pairing energy terms of the semiempirical liquid drop model mass formula have been determined by furnishing best fit to the observed mass excesses. Slightly different sets of the weighting parameters for liquid drop model mass formula have been obtained from minimizations of \\chi 2 and mean square deviation. The most recent experimental and estimated mass excesses from Audi-Wapstra-Thibault atomic mass table have been used for the least square fitting procedure. Equation of state, nuclear incompressibility, nuclear mean free path and the most stable nuclei for corresponding atomic numbers, all are in good agreement with the experimental results.

The Apollo 16 regolith - A petrographically-constrained chemical mixing model

NASA Technical Reports Server (NTRS)

Kempa, M. J.; Papike, J. J.; White, C.

1980-01-01

A mixing model for Apollo 16 regolith samples has been developed, which differs from other A-16 mixing models in that it is both petrographically constrained and statistically sound. The model was developed using three components representative of rock types present at the A-16 site, plus a representative mare basalt. A linear least-squares fitting program employing the chi-squared test and sum of components was used to determine goodness of fit. Results for surface soils indicate that either there are no significant differences between Cayley and Descartes material at the A-16 site or, if differences do exist, they have been obscured by meteoritic reworking and mixing of the lithologies.

Wavelength calibration of an imaging spectrometer based on Savart interferometer

NASA Astrophysics Data System (ADS)

Li, Qiwei; Zhang, Chunmin; Yan, Tingyu; Quan, Naicheng; Wei, Yutong; Tong, Cuncun

2017-09-01

The basic principle of Fourier-transform imaging spectrometer (FTIS) based on Savart interferometer is outlined. The un-identical distribution of the optical path difference which leads to the wavelength drift of each row of the interferogram is analyzed. Two typical methods for wavelength calibration of the presented system are described. The first method unifies different spectral intervals and maximum spectral frequencies of each row by a reference monochromatic light with known wavelength, and the dispersion compensation of Savart interferometer is also involved. The second approach is based on the least square fitting which builds the functional relation between recovered wavelength, row number and calibrated wavelength by concise equations. The effectiveness of the two methods is experimentally demonstrated with monochromatic lights and mixed light source across the detecting band of the system, and the results indicate that the first method has higher precision and the mean root-mean-square error of the recovered wavelengths is significantly reduced from 19.896 nm to 1.353 nm, while the second method is more convenient to implement and also has good precision of 2.709 nm.

Penalized Nonlinear Least Squares Estimation of Time-Varying Parameters in Ordinary Differential Equations

PubMed Central

Cao, Jiguo; Huang, Jianhua Z.; Wu, Hulin

2012-01-01

Ordinary differential equations (ODEs) are widely used in biomedical research and other scientific areas to model complex dynamic systems. It is an important statistical problem to estimate parameters in ODEs from noisy observations. In this article we propose a method for estimating the time-varying coefficients in an ODE. Our method is a variation of the nonlinear least squares where penalized splines are used to model the functional parameters and the ODE solutions are approximated also using splines. We resort to the implicit function theorem to deal with the nonlinear least squares objective function that is only defined implicitly. The proposed penalized nonlinear least squares method is applied to estimate a HIV dynamic model from a real dataset. Monte Carlo simulations show that the new method can provide much more accurate estimates of functional parameters than the existing two-step local polynomial method which relies on estimation of the derivatives of the state function. Supplemental materials for the article are available online. PMID:23155351

Measurement System Characterization in the Presence of Measurement Errors

NASA Technical Reports Server (NTRS)

Commo, Sean A.

2012-01-01

In the calibration of a measurement system, data are collected in order to estimate a mathematical model between one or more factors of interest and a response. Ordinary least squares is a method employed to estimate the regression coefficients in the model. The method assumes that the factors are known without error; yet, it is implicitly known that the factors contain some uncertainty. In the literature, this uncertainty is known as measurement error. The measurement error affects both the estimates of the model coefficients and the prediction, or residual, errors. There are some methods, such as orthogonal least squares, that are employed in situations where measurement errors exist, but these methods do not directly incorporate the magnitude of the measurement errors. This research proposes a new method, known as modified least squares, that combines the principles of least squares with knowledge about the measurement errors. This knowledge is expressed in terms of the variance ratio - the ratio of response error variance to measurement error variance.

Computer user's manual for a generalized curve fit and plotting program

NASA Technical Reports Server (NTRS)

Schlagheck, R. A.; Beadle, B. D., II; Dolerhie, B. D., Jr.; Owen, J. W.

1973-01-01

A FORTRAN coded program has been developed for generating plotted output graphs on 8-1/2 by 11-inch paper. The program is designed to be used by engineers, scientists, and non-programming personnel on any IBM 1130 system that includes a 1627 plotter. The program has been written to provide a fast and efficient method of displaying plotted data without having to generate any additions. Various output options are available to the program user for displaying data in four different types of formatted plots. These options include discrete linear, continuous, and histogram graphical outputs. The manual contains information about the use and operation of this program. A mathematical description of the least squares goodness of fit test is presented. A program listing is also included.

Dielectric properties of benzylamine in 1,2,6-hexanetriol mixture using time domain reflectometry technique

NASA Astrophysics Data System (ADS)

Swami, M. B.; Hudge, P. G.; Pawar, V. P.

The dielectric properties of binary mixtures of benzylamine-1,2,6-hexantriol mixtures at different volume fractions of 1,2,6-hexanetriol have been measured using Time Domain Reflectometry (TDR) technique in the frequency range of 10 MHz to 30 GHz. Complex permittivity spectra were fitted using Havriliak-Negami equation. By using least square fit method the dielectric parameters such as static dielectric constant (ɛ0), dielectric constant at high frequency (ɛ∞), relaxation time τ (ps) and relaxation distribution parameter (β) were extracted from complex permittivity spectra at 25∘C. The intramolecular interaction of different molecules has been discussed using the Kirkwood correlation factor, Bruggeman factor. The Kirkwood correlation factor (gf) and effective Kirkwood correlation factor (geff) indicate the dipole ordering of the binary mixtures.

Use of inequality constrained least squares estimation in small area estimation

NASA Astrophysics Data System (ADS)

Abeygunawardana, R. A. B.; Wickremasinghe, W. N.

2017-05-01

Traditional surveys provide estimates that are based only on the sample observations collected for the population characteristic of interest. However, these estimates may have unacceptably large variance for certain domains. Small Area Estimation (SAE) deals with determining precise and accurate estimates for population characteristics of interest for such domains. SAE usually uses least squares or maximum likelihood procedures incorporating prior information and current survey data. Many available methods in SAE use constraints in equality form. However there are practical situations where certain inequality restrictions on model parameters are more realistic. It will lead to Inequality Constrained Least Squares (ICLS) estimates if the method used is least squares. In this study ICLS estimation procedure is applied to many proposed small area estimates.

Quantitative photoplethysmography: Lambert-Beer law or inverse function incorporating light scatter.

PubMed

Cejnar, M; Kobler, H; Hunyor, S N

1993-03-01

Finger blood volume is commonly determined from measurement of infra-red (IR) light transmittance using the Lambert-Beer law of light absorption derived for use in non-scattering media, even when such transmission involves light scatter around the phalangeal bone. Simultaneous IR transmittance and finger volume were measured over the full dynamic range of vascular volumes in seven subjects and outcomes compared with data fitted according to the Lambert-Beer exponential function and an inverse function derived for light attenuation by scattering materials. Curves were fitted by the least-squares method and goodness of fit was compared using standard errors of estimate (SEE). The inverse function gave a better data fit in six of the subjects: mean SEE 1.9 (SD 0.7, range 0.7-2.8) and 4.6 (2.2, 2.0-8.0) respectively (p < 0.02, paired t-test). Thus, when relating IR transmittance to blood volume, as occurs in the finger during measurements of arterial compliance, an inverse function derived from a model of light attenuation by scattering media gives more accurate results than the traditional exponential fit.

A unifying theoretical and algorithmic framework for least squares methods of estimation in diffusion tensor imaging.

PubMed

Koay, Cheng Guan; Chang, Lin-Ching; Carew, John D; Pierpaoli, Carlo; Basser, Peter J

2006-09-01

A unifying theoretical and algorithmic framework for diffusion tensor estimation is presented. Theoretical connections among the least squares (LS) methods, (linear least squares (LLS), weighted linear least squares (WLLS), nonlinear least squares (NLS) and their constrained counterparts), are established through their respective objective functions, and higher order derivatives of these objective functions, i.e., Hessian matrices. These theoretical connections provide new insights in designing efficient algorithms for NLS and constrained NLS (CNLS) estimation. Here, we propose novel algorithms of full Newton-type for the NLS and CNLS estimations, which are evaluated with Monte Carlo simulations and compared with the commonly used Levenberg-Marquardt method. The proposed methods have a lower percent of relative error in estimating the trace and lower reduced chi2 value than those of the Levenberg-Marquardt method. These results also demonstrate that the accuracy of an estimate, particularly in a nonlinear estimation problem, is greatly affected by the Hessian matrix. In other words, the accuracy of a nonlinear estimation is algorithm-dependent. Further, this study shows that the noise variance in diffusion weighted signals is orientation dependent when signal-to-noise ratio (SNR) is low (

The crux of the method: assumptions in ordinary least squares and logistic regression.

PubMed

Long, Rebecca G

2008-10-01

Logistic regression has increasingly become the tool of choice when analyzing data with a binary dependent variable. While resources relating to the technique are widely available, clear discussions of why logistic regression should be used in place of ordinary least squares regression are difficult to find. The current paper compares and contrasts the assumptions of ordinary least squares with those of logistic regression and explains why logistic regression's looser assumptions make it adept at handling violations of the more important assumptions in ordinary least squares.

Landsat-4 (TDRSS-user) orbit determination using batch least-squares and sequential methods

NASA Technical Reports Server (NTRS)

Oza, D. H.; Jones, T. L.; Hakimi, M.; Samii, M. V.; Doll, C. E.; Mistretta, G. D.; Hart, R. C.

1992-01-01

TDRSS user orbit determination is analyzed using a batch least-squares method and a sequential estimation method. It was found that in the batch least-squares method analysis, the orbit determination consistency for Landsat-4, which was heavily tracked by TDRSS during January 1991, was about 4 meters in the rms overlap comparisons and about 6 meters in the maximum position differences in overlap comparisons. The consistency was about 10 to 30 meters in the 3 sigma state error covariance function in the sequential method analysis. As a measure of consistency, the first residual of each pass was within the 3 sigma bound in the residual space.

Multiway analysis methods applied to the fluorescence excitation-emission dataset for the simultaneous quantification of valsartan and amlodipine in tablets

NASA Astrophysics Data System (ADS)

Dinç, Erdal; Ertekin, Zehra Ceren; Büker, Eda

2017-09-01

In this study, excitation-emission matrix datasets, which have strong overlapping bands, were processed by using four different chemometric calibration algorithms consisting of parallel factor analysis, Tucker3, three-way partial least squares and unfolded partial least squares for the simultaneous quantitative estimation of valsartan and amlodipine besylate in tablets. In analyses, preliminary separation step was not used before the application of parallel factor analysis Tucker3, three-way partial least squares and unfolded partial least squares approaches for the analysis of the related drug substances in samples. Three-way excitation-emission matrix data array was obtained by concatenating excitation-emission matrices of the calibration set, validation set, and commercial tablet samples. The excitation-emission matrix data array was used to get parallel factor analysis, Tucker3, three-way partial least squares and unfolded partial least squares calibrations and to predict the amounts of valsartan and amlodipine besylate in samples. For all the methods, calibration and prediction of valsartan and amlodipine besylate were performed in the working concentration ranges of 0.25-4.50 μg/mL. The validity and the performance of all the proposed methods were checked by using the validation parameters. From the analysis results, it was concluded that the described two-way and three-way algorithmic methods were very useful for the simultaneous quantitative resolution and routine analysis of the related drug substances in marketed samples.

Accuracy of least-squares methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Bochev, Pavel B.; Gunzburger, Max D.

1993-01-01

Recently there has been substantial interest in least-squares finite element methods for velocity-vorticity-pressure formulations of the incompressible Navier-Stokes equations. The main cause for this interest is the fact that algorithms for the resulting discrete equations can be devised which require the solution of only symmetric, positive definite systems of algebraic equations. On the other hand, it is well-documented that methods using the vorticity as a primary variable often yield very poor approximations. Thus, here we study the accuracy of these methods through a series of computational experiments, and also comment on theoretical error estimates. It is found, despite the failure of standard methods for deriving error estimates, that computational evidence suggests that these methods are, at the least, nearly optimally accurate. Thus, in addition to the desirable matrix properties yielded by least-squares methods, one also obtains accurate approximations.

Computer Calculation of First-Order Rate Constants

ERIC Educational Resources Information Center

Williams, Robert C.; Taylor, James W.

1970-01-01

Discusses the computer program used to calculate first-order rate constants. Discussion includes data preparation, weighting options, comparison techniques, infinity point adjustment, least-square fit, Guggenheim calculation, and printed outputs. Exemplifies the utility of the computer program by two experiments: (1) the thermal decomposition of…

Uncertainties in extracted parameters of a Gaussian emission line profile with continuum background.

PubMed

Minin, Serge; Kamalabadi, Farzad

2009-12-20

We derive analytical equations for uncertainties in parameters extracted by nonlinear least-squares fitting of a Gaussian emission function with an unknown continuum background component in the presence of additive white Gaussian noise. The derivation is based on the inversion of the full curvature matrix (equivalent to Fisher information matrix) of the least-squares error, chi(2), in a four-variable fitting parameter space. The derived uncertainty formulas (equivalent to Cramer-Rao error bounds) are found to be in good agreement with the numerically computed uncertainties from a large ensemble of simulated measurements. The derived formulas can be used for estimating minimum achievable errors for a given signal-to-noise ratio and for investigating some aspects of measurement setup trade-offs and optimization. While the intended application is Fabry-Perot spectroscopy for wind and temperature measurements in the upper atmosphere, the derivation is generic and applicable to other spectroscopy problems with a Gaussian line shape.

Ground-truthing AVIRIS mineral mapping at Cuprite, Nevada

NASA Technical Reports Server (NTRS)

Swayze, Gregg; Clark, Roger N.; Kruse, Fred; Sutley, Steve; Gallagher, Andrea

1992-01-01

Mineral abundance maps of 18 minerals were made of the Cuprite Mining District using 1990 AVIRIS data and the Multiple Spectral Feature Mapping Algorithm (MSFMA) as discussed in Clark et al. This technique uses least-squares fitting between a scaled laboratory reference spectrum and ground calibrated AVIRIS data for each pixel. Multiple spectral features can be fitted for each mineral and an unlimited number of minerals can be mapped simultaneously. Quality of fit and depth from continuum numbers for each mineral are calculated for each pixel and the results displayed as a multicolor image.

Calculation of earthquake rupture histories using a hybrid global search algorithm: Application to the 1992 Landers, California, earthquake

USGS Publications Warehouse

Hartzell, S.; Liu, P.

1996-01-01

A method is presented for the simultaneous calculation of slip amplitudes and rupture times for a finite fault using a hybrid global search algorithm. The method we use combines simulated annealing with the downhill simplex method to produce a more efficient search algorithm then either of the two constituent parts. This formulation has advantages over traditional iterative or linearized approaches to the problem because it is able to escape local minima in its search through model space for the global optimum. We apply this global search method to the calculation of the rupture history for the Landers, California, earthquake. The rupture is modeled using three separate finite-fault planes to represent the three main fault segments that failed during this earthquake. Both the slip amplitude and the time of slip are calculated for a grid work of subfaults. The data used consist of digital, teleseismic P and SH body waves. Long-period, broadband, and short-period records are utilized to obtain a wideband characterization of the source. The results of the global search inversion are compared with a more traditional linear-least-squares inversion for only slip amplitudes. We use a multi-time-window linear analysis to relax the constraints on rupture time and rise time in the least-squares inversion. Both inversions produce similar slip distributions, although the linear-least-squares solution has a 10% larger moment (7.3 ?? 1026 dyne-cm compared with 6.6 ?? 1026 dyne-cm). Both inversions fit the data equally well and point out the importance of (1) using a parameterization with sufficient spatial and temporal flexibility to encompass likely complexities in the rupture process, (2) including suitable physically based constraints on the inversion to reduce instabilities in the solution, and (3) focusing on those robust rupture characteristics that rise above the details of the parameterization and data set.

On sufficient statistics of least-squares superposition of vector sets.

PubMed

Konagurthu, Arun S; Kasarapu, Parthan; Allison, Lloyd; Collier, James H; Lesk, Arthur M

2015-06-01

The problem of superposition of two corresponding vector sets by minimizing their sum-of-squares error under orthogonal transformation is a fundamental task in many areas of science, notably structural molecular biology. This problem can be solved exactly using an algorithm whose time complexity grows linearly with the number of correspondences. This efficient solution has facilitated the widespread use of the superposition task, particularly in studies involving macromolecular structures. This article formally derives a set of sufficient statistics for the least-squares superposition problem. These statistics are additive. This permits a highly efficient (constant time) computation of superpositions (and sufficient statistics) of vector sets that are composed from its constituent vector sets under addition or deletion operation, where the sufficient statistics of the constituent sets are already known (that is, the constituent vector sets have been previously superposed). This results in a drastic improvement in the run time of the methods that commonly superpose vector sets under addition or deletion operations, where previously these operations were carried out ab initio (ignoring the sufficient statistics). We experimentally demonstrate the improvement our work offers in the context of protein structural alignment programs that assemble a reliable structural alignment from well-fitting (substructural) fragment pairs. A C++ library for this task is available online under an open-source license.

Combinatorics of least-squares trees.

PubMed

Mihaescu, Radu; Pachter, Lior

2008-09-09

A recurring theme in the least-squares approach to phylogenetics has been the discovery of elegant combinatorial formulas for the least-squares estimates of edge lengths. These formulas have proved useful for the development of efficient algorithms, and have also been important for understanding connections among popular phylogeny algorithms. For example, the selection criterion of the neighbor-joining algorithm is now understood in terms of the combinatorial formulas of Pauplin for estimating tree length. We highlight a phylogenetically desirable property that weighted least-squares methods should satisfy, and provide a complete characterization of methods that satisfy the property. The necessary and sufficient condition is a multiplicative four-point condition that the variance matrix needs to satisfy. The proof is based on the observation that the Lagrange multipliers in the proof of the Gauss-Markov theorem are tree-additive. Our results generalize and complete previous work on ordinary least squares, balanced minimum evolution, and the taxon-weighted variance model. They also provide a time-optimal algorithm for computation.

Post-flight trajectory reconstruction of suborbital free-flyers using GPS raw data

NASA Astrophysics Data System (ADS)

Ivchenko, N.; Yuan, Y.; Linden, E.

2017-08-01

This paper describes the reconstruction of postflight trajectories of suborbital free flying units by using logged GPS raw data. We took the reconstruction as a global least squares optimization problem, using both the pseudo-range and Doppler observables, and solved it by using the trust-region-reflective algorithm, which enabled navigational solutions of high accuracy. The code tracking was implemented with a large number of correlators and least squares curve fitting, in order to improve the precision of the code start times, while a more conventional phased lock loop was used for Doppler tracking. We proposed a weighting scheme to account for fast signal strength variation due to free-flier fast rotation, and a penalty for jerk to achieve a smooth solution. We applied these methods to flight data of two suborbital free flying units launched on REXUS 12 sounding rocket, reconstructing the trajectory, receiver clock error and wind up rates. The trajectory exhibits a parabola with the apogee around 80 km, and the velocity profile shows the details of payloadwobbling. The wind up rates obtained match the measurements from onboard angular rate sensors.

Computing ordinary least-squares parameter estimates for the National Descriptive Model of Mercury in Fish

USGS Publications Warehouse

Donato, David I.

2013-01-01

A specialized technique is used to compute weighted ordinary least-squares (OLS) estimates of the parameters of the National Descriptive Model of Mercury in Fish (NDMMF) in less time using less computer memory than general methods. The characteristics of the NDMMF allow the two products X'X and X'y in the normal equations to be filled out in a second or two of computer time during a single pass through the N data observations. As a result, the matrix X does not have to be stored in computer memory and the computationally expensive matrix multiplications generally required to produce X'X and X'y do not have to be carried out. The normal equations may then be solved to determine the best-fit parameters in the OLS sense. The computational solution based on this specialized technique requires O(8p2+16p) bytes of computer memory for p parameters on a machine with 8-byte double-precision numbers. This publication includes a reference implementation of this technique and a Gaussian-elimination solver in preliminary custom software.

First-Order System Least-Squares for Second-Order Elliptic Problems with Discontinuous Coefficients

NASA Technical Reports Server (NTRS)

Manteuffel, Thomas A.; McCormick, Stephen F.; Starke, Gerhard

1996-01-01

The first-order system least-squares methodology represents an alternative to standard mixed finite element methods. Among its advantages is the fact that the finite element spaces approximating the pressure and flux variables are not restricted by the inf-sup condition and that the least-squares functional itself serves as an appropriate error measure. This paper studies the first-order system least-squares approach for scalar second-order elliptic boundary value problems with discontinuous coefficients. Ellipticity of an appropriately scaled least-squares bilinear form of the size of the jumps in the coefficients leading to adequate finite element approximation results. The occurrence of singularities at interface corners and cross-points is discussed. and a weighted least-squares functional is introduced to handle such cases. Numerical experiments are presented for two test problems to illustrate the performance of this approach.

Speckle noise removal applied to ultrasound image of carotid artery based on total least squares model.

PubMed

Yang, Lei; Lu, Jun; Dai, Ming; Ren, Li-Jie; Liu, Wei-Zong; Li, Zhen-Zhou; Gong, Xue-Hao

2016-10-06

An ultrasonic image speckle noise removal method by using total least squares model is proposed and applied onto images of cardiovascular structures such as the carotid artery. On the basis of the least squares principle, the related principle of minimum square method is applied to cardiac ultrasound image speckle noise removal process to establish the model of total least squares, orthogonal projection transformation processing is utilized for the output of the model, and the denoising processing for the cardiac ultrasound image speckle noise is realized. Experimental results show that the improved algorithm can greatly improve the resolution of the image, and meet the needs of clinical medical diagnosis and treatment of the cardiovascular system for the head and neck. Furthermore, the success in imaging of carotid arteries has strong implications in neurological complications such as stroke.

Calculated shock pressures in the aquarium test

NASA Astrophysics Data System (ADS)

Johnson, J. N.

1982-04-01

A new method of analysis has been developed for determintion of shock pressures in aquarium tests on commercial explosives. This test consists of photographing the expanding cylindrical tube wall (which contains the detonation products) and the shock wave in water surrounding the explosive charge. By making a least-squares fit to the shock-front data, it is possible to determine the peak shock-front pressure as a function of distance from the cylinder wall. This has been done for 10-cm and 20-cm-diam ANFO (ammonium nitrate/fuel oil) and aluminized ANFO (7.5 wt% Al) aquarium test data.

SIMULATIONS OF 2D AND 3D THERMOCAPILLARY FLOWS BY A LEAST-SQUARES FINITE ELEMENT METHOD. (R825200)

EPA Science Inventory

Numerical results for time-dependent 2D and 3D thermocapillary flows are presented in this work. The numerical algorithm is based on the Crank-Nicolson scheme for time integration, Newton's method for linearization, and a least-squares finite element method, together with a matri...

Chi-Squared Test of Fit and Sample Size-A Comparison between a Random Sample Approach and a Chi-Square Value Adjustment Method.

PubMed

Bergh, Daniel

2015-01-01

Chi-square statistics are commonly used for tests of fit of measurement models. Chi-square is also sensitive to sample size, which is why several approaches to handle large samples in test of fit analysis have been developed. One strategy to handle the sample size problem may be to adjust the sample size in the analysis of fit. An alternative is to adopt a random sample approach. The purpose of this study was to analyze and to compare these two strategies using simulated data. Given an original sample size of 21,000, for reductions of sample sizes down to the order of 5,000 the adjusted sample size function works as good as the random sample approach. In contrast, when applying adjustments to sample sizes of lower order the adjustment function is less effective at approximating the chi-square value for an actual random sample of the relevant size. Hence, the fit is exaggerated and misfit under-estimated using the adjusted sample size function. Although there are big differences in chi-square values between the two approaches at lower sample sizes, the inferences based on the p-values may be the same.

A new linear least squares method for T1 estimation from SPGR signals with multiple TRs

NASA Astrophysics Data System (ADS)

Chang, Lin-Ching; Koay, Cheng Guan; Basser, Peter J.; Pierpaoli, Carlo

2009-02-01

The longitudinal relaxation time, T1, can be estimated from two or more spoiled gradient recalled echo x (SPGR) images with two or more flip angles and one or more repetition times (TRs). The function relating signal intensity and the parameters are nonlinear; T1 maps can be computed from SPGR signals using nonlinear least squares regression. A widely-used linear method transforms the nonlinear model by assuming a fixed TR in SPGR images. This constraint is not desirable since multiple TRs are a clinically practical way to reduce the total acquisition time, to satisfy the required resolution, and/or to combine SPGR data acquired at different times. A new linear least squares method is proposed using the first order Taylor expansion. Monte Carlo simulations of SPGR experiments are used to evaluate the accuracy and precision of the estimated T1 from the proposed linear and the nonlinear methods. We show that the new linear least squares method provides T1 estimates comparable in both precision and accuracy to those from the nonlinear method, allowing multiple TRs and reducing computation time significantly.

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mu, Lin; Wang, Junping; Ye, Xiu

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore » the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.« less

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu

2017-08-17

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore » the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.« less

Generalized Structured Component Analysis

ERIC Educational Resources Information Center

Hwang, Heungsun; Takane, Yoshio

2004-01-01

We propose an alternative method to partial least squares for path analysis with components, called generalized structured component analysis. The proposed method replaces factors by exact linear combinations of observed variables. It employs a well-defined least squares criterion to estimate model parameters. As a result, the proposed method…

Recursive least squares method of regression coefficients estimation as a special case of Kalman filter

NASA Astrophysics Data System (ADS)

Borodachev, S. M.

2016-06-01

The simple derivation of recursive least squares (RLS) method equations is given as special case of Kalman filter estimation of a constant system state under changing observation conditions. A numerical example illustrates application of RLS to multicollinearity problem.

A User's Version View of a Robustified, Bayesian Weighted Least-Squares Recursive Algorithm for Interpolating AVHRR-NDVI Data: Applications to an Animated Visualization of the Phenology of a Semi-Arid Study Area

NASA Astrophysics Data System (ADS)

Hermance, J. F.; Jacob, R. W.; Bradley, B. A.; Mustard, J. F.

2005-12-01

In studying vegetation patterns remotely, the objective is to draw inferences on the development of specific or general land surface phenology (LSP) as a function of space and time by determining the behavior of a parameter (in our case NDVI), when the parameter estimate may be biased by noise, data dropouts and obfuscations from atmospheric and other effects. We describe the underpinning concepts of a procedure for a robust interpolation of NDVI data that does not have the limitations of other mathematical approaches which require orthonormal basis functions (e.g. Fourier analysis). In this approach, data need not be uniformly sampled in time, nor do we expect noise to be Gaussian-distributed. Our approach is intuitive and straightforward, and is applied here to the refined modeling of LSP using 7 years of weekly and biweekly AVHRR NDVI data for a 150 x 150 km study area in central Nevada. This site is a microcosm of a broad range of vegetation classes, from irrigated agriculture with annual NDVIvalues of up to 0.7 to playas and alkali salt flats with annual NDVI values of only 0.07. Our procedure involves a form of parameter estimation employing Bayesian statistics. In utilitarian terms, the latter procedure is a method of statistical analysis (in our case, robustified, weighted least-squares recursive curve-fitting) that incorporates a variety of prior knowledge when forming current estimates of a particular process or parameter. In addition to the standard Bayesian approach, we account for outliers due to data dropouts or obfuscations because of clouds and snow cover. An initial "starting model" for the average annual cycle and long term (7 year) trend is determined by jointly fitting a common set of complex annual harmonics and a low order polynomial to an entire multi-year time series in one step. This is not a formal Fourier series in the conventional sense, but rather a set of 4 cosine and 4 sine coefficients with fundamental periods of 12, 6, 3 and 1.5 months. Instabilities during large time gaps in the data are suppressed by introducing an expectation of minimum roughness on the fitted time series. Our next significant computational step involves a constrained least squares fit to the observed NDVI data. Residuals between the observed NDVI value and the predicted starting model are computed, and the inverse of these residuals provide the weights for a weighted least squares analysis whereby a set of annual eighth-order splines are fit to the 7 years of NDVI data. Although a series of independent 8-th order annual functionals over a period of 7 years is intrinsically unstable when there are significant data gaps, the splined versions for this specific application are quite stable due to explicit continuity conditions on the values and derivatives of the functionals across contiguous years, as well as a priori constraints on the predicted values vis-a-vis the assumed initial model. Our procedure allows us to robustly interpolate original unequally-spaced NDVI data with a new time series having the most-appropriate, user-defined time base. We apply this approach to the temporal behavior of vegetation in our 150 x 150 km study area. Such a small area, being so rich in vegetation diversity, is particularly useful to view in map form and by animated annual and multi-year time sequences, since the interrelation between phenology, topography and specific usage patterns becomes clear.

A Hybrid Method to Estimate Specific Differential Phase and Rainfall With Linear Programming and Physics Constraints

DOE PAGES

Huang, Hao; Zhang, Guifu; Zhao, Kun; ...

2016-10-20

A hybrid method of combining linear programming (LP) and physical constraints is developed to estimate specific differential phase (K DP) and to improve rain estimation. Moreover, the hybrid K DP estimator and the existing estimators of LP, least squares fitting, and a self-consistent relation of polarimetric radar variables are evaluated and compared using simulated data. Our simulation results indicate the new estimator's superiority, particularly in regions where backscattering phase (δ hv) dominates. Further, a quantitative comparison between auto-weather-station rain-gauge observations and K DP-based radar rain estimates for a Meiyu event also demonstrate the superiority of the hybrid K DP estimatormore » over existing methods.« less

A novel line segment detection algorithm based on graph search

NASA Astrophysics Data System (ADS)

Zhao, Hong-dan; Liu, Guo-ying; Song, Xu

2018-02-01

To overcome the problem of extracting line segment from an image, a method of line segment detection was proposed based on the graph search algorithm. After obtaining the edge detection result of the image, the candidate straight line segments are obtained in four directions. For the candidate straight line segments, their adjacency relationships are depicted by a graph model, based on which the depth-first search algorithm is employed to determine how many adjacent line segments need to be merged. Finally we use the least squares method to fit the detected straight lines. The comparative experimental results verify that the proposed algorithm has achieved better results than the line segment detector (LSD).

Estimating standard errors in feature network models.

PubMed

Frank, Laurence E; Heiser, Willem J

2007-05-01

Feature network models are graphical structures that represent proximity data in a discrete space while using the same formalism that is the basis of least squares methods employed in multidimensional scaling. Existing methods to derive a network model from empirical data only give the best-fitting network and yield no standard errors for the parameter estimates. The additivity properties of networks make it possible to consider the model as a univariate (multiple) linear regression problem with positivity restrictions on the parameters. In the present study, both theoretical and empirical standard errors are obtained for the constrained regression parameters of a network model with known features. The performance of both types of standard error is evaluated using Monte Carlo techniques.

Analysis and computation of a least-squares method for consistent mesh tying

DOE PAGES

Day, David; Bochev, Pavel

2007-07-10

We report in the finite element method, a standard approach to mesh tying is to apply Lagrange multipliers. If the interface is curved, however, discretization generally leads to adjoining surfaces that do not coincide spatially. Straightforward Lagrange multiplier methods lead to discrete formulations failing a first-order patch test [T.A. Laursen, M.W. Heinstein, Consistent mesh-tying methods for topologically distinct discretized surfaces in non-linear solid mechanics, Internat. J. Numer. Methods Eng. 57 (2003) 1197–1242]. This paper presents a theoretical and computational study of a least-squares method for mesh tying [P. Bochev, D.M. Day, A least-squares method for consistent mesh tying, Internat. J.more » Numer. Anal. Modeling 4 (2007) 342–352], applied to the partial differential equation -∇ 2φ+αφ=f. We prove optimal convergence rates for domains represented as overlapping subdomains and show that the least-squares method passes a patch test of the order of the finite element space by construction. To apply the method to subdomain configurations with gaps and overlaps we use interface perturbations to eliminate the gaps. Finally, theoretical error estimates are illustrated by numerical experiments.« less

Analysis of the Magnitude and Frequency of Peak Discharge and Maximum Observed Peak Discharge in New Mexico and Surrounding Areas

USGS Publications Warehouse

Waltemeyer, Scott D.

2008-01-01

Estimates of the magnitude and frequency of peak discharges are necessary for the reliable design of bridges, culverts, and open-channel hydraulic analysis, and for flood-hazard mapping in New Mexico and surrounding areas. The U.S. Geological Survey, in cooperation with the New Mexico Department of Transportation, updated estimates of peak-discharge magnitude for gaging stations in the region and updated regional equations for estimation of peak discharge and frequency at ungaged sites. Equations were developed for estimating the magnitude of peak discharges for recurrence intervals of 2, 5, 10, 25, 50, 100, and 500 years at ungaged sites by use of data collected through 2004 for 293 gaging stations on unregulated streams that have 10 or more years of record. Peak discharges for selected recurrence intervals were determined at gaging stations by fitting observed data to a log-Pearson Type III distribution with adjustments for a low-discharge threshold and a zero skew coefficient. A low-discharge threshold was applied to frequency analysis of 140 of the 293 gaging stations. This application provides an improved fit of the log-Pearson Type III frequency distribution. Use of the low-discharge threshold generally eliminated the peak discharge by having a recurrence interval of less than 1.4 years in the probability-density function. Within each of the nine regions, logarithms of the maximum peak discharges for selected recurrence intervals were related to logarithms of basin and climatic characteristics by using stepwise ordinary least-squares regression techniques for exploratory data analysis. Generalized least-squares regression techniques, an improved regression procedure that accounts for time and spatial sampling errors, then were applied to the same data used in the ordinary least-squares regression analyses. The average standard error of prediction, which includes average sampling error and average standard error of regression, ranged from 38 to 93 percent (mean value is 62, and median value is 59) for the 100-year flood. The 1996 investigation standard error of prediction for the flood regions ranged from 41 to 96 percent (mean value is 67, and median value is 68) for the 100-year flood that was analyzed by using generalized least-squares regression analysis. Overall, the equations based on generalized least-squares regression techniques are more reliable than those in the 1996 report because of the increased length of record and improved geographic information system (GIS) method to determine basin and climatic characteristics. Flood-frequency estimates can be made for ungaged sites upstream or downstream from gaging stations by using a method that transfers flood-frequency data at the gaging station to the ungaged site by using a drainage-area ratio adjustment equation. The peak discharge for a given recurrence interval at the gaging station, drainage-area ratio, and the drainage-area exponent from the regional regression equation of the respective region is used to transfer the peak discharge for the recurrence interval to the ungaged site. Maximum observed peak discharge as related to drainage area was determined for New Mexico. Extreme events are commonly used in the design and appraisal of bridge crossings and other structures. Bridge-scour evaluations are commonly made by using the 500-year peak discharge for these appraisals. Peak-discharge data collected at 293 gaging stations and 367 miscellaneous sites were used to develop a maximum peak-discharge relation as an alternative method of estimating peak discharge of an extreme event such as a maximum probable flood.

DIFFERENTIATION OF AURANTII FRUCTUS IMMATURUS AND FRUCTUS PONICIRI TRIFOLIATAE IMMATURUS BY FLOW-INJECTION WITH ULTRAVIOLET SPECTROSCOPIC DETECTION AND PROTON NUCLEAR MAGNETIC RESONANCE USING PARTIAL LEAST-SQUARES DISCRIMINANT ANALYSIS.

PubMed

Zhang, Mengliang; Zhao, Yang; Harrington, Peter de B; Chen, Pei

2016-03-01

Two simple fingerprinting methods, flow-injection coupled to ultraviolet spectroscopy and proton nuclear magnetic resonance, were used for discriminating between Aurantii fructus immaturus and Fructus poniciri trifoliatae immaturus . Both methods were combined with partial least-squares discriminant analysis. In the flow-injection method, four data representations were evaluated: total ultraviolet absorbance chromatograms, averaged ultraviolet spectra, absorbance at 193, 205, 225, and 283 nm, and absorbance at 225 and 283 nm. Prediction rates of 100% were achieved for all data representations by partial least-squares discriminant analysis using leave-one-sample-out cross-validation. The prediction rate for the proton nuclear magnetic resonance data by partial least-squares discriminant analysis with leave-one-sample-out cross-validation was also 100%. A new validation set of data was collected by flow-injection with ultraviolet spectroscopic detection two weeks later and predicted by partial least-squares discriminant analysis models constructed by the initial data representations with no parameter changes. The classification rates were 95% with the total ultraviolet absorbance chromatograms datasets and 100% with the other three datasets. Flow-injection with ultraviolet detection and proton nuclear magnetic resonance are simple, high throughput, and low-cost methods for discrimination studies.

On Browne's Solution for Oblique Procrustes Rotation

ERIC Educational Resources Information Center

Cramer, Elliot M.

1974-01-01

A form of Browne's (1967) solution of finding a least squares fit to a specified factor structure is given which does not involve solution of an eigenvalue problem. It suggests the possible existence of a singularity, and a simple modification of Browne's computational procedure is proposed. (Author/RC)

40 CFR 89.320 - Carbon monoxide analyzer calibration.

Code of Federal Regulations, 2010 CFR

2010-07-01

... introduction into service and annually thereafter, the NDIR carbon monoxide analyzer shall be checked for... to its introduction into service, after any maintenance which could alter calibration, and every two... engineering practice. For each range calibrated, if the deviation from a least-squares best-fit straight line...

Nuclear matter compressibility from isoscalar giant monopole resonance

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shlomo, S.; Youngblood, D.H.

1993-02-01

We examine the status of the nuclear matter compressibility [ital K][sub nm] obtained from experimental data of the strength distribution of the giant monopole resonance in nuclei and employing a least-squares fit to a semiempirical expansion of the nucleus compressibility [ital K][sub [ital A

Accurate reconstruction of the thermal conductivity depth profile in case hardened steel

NASA Astrophysics Data System (ADS)

Celorrio, Ricardo; Apiñaniz, Estibaliz; Mendioroz, Arantza; Salazar, Agustín; Mandelis, Andreas

2010-04-01

The problem of retrieving a nonhomogeneous thermal conductivity profile from photothermal radiometry data is addressed from the perspective of a stabilized least square fitting algorithm. We have implemented an inversion method with several improvements: (a) a renormalization of the experimental data which removes not only the instrumental factor, but the constants affecting the amplitude and the phase as well, (b) the introduction of a frequency weighting factor in order to balance the contribution of high and low frequencies in the inversion algorithm, (c) the simultaneous fitting of amplitude and phase data, balanced according to their experimental noises, (d) a modified Tikhonov regularization procedure has been introduced to stabilize the inversion, and (e) the Morozov discrepancy principle has been used to stop the iterative process automatically, according to the experimental noise, to avoid "overfitting" of the experimental data. We have tested this improved method by fitting theoretical data generated from a known conductivity profile. Finally, we have applied our method to real data obtained in a hardened stainless steel plate. The reconstructed in-depth thermal conductivity profile exhibits low dispersion, even at the deepest locations, and is in good anticorrelation with the hardness indentation test.

A class of least-squares filtering and identification algorithms with systolic array architectures

NASA Technical Reports Server (NTRS)

Kalson, Seth Z.; Yao, Kung

1991-01-01

A unified approach is presented for deriving a large class of new and previously known time- and order-recursive least-squares algorithms with systolic array architectures, suitable for high-throughput-rate and VLSI implementations of space-time filtering and system identification problems. The geometrical derivation given is unique in that no assumption is made concerning the rank of the sample data correlation matrix. This method utilizes and extends the concept of oblique projections, as used previously in the derivations of the least-squares lattice algorithms. Exponentially weighted least-squares criteria are considered for both sliding and growing memory.

Least squares estimation of avian molt rates

USGS Publications Warehouse

Johnson, D.H.

1989-01-01

A straightforward least squares method of estimating the rate at which birds molt feathers is presented, suitable for birds captured more than once during the period of molt. The date of molt onset can also be estimated. The method is applied to male and female mourning doves.

New fit of thermal neutron constants (TNC) for 233,235U, 239,241Pu and 252Cf(sf): Microscopic vs. maxwellian data

NASA Astrophysics Data System (ADS)

Pronyaev, Vladimir G.; Capote, Roberto; Trkov, Andrej; Noguere, Gilles; Wallner, Anton

2017-09-01

An IAEA project to update the Neutron Standards is near completion. Traditionally, the Thermal Neutron Constants (TNC) evaluated data by Axton for thermal-neutron scattering, capture and fission on four fissile nuclei and the total nu-bar of 252Cf(sf) are used as input in the combined least-square fit with neutron cross section standards. The evaluation by Axton (1986) was based on a least-square fit of both thermal-spectrum averaged cross sections (Maxwellian data) and microscopic cross sections at 2200 m/s. There is a second Axton evaluation based exclusively on measured microscopic cross sections at 2200 m/s (excluding Maxwellian data). Both evaluations disagree within quoted uncertainties for fission and capture cross sections and total multiplicities of uranium isotopes. There are two factors, which may lead to such difference: Westcott g-factors with estimated 0.2% uncertainties used in the Axton's fit, and deviation of the thermal spectra from Maxwellian shape. To exclude or mitigate the impact of these factors, a new combined GMA fit of standards was undertaken with Axton's TNC evaluation based on 2200 m/s data used as a prior. New microscopic data at the thermal point, available since 1986, were added to the combined fit. Additionally, an independent evaluation of TNC was undertaken using CONRAD code. Both GMA and CONRAD results are consistent within quoted uncertainties. New evaluation shows a small increase of fission and capture thermal cross sections, and a corresponding decrease in evaluated thermal nubar for uranium isotopes and 239Pu.

How to deal with the high condition number of the noise covariance matrix of gravity field functionals synthesised from a satellite-only global gravity field model?

NASA Astrophysics Data System (ADS)

Klees, R.; Slobbe, D. C.; Farahani, H. H.

2018-03-01

The posed question arises for instance in regional gravity field modelling using weighted least-squares techniques if the gravity field functionals are synthesised from the spherical harmonic coefficients of a satellite-only global gravity model (GGM), and are used as one of the noisy datasets. The associated noise covariance matrix, appeared to be extremely ill-conditioned with a singular value spectrum that decayed gradually to zero without any noticeable gap. We analysed three methods to deal with the ill-conditioned noise covariance matrix: Tihonov regularisation of the noise covariance matrix in combination with the standard formula for the weighted least-squares estimator, a formula of the weighted least-squares estimator, which does not involve the inverse noise covariance matrix, and an estimator based on Rao's unified theory of least-squares. Our analysis was based on a numerical experiment involving a set of height anomalies synthesised from the GGM GOCO05s, which is provided with a full noise covariance matrix. We showed that the three estimators perform similar, provided that the two regularisation parameters each method knows were chosen properly. As standard regularisation parameter choice rules do not apply here, we suggested a new parameter choice rule, and demonstrated its performance. Using this rule, we found that the differences between the three least-squares estimates were within noise. For the standard formulation of the weighted least-squares estimator with regularised noise covariance matrix, this required an exceptionally strong regularisation, much larger than one expected from the condition number of the noise covariance matrix. The preferred method is the inversion-free formulation of the weighted least-squares estimator, because of its simplicity with respect to the choice of the two regularisation parameters.

Mapping conduction velocity of early embryonic hearts with a robust fitting algorithm

PubMed Central

Gu, Shi; Wang, Yves T; Ma, Pei; Werdich, Andreas A; Rollins, Andrew M; Jenkins, Michael W

2015-01-01

Cardiac conduction maturation is an important and integral component of heart development. Optical mapping with voltage-sensitive dyes allows sensitive measurements of electrophysiological signals over the entire heart. However, accurate measurements of conduction velocity during early cardiac development is typically hindered by low signal-to-noise ratio (SNR) measurements of action potentials. Here, we present a novel image processing approach based on least squares optimizations, which enables high-resolution, low-noise conduction velocity mapping of smaller tubular hearts. First, the action potential trace measured at each pixel is fit to a curve consisting of two cumulative normal distribution functions. Then, the activation time at each pixel is determined based on the fit, and the spatial gradient of activation time is determined with a two-dimensional (2D) linear fit over a square-shaped window. The size of the window is adaptively enlarged until the gradients can be determined within a preset precision. Finally, the conduction velocity is calculated based on the activation time gradient, and further corrected for three-dimensional (3D) geometry that can be obtained by optical coherence tomography (OCT). We validated the approach using published activation potential traces based on computer simulations. We further validated the method by adding artificially generated noise to the signal to simulate various SNR conditions using a curved simulated image (digital phantom) that resembles a tubular heart. This method proved to be robust, even at very low SNR conditions (SNR = 2-5). We also established an empirical equation to estimate the maximum conduction velocity that can be accurately measured under different conditions (e.g. sampling rate, SNR, and pixel size). Finally, we demonstrated high-resolution conduction velocity maps of the quail embryonic heart at a looping stage of development. PMID:26114034

Method of determining effects of heat-induced irregular refractive index on an optical system.

PubMed

Song, Xifa; Li, Lin; Huang, Yifan

2015-09-01

The effects of an irregular refractive index on optical performance are examined. A method was developed to express a lens's irregular refractive index distribution. An optical system and its mountings were modeled by a thermomechanical finite element (FE) program in the predicted operating temperature range, -45°C-50°C. FE outputs were elaborated using a MATLAB optimization routine; a nonlinear least squares algorithm was adopted to determine which gradient equation best fit each lens's refractive index distribution. The obtained gradient data were imported into Zemax for sequential ray-tracing analysis. The root mean square spot diameter, modulation transfer function, and diffraction ensquared energy were computed for an optical system under an irregular refractive index and under thermoelastic deformation. These properties are greatly reduced by the irregular refractive index effect, which is one-third to five-sevenths the size of the thermoelastic deformation effect. Thus, thermal analyses of optical systems should consider not only thermoelastic deformation but also refractive index irregularities caused by inhomogeneous temperature.

A weighted least squares estimation of the polynomial regression model on paddy production in the area of Kedah and Perlis

NASA Astrophysics Data System (ADS)

Musa, Rosliza; Ali, Zalila; Baharum, Adam; Nor, Norlida Mohd

2017-08-01

The linear regression model assumes that all random error components are identically and independently distributed with constant variance. Hence, each data point provides equally precise information about the deterministic part of the total variation. In other words, the standard deviations of the error terms are constant over all values of the predictor variables. When the assumption of constant variance is violated, the ordinary least squares estimator of regression coefficient lost its property of minimum variance in the class of linear and unbiased estimators. Weighted least squares estimation are often used to maximize the efficiency of parameter estimation. A procedure that treats all of the data equally would give less precisely measured points more influence than they should have and would give highly precise points too little influence. Optimizing the weighted fitting criterion to find the parameter estimates allows the weights to determine the contribution of each observation to the final parameter estimates. This study used polynomial model with weighted least squares estimation to investigate paddy production of different paddy lots based on paddy cultivation characteristics and environmental characteristics in the area of Kedah and Perlis. The results indicated that factors affecting paddy production are mixture fertilizer application cycle, average temperature, the squared effect of average rainfall, the squared effect of pest and disease, the interaction between acreage with amount of mixture fertilizer, the interaction between paddy variety and NPK fertilizer application cycle and the interaction between pest and disease and NPK fertilizer application cycle.

Estimation of fast and slow wave properties in cancellous bone using Prony's method and curve fitting.

PubMed

Wear, Keith A

2013-04-01

The presence of two longitudinal waves in poroelastic media is predicted by Biot's theory and has been confirmed experimentally in through-transmission measurements in cancellous bone. Estimation of attenuation coefficients and velocities of the two waves is challenging when the two waves overlap in time. The modified least squares Prony's (MLSP) method in conjuction with curve-fitting (MLSP + CF) is tested using simulations based on published values for fast and slow wave attenuation coefficients and velocities in cancellous bone from several studies in bovine femur, human femur, and human calcaneus. The search algorithm is accelerated by exploiting correlations among search parameters. The performance of the algorithm is evaluated as a function of signal-to-noise ratio (SNR). For a typical experimental SNR (40 dB), the root-mean-square errors (RMSEs) for one example (human femur) with fast and slow waves separated by approximately half of a pulse duration were 1 m/s (slow wave velocity), 4 m/s (fast wave velocity), 0.4 dB/cm MHz (slow wave attenuation slope), and 1.7 dB/cm MHz (fast wave attenuation slope). The MLSP + CF method is fast (requiring less than 2 s at SNR = 40 dB on a consumer-grade notebook computer) and is flexible with respect to the functional form of the parametric model for the transmission coefficient. The MLSP + CF method provides sufficient accuracy and precision for many applications such that experimental error is a greater limiting factor than estimation error.

Resimulation of noise: a precision estimator for least square error curve-fitting tested for axial strain time constant imaging

NASA Astrophysics Data System (ADS)

Nair, S. P.; Righetti, R.

2015-05-01

Recent elastography techniques focus on imaging information on properties of materials which can be modeled as viscoelastic or poroelastic. These techniques often require the fitting of temporal strain data, acquired from either a creep or stress-relaxation experiment to a mathematical model using least square error (LSE) parameter estimation. It is known that the strain versus time relationships for tissues undergoing creep compression have a non-linear relationship. In non-linear cases, devising a measure of estimate reliability can be challenging. In this article, we have developed and tested a method to provide non linear LSE parameter estimate reliability: which we called Resimulation of Noise (RoN). RoN provides a measure of reliability by estimating the spread of parameter estimates from a single experiment realization. We have tested RoN specifically for the case of axial strain time constant parameter estimation in poroelastic media. Our tests show that the RoN estimated precision has a linear relationship to the actual precision of the LSE estimator. We have also compared results from the RoN derived measure of reliability against a commonly used reliability measure: the correlation coefficient (CorrCoeff). Our results show that CorrCoeff is a poor measure of estimate reliability for non-linear LSE parameter estimation. While the RoN is specifically tested only for axial strain time constant imaging, a general algorithm is provided for use in all LSE parameter estimation.

Tmax Determined Using a Bayesian Estimation Deconvolution Algorithm Applied to Bolus Tracking Perfusion Imaging: A Digital Phantom Validation Study.

PubMed

Uwano, Ikuko; Sasaki, Makoto; Kudo, Kohsuke; Boutelier, Timothé; Kameda, Hiroyuki; Mori, Futoshi; Yamashita, Fumio

2017-01-10

The Bayesian estimation algorithm improves the precision of bolus tracking perfusion imaging. However, this algorithm cannot directly calculate Tmax, the time scale widely used to identify ischemic penumbra, because Tmax is a non-physiological, artificial index that reflects the tracer arrival delay (TD) and other parameters. We calculated Tmax from the TD and mean transit time (MTT) obtained by the Bayesian algorithm and determined its accuracy in comparison with Tmax obtained by singular value decomposition (SVD) algorithms. The TD and MTT maps were generated by the Bayesian algorithm applied to digital phantoms with time-concentration curves that reflected a range of values for various perfusion metrics using a global arterial input function. Tmax was calculated from the TD and MTT using constants obtained by a linear least-squares fit to Tmax obtained from the two SVD algorithms that showed the best benchmarks in a previous study. Correlations between the Tmax values obtained by the Bayesian and SVD methods were examined. The Bayesian algorithm yielded accurate TD and MTT values relative to the true values of the digital phantom. Tmax calculated from the TD and MTT values with the least-squares fit constants showed excellent correlation (Pearson's correlation coefficient = 0.99) and agreement (intraclass correlation coefficient = 0.99) with Tmax obtained from SVD algorithms. Quantitative analyses of Tmax values calculated from Bayesian-estimation algorithm-derived TD and MTT from a digital phantom correlated and agreed well with Tmax values determined using SVD algorithms.

Estimation of parameters in rational reaction rates of molecular biological systems via weighted least squares

NASA Astrophysics Data System (ADS)

Wu, Fang-Xiang; Mu, Lei; Shi, Zhong-Ke

2010-01-01

The models of gene regulatory networks are often derived from statistical thermodynamics principle or Michaelis-Menten kinetics equation. As a result, the models contain rational reaction rates which are nonlinear in both parameters and states. It is challenging to estimate parameters nonlinear in a model although there have been many traditional nonlinear parameter estimation methods such as Gauss-Newton iteration method and its variants. In this article, we develop a two-step method to estimate the parameters in rational reaction rates of gene regulatory networks via weighted linear least squares. This method takes the special structure of rational reaction rates into consideration. That is, in the rational reaction rates, the numerator and the denominator are linear in parameters. By designing a special weight matrix for the linear least squares, parameters in the numerator and the denominator can be estimated by solving two linear least squares problems. The main advantage of the developed method is that it can produce the analytical solutions to the estimation of parameters in rational reaction rates which originally is nonlinear parameter estimation problem. The developed method is applied to a couple of gene regulatory networks. The simulation results show the superior performance over Gauss-Newton method.

Multi-Parameter Linear Least-Squares Fitting to Poisson Data One Count at a Time

NASA Technical Reports Server (NTRS)

Wheaton, W.; Dunklee, A.; Jacobson, A.; Ling, J.; Mahoney, W.; Radocinski, R.

1993-01-01

A standard problem in gamma-ray astronomy data analysis is the decomposition of a set of observed counts, described by Poisson statistics, according to a given multi-component linear model, with underlying physical count rates or fluxes which are to be estimated from the data.

40 CFR 89.322 - Carbon dioxide analyzer calibration.

Code of Federal Regulations, 2010 CFR

2010-07-01

... Test Equipment Provisions § 89.322 Carbon dioxide analyzer calibration. (a) Prior to its introduction... requirements of paragraph (a)(3) of this section. Proceed as follows: (1) Follow good engineering practices for... engineering practice. For each range calibrated, if the deviation from a least-squares best-fit straight line...

Effects of Employing Ridge Regression in Structural Equation Models.

ERIC Educational Resources Information Center

McQuitty, Shaun

1997-01-01

LISREL 8 invokes a ridge option when maximum likelihood or generalized least squares are used to estimate a structural equation model with a nonpositive definite covariance or correlation matrix. Implications of the ridge option for model fit, parameter estimates, and standard errors are explored through two examples. (SLD)

Improved estimation of parametric images of cerebral glucose metabolic rate from dynamic FDG-PET using volume-wise principle component analysis

NASA Astrophysics Data System (ADS)

Dai, Xiaoqian; Tian, Jie; Chen, Zhe

2010-03-01

Parametric images can represent both spatial distribution and quantification of the biological and physiological parameters of tracer kinetics. The linear least square (LLS) method is a well-estimated linear regression method for generating parametric images by fitting compartment models with good computational efficiency. However, bias exists in LLS-based parameter estimates, owing to the noise present in tissue time activity curves (TTACs) that propagates as correlated error in the LLS linearized equations. To address this problem, a volume-wise principal component analysis (PCA) based method is proposed. In this method, firstly dynamic PET data are properly pre-transformed to standardize noise variance as PCA is a data driven technique and can not itself separate signals from noise. Secondly, the volume-wise PCA is applied on PET data. The signals can be mostly represented by the first few principle components (PC) and the noise is left in the subsequent PCs. Then the noise-reduced data are obtained using the first few PCs by applying 'inverse PCA'. It should also be transformed back according to the pre-transformation method used in the first step to maintain the scale of the original data set. Finally, the obtained new data set is used to generate parametric images using the linear least squares (LLS) estimation method. Compared with other noise-removal method, the proposed method can achieve high statistical reliability in the generated parametric images. The effectiveness of the method is demonstrated both with computer simulation and with clinical dynamic FDG PET study.

Ultrasonic tracking of shear waves using a particle filter

PubMed Central

Ingle, Atul N.; Ma, Chi; Varghese, Tomy

2015-01-01

Purpose: This paper discusses an application of particle filtering for estimating shear wave velocity in tissue using ultrasound elastography data. Shear wave velocity estimates are of significant clinical value as they help differentiate stiffer areas from softer areas which is an indicator of potential pathology. Methods: Radio-frequency ultrasound echo signals are used for tracking axial displacements and obtaining the time-to-peak displacement at different lateral locations. These time-to-peak data are usually very noisy and cannot be used directly for computing velocity. In this paper, the denoising problem is tackled using a hidden Markov model with the hidden states being the unknown (noiseless) time-to-peak values. A particle filter is then used for smoothing out the time-to-peak curve to obtain a fit that is optimal in a minimum mean squared error sense. Results: Simulation results from synthetic data and finite element modeling suggest that the particle filter provides lower mean squared reconstruction error with smaller variance as compared to standard filtering methods, while preserving sharp boundary detail. Results from phantom experiments show that the shear wave velocity estimates in the stiff regions of the phantoms were within 20% of those obtained from a commercial ultrasound scanner and agree with estimates obtained using a standard method using least-squares fit. Estimates of area obtained from the particle filtered shear wave velocity maps were within 10% of those obtained from B-mode ultrasound images. Conclusions: The particle filtering approach can be used for producing visually appealing SWV reconstructions by effectively delineating various areas of the phantom with good image quality properties comparable to existing techniques. PMID:26520761

LIF and emission studies of copper and nitrogen

NASA Technical Reports Server (NTRS)

Akundi, Murty A.

1990-01-01

A technique is developed to determine the rotational temperature of nitrogen molecular ion, N2(+), from the emission spectra of B-X transition, when P and R branches are not resolved. Its validity is tested on simulated spectra of the 0-1 band of N2(+) produced under low resolution. The method is applied to experimental spectra of N2(+) taken in the shock layer of a blunt body at distances of 1.91, 2.54, and 3.18 cm from the body. The laser induced fluorescence (LIF) spectra of copper atoms is analyzed to obtain the free stream velocities and temperatures. The only broadening mechanism considered is Doppler broadening. The temperatures are obtained by manual curve fitting, and the results are compared with least square fits. The agreement on the average is within 10 percent.

Nucleus detection using gradient orientation information and linear least squares regression

NASA Astrophysics Data System (ADS)

Kwak, Jin Tae; Hewitt, Stephen M.; Xu, Sheng; Pinto, Peter A.; Wood, Bradford J.

2015-03-01

Computerized histopathology image analysis enables an objective, efficient, and quantitative assessment of digitized histopathology images. Such analysis often requires an accurate and efficient detection and segmentation of histological structures such as glands, cells and nuclei. The segmentation is used to characterize tissue specimens and to determine the disease status or outcomes. The segmentation of nuclei, in particular, is challenging due to the overlapping or clumped nuclei. Here, we propose a nuclei seed detection method for the individual and overlapping nuclei that utilizes the gradient orientation or direction information. The initial nuclei segmentation is provided by a multiview boosting approach. The angle of the gradient orientation is computed and traced for the nuclear boundaries. Taking the first derivative of the angle of the gradient orientation, high concavity points (junctions) are discovered. False junctions are found and removed by adopting a greedy search scheme with the goodness-of-fit statistic in a linear least squares sense. Then, the junctions determine boundary segments. Partial boundary segments belonging to the same nucleus are identified and combined by examining the overlapping area between them. Using the final set of the boundary segments, we generate the list of seeds in tissue images. The method achieved an overall precision of 0.89 and a recall of 0.88 in comparison to the manual segmentation.

Estimating pole/zero errors in GSN-IRIS/USGS network calibration metadata

USGS Publications Warehouse

Ringler, A.T.; Hutt, C.R.; Aster, R.; Bolton, H.; Gee, L.S.; Storm, T.

2012-01-01

Mapping the digital record of a seismograph into true ground motion requires the correction of the data by some description of the instrument's response. For the Global Seismographic Network (Butler et al., 2004), as well as many other networks, this instrument response is represented as a Laplace domain pole–zero model and published in the Standard for the Exchange of Earthquake Data (SEED) format. This Laplace representation assumes that the seismometer behaves as a linear system, with any abrupt changes described adequately via multiple time-invariant epochs. The SEED format allows for published instrument response errors as well, but these typically have not been estimated or provided to users. We present an iterative three-step method to estimate the instrument response parameters (poles and zeros) and their associated errors using random calibration signals. First, we solve a coarse nonlinear inverse problem using a least-squares grid search to yield a first approximation to the solution. This approach reduces the likelihood of poorly estimated parameters (a local-minimum solution) caused by noise in the calibration records and enhances algorithm convergence. Second, we iteratively solve a nonlinear parameter estimation problem to obtain the least-squares best-fit Laplace pole–zero–gain model. Third, by applying the central limit theorem, we estimate the errors in this pole–zero model by solving the inverse problem at each frequency in a two-thirds octave band centered at each best-fit pole–zero frequency. This procedure yields error estimates of the 99% confidence interval. We demonstrate the method by applying it to a number of recent Incorporated Research Institutions in Seismology/United States Geological Survey (IRIS/USGS) network calibrations (network code IU).

Penalized Multi-Way Partial Least Squares for Smooth Trajectory Decoding from Electrocorticographic (ECoG) Recording

PubMed Central

Eliseyev, Andrey; Aksenova, Tetiana

2016-01-01

In the current paper the decoding algorithms for motor-related BCI systems for continuous upper limb trajectory prediction are considered. Two methods for the smooth prediction, namely Sobolev and Polynomial Penalized Multi-Way Partial Least Squares (PLS) regressions, are proposed. The methods are compared to the Multi-Way Partial Least Squares and Kalman Filter approaches. The comparison demonstrated that the proposed methods combined the prediction accuracy of the algorithms of the PLS family and trajectory smoothness of the Kalman Filter. In addition, the prediction delay is significantly lower for the proposed algorithms than for the Kalman Filter approach. The proposed methods could be applied in a wide range of applications beyond neuroscience. PMID:27196417

Effect of genetic algorithm as a variable selection method on different chemometric models applied for the analysis of binary mixture of amoxicillin and flucloxacillin: A comparative study

NASA Astrophysics Data System (ADS)

Attia, Khalid A. M.; Nassar, Mohammed W. I.; El-Zeiny, Mohamed B.; Serag, Ahmed

2016-03-01

Different chemometric models were applied for the quantitative analysis of amoxicillin (AMX), and flucloxacillin (FLX) in their binary mixtures, namely, partial least squares (PLS), spectral residual augmented classical least squares (SRACLS), concentration residual augmented classical least squares (CRACLS) and artificial neural networks (ANNs). All methods were applied with and without variable selection procedure (genetic algorithm GA). The methods were used for the quantitative analysis of the drugs in laboratory prepared mixtures and real market sample via handling the UV spectral data. Robust and simpler models were obtained by applying GA. The proposed methods were found to be rapid, simple and required no preliminary separation steps.

Simulation of Foam Divot Weight on External Tank Utilizing Least Squares and Neural Network Methods

NASA Technical Reports Server (NTRS)

Chamis, Christos C.; Coroneos, Rula M.

2007-01-01

Simulation of divot weight in the insulating foam, associated with the external tank of the U.S. space shuttle, has been evaluated using least squares and neural network concepts. The simulation required models based on fundamental considerations that can be used to predict under what conditions voids form, the size of the voids, and subsequent divot ejection mechanisms. The quadratic neural networks were found to be satisfactory for the simulation of foam divot weight in various tests associated with the external tank. Both linear least squares method and the nonlinear neural network predicted identical results.

Improved modeling of in vivo confocal Raman data using multivariate curve resolution (MCR) augmentation of ordinary least squares models.

PubMed

Hancewicz, Thomas M; Xiao, Chunhong; Zhang, Shuliang; Misra, Manoj

2013-12-01

In vivo confocal Raman spectroscopy has become the measurement technique of choice for skin health and skin care related communities as a way of measuring functional chemistry aspects of skin that are key indicators for care and treatment of various skin conditions. Chief among these techniques are stratum corneum water content, a critical health indicator for severe skin condition related to dryness, and natural moisturizing factor components that are associated with skin protection and barrier health. In addition, in vivo Raman spectroscopy has proven to be a rapid and effective method for quantifying component penetration in skin for topically applied skin care formulations. The benefit of such a capability is that noninvasive analytical chemistry can be performed in vivo in a clinical setting, significantly simplifying studies aimed at evaluating product performance. This presumes, however, that the data and analysis methods used are compatible and appropriate for the intended purpose. The standard analysis method used by most researchers for in vivo Raman data is ordinary least squares (OLS) regression. The focus of work described in this paper is the applicability of OLS for in vivo Raman analysis with particular attention given to use for non-ideal data that often violate the inherent limitations and deficiencies associated with proper application of OLS. We then describe a newly developed in vivo Raman spectroscopic analysis methodology called multivariate curve resolution-augmented ordinary least squares (MCR-OLS), a relatively simple route to addressing many of the issues with OLS. The method is compared with the standard OLS method using the same in vivo Raman data set and using both qualitative and quantitative comparisons based on model fit error, adherence to known data constraints, and performance against calibration samples. A clear improvement is shown in each comparison for MCR-OLS over standard OLS, thus supporting the premise that the MCR-OLS method is better suited for general-purpose multicomponent analysis of in vivo Raman spectral data. This suggests that the methodology is more readily adaptable to a wide range of component systems and is thus more generally applicable than standard OLS.

Variable selection based on clustering analysis for improvement of polyphenols prediction in green tea using synchronous fluorescence spectra

NASA Astrophysics Data System (ADS)

Shan, Jiajia; Wang, Xue; Zhou, Hao; Han, Shuqing; Riza, Dimas Firmanda Al; Kondo, Naoshi

2018-04-01

Synchronous fluorescence spectra, combined with multivariate analysis were used to predict flavonoids content in green tea rapidly and nondestructively. This paper presented a new and efficient spectral intervals selection method called clustering based partial least square (CL-PLS), which selected informative wavelengths by combining clustering concept and partial least square (PLS) methods to improve models’ performance by synchronous fluorescence spectra. The fluorescence spectra of tea samples were obtained and k-means and kohonen-self organizing map clustering algorithms were carried out to cluster full spectra into several clusters, and sub-PLS regression model was developed on each cluster. Finally, CL-PLS models consisting of gradually selected clusters were built. Correlation coefficient (R) was used to evaluate the effect on prediction performance of PLS models. In addition, variable influence on projection partial least square (VIP-PLS), selectivity ratio partial least square (SR-PLS), interval partial least square (iPLS) models and full spectra PLS model were investigated and the results were compared. The results showed that CL-PLS presented the best result for flavonoids prediction using synchronous fluorescence spectra.

Variable selection based on clustering analysis for improvement of polyphenols prediction in green tea using synchronous fluorescence spectra.

PubMed

Shan, Jiajia; Wang, Xue; Zhou, Hao; Han, Shuqing; Riza, Dimas Firmanda Al; Kondo, Naoshi

2018-03-13

Synchronous fluorescence spectra, combined with multivariate analysis were used to predict flavonoids content in green tea rapidly and nondestructively. This paper presented a new and efficient spectral intervals selection method called clustering based partial least square (CL-PLS), which selected informative wavelengths by combining clustering concept and partial least square (PLS) methods to improve models' performance by synchronous fluorescence spectra. The fluorescence spectra of tea samples were obtained and k-means and kohonen-self organizing map clustering algorithms were carried out to cluster full spectra into several clusters, and sub-PLS regression model was developed on each cluster. Finally, CL-PLS models consisting of gradually selected clusters were built. Correlation coefficient (R) was used to evaluate the effect on prediction performance of PLS models. In addition, variable influence on projection partial least square (VIP-PLS), selectivity ratio partial least square (SR-PLS), interval partial least square (iPLS) models and full spectra PLS model were investigated and the results were compared. The results showed that CL-PLS presented the best result for flavonoids prediction using synchronous fluorescence spectra.

Calibration data Analysis Package (CAP): An IDL based widget application for analysis of X-ray calibration data

NASA Astrophysics Data System (ADS)

Vaishali, S.; Narendranath, S.; Sreekumar, P.

An IDL (interactive data language) based widget application developed for the calibration of C1XS (Narendranath et al., 2010) instrument on Chandrayaan-1 is modified to provide a generic package for the analysis of data from x-ray detectors. The package supports files in ascii as well as FITS format. Data can be fitted with a list of inbuilt functions to derive the spectral redistribution function (SRF). We have incorporated functions such as `HYPERMET' (Philips & Marlow 1976) including non Gaussian components in the SRF such as low energy tail, low energy shelf and escape peak. In addition users can incorporate additional models which may be required to model detector specific features. Spectral fits use a routine `mpfit' which uses Leven-Marquardt least squares fitting method. The SRF derived from this tool can be fed into an accompanying program to generate a redistribution matrix file (RMF) compatible with the X-ray spectral analysis package XSPEC. The tool provides a user friendly interface of help to beginners and also provides transparency and advanced features for experts.

Ultrasonic tracking of shear waves using a particle filter.

PubMed

Ingle, Atul N; Ma, Chi; Varghese, Tomy

2015-11-01

This paper discusses an application of particle filtering for estimating shear wave velocity in tissue using ultrasound elastography data. Shear wave velocity estimates are of significant clinical value as they help differentiate stiffer areas from softer areas which is an indicator of potential pathology. Radio-frequency ultrasound echo signals are used for tracking axial displacements and obtaining the time-to-peak displacement at different lateral locations. These time-to-peak data are usually very noisy and cannot be used directly for computing velocity. In this paper, the denoising problem is tackled using a hidden Markov model with the hidden states being the unknown (noiseless) time-to-peak values. A particle filter is then used for smoothing out the time-to-peak curve to obtain a fit that is optimal in a minimum mean squared error sense. Simulation results from synthetic data and finite element modeling suggest that the particle filter provides lower mean squared reconstruction error with smaller variance as compared to standard filtering methods, while preserving sharp boundary detail. Results from phantom experiments show that the shear wave velocity estimates in the stiff regions of the phantoms were within 20% of those obtained from a commercial ultrasound scanner and agree with estimates obtained using a standard method using least-squares fit. Estimates of area obtained from the particle filtered shear wave velocity maps were within 10% of those obtained from B-mode ultrasound images. The particle filtering approach can be used for producing visually appealing SWV reconstructions by effectively delineating various areas of the phantom with good image quality properties comparable to existing techniques.

Chi-squared and C statistic minimization for low count per bin data

NASA Astrophysics Data System (ADS)

Nousek, John A.; Shue, David R.

1989-07-01

Results are presented from a computer simulation comparing two statistical fitting techniques on data samples with large and small counts per bin; the results are then related specifically to X-ray astronomy. The Marquardt and Powell minimization techniques are compared by using both to minimize the chi-squared statistic. In addition, Cash's C statistic is applied, with Powell's method, and it is shown that the C statistic produces better fits in the low-count regime than chi-squared.

Chi-squared and C statistic minimization for low count per bin data. [sampling in X ray astronomy

NASA Technical Reports Server (NTRS)

Nousek, John A.; Shue, David R.

1989-01-01

Results are presented from a computer simulation comparing two statistical fitting techniques on data samples with large and small counts per bin; the results are then related specifically to X-ray astronomy. The Marquardt and Powell minimization techniques are compared by using both to minimize the chi-squared statistic. In addition, Cash's C statistic is applied, with Powell's method, and it is shown that the C statistic produces better fits in the low-count regime than chi-squared.

Four points function fitted and first derivative procedure for determining the end points in potentiometric titration curves: statistical analysis and method comparison.

PubMed

Kholeif, S A

2001-06-01

A new method that belongs to the differential category for determining the end points from potentiometric titration curves is presented. It uses a preprocess to find first derivative values by fitting four data points in and around the region of inflection to a non-linear function, and then locate the end point, usually as a maximum or minimum, using an inverse parabolic interpolation procedure that has an analytical solution. The behavior and accuracy of the sigmoid and cumulative non-linear functions used are investigated against three factors. A statistical evaluation of the new method using linear least-squares method validation and multifactor data analysis are covered. The new method is generally applied to symmetrical and unsymmetrical potentiometric titration curves, and the end point is calculated using numerical procedures only. It outperforms the "parent" regular differential method in almost all factors levels and gives accurate results comparable to the true or estimated true end points. Calculated end points from selected experimental titration curves compatible with the equivalence point category of methods, such as Gran or Fortuin, are also compared with the new method.

An Alternating Least Squares Method for the Weighted Approximation of a Symmetric Matrix.

ERIC Educational Resources Information Center

ten Berge, Jos M. F.; Kiers, Henk A. L.

1993-01-01

R. A. Bailey and J. C. Gower explored approximating a symmetric matrix "B" by another, "C," in the least squares sense when the squared discrepancies for diagonal elements receive specific nonunit weights. A solution is proposed where "C" is constrained to be positive semidefinite and of a fixed rank. (SLD)

Tidal Volume Estimation Using the Blanket Fractal Dimension of the Tracheal Sounds Acquired by Smartphone

PubMed Central

Reljin, Natasa; Reyes, Bersain A.; Chon, Ki H.

2015-01-01

In this paper, we propose the use of blanket fractal dimension (BFD) to estimate the tidal volume from smartphone-acquired tracheal sounds. We collected tracheal sounds with a Samsung Galaxy S4 smartphone, from five (N = 5) healthy volunteers. Each volunteer performed the experiment six times; first to obtain linear and exponential fitting models, and then to fit new data onto the existing models. Thus, the total number of recordings was 30. The estimated volumes were compared to the true values, obtained with a Respitrace system, which was considered as a reference. Since Shannon entropy (SE) is frequently used as a feature in tracheal sound analyses, we estimated the tidal volume from the same sounds by using SE as well. The evaluation of the performed estimation, using BFD and SE methods, was quantified by the normalized root-mean-squared error (NRMSE). The results show that the BFD outperformed the SE (at least twice smaller NRMSE was obtained). The smallest NRMSE error of 15.877% ± 9.246% (mean ± standard deviation) was obtained with the BFD and exponential model. In addition, it was shown that the fitting curves calculated during the first day of experiments could be successfully used for at least the five following days. PMID:25923929

Tidal volume estimation using the blanket fractal dimension of the tracheal sounds acquired by smartphone.

PubMed

Reljin, Natasa; Reyes, Bersain A; Chon, Ki H

2015-04-27

In this paper, we propose the use of blanket fractal dimension (BFD) to estimate the tidal volume from smartphone-acquired tracheal sounds. We collected tracheal sounds with a Samsung Galaxy S4 smartphone, from five (N = 5) healthy volunteers. Each volunteer performed the experiment six times; first to obtain linear and exponential fitting models, and then to fit new data onto the existing models. Thus, the total number of recordings was 30. The estimated volumes were compared to the true values, obtained with a Respitrace system, which was considered as a reference. Since Shannon entropy (SE) is frequently used as a feature in tracheal sound analyses, we estimated the tidal volume from the same sounds by using SE as well. The evaluation of the performed estimation, using BFD and SE methods, was quantified by the normalized root-mean-squared error (NRMSE). The results show that the BFD outperformed the SE (at least twice smaller NRMSE was obtained). The smallest NRMSE error of 15.877% ± 9.246% (mean ± standard deviation) was obtained with the BFD and exponential model. In addition, it was shown that the fitting curves calculated during the first day of experiments could be successfully used for at least the five following days.

A simplified fractional order impedance model and parameter identification method for lithium-ion batteries

PubMed Central

Yang, Qingxia; Xu, Jun; Cao, Binggang; Li, Xiuqing

2017-01-01

Identification of internal parameters of lithium-ion batteries is a useful tool to evaluate battery performance, and requires an effective model and algorithm. Based on the least square genetic algorithm, a simplified fractional order impedance model for lithium-ion batteries and the corresponding parameter identification method were developed. The simplified model was derived from the analysis of the electrochemical impedance spectroscopy data and the transient response of lithium-ion batteries with different states of charge. In order to identify the parameters of the model, an equivalent tracking system was established, and the method of least square genetic algorithm was applied using the time-domain test data. Experiments and computer simulations were carried out to verify the effectiveness and accuracy of the proposed model and parameter identification method. Compared with a second-order resistance-capacitance (2-RC) model and recursive least squares method, small tracing voltage fluctuations were observed. The maximum battery voltage tracing error for the proposed model and parameter identification method is within 0.5%; this demonstrates the good performance of the model and the efficiency of the least square genetic algorithm to estimate the internal parameters of lithium-ion batteries. PMID:28212405

TaiWan Ionospheric Model (TWIM) prediction based on time series autoregressive analysis

NASA Astrophysics Data System (ADS)

Tsai, L. C.; Macalalad, Ernest P.; Liu, C. H.

2014-10-01

As described in a previous paper, a three-dimensional ionospheric electron density (Ne) model has been constructed from vertical Ne profiles retrieved from the FormoSat3/Constellation Observing System for Meteorology, Ionosphere, and Climate GPS radio occultation measurements and worldwide ionosonde foF2 and foE data and named the TaiWan Ionospheric Model (TWIM). The TWIM exhibits vertically fitted α-Chapman-type layers with distinct F2, F1, E, and D layers, and surface spherical harmonic approaches for the fitted layer parameters including peak density, peak density height, and scale height. To improve the TWIM into a real-time model, we have developed a time series autoregressive model to forecast short-term TWIM coefficients. The time series of TWIM coefficients are considered as realizations of stationary stochastic processes within a processing window of 30 days. These autocorrelation coefficients are used to derive the autoregressive parameters and then forecast the TWIM coefficients, based on the least squares method and Lagrange multiplier technique. The forecast root-mean-square relative TWIM coefficient errors are generally <30% for 1 day predictions. The forecast TWIM values of foE and foF2 values are also compared and evaluated using worldwide ionosonde data.

Curve fitting methods for solar radiation data modeling

NASA Astrophysics Data System (ADS)

Karim, Samsul Ariffin Abdul; Singh, Balbir Singh Mahinder

2014-10-01

This paper studies the use of several type of curve fitting method to smooth the global solar radiation data. After the data have been fitted by using curve fitting method, the mathematical model of global solar radiation will be developed. The error measurement was calculated by using goodness-fit statistics such as root mean square error (RMSE) and the value of R2. The best fitting methods will be used as a starting point for the construction of mathematical modeling of solar radiation received in Universiti Teknologi PETRONAS (UTP) Malaysia. Numerical results indicated that Gaussian fitting and sine fitting (both with two terms) gives better results as compare with the other fitting methods.

Curve fitting methods for solar radiation data modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Karim, Samsul Ariffin Abdul, E-mail: samsul-ariffin@petronas.com.my, E-mail: balbir@petronas.com.my; Singh, Balbir Singh Mahinder, E-mail: samsul-ariffin@petronas.com.my, E-mail: balbir@petronas.com.my

2014-10-24

This paper studies the use of several type of curve fitting method to smooth the global solar radiation data. After the data have been fitted by using curve fitting method, the mathematical model of global solar radiation will be developed. The error measurement was calculated by using goodness-fit statistics such as root mean square error (RMSE) and the value of R{sup 2}. The best fitting methods will be used as a starting point for the construction of mathematical modeling of solar radiation received in Universiti Teknologi PETRONAS (UTP) Malaysia. Numerical results indicated that Gaussian fitting and sine fitting (both withmore » two terms) gives better results as compare with the other fitting methods.« less

Parameter estimation using weighted total least squares in the two-compartment exchange model.

PubMed

Garpebring, Anders; Löfstedt, Tommy

2018-01-01

The linear least squares (LLS) estimator provides a fast approach to parameter estimation in the linearized two-compartment exchange model. However, the LLS method may introduce a bias through correlated noise in the system matrix of the model. The purpose of this work is to present a new estimator for the linearized two-compartment exchange model that takes this noise into account. To account for the noise in the system matrix, we developed an estimator based on the weighted total least squares (WTLS) method. Using simulations, the proposed WTLS estimator was compared, in terms of accuracy and precision, to an LLS estimator and a nonlinear least squares (NLLS) estimator. The WTLS method improved the accuracy compared to the LLS method to levels comparable to the NLLS method. This improvement was at the expense of increased computational time; however, the WTLS was still faster than the NLLS method. At high signal-to-noise ratio all methods provided similar precisions while inconclusive results were observed at low signal-to-noise ratio. The proposed method provides improvements in accuracy compared to the LLS method, however, at an increased computational cost. Magn Reson Med 79:561-567, 2017. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

On the accuracy of least squares methods in the presence of corner singularities

NASA Technical Reports Server (NTRS)

Cox, C. L.; Fix, G. J.

1985-01-01

Elliptic problems with corner singularities are discussed. Finite element approximations based on variational principles of the least squares type tend to display poor convergence properties in such contexts. Moreover, mesh refinement or the use of special singular elements do not appreciably improve matters. It is shown that if the least squares formulation is done in appropriately weighted space, then optimal convergence results in unweighted spaces like L(2).

Accuracy of neutron self-activation method with iodine-containing scintillators for quantifying 128I generation using decay-fitting technique

NASA Astrophysics Data System (ADS)

Nohtomi, Akihiro; Wakabayashi, Genichiro

2015-11-01

We evaluated the accuracy of a self-activation method with iodine-containing scintillators in quantifying 128I generation in an activation detector; the self-activation method was recently proposed for photo-neutron on-line measurements around X-ray radiotherapy machines. Here, we consider the accuracy of determining the initial count rate R0, observed just after termination of neutron irradiation of the activation detector. The value R0 is directly related to the amount of activity generated by incident neutrons; the detection efficiency of radiation emitted from the activity should be taken into account for such an evaluation. Decay curves of 128I activity were numerically simulated by a computer program for various conditions including different initial count rates (R0) and background rates (RB), as well as counting statistical fluctuations. The data points sampled at minute intervals and integrated over the same period were fit by a non-linear least-squares fitting routine to obtain the value R0 as a fitting parameter with an associated uncertainty. The corresponding background rate RB was simultaneously calculated in the same fitting routine. Identical data sets were also evaluated by a well-known integration algorithm used for conventional activation methods and the results were compared with those of the proposed fitting method. When we fixed RB = 500 cpm, the relative uncertainty σR0 /R0 ≤ 0.02 was achieved for R0/RB ≥ 20 with 20 data points from 1 min to 20 min following the termination of neutron irradiation used in the fitting; σR0 /R0 ≤ 0.01 was achieved for R0/RB ≥ 50 with the same data points. Reasonable relative uncertainties to evaluate initial count rates were reached by the decay-fitting method using practically realistic sampling numbers. These results clarified the theoretical limits of the fitting method. The integration method was found to be potentially vulnerable to short-term variations in background levels, especially instantaneous contaminations by spike-like noise. The fitting method easily detects and removes such spike-like noise.

Sea surface mean square slope from Ku-band backscatter data

NASA Technical Reports Server (NTRS)

Jackson, F. C.; Walton, W. T.; Hines, D. E.; Walter, B. A.; Peng, C. Y.

1992-01-01

A surface mean-square-slope parameter analysis is conducted for 14-GHz airborne radar altimeter near-nadir, quasi-specular backscatter data, which in raw form obtained by least-squares fitting of an optical scattering model to the return waveform show an approximately linear dependence over the 7-15 m/sec wind speed range. Slope data are used to draw inferences on the structure of the high-wavenumber portion of the spectrum. A directionally-integrated model height spectrum that encompasses wind speed-dependent k exp -5/2 and classical Phillips k exp -3 power laws subranges in the range of gravity waves is supported by the data.

Meteoroid and debris special investigation group; status of 3-D crater analysis from binocular imagery

NASA Technical Reports Server (NTRS)

Sapp, Clyde A.; See, Thomas H.; Zolensky, Michael E.

1992-01-01

During the 3 month deintegration of the LDEF, the M&D SIG generated approximately 5000 digital color stereo image pairs of impact related features from all space exposed surfaces. Currently, these images are being processed at JSC to yield more accurate feature information. Work is currently underway to determine the minimum number of data points necessary to parametrically define impact crater morphologies in order to minimize the man-hour intensive task of tie point selection. Initial attempts at deriving accurate crater depth and diameter measurements from binocular imagery were based on the assumption that the crater geometries were best defined by paraboloid. We made no assumptions regarding the crater depth/diameter ratios but instead allowed each crater to define its own coefficients by performing a least-squares fit based on user-selected tiepoints. Initial test cases resulted in larger errors than desired, so it was decided to test our basic assumptions that the crater geometries could be parametrically defined as paraboloids. The method for testing this assumption was to carefully slice test craters (experimentally produced in an appropriate aluminum alloy) vertically through the center resulting in a readily visible cross-section of the crater geometry. Initially, five separate craters were cross-sectioned in this fashion. A digital image of each cross-section was then created, and the 2-D crater geometry was then hand-digitized to create a table of XY position for each crater. A 2nd order polynomial (parabolic) was fitted to the data using a least-squares approach. The differences between the fit equation and the actual data were fairly significant, and easily large enough to account for the errors found in the 3-D fits. The differences between the curve fit and the actual data were consistent between the caters. This consistency suggested that the differences were due to the fact that a parabola did not sufficiently define the generic crater geometry. Fourth and 6th order equations were then fitted to each crater cross-section, and significantly better estimates of the crater geometry were obtained with each fit. Work is presently underway to determine the best way to make use of this new parametric crater definition.

Parametric output-only identification of time-varying structures using a kernel recursive extended least squares TARMA approach

NASA Astrophysics Data System (ADS)

Ma, Zhi-Sai; Liu, Li; Zhou, Si-Da; Yu, Lei; Naets, Frank; Heylen, Ward; Desmet, Wim

2018-01-01

The problem of parametric output-only identification of time-varying structures in a recursive manner is considered. A kernelized time-dependent autoregressive moving average (TARMA) model is proposed by expanding the time-varying model parameters onto the basis set of kernel functions in a reproducing kernel Hilbert space. An exponentially weighted kernel recursive extended least squares TARMA identification scheme is proposed, and a sliding-window technique is subsequently applied to fix the computational complexity for each consecutive update, allowing the method to operate online in time-varying environments. The proposed sliding-window exponentially weighted kernel recursive extended least squares TARMA method is employed for the identification of a laboratory time-varying structure consisting of a simply supported beam and a moving mass sliding on it. The proposed method is comparatively assessed against an existing recursive pseudo-linear regression TARMA method via Monte Carlo experiments and shown to be capable of accurately tracking the time-varying dynamics. Furthermore, the comparisons demonstrate the superior achievable accuracy, lower computational complexity and enhanced online identification capability of the proposed kernel recursive extended least squares TARMA approach.

Radial artery pulse waveform analysis based on curve fitting using discrete Fourier series.

PubMed

Jiang, Zhixing; Zhang, David; Lu, Guangming

2018-04-19

Radial artery pulse diagnosis has been playing an important role in traditional Chinese medicine (TCM). For its non-invasion and convenience, the pulse diagnosis has great significance in diseases analysis of modern medicine. The practitioners sense the pulse waveforms in patients' wrist to make diagnoses based on their non-objective personal experience. With the researches of pulse acquisition platforms and computerized analysis methods, the objective study on pulse diagnosis can help the TCM to keep up with the development of modern medicine. In this paper, we propose a new method to extract feature from pulse waveform based on discrete Fourier series (DFS). It regards the waveform as one kind of signal that consists of a series of sub-components represented by sine and cosine (SC) signals with different frequencies and amplitudes. After the pulse signals are collected and preprocessed, we fit the average waveform for each sample using discrete Fourier series by least squares. The feature vector is comprised by the coefficients of discrete Fourier series function. Compared with the fitting method using Gaussian mixture function, the fitting errors of proposed method are smaller, which indicate that our method can represent the original signal better. The classification performance of proposed feature is superior to the other features extracted from waveform, liking auto-regression model and Gaussian mixture model. The coefficients of optimized DFS function, who is used to fit the arterial pressure waveforms, can obtain better performance in modeling the waveforms and holds more potential information for distinguishing different psychological states. Copyright © 2018 Elsevier B.V. All rights reserved.

Missing value imputation in DNA microarrays based on conjugate gradient method.

PubMed

Dorri, Fatemeh; Azmi, Paeiz; Dorri, Faezeh

2012-02-01

Analysis of gene expression profiles needs a complete matrix of gene array values; consequently, imputation methods have been suggested. In this paper, an algorithm that is based on conjugate gradient (CG) method is proposed to estimate missing values. k-nearest neighbors of the missed entry are first selected based on absolute values of their Pearson correlation coefficient. Then a subset of genes among the k-nearest neighbors is labeled as the best similar ones. CG algorithm with this subset as its input is then used to estimate the missing values. Our proposed CG based algorithm (CGimpute) is evaluated on different data sets. The results are compared with sequential local least squares (SLLSimpute), Bayesian principle component analysis (BPCAimpute), local least squares imputation (LLSimpute), iterated local least squares imputation (ILLSimpute) and adaptive k-nearest neighbors imputation (KNNKimpute) methods. The average of normalized root mean squares error (NRMSE) and relative NRMSE in different data sets with various missing rates shows CGimpute outperforms other methods. Copyright © 2011 Elsevier Ltd. All rights reserved.

Weighted linear least squares estimation of diffusion MRI parameters: strengths, limitations, and pitfalls.

PubMed

Veraart, Jelle; Sijbers, Jan; Sunaert, Stefan; Leemans, Alexander; Jeurissen, Ben

2013-11-01

Linear least squares estimators are widely used in diffusion MRI for the estimation of diffusion parameters. Although adding proper weights is necessary to increase the precision of these linear estimators, there is no consensus on how to practically define them. In this study, the impact of the commonly used weighting strategies on the accuracy and precision of linear diffusion parameter estimators is evaluated and compared with the nonlinear least squares estimation approach. Simulation and real data experiments were done to study the performance of the weighted linear least squares estimators with weights defined by (a) the squares of the respective noisy diffusion-weighted signals; and (b) the squares of the predicted signals, which are reconstructed from a previous estimate of the diffusion model parameters. The negative effect of weighting strategy (a) on the accuracy of the estimator was surprisingly high. Multi-step weighting strategies yield better performance and, in some cases, even outperformed the nonlinear least squares estimator. If proper weighting strategies are applied, the weighted linear least squares approach shows high performance characteristics in terms of accuracy/precision and may even be preferred over nonlinear estimation methods. Copyright © 2013 Elsevier Inc. All rights reserved.

Mapping Hydrothermal Alterations in the Muteh Gold Mining Area in Iran by using ASTER satellite Imagery data

NASA Astrophysics Data System (ADS)

Asadi Haroni, Hooshang; Hassan Tabatabaei, Seyed

2016-04-01

Muteh gold mining area is located in 160 km NW of Isfahan town. Gold mineralization is meso-thermal type and associated with silisic, seresitic and carbonate alterations as well as with hematite and goethite. Image processing and interpretation were applied on the ASTER satellite imagery data of about 400 km2 at the Muteh gold mining area to identify hydrothermal alterations and iron oxides associated with gold mineralization. After applying preprocessing methods such as radiometric and geometric corrections, image processing methods of Principal Components Analysis (PCA), Least Square Fit (Ls-Fit) and Spectral Angle Mapper (SAM) were applied on the ASTER data to identify hydrothermal alterations and iron oxides. In this research reference spectra of minerals such as chlorite, hematite, clay minerals and phengite identified from laboratory spectral analysis of collected samples were used to map the hydrothermal alterations. Finally, identified hydrothermal alteration and iron oxides were validated by visiting and sampling some of the mapped hydrothermal alterations.

Investigation on phase transitions of 1-decylammonium hydrochloride as the potential thermal energy storage material

NASA Astrophysics Data System (ADS)

Dan, Wen-Yan; Di, You-Ying; He, Dong-Hua; Liu, Yu-Pu

2011-02-01

1-Decylammonium hydrochloride was synthesized by the method of liquid phase synthesis. Chemical analysis, elemental analysis, and X-ray single crystal diffraction techniques were applied to characterize its composition and structure. Low-temperature heat capacities of the compounds were measured with a precision automated adiabatic calorimeter over the temperature range from 78 to 380 K. Three solid-solid phase transitions have been observed at the peak temperatures of 307.52 ± 0.13, 325.02 ± 0.19, and 327.26 ± 0.07 K. The molar enthalpies and entropies of three phase transitions were determined based on the analysis of heat capacity curves. Experimental molar heat capacities were fitted to two polynomial equations of the heat capacities as a function of temperature by least square method. Smoothed heat capacities and thermodynamic functions of the compound relative to the standard reference temperature 298.15 K were calculated and tabulated at intervals of 5 K based on the fitted polynomials.

Realistic Subsurface Anomaly Discrimination Using Electromagnetic Induction and an SVM Classifier

DTIC Science & Technology

2010-01-01

proposed by Pasion and Oldenburg [25]: Q(t) = kt−βe−γt. (10) Various combinations of these fitting parameters can be used as inputs to classifier... Pasion -Oldenburg parameters k, β, and γ for each anomaly by a direct nonlinear least-squares fit of (10) and by linear (pseudo)inversion of its...combinations of the Pasion -Oldenburg parameters. Com- bining k and γ yields results similar to those of k and R, as Figure 7 and Table 2 show. Figure 8 and

Mixture Model for Determination of Shock Equation of State

DTIC Science & Technology

2012-07-25

not considered in this paper. III. COMPARISON WITH EXPERIMENTAL DATA A. Two-constituent composites 1. Uranium- rhodium composite Uranium- rhodium (U...sound speed, Co, and S were determined from linear least squares fit to the available data22 as shown in Figs. 1(a) and 1(b) for uranium and rhodium ...overpredicts the experimental data, with an average deviation, dUs,/Us of 0.05, shown in Fig. 2(b). The linear fits for uranium and rhodium are shown for

A Monte Carlo Library Least Square approach in the Neutron Inelastic-scattering and Thermal-capture Analysis (NISTA) process in bulk coal samples

NASA Astrophysics Data System (ADS)

Reyhancan, Iskender Atilla; Ebrahimi, Alborz; Çolak, Üner; Erduran, M. Nizamettin; Angin, Nergis

2017-01-01

A new Monte-Carlo Library Least Square (MCLLS) approach for treating non-linear radiation analysis problem in Neutron Inelastic-scattering and Thermal-capture Analysis (NISTA) was developed. 14 MeV neutrons were produced by a neutron generator via the 3H (2H , n) 4He reaction. The prompt gamma ray spectra from bulk samples of seven different materials were measured by a Bismuth Germanate (BGO) gamma detection system. Polyethylene was used as neutron moderator along with iron and lead as neutron and gamma ray shielding, respectively. The gamma detection system was equipped with a list mode data acquisition system which streams spectroscopy data directly to the computer, event-by-event. A GEANT4 simulation toolkit was used for generating the single-element libraries of all the elements of interest. These libraries were then used in a Linear Library Least Square (LLLS) approach with an unknown experimental sample spectrum to fit it with the calculated elemental libraries. GEANT4 simulation results were also used for the selection of the neutron shielding material.

Applied Algebra: The Modeling Technique of Least Squares

ERIC Educational Resources Information Center

Zelkowski, Jeremy; Mayes, Robert

2008-01-01

The article focuses on engaging students in algebra through modeling real-world problems. The technique of least squares is explored, encouraging students to develop a deeper understanding of the method. (Contains 2 figures and a bibliography.)

Comparison between results of solution of Burgers' equation and Laplace's equation by Galerkin and least-square finite element methods

NASA Astrophysics Data System (ADS)

Adib, Arash; Poorveis, Davood; Mehraban, Farid

2018-03-01

In this research, two equations are considered as examples of hyperbolic and elliptic equations. In addition, two finite element methods are applied for solving of these equations. The purpose of this research is the selection of suitable method for solving each of two equations. Burgers' equation is a hyperbolic equation. This equation is a pure advection (without diffusion) equation. This equation is one-dimensional and unsteady. A sudden shock wave is introduced to the model. This wave moves without deformation. In addition, Laplace's equation is an elliptical equation. This equation is steady and two-dimensional. The solution of Laplace's equation in an earth dam is considered. By solution of Laplace's equation, head pressure and the value of seepage in the directions X and Y are calculated in different points of earth dam. At the end, water table is shown in the earth dam. For Burgers' equation, least-square method can show movement of wave with oscillation but Galerkin method can not show it correctly (the best method for solving of the Burgers' equation is discrete space by least-square finite element method and discrete time by forward difference.). For Laplace's equation, Galerkin and least square methods can show water table correctly in earth dam.

Curve fits of predicted inviscid stagnation-point radiative heating rates, cooling factors, and shock standoff distances for hyperbolic earth entry

NASA Technical Reports Server (NTRS)

Suttles, J. T.; Sullivan, E. M.; Margolis, S. B.

1974-01-01

Curve-fit formulas are presented for the stagnation-point radiative heating rate, cooling factor, and shock standoff distance for inviscid flow over blunt bodies at conditions corresponding to high-speed earth entry. The data which were curve fitted were calculated by using a technique which utilizes a one-strip integral method and a detailed nongray radiation model to generate a radiatively coupled flow-field solution for air in chemical and local thermodynamic equilibrium. The range of free-stream parameters considered were altitudes from about 55 to 70 km and velocities from about 11 to 16 km.sec. Spherical bodies with nose radii from 30 to 450 cm and elliptical bodies with major-to-minor axis ratios of 2, 4, and 6 were treated. Powerlaw formulas are proposed and a least-squares logarithmic fit is used to evaluate the constants. It is shown that the data can be described in this manner with an average deviation of about 3 percent (or less) and a maximum deviation of about 10 percent (or less). The curve-fit formulas provide an effective and economic means for making preliminary design studies for situations involving high-speed earth entry.

Determination of Diffusion Parameters of CO2 Through Microporous PTFE Using a Potentiometric Method

NASA Astrophysics Data System (ADS)

Tarsiche, I.; Ciurchea, D.

Dk values at the diffusion of CO2 through microporous PTFE of 1 to 7 × 10- 7 cm2 s- 1 in the concentration range from 4 × 10- 4 to 0.22 g/l CO2 are determined using a simple, fast and reliable potentiometric method. The method is based on the least-squares fitting of the potential versus time response of a self made CO2 sensitive Severinghaus type sensor with PTFE as a gas-permeable membrane. The obtained results are in good agreement with other reported literature data, both experimental or calculated ones using molecular dynamics simulations. The proposed technique is very sensitive especially at low concentrations of gas and may be used for the study of other polymeric membranes too.

Least-squares finite element methods for compressible Euler equations

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Carey, G. F.

1990-01-01

A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.

Hybrid least squares multivariate spectral analysis methods

DOEpatents

Haaland, David M.

2002-01-01

A set of hybrid least squares multivariate spectral analysis methods in which spectral shapes of components or effects not present in the original calibration step are added in a following estimation or calibration step to improve the accuracy of the estimation of the amount of the original components in the sampled mixture. The "hybrid" method herein means a combination of an initial classical least squares analysis calibration step with subsequent analysis by an inverse multivariate analysis method. A "spectral shape" herein means normally the spectral shape of a non-calibrated chemical component in the sample mixture but can also mean the spectral shapes of other sources of spectral variation, including temperature drift, shifts between spectrometers, spectrometer drift, etc. The "shape" can be continuous, discontinuous, or even discrete points illustrative of the particular effect.

Lameness detection challenges in automated milking systems addressed with partial least squares discriminant analysis.

PubMed

Garcia, E; Klaas, I; Amigo, J M; Bro, R; Enevoldsen, C

2014-12-01

Lameness causes decreased animal welfare and leads to higher production costs. This study explored data from an automatic milking system (AMS) to model on-farm gait scoring from a commercial farm. A total of 88 cows were gait scored once per week, for 2 5-wk periods. Eighty variables retrieved from AMS were summarized week-wise and used to predict 2 defined classes: nonlame and clinically lame cows. Variables were represented with 2 transformations of the week summarized variables, using 2-wk data blocks before gait scoring, totaling 320 variables (2 × 2 × 80). The reference gait scoring error was estimated in the first week of the study and was, on average, 15%. Two partial least squares discriminant analysis models were fitted to parity 1 and parity 2 groups, respectively, to assign the lameness class according to the predicted probability of being lame (score 3 or 4/4) or not lame (score 1/4). Both models achieved sensitivity and specificity values around 80%, both in calibration and cross-validation. At the optimum values in the receiver operating characteristic curve, the false-positive rate was 28% in the parity 1 model, whereas in the parity 2 model it was about half (16%), which makes it more suitable for practical application; the model error rates were, 23 and 19%, respectively. Based on data registered automatically from one AMS farm, we were able to discriminate nonlame and lame cows, where partial least squares discriminant analysis achieved similar performance to the reference method. Copyright © 2014 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Computational methods for the identification of spatially varying stiffness and damping in beams

NASA Technical Reports Server (NTRS)

Banks, H. T.; Rosen, I. G.

1986-01-01

A numerical approximation scheme for the estimation of functional parameters in Euler-Bernoulli models for the transverse vibration of flexible beams with tip bodies is developed. The method permits the identification of spatially varying flexural stiffness and Voigt-Kelvin viscoelastic damping coefficients which appear in the hybrid system of ordinary and partial differential equations and boundary conditions describing the dynamics of such structures. An inverse problem is formulated as a least squares fit to data subject to constraints in the form of a vector system of abstract first order evolution equations. Spline-based finite element approximations are used to finite dimensionalize the problem. Theoretical convergence results are given and numerical studies carried out on both conventional (serial) and vector computers are discussed.

Assessment of Gait Characteristics in Total Knee Arthroplasty Patients Using a Hierarchical Partial Least Squares Method.

PubMed

Wang, Wei; Ackland, David C; McClelland, Jodie A; Webster, Kate E; Halgamuge, Saman

2018-01-01

Quantitative gait analysis is an important tool in objective assessment and management of total knee arthroplasty (TKA) patients. Studies evaluating gait patterns in TKA patients have tended to focus on discrete data such as spatiotemporal information, joint range of motion and peak values of kinematics and kinetics, or consider selected principal components of gait waveforms for analysis. These strategies may not have the capacity to capture small variations in gait patterns associated with each joint across an entire gait cycle, and may ultimately limit the accuracy of gait classification. The aim of this study was to develop an automatic feature extraction method to analyse patterns from high-dimensional autocorrelated gait waveforms. A general linear feature extraction framework was proposed and a hierarchical partial least squares method derived for discriminant analysis of multiple gait waveforms. The effectiveness of this strategy was verified using a dataset of joint angle and ground reaction force waveforms from 43 patients after TKA surgery and 31 healthy control subjects. Compared with principal component analysis and partial least squares methods, the hierarchical partial least squares method achieved generally better classification performance on all possible combinations of waveforms, with the highest classification accuracy . The novel hierarchical partial least squares method proposed is capable of capturing virtually all significant differences between TKA patients and the controls, and provides new insights into data visualization. The proposed framework presents a foundation for more rigorous classification of gait, and may ultimately be used to evaluate the effects of interventions such as surgery and rehabilitation.

Applying Statistics in the Undergraduate Chemistry Laboratory: Experiments with Food Dyes.

ERIC Educational Resources Information Center

Thomasson, Kathryn; Lofthus-Merschman, Sheila; Humbert, Michelle; Kulevsky, Norman

1998-01-01

Describes several experiments to teach different aspects of the statistical analysis of data using household substances and a simple analysis technique. Each experiment can be performed in three hours. Students learn about treatment of spurious data, application of a pooled variance, linear least-squares fitting, and simultaneous analysis of dyes…

Taper equation and volume tables for plantation-grown red alder.

Treesearch

Andrew A. Bluhm; Sean M. Garber; David E. Hibbs

2007-01-01

A taper equation and associated tables are presented for red alder (Alnus rubra Bong.) trees grown in plantations. The data were gathered from variable-density experimental plantations throughout the Pacific Northwest. Diameter inside bark along the stem was fitted to a variable exponent model form by using generalized nonlinear least squares and a...

The Rigid Orthogonal Procrustes Rotation Problem

ERIC Educational Resources Information Center

ten Berge, Jos M. F.

2006-01-01

The problem of rotating a matrix orthogonally to a best least squares fit with another matrix of the same order has a closed-form solution based on a singular value decomposition. The optimal rotation matrix is not necessarily rigid, but may also involve a reflection. In some applications, only rigid rotations are permitted. Gower (1976) has…

Factor Covariance Analysis in Subgroups.

ERIC Educational Resources Information Center

Pennell, Roger

The problem considered is that of an investigator sampling two or more correlation matrices and desiring to fit a model where a factor pattern matrix is assumed to be identical across samples and we need to estimate only the factor covariance matrix and the unique variance for each sample. A flexible, least squares solution is worked out and…

Recursive Inversion By Finite-Impulse-Response Filters

NASA Technical Reports Server (NTRS)

Bach, Ralph E., Jr.; Baram, Yoram

1991-01-01

Recursive approximation gives least-squares best fit to exact response. Algorithm yields finite-impulse-response approximation of unknown single-input/single-output, causal, time-invariant, linear, real system, response of which is sequence of impulses. Applicable to such system-inversion problems as suppression of echoes and identification of target from its scatter response to incident impulse.

Deriving the Quadratic Regression Equation Using Algebra

ERIC Educational Resources Information Center

Gordon, Sheldon P.; Gordon, Florence S.

2004-01-01

In discussions with leading educators from many different fields, MAA's CRAFTY (Curriculum Renewal Across the First Two Years) committee found that one of the most common mathematical themes in those other disciplines is the idea of fitting a function to a set of data in the least squares sense. The representatives of those partner disciplines…

Laser-Excited Opto-Acoustic Pulses in a Flame

DTIC Science & Technology

1981-06-01

I. INTRODUCTION ........... ....................... . A. Laser Probes and Combustion Chemistry ............. ... B. Cpto...unweighted least-squares fit ...... ................ 32 |Z I: **. t•I U 5-u•. ,. I. .-IRODUCTION A. Laser Probes and Combustion Chemistry The...influencing the chemistry . Although th; presence of particulate matter can be a serious problem, extremes of temperature and pressure offer no hostility

PINS chemical identification software

DOEpatents

Caffrey, Augustine J.; Krebs, Kennth M.

2004-09-14

An apparatus and method for identifying a chemical compound. A neutron source delivers neutrons into the chemical compound. The nuclei of chemical elements constituting the chemical compound emit gamma rays upon interaction with the neutrons. The gamma rays are characteristic of the chemical elements constituting the chemical compound. A spectrum of the gamma rays is generated having a detection count and an energy scale. The energy scale is calibrated by comparing peaks in the spectrum to energies of pre-selected chemical elements in the spectrum. A least-squares fit completes the calibration. The chemical elements constituting the chemical compound can be readily determined, which then allows for identification of the chemical compound.

Catálogo de supercáscaras de hidrógeno neutro en la Vía Láctea

NASA Astrophysics Data System (ADS)

Suad, L. A.; Arnal, E. M.; Cichowolski, S.

We present a number of neutral hydrogen supershells (SC-HI) found in the outer part of the Galaxy (80 l 130 and -50 b 50 ). These struc- tures were indentified through visual inspection of the neutral hydrogen data cube and will be part of a catalog, which will complement the existing ones (Heiles 1979, McClure-Griffiths et al. 2002). We have only catalogued those structures whose linear diameters, at the SC-HI's kinematic distance, exceeds 200 pc. Using a least square method we have characterized the ellipse that best fits each structure. FULL TEXT IN SPANISH