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.

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.

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.

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

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.

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.

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

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.

Three Perspectives on Teaching Least Squares

ERIC Educational Resources Information Center

Scariano, Stephen M.; Calzada, Maria

2004-01-01

The method of Least Squares is the most widely used technique for fitting a straight line to data, and it is typically discussed in several undergraduate courses. This article focuses on three developmentally different approaches for solving the Least Squares problem that are suitable for classroom exposition.

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.

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

Interactive application of quadratic expansion of chi-square statistic to nonlinear curve fitting

NASA Technical Reports Server (NTRS)

Badavi, F. F.; Everhart, Joel L.

1987-01-01

This report contains a detailed theoretical description of an all-purpose, interactive curve-fitting routine that is based on P. R. Bevington's description of the quadratic expansion of the Chi-Square statistic. The method is implemented in the associated interactive, graphics-based computer program. Taylor's expansion of Chi-Square is first introduced, and justifications for retaining only the first term are presented. From the expansion, a set of n simultaneous linear equations is derived, then solved by matrix algebra. A brief description of the code is presented along with a limited number of changes that are required to customize the program of a particular task. To evaluate the performance of the method and the goodness of nonlinear curve fitting, two typical engineering problems are examined and the graphical and tabular output of each is discussed. A complete listing of the entire package is included as an appendix.

Using Least Squares for Error Propagation

ERIC Educational Resources Information Center

Tellinghuisen, Joel

2015-01-01

The method of least-squares (LS) has a built-in procedure for estimating the standard errors (SEs) of the adjustable parameters in the fit model: They are the square roots of the diagonal elements of the covariance matrix. This means that one can use least-squares to obtain numerical values of propagated errors by defining the target quantities as…

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.

Evaluating the performance of the Lee-Carter method and its variants in modelling and forecasting Malaysian mortality

NASA Astrophysics Data System (ADS)

Zakiyatussariroh, W. H. Wan; Said, Z. Mohammad; Norazan, M. R.

2014-12-01

This study investigated the performance of the Lee-Carter (LC) method and it variants in modeling and forecasting Malaysia mortality. These include the original LC, the Lee-Miller (LM) variant and the Booth-Maindonald-Smith (BMS) variant. These methods were evaluated using Malaysia's mortality data which was measured based on age specific death rates (ASDR) for 1971 to 2009 for overall population while those for 1980-2009 were used in separate models for male and female population. The performance of the variants has been examined in term of the goodness of fit of the models and forecasting accuracy. Comparison was made based on several criteria namely, mean square error (MSE), root mean square error (RMSE), mean absolute deviation (MAD) and mean absolute percentage error (MAPE). The results indicate that BMS method was outperformed in in-sample fitting for overall population and when the models were fitted separately for male and female population. However, in the case of out-sample forecast accuracy, BMS method only best when the data were fitted to overall population. When the data were fitted separately for male and female, LCnone performed better for male population and LM method is good for female population.

Least-Squares Curve-Fitting Program

NASA Technical Reports Server (NTRS)

Kantak, Anil V.

1990-01-01

Least Squares Curve Fitting program, AKLSQF, easily and efficiently computes polynomial providing least-squares best fit to uniformly spaced data. Enables user to specify tolerable least-squares error in fit or degree of polynomial. AKLSQF returns polynomial and actual least-squares-fit error incurred in operation. Data supplied to routine either by direct keyboard entry or via file. Written for an IBM PC X/AT or compatible using Microsoft's Quick Basic compiler.

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.

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.

An Empirical Investigation of Methods for Assessing Item Fit for Mixed Format Tests

ERIC Educational Resources Information Center

Chon, Kyong Hee; Lee, Won-Chan; Ansley, Timothy N.

2013-01-01

Empirical information regarding performance of model-fit procedures has been a persistent need in measurement practice. Statistical procedures for evaluating item fit were applied to real test examples that consist of both dichotomously and polytomously scored items. The item fit statistics used in this study included the PARSCALE's G[squared],…

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.

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.

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.

AKLSQF - LEAST SQUARES CURVE FITTING

NASA Technical Reports Server (NTRS)

Kantak, A. V.

1994-01-01

The Least Squares Curve Fitting program, AKLSQF, computes the polynomial which will least square fit uniformly spaced data easily and efficiently. The program allows the user to specify the tolerable least squares error in the fitting or allows the user to specify the polynomial degree. In both cases AKLSQF returns the polynomial and the actual least squares fit error incurred in the operation. The data may be supplied to the routine either by direct keyboard entry or via a file. AKLSQF produces the least squares polynomial in two steps. First, the data points are least squares fitted using the orthogonal factorial polynomials. The result is then reduced to a regular polynomial using Sterling numbers of the first kind. If an error tolerance is specified, the program starts with a polynomial of degree 1 and computes the least squares fit error. The degree of the polynomial used for fitting is then increased successively until the error criterion specified by the user is met. At every step the polynomial as well as the least squares fitting error is printed to the screen. In general, the program can produce a curve fitting up to a 100 degree polynomial. All computations in the program are carried out under Double Precision format for real numbers and under long integer format for integers to provide the maximum accuracy possible. AKLSQF was written for an IBM PC X/AT or compatible using Microsoft's Quick Basic compiler. It has been implemented under DOS 3.2.1 using 23K of RAM. AKLSQF was developed in 1989.

Rasch fit statistics and sample size considerations for polytomous data

PubMed Central

Smith, Adam B; Rush, Robert; Fallowfield, Lesley J; Velikova, Galina; Sharpe, Michael

2008-01-01

Background Previous research on educational data has demonstrated that Rasch fit statistics (mean squares and t-statistics) are highly susceptible to sample size variation for dichotomously scored rating data, although little is known about this relationship for polytomous data. These statistics help inform researchers about how well items fit to a unidimensional latent trait, and are an important adjunct to modern psychometrics. Given the increasing use of Rasch models in health research the purpose of this study was therefore to explore the relationship between fit statistics and sample size for polytomous data. Methods Data were collated from a heterogeneous sample of cancer patients (n = 4072) who had completed both the Patient Health Questionnaire – 9 and the Hospital Anxiety and Depression Scale. Ten samples were drawn with replacement for each of eight sample sizes (n = 25 to n = 3200). The Rating and Partial Credit Models were applied and the mean square and t-fit statistics (infit/outfit) derived for each model. Results The results demonstrated that t-statistics were highly sensitive to sample size, whereas mean square statistics remained relatively stable for polytomous data. Conclusion It was concluded that mean square statistics were relatively independent of sample size for polytomous data and that misfit to the model could be identified using published recommended ranges. PMID:18510722

Model Fit and Item Factor Analysis: Overfactoring, Underfactoring, and a Program to Guide Interpretation.

PubMed

Clark, D Angus; Bowles, Ryan P

2018-04-23

In exploratory item factor analysis (IFA), researchers may use model fit statistics and commonly invoked fit thresholds to help determine the dimensionality of an assessment. However, these indices and thresholds may mislead as they were developed in a confirmatory framework for models with continuous, not categorical, indicators. The present study used Monte Carlo simulation methods to investigate the ability of popular model fit statistics (chi-square, root mean square error of approximation, the comparative fit index, and the Tucker-Lewis index) and their standard cutoff values to detect the optimal number of latent dimensions underlying sets of dichotomous items. Models were fit to data generated from three-factor population structures that varied in factor loading magnitude, factor intercorrelation magnitude, number of indicators, and whether cross loadings or minor factors were included. The effectiveness of the thresholds varied across fit statistics, and was conditional on many features of the underlying model. Together, results suggest that conventional fit thresholds offer questionable utility in the context of IFA.

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)

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 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.

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.

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.

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)

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.

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.

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.

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.

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…

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…

Performance of the Generalized S-X[squared] Item Fit Index for the Graded Response Model

ERIC Educational Resources Information Center

Kang, Taehoon; Chen, Troy T.

2011-01-01

The utility of Orlando and Thissen's ("2000", "2003") S-X[squared] fit index was extended to the model-fit analysis of the graded response model (GRM). The performance of a modified S-X[squared] in assessing item-fit of the GRM was investigated in light of empirical Type I error rates and power with a simulation study having…

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

[Analysis of the impact of job characteristics and organizational support for workplace violence].

PubMed

Li, M L; Chen, P; Zeng, F H; Cui, Q L; Zeng, J; Zhao, X S; Li, Z N

2017-12-20

Objective: To analyze the effect of job characteristics and organizational support for workplace violence, explore the influence path and the theoretical model, and provide a theoretical basis for reducing workplace violence. Methods: Stratified random sampling was used to select 813 medical staff, conductors and bus drivers in Chongqing with a self-made questionnaire to investigate job characteristics, organization attitude toward workplace violence, workplace violence, fear of violence, workplace violence, etc from February to October, 2014. Amos 21.0 was used to analyze the path and to establish a theoretical model of workplace violence. Results: The odds ratio of work characteristics and organizational attitude to workplace violence were 6.033 and 0.669, respectively, and the path coefficients were 0.41 and-0.14, respectively ( P <0.05). The Fitting indexes of the model: Chi-square (χ(2)) =67.835, The ratio of the chi-square to the degree of freedom (χ(2)/df) =5.112, Good-of-fit index (GFI) =0.970, Adjusted good-of-fit index (AGFI) =0.945, Normed fit index (NFI) =0.923, Root mean square error of approximation (RMSEA) =0.071, Fit criterion (Fmin) =0.092, so the model fit well with the data. Conclusion: The job characteristic is a risk factor for workplace violence while organizational attitude is a protective factor for workplace violence, so changing the job characteristics and improving the enthusiasm of the organization to deal with workplace violence are conducive to reduce workplace violence and increase loyalty to the unit.

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.

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.

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.

Asteroid orbit fitting with radar and angular observations

NASA Astrophysics Data System (ADS)

Baturin, A. P.

2013-12-01

The asteroid orbit fitting problem using their radar and angular observations has been considered. The problem was solved in a standanrd way by means of minimization of weighted sum of squares of residuals. In the orbit fitting both kinds of radar observa-tions have been used: the observations of time delays and of Doppler frequency shifts. The weight for angular observations has been set the same for all of them and has been determined as inverse mean-square residual obtained in the orbit fitting using just angular observations. The weights of radar observations have been set as inverse squared errors of these observations published together with them in the Minor Planet Center electronical circulars (MPECs). For the orbit fitting some five asteroids have been taken from these circulars. The asteroids have been chosen fulfilling the requirement of more than six radar observations of them to be available. The asteroids are 1950 DA, 1999 RQ36, 2002 NY40, 2004 DC and 2005 EU2. Several orbit fittings for these aster-oids have been done: with just angular observations; with just radar observations; with both angular and radar observations. The obtained results are quite acceptable because in the last case the mean-square angular residuals are approximately equal to the same ones obtained in the fitting with just angular observations. As to radar observations mean-square residuals, the time delay residuals for three asteroids do not exceed 1 μs, for two others ˜ 10 μs and the Doppler shift residuals for three asteroids do not exceed 1 Hz, for two others ˜ 10 Hz. The motion equations included perturbations from 9 planets and the Moon using their ephemerides DE422. The numerical integration has been performed with Everhart 27-order method with variable step. All calculations have been exe-cuted to a 34-digit decimal precision (i.e. using 128-bit floating-point numbers). Further, the sizes of confidence ellipsoids of im-proved orbit parameters have been compared. It has been accepted that an indicator of ellipsoid size is a geometric mean of its six semi-axes. A comparison of sizes has shown that confidence ellipsoids obtained in orbit fitting with both angular and radar obser-vations are several times less than ellipsoids obtained with just angular observations.

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.

Non-linear Multidimensional Optimization for use in Wire Scanner Fitting

NASA Astrophysics Data System (ADS)

Henderson, Alyssa; Terzic, Balsa; Hofler, Alicia; Center Advanced Studies of Accelerators Collaboration

2014-03-01

To ensure experiment efficiency and quality from the Continuous Electron Beam Accelerator at Jefferson Lab, beam energy, size, and position must be measured. Wire scanners are devices inserted into the beamline to produce measurements which are used to obtain beam properties. Extracting physical information from the wire scanner measurements begins by fitting Gaussian curves to the data. This study focuses on optimizing and automating this curve-fitting procedure. We use a hybrid approach combining the efficiency of Newton Conjugate Gradient (NCG) method with the global convergence of three nature-inspired (NI) optimization approaches: genetic algorithm, differential evolution, and particle-swarm. In this Python-implemented approach, augmenting the locally-convergent NCG with one of the globally-convergent methods ensures the quality, robustness, and automation of curve-fitting. After comparing the methods, we establish that given an initial data-derived guess, each finds a solution with the same chi-square- a measurement of the agreement of the fit to the data. NCG is the fastest method, so it is the first to attempt data-fitting. The curve-fitting procedure escalates to one of the globally-convergent NI methods only if NCG fails, thereby ensuring a successful fit. This method allows for the most optimal signal fit and can be easily applied to similar problems.

Development of the Chinese version of the Hospital Autonomy Questionnaire: a cross-sectional study in Guangdong Province

PubMed Central

Liu, Zifeng; Yuan, Lianxiong; Huang, Yixiang; Zhang, Lingling; Luo, Futian

2016-01-01

Objective We aimed to develop a questionnaire for quantitative evaluation of the autonomy of public hospitals in China. Method An extensive literature review was conducted to select possible items for inclusion in the questionnaire, which was then reviewed by 5 experts. After a two-round Delphi method, we distributed the questionnaire to 404 secondary and tertiary hospitals in Guangdong Province, China, and 379 completed questionnaires were collected. The final questionnaire was then developed on the basis of the results of exploratory and confirmatory factor analysis. Results Analysis suggested that all internal consistency reliabilities exceeded the minimum reliability standard of 0.70 for the α coefficient. The overall scale coefficient was 0.87, and 6 subscale coefficients were 0.92 (strategic management), 0.81 (budget and expenditure), 0.85 (financing), 0.75 (financing, medical management), 0.86 (human resources) and 0.86 (accountability). Correlation coefficients between and among items and their hypothesised subscales were higher than those with other subscales. The value of average variance extracted (AVE) was higher than 0.5, the value of construct reliability (CR) was higher than 0.7, and the square roots of the AVE of each subscale were larger than the correlation of the specific subscale with the other subscales, supporting the convergent and discriminant validity of the Chinese version of the Hospital Autonomy Questionnaire (CVHAQ). The model fit indices were all acceptable: χ2/df=1.73, Goodness of Fit Index (GFI) = 0.93, Adjusted Goodness of Fit Index (AGFI) = 0.91, Non-Normed Fit Index (NNFI) = 0.96, Comparative Fit Index (CFI) = 0.97, Root Mean Square Error of Approximation (RMSEA) = 0.04, Standardised Root Mean Square Residual (SRMR) = 0.07. Conclusions This study demonstrated the reliability and validity of a CVHAQ and provides a quantitative method for the assessment of hospital autonomy. PMID:26911587

Effect of scrape-off-layer current on reconstructed tokamak equilibrium

DOE PAGES

King, J. R.; Kruger, S. E.; Groebner, R. J.; ...

2017-01-13

Methods are described that extend fields from reconstructed equilibria to include scrape-off-layer current through extrapolated parametrized and experimental fits. The extrapolation includes both the effects of the toroidal-field and pressure gradients which produce scrape-off-layer current after recomputation of the Grad-Shafranov solution. To quantify the degree that inclusion of scrape-off-layer current modifies the equilibrium, the χ-squared goodness-of-fit parameter is calculated for cases with and without scrape-off-layer current. The change in χ-squared is found to be minor when scrape-off-layer current is included however flux surfaces are shifted by up to 3 cm. Here the impact on edge modes of these scrape-off-layer modificationsmore » is also found to be small and the importance of these methods to nonlinear computation is discussed.« less

Full two-dimensional transient solutions of electrothermal aircraft blade deicing

NASA Technical Reports Server (NTRS)

Masiulaniec, K. C.; Keith, T. G., Jr.; Dewitt, K. J.; Leffel, K. L.

1985-01-01

Two finite difference methods are presented for the analysis of transient, two-dimensional responses of an electrothermal de-icer pad of an aircraft wing or blade with attached variable ice layer thickness. Both models employ a Crank-Nicholson iterative scheme, and use an enthalpy formulation to handle the phase change in the ice layer. The first technique makes use of a 'staircase' approach, fitting the irregular ice boundary with square computational cells. The second technique uses a body fitted coordinate transform, and maps the exact shape of the irregular boundary into a rectangular body, with uniformally square computational cells. The numerical solution takes place in the transformed plane. Initial results accounting for variable ice layer thickness are presented. Details of planned de-icing tests at NASA-Lewis, which will provide empirical verification for the above two methods, are also presented.

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.

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.

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.

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.

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.

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.

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.

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;

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.

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.

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.

Non-linear Multidimensional Optimization for use in Wire Scanner Fitting

NASA Astrophysics Data System (ADS)

Henderson, Alyssa; Terzic, Balsa; Hofler, Alicia; CASA and Accelerator Ops Collaboration

2013-10-01

To ensure experiment efficiency and quality from the Continuous Electron Beam Accelerator at Jefferson Lab, beam energy, size, and position must be measured. Wire scanners are devices inserted into the beamline to produce measurements which are used to obtain beam properties. Extracting physical information from the wire scanner measurements begins by fitting Gaussian curves to the data. This study focuses on optimizing and automating this curve-fitting procedure. We use a hybrid approach combining the efficiency of Newton Conjugate Gradient (NCG) method with the global convergence of three nature-inspired (NI) optimization approaches: genetic algorithm, differential evolution, and particle-swarm. In this Python-implemented approach, augmenting the locally-convergent NCG with one of the globally-convergent methods ensures the quality, robustness, and automation of curve-fitting. After comparing the methods, we establish that given an initial data-derived guess, each finds a solution with the same chi-square- a measurement of the agreement of the fit to the data. NCG is the fastest method, so it is the first to attempt data-fitting. The curve-fitting procedure escalates to one of the globally-convergent NI methods only if NCG fails, thereby ensuring a successful fit. This method allows for the most optimal signal fit and can be easily applied to similar problems. Financial support from DoE, NSF, ODU, DoD, and Jefferson Lab.

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…

Reliability and validity in measurement of true humeral retroversion by a three-dimensional cylinder fitting method.

PubMed

Saka, Masayuki; Yamauchi, Hiroki; Hoshi, Kenji; Yoshioka, Toru; Hamada, Hidetoshi; Gamada, Kazuyoshi

2015-05-01

Humeral retroversion is defined as the orientation of the humeral head relative to the distal humerus. Because none of the previous methods used to measure humeral retroversion strictly follow this definition, values obtained by these techniques vary and may be biased by morphologic variations of the humerus. The purpose of this study was 2-fold: to validate a method to define the axis of the distal humerus with a virtual cylinder and to establish the reliability of 3-dimensional (3D) measurement of humeral retroversion by this cylinder fitting method. Humeral retroversion in 14 baseball players (28 humeri) was measured by the 3D cylinder fitting method. The root mean square error was calculated to compare values obtained by a single tester and by 2 different testers using the embedded coordinate system. To establish the reliability, intraclass correlation coefficient (ICC) and precision (standard error of measurement [SEM]) were calculated. The root mean square errors for the humeral coordinate system were <1.0 mm/1.0° for comparison of all translations/rotations obtained by a single tester and <1.0 mm/2.0° for comparison obtained by 2 different testers. Assessment of reliability and precision of the 3D measurement of retroversion yielded an intratester ICC of 0.99 (SEM, 1.0°) and intertester ICC of 0.96 (SEM, 2.8°). The error in measurements obtained by a distal humerus cylinder fitting method was small enough not to affect retroversion measurement. The 3D measurement of retroversion by this method provides excellent intratester and intertester reliability. Copyright © 2015 Journal of Shoulder and Elbow Surgery Board of Trustees. Published by Elsevier Inc. All rights reserved.

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/.

Comments on Different techniques for finding best-fit parameters

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

Fenimore, Edward E.; Triplett, Laurie A.

2014-07-01

A common data analysis problem is to find best-fit parameters through chi-square minimization. Levenberg-Marquardt is an often used system that depends on gradients and converges when successive iterations do not change chi-square more than a specified amount. We point out in cases where the sought-after parameter weakly affects the fit and cases where the overall scale factor is a parameter, that a Golden Search technique can often do better. The Golden Search converges when the best-fit point is within a specified range and that range can be made arbitrarily small. It does not depend on the value of chi-square.

Predicting First Traversal Times for Virions and Nanoparticles in Mucus with Slowed Diffusion

PubMed Central

Erickson, Austen M.; Henry, Bruce I.; Murray, John M.; Klasse, Per Johan; Angstmann, Christopher N.

2015-01-01

Particle-tracking experiments focusing on virions or nanoparticles in mucus have measured mean-square displacements and reported diffusion coefficients that are orders of magnitude smaller than the diffusion coefficients of such particles in water. Accurate description of this subdiffusion is important to properly estimate the likelihood of virions traversing the mucus boundary layer and infecting cells in the epithelium. However, there are several candidate models for diffusion that can fit experimental measurements of mean-square displacements. We show that these models yield very different estimates for the time taken for subdiffusive virions to traverse through a mucus layer. We explain why fits of subdiffusive mean-square displacements to standard diffusion models may be misleading. Relevant to human immunodeficiency virus infection, using computational methods for fractional subdiffusion, we show that subdiffusion in normal acidic mucus provides a more effective barrier against infection than previously thought. By contrast, the neutralization of the mucus by alkaline semen, after sexual intercourse, allows virions to cross the mucus layer and reach the epithelium in a short timeframe. The computed barrier protection from fractional subdiffusion is some orders of magnitude greater than that derived by fitting standard models of diffusion to subdiffusive data. PMID:26153713

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.

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.

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.

Landslide susceptibility mapping using decision-tree based CHi-squared automatic interaction detection (CHAID) and Logistic regression (LR) integration

NASA Astrophysics Data System (ADS)

Althuwaynee, Omar F.; Pradhan, Biswajeet; Ahmad, Noordin

2014-06-01

This article uses methodology based on chi-squared automatic interaction detection (CHAID), as a multivariate method that has an automatic classification capacity to analyse large numbers of landslide conditioning factors. This new algorithm was developed to overcome the subjectivity of the manual categorization of scale data of landslide conditioning factors, and to predict rainfall-induced susceptibility map in Kuala Lumpur city and surrounding areas using geographic information system (GIS). The main objective of this article is to use CHi-squared automatic interaction detection (CHAID) method to perform the best classification fit for each conditioning factor, then, combining it with logistic regression (LR). LR model was used to find the corresponding coefficients of best fitting function that assess the optimal terminal nodes. A cluster pattern of landslide locations was extracted in previous study using nearest neighbor index (NNI), which were then used to identify the clustered landslide locations range. Clustered locations were used as model training data with 14 landslide conditioning factors such as; topographic derived parameters, lithology, NDVI, land use and land cover maps. Pearson chi-squared value was used to find the best classification fit between the dependent variable and conditioning factors. Finally the relationship between conditioning factors were assessed and the landslide susceptibility map (LSM) was produced. An area under the curve (AUC) was used to test the model reliability and prediction capability with the training and validation landslide locations respectively. This study proved the efficiency and reliability of decision tree (DT) model in landslide susceptibility mapping. Also it provided a valuable scientific basis for spatial decision making in planning and urban management studies.

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.

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.

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…

A non-linear regression analysis program for describing electrophysiological data with multiple functions using Microsoft Excel.

PubMed

Brown, Angus M

2006-04-01

The objective of this present study was to demonstrate a method for fitting complex electrophysiological data with multiple functions using the SOLVER add-in of the ubiquitous spreadsheet Microsoft Excel. SOLVER minimizes the difference between the sum of the squares of the data to be fit and the function(s) describing the data using an iterative generalized reduced gradient method. While it is a straightforward procedure to fit data with linear functions, and we have previously demonstrated a method of non-linear regression analysis of experimental data based upon a single function, it is more complex to fit data with multiple functions, usually requiring specialized expensive computer software. In this paper we describe an easily understood program for fitting experimentally acquired data, in this case the stimulus-evoked compound action potential from the mouse optic nerve, with multiple Gaussian functions. The program is flexible and can be applied to describe data with a wide variety of user-input functions.

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

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.

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.

Improvements in Spectrum's fit to program data tool.

PubMed

Mahiane, Severin G; Marsh, Kimberly; Grantham, Kelsey; Crichlow, Shawna; Caceres, Karen; Stover, John

2017-04-01

The Joint United Nations Program on HIV/AIDS-supported Spectrum software package (Glastonbury, Connecticut, USA) is used by most countries worldwide to monitor the HIV epidemic. In Spectrum, HIV incidence trends among adults (aged 15-49 years) are derived by either fitting to seroprevalence surveillance and survey data or generating curves consistent with program and vital registration data, such as historical trends in the number of newly diagnosed infections or people living with HIV and AIDS related deaths. This article describes development and application of the fit to program data (FPD) tool in Joint United Nations Program on HIV/AIDS' 2016 estimates round. In the FPD tool, HIV incidence trends are described as a simple or double logistic function. Function parameters are estimated from historical program data on newly reported HIV cases, people living with HIV or AIDS-related deaths. Inputs can be adjusted for proportions undiagnosed or misclassified deaths. Maximum likelihood estimation or minimum chi-squared distance methods are used to identify the best fitting curve. Asymptotic properties of the estimators from these fits are used to estimate uncertainty. The FPD tool was used to fit incidence for 62 countries in 2016. Maximum likelihood and minimum chi-squared distance methods gave similar results. A double logistic curve adequately described observed trends in all but four countries where a simple logistic curve performed better. Robust HIV-related program and vital registration data are routinely available in many middle-income and high-income countries, whereas HIV seroprevalence surveillance and survey data may be scarce. In these countries, the FPD tool offers a simpler, improved approach to estimating HIV incidence trends.

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.

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.

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.

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 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.

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.

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.

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.

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.

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.

Pre-processing by data augmentation for improved ellipse fitting.

PubMed

Kumar, Pankaj; Belchamber, Erika R; Miklavcic, Stanley J

2018-01-01

Ellipse fitting is a highly researched and mature topic. Surprisingly, however, no existing method has thus far considered the data point eccentricity in its ellipse fitting procedure. Here, we introduce the concept of eccentricity of a data point, in analogy with the idea of ellipse eccentricity. We then show empirically that, irrespective of ellipse fitting method used, the root mean square error (RMSE) of a fit increases with the eccentricity of the data point set. The main contribution of the paper is based on the hypothesis that if the data point set were pre-processed to strategically add additional data points in regions of high eccentricity, then the quality of a fit could be improved. Conditional validity of this hypothesis is demonstrated mathematically using a model scenario. Based on this confirmation we propose an algorithm that pre-processes the data so that data points with high eccentricity are replicated. The improvement of ellipse fitting is then demonstrated empirically in real-world application of 3D reconstruction of a plant root system for phenotypic analysis. The degree of improvement for different underlying ellipse fitting methods as a function of data noise level is also analysed. We show that almost every method tested, irrespective of whether it minimizes algebraic error or geometric error, shows improvement in the fit following data augmentation using the proposed pre-processing algorithm.

Analysis of the multigroup model for muon tomography based threat detection

NASA Astrophysics Data System (ADS)

Perry, J. O.; Bacon, J. D.; Borozdin, K. N.; Fabritius, J. M.; Morris, C. L.

2014-02-01

We compare different algorithms for detecting a 5 cm tungsten cube using cosmic ray muon technology. In each case, a simple tomographic technique was used for position reconstruction, but the scattering angles were used differently to obtain a density signal. Receiver operating characteristic curves were used to compare images made using average angle squared, median angle squared, average of the squared angle, and a multi-energy group fit of the angular distributions for scenes with and without a 5 cm tungsten cube. The receiver operating characteristic curves show that the multi-energy group treatment of the scattering angle distributions is the superior method for image reconstruction.

Fit between Africa and Antarctica: A Continental Drift Reconstruction.

PubMed

Dietz, R S; Sproll, W P

1970-03-20

A computerized (smallest average misfit) best fit position is obtained for the juxtaposition of Africa and Antarctica in a continental drift reconstruction. An S-shaped portion of the Weddell and Princess Martha Coast regions of western East Antarctica is fitted into a similar profile along southeastern Africa. The total amount of overlap is 36,300 square kilometers, and the underlap is 23,600 square kilometers; the total mismatch is thus of 59,900 square kilometers. The congruency along the 1000-fathom isobath is remarkably good and suggests that this reconstruction is valid within the overall framework of the Gondwana supercontinent.

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.

Ridit Analysis for Cooper-Harper and Other Ordinal Ratings for Sparse Data - A Distance-based Approach

DTIC Science & Technology

2016-09-01

is to fit empirical Beta distributions to observed data, and then to use a randomization approach to make inferences on the difference between...a Ridit analysis on the often sparse data sets in many Flying Qualities applicationsi. The method of this paper is to fit empirical Beta ...One such measure is the discrete- probability-distribution version of the (squared) ‘Hellinger Distance’ (Yang & Le Cam , 2000) 2(, ) = 1

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.

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.

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.

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.

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 quasi-Monte-Carlo comparison of parametric and semiparametric regression methods for heavy-tailed and non-normal data: an application to healthcare costs.

PubMed

Jones, Andrew M; Lomas, James; Moore, Peter T; Rice, Nigel

2016-10-01

We conduct a quasi-Monte-Carlo comparison of the recent developments in parametric and semiparametric regression methods for healthcare costs, both against each other and against standard practice. The population of English National Health Service hospital in-patient episodes for the financial year 2007-2008 (summed for each patient) is randomly divided into two equally sized subpopulations to form an estimation set and a validation set. Evaluating out-of-sample using the validation set, a conditional density approximation estimator shows considerable promise in forecasting conditional means, performing best for accuracy of forecasting and among the best four for bias and goodness of fit. The best performing model for bias is linear regression with square-root-transformed dependent variables, whereas a generalized linear model with square-root link function and Poisson distribution performs best in terms of goodness of fit. Commonly used models utilizing a log-link are shown to perform badly relative to other models considered in our comparison.

Response Surface Analysis of Experiments with Random Blocks

DTIC Science & Technology

1988-09-01

partitioned into a lack of fit sum of squares, SSLOF, and a pure error sum of squares, SSPE . The latter is obtained by pooling the pure error sums of squares...from the blocks. Tests concerning the polynomial effects can then proceed using SSPE as the error term in the denominators of the F test statistics. 3.2...the center point in each of the three blocks is equal to SSPE = 2.0127 with 5 degrees of freedom. Hence, the lack of fit sum of squares is SSLoF

Fitting membrane resistance along with action potential shape in cardiac myocytes improves convergence: application of a multi-objective parallel genetic algorithm.

PubMed

Kaur, Jaspreet; Nygren, Anders; Vigmond, Edward J

2014-01-01

Fitting parameter sets of non-linear equations in cardiac single cell ionic models to reproduce experimental behavior is a time consuming process. The standard procedure is to adjust maximum channel conductances in ionic models to reproduce action potentials (APs) recorded in isolated cells. However, vastly different sets of parameters can produce similar APs. Furthermore, even with an excellent AP match in case of single cell, tissue behaviour may be very different. We hypothesize that this uncertainty can be reduced by additionally fitting membrane resistance (Rm). To investigate the importance of Rm, we developed a genetic algorithm approach which incorporated Rm data calculated at a few points in the cycle, in addition to AP morphology. Performance was compared to a genetic algorithm using only AP morphology data. The optimal parameter sets and goodness of fit as computed by the different methods were compared. First, we fit an ionic model to itself, starting from a random parameter set. Next, we fit the AP of one ionic model to that of another. Finally, we fit an ionic model to experimentally recorded rabbit action potentials. Adding the extra objective (Rm, at a few voltages) to the AP fit, lead to much better convergence. Typically, a smaller MSE (mean square error, defined as the average of the squared error between the target AP and AP that is to be fitted) was achieved in one fifth of the number of generations compared to using only AP data. Importantly, the variability in fit parameters was also greatly reduced, with many parameters showing an order of magnitude decrease in variability. Adding Rm to the objective function improves the robustness of fitting, better preserving tissue level behavior, and should be incorporated.

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.

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.

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.

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.

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.

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.

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.

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.

Group Influences on Young Adult Warfighters’ Risk Taking

DTIC Science & Technology

2016-12-01

Statistical Analysis Latent linear growth models were fitted using the maximum likelihood estimation method in Mplus (version 7.0; Muthen & Muthen...condition had a higher net score than those in the alone condition (b = 20.53, SE = 6.29, p < .001). Results of the relevant statistical analyses are...8.56 110.86*** 22.01 158.25*** 29.91 Model fit statistics BIC 4004.50 5302.539 5540.58 Chi-square (df) 41.51*** (16) 38.10** (20) 42.19** (20

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.

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

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…

A nonparametric smoothing method for assessing GEE models with longitudinal binary data.

PubMed

Lin, Kuo-Chin; Chen, Yi-Ju; Shyr, Yu

2008-09-30

Studies involving longitudinal binary responses are widely applied in the health and biomedical sciences research and frequently analyzed by generalized estimating equations (GEE) method. This article proposes an alternative goodness-of-fit test based on the nonparametric smoothing approach for assessing the adequacy of GEE fitted models, which can be regarded as an extension of the goodness-of-fit test of le Cessie and van Houwelingen (Biometrics 1991; 47:1267-1282). The expectation and approximate variance of the proposed test statistic are derived. The asymptotic distribution of the proposed test statistic in terms of a scaled chi-squared distribution and the power performance of the proposed test are discussed by simulation studies. The testing procedure is demonstrated by two real data. Copyright (c) 2008 John Wiley & Sons, Ltd.

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.

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 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.

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.

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.

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.

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.

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.

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

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…

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.

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.

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.

Smoothness of In vivo Spectral Baseline Determined by Mean Squared Error

PubMed Central

Zhang, Yan; Shen, Jun

2013-01-01

Purpose A nonparametric smooth line is usually added to spectral model to account for background signals in vivo magnetic resonance spectroscopy (MRS). The assumed smoothness of the baseline significantly influences quantitative spectral fitting. In this paper, a method is proposed to minimize baseline influences on estimated spectral parameters. Methods In this paper, the non-parametric baseline function with a given smoothness was treated as a function of spectral parameters. Its uncertainty was measured by root-mean-squared error (RMSE). The proposed method was demonstrated with a simulated spectrum and in vivo spectra of both short echo time (TE) and averaged echo times. The estimated in vivo baselines were compared with the metabolite-nulled spectra, and the LCModel-estimated baselines. The accuracies of estimated baseline and metabolite concentrations were further verified by cross-validation. Results An optimal smoothness condition was found that led to the minimal baseline RMSE. In this condition, the best fit was balanced against minimal baseline influences on metabolite concentration estimates. Conclusion Baseline RMSE can be used to indicate estimated baseline uncertainties and serve as the criterion for determining the baseline smoothness of in vivo MRS. PMID:24259436

Rasch fit statistics and sample size considerations for polytomous data.

PubMed

Smith, Adam B; Rush, Robert; Fallowfield, Lesley J; Velikova, Galina; Sharpe, Michael

2008-05-29

Previous research on educational data has demonstrated that Rasch fit statistics (mean squares and t-statistics) are highly susceptible to sample size variation for dichotomously scored rating data, although little is known about this relationship for polytomous data. These statistics help inform researchers about how well items fit to a unidimensional latent trait, and are an important adjunct to modern psychometrics. Given the increasing use of Rasch models in health research the purpose of this study was therefore to explore the relationship between fit statistics and sample size for polytomous data. Data were collated from a heterogeneous sample of cancer patients (n = 4072) who had completed both the Patient Health Questionnaire - 9 and the Hospital Anxiety and Depression Scale. Ten samples were drawn with replacement for each of eight sample sizes (n = 25 to n = 3200). The Rating and Partial Credit Models were applied and the mean square and t-fit statistics (infit/outfit) derived for each model. The results demonstrated that t-statistics were highly sensitive to sample size, whereas mean square statistics remained relatively stable for polytomous data. It was concluded that mean square statistics were relatively independent of sample size for polytomous data and that misfit to the model could be identified using published recommended ranges.

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.

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.

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.

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…

A chi-square goodness-of-fit test for non-identically distributed random variables: with application to empirical Bayes

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

Conover, W.J.; Cox, D.D.; Martz, H.F.

1997-12-01

When using parametric empirical Bayes estimation methods for estimating the binomial or Poisson parameter, the validity of the assumed beta or gamma conjugate prior distribution is an important diagnostic consideration. Chi-square goodness-of-fit tests of the beta or gamma prior hypothesis are developed for use when the binomial sample sizes or Poisson exposure times vary. Nine examples illustrate the application of the methods, using real data from such diverse applications as the loss of feedwater flow rates in nuclear power plants, the probability of failure to run on demand and the failure rates of the high pressure coolant injection systems atmore » US commercial boiling water reactors, the probability of failure to run on demand of emergency diesel generators in US commercial nuclear power plants, the rate of failure of aircraft air conditioners, baseball batting averages, the probability of testing positive for toxoplasmosis, and the probability of tumors in rats. The tests are easily applied in practice by means of corresponding Mathematica{reg_sign} computer programs which are provided.« less

A note on the misuses of the variance test in meteorological studies

NASA Astrophysics Data System (ADS)

Hazra, Arnab; Bhattacharya, Sourabh; Banik, Pabitra; Bhattacharya, Sabyasachi

2017-12-01

Stochastic modeling of rainfall data is an important area in meteorology. The gamma distribution is a widely used probability model for non-zero rainfall. Typically the choice of the distribution for such meteorological studies is based on two goodness-of-fit tests—the Pearson's Chi-square test and the Kolmogorov-Smirnov test. Inspired by the index of dispersion introduced by Fisher (Statistical methods for research workers. Hafner Publishing Company Inc., New York, 1925), Mooley (Mon Weather Rev 101:160-176, 1973) proposed the variance test as a goodness-of-fit measure in this context and a number of researchers have implemented it since then. We show that the asymptotic distribution of the test statistic for the variance test is generally not comparable to any central Chi-square distribution and hence the test is erroneous. We also describe a method for checking the validity of the asymptotic distribution for a class of distributions. We implement the erroneous test on some simulated, as well as real datasets and demonstrate how it leads to some wrong conclusions.

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.

Perceptions and receptivity of non-spousal family support: A mixed methods study of psychological distress among older, church-going African American men

PubMed Central

Watkins, Daphne C.; Wharton, Tracy; Mitchell, Jamie A.; Matusko, Niki; Kales, Helen

2016-01-01

The purpose of this study was to explore the role of non-spousal family support on mental health among older, church-going African American men. The mixed methods objective was to employ a design that used existing qualitative and quantitative data to explore the interpretive context within which social and cultural experiences occur. Qualitative data (n=21) were used to build a conceptual model that was tested using quantitative data (n= 401). Confirmatory factor analysis indicated an inverse association between non-spousal family support and distress. The comparative fit index, Tucker-Lewis fit index, and root mean square error of approximation indicated good model fit. This study offers unique methodological approaches to using existing, complementary data sources to understand the health of African American men. PMID:28943829

SU-F-T-130: [18F]-FDG Uptake Dose Response in Lung Correlates Linearly with Proton Therapy Dose

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

Kim, D; Titt, U; Mirkovic, D

2016-06-15

Purpose: Analysis of clinical outcomes in lung cancer patients treated with protons using 18F-FDG uptake in lung as a measure of dose response. Methods: A test case lung cancer patient was selected in an unbiased way. The test patient’s treatment planning and post treatment positron emission tomography (PET) were collected from picture archiving and communication system at the UT M.D. Anderson Cancer Center. Average computerized tomography scan was registered with post PET/CT through both rigid and deformable registrations for selected region of interest (ROI) via VelocityAI imaging informatics software. For the voxels in the ROI, a system that extracts themore » Standard Uptake Value (SUV) from PET was developed, and the corresponding relative biological effectiveness (RBE) weighted (both variable and constant) dose was computed using the Monte Carlo (MC) methods. The treatment planning system (TPS) dose was also obtained. Using histogram analysis, the voxel average normalized SUV vs. 3 different doses was obtained and linear regression fit was performed. Results: From the registration process, there were some regions that showed significant artifacts near the diaphragm and heart region, which yielded poor r-squared values when the linear regression fit was performed on normalized SUV vs. dose. Excluding these values, TPS fit yielded mean r-squared value of 0.79 (range 0.61–0.95), constant RBE fit yielded 0.79 (range 0.52–0.94), and variable RBE fit yielded 0.80 (range 0.52–0.94). Conclusion: A system that extracts SUV from PET to correlate between normalized SUV and various dose calculations was developed. A linear relation between normalized SUV and all three different doses was found.« less

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

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.

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.

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.

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.

An evaluation of the structural validity of the shoulder pain and disability index (SPADI) using the Rasch model.

PubMed

Jerosch-Herold, Christina; Chester, Rachel; Shepstone, Lee; Vincent, Joshua I; MacDermid, Joy C

2018-02-01

The shoulder pain and disability index (SPADI) has been extensively evaluated for its psychometric properties using classical test theory (CTT). The purpose of this study was to evaluate its structural validity using Rasch model analysis. Responses to the SPADI from 1030 patients referred for physiotherapy with shoulder pain and enrolled in a prospective cohort study were available for Rasch model analysis. Overall fit, individual person and item fit, response format, dependence, unidimensionality, targeting, reliability and differential item functioning (DIF) were examined. The SPADI pain subscale initially demonstrated a misfit due to DIF by age and gender. After iterative analysis it showed good fit to the Rasch model with acceptable targeting and unidimensionality (overall fit Chi-square statistic 57.2, p = 0.1; mean item fit residual 0.19 (1.5) and mean person fit residual 0.44 (1.1); person separation index (PSI) of 0.83. The disability subscale however shows significant misfit due to uniform DIF even after iterative analyses were used to explore different solutions to the sources of misfit (overall fit (Chi-square statistic 57.2, p = 0.1); mean item fit residual 0.54 (1.26) and mean person fit residual 0.38 (1.0); PSI 0.84). Rasch Model analysis of the SPADI has identified some strengths and limitations not previously observed using CTT methods. The SPADI should be treated as two separate subscales. The SPADI is a widely used outcome measure in clinical practice and research; however, the scores derived from it must be interpreted with caution. The pain subscale fits the Rasch model expectations well. The disability subscale does not fit the Rasch model and its current format does not meet the criteria for true interval-level measurement required for use as a primary endpoint in clinical trials. Clinicians should therefore exercise caution when interpreting score changes on the disability subscale and attempt to compare their scores to age- and sex-stratified data.

A global goodness-of-fit statistic for Cox regression models.

PubMed

Parzen, M; Lipsitz, S R

1999-06-01

In this paper, a global goodness-of-fit test statistic for a Cox regression model, which has an approximate chi-squared distribution when the model has been correctly specified, is proposed. Our goodness-of-fit statistic is global and has power to detect if interactions or higher order powers of covariates in the model are needed. The proposed statistic is similar to the Hosmer and Lemeshow (1980, Communications in Statistics A10, 1043-1069) goodness-of-fit statistic for binary data as well as Schoenfeld's (1980, Biometrika 67, 145-153) statistic for the Cox model. The methods are illustrated using data from a Mayo Clinic trial in primary billiary cirrhosis of the liver (Fleming and Harrington, 1991, Counting Processes and Survival Analysis), in which the outcome is the time until liver transplantation or death. The are 17 possible covariates. Two Cox proportional hazards models are fit to the data, and the proposed goodness-of-fit statistic is applied to the fitted models.

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.

Statistical analysis of multivariate atmospheric variables. [cloud cover

NASA Technical Reports Server (NTRS)

Tubbs, J. D.

1979-01-01

Topics covered include: (1) estimation in discrete multivariate distributions; (2) a procedure to predict cloud cover frequencies in the bivariate case; (3) a program to compute conditional bivariate normal parameters; (4) the transformation of nonnormal multivariate to near-normal; (5) test of fit for the extreme value distribution based upon the generalized minimum chi-square; (6) test of fit for continuous distributions based upon the generalized minimum chi-square; (7) effect of correlated observations on confidence sets based upon chi-square statistics; and (8) generation of random variates from specified distributions.

Probability analysis for consecutive-day maximum rainfall for Tiruchirapalli City (south India, Asia)

NASA Astrophysics Data System (ADS)

Sabarish, R. Mani; Narasimhan, R.; Chandhru, A. R.; Suribabu, C. R.; Sudharsan, J.; Nithiyanantham, S.

2017-05-01

In the design of irrigation and other hydraulic structures, evaluating the magnitude of extreme rainfall for a specific probability of occurrence is of much importance. The capacity of such structures is usually designed to cater to the probability of occurrence of extreme rainfall during its lifetime. In this study, an extreme value analysis of rainfall for Tiruchirapalli City in Tamil Nadu was carried out using 100 years of rainfall data. Statistical methods were used in the analysis. The best-fit probability distribution was evaluated for 1, 2, 3, 4 and 5 days of continuous maximum rainfall. The goodness of fit was evaluated using Chi-square test. The results of the goodness-of-fit tests indicate that log-Pearson type III method is the overall best-fit probability distribution for 1-day maximum rainfall and consecutive 2-, 3-, 4-, 5- and 6-day maximum rainfall series of Tiruchirapalli. To be reliable, the forecasted maximum rainfalls for the selected return periods are evaluated in comparison with the results of the plotting position.

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.

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).

Retransformation bias in a stem profile model

Treesearch

Raymond L. Czaplewski; David Bruce

1990-01-01

An unbiased profile model, fit to diameter divided by diameter at breast height, overestimated volume of 5.3-m log sections by 0.5 to 3.5%. Another unbiased profile model, fit to squared diameter divided by squared diameter at breast height, underestimated bole diameters by 0.2 to 2.1%. These biases are caused by retransformation of the predicted dependent variable;...

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.

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.

Improved cutback method measuring beat-length for high-birefringence optical fiber by fitting data of photoelectric signal

NASA Astrophysics Data System (ADS)

Shi, Zhi-Dong; Lin, Jian-Qiang; Bao, Huan-Huan; Liu, Shu; Xiang, Xue-Nong

2008-03-01

A photoelectric measurement system for measuring the beat length of birefringence fiber is set up including a set of rotating-wave-plate polarimeter using single photodiode. And two improved cutback methods suitable for measuring beat-length within millimeter range of high birefringence fiber are proposed through data processing technique. The cut length needs not to be restricted shorter than one centimeter so that the auto-cleaving machine is freely used, and no need to carefully operate the manually cleaving blade with low efficiency and poor success. The first method adopts the parameter-fitting to a saw-tooth function of tried beat length by the criterion of minimum square deviations, without special limitation on the cut length. The second method adopts linear-fitting in the divided length ranges, only restrict condition is the increment between different cut lengths less than one beat-length. For a section of holey high-birefringence fiber, we do experiments respectively by the two methods. The detecting error of beat-length is discussed and the advantage is compared.

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...

A Response to Holster and Lake Regarding Guessing and the Rasch Model

ERIC Educational Resources Information Center

Stewart, Jeffrey; McLean, Stuart; Kramer, Brandon

2017-01-01

Stewart questioned vocabulary size estimation methods proposed by Beglar and Nation for the Vocabulary Size Test, further arguing Rasch mean square (MSQ) fit statistics cannot determine the proportion of random guesses contained in the average learner's raw score, because the average value will be near 1 by design. He illustrated this by…

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.

Evaluating the relationship between job stress and job satisfaction among female hospital nurses in Babol: An application of structural equation modeling.

PubMed

Bagheri Hosseinabadi, Majid; Etemadinezhad, Siavash; Khanjani, Narges; Ahmadi, Omran; Gholinia, Hemat; Galeshi, Mina; Samaei, Seyed Ehsan

2018-01-01

Background: This study was designed to investigate job satisfaction and its relation to perceived job stress among hospital nurses in Babol County, Iran. Methods: This cross-sectional study was conducted on 406 female nurses in 6 Babol hospitals. Respondents completed the Minnesota Satisfaction Questionnaire (MSQ), the health and safety executive (HSE) indicator tool and a demographic questionnaire. Descriptive, analytical and structural equation modeling (SEM) analyses were carried out applying SPSS v. 22 and AMOS v. 22. Results: The Normed Fit Index (NFI), Non-normed Fit Index (NNFI), Incremental Fit Index (IFI)and Comparative Fit Index (CFI) were greater than 0.9. Also, goodness of fit index (GFI=0.99)and adjusted goodness of fit index (AGFI) were greater than 0.8, and root mean square error of approximation (RMSEA) were 0.04, The model was found to be with an appropriate fit. The R-squared was 0.42 for job satisfaction, and all its dimensions were related to job stress. The dimensions of job stress explained 42% of changes in the variance of job satisfaction. There was a significant relationship between the dimensions of job stress such as demand (β =0.173,CI =0.095 - 0.365, P≤0.001), control (β =0.135, CI =0.062 - 0.404, P =0.008), relationships(β =-0.208, CI =-0.637- -0.209; P≤0.001) and changes (β =0.247, CI =0.360 - 1.026, P≤0.001)with job satisfaction. Conclusion: One of the important interventions to increase job satisfaction among nurses maybe improvement in the workplace. Reducing the level of workload in order to improve job demand and minimizing role conflict through reducing conflicting demands are recommended.

Evaluating the relationship between job stress and job satisfaction among female hospital nurses in Babol: An application of structural equation modeling

PubMed Central

Bagheri Hosseinabadi, Majid; Etemadinezhad, Siavash; khanjani, Narges; Ahmadi, Omran; Gholinia, Hemat; Galeshi, Mina; Samaei, Seyed Ehsan

2018-01-01

Background: This study was designed to investigate job satisfaction and its relation to perceived job stress among hospital nurses in Babol County, Iran. Methods: This cross-sectional study was conducted on 406 female nurses in 6 Babol hospitals. Respondents completed the Minnesota Satisfaction Questionnaire (MSQ), the health and safety executive (HSE) indicator tool and a demographic questionnaire. Descriptive, analytical and structural equation modeling (SEM) analyses were carried out applying SPSS v. 22 and AMOS v. 22. Results: The Normed Fit Index (NFI), Non-normed Fit Index (NNFI), Incremental Fit Index (IFI)and Comparative Fit Index (CFI) were greater than 0.9. Also, goodness of fit index (GFI=0.99)and adjusted goodness of fit index (AGFI) were greater than 0.8, and root mean square error of approximation (RMSEA) were 0.04, The model was found to be with an appropriate fit. The R-squared was 0.42 for job satisfaction, and all its dimensions were related to job stress. The dimensions of job stress explained 42% of changes in the variance of job satisfaction. There was a significant relationship between the dimensions of job stress such as demand (β =0.173,CI =0.095 - 0.365, P≤0.001), control (β =0.135, CI =0.062 - 0.404, P =0.008), relationships(β =-0.208, CI =-0.637– -0.209; P≤0.001) and changes (β =0.247, CI =0.360 - 1.026, P≤0.001)with job satisfaction. Conclusion: One of the important interventions to increase job satisfaction among nurses maybe improvement in the workplace. Reducing the level of workload in order to improve job demand and minimizing role conflict through reducing conflicting demands are recommended. PMID:29744305

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.

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.

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.

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.

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.

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.

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.

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.

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.

Modeling protein conformational changes by iterative fitting of distance constraints using reoriented normal modes.

PubMed

Zheng, Wenjun; Brooks, Bernard R

2006-06-15

Recently we have developed a normal-modes-based algorithm that predicts the direction of protein conformational changes given the initial state crystal structure together with a small number of pairwise distance constraints for the end state. Here we significantly extend this method to accurately model both the direction and amplitude of protein conformational changes. The new protocol implements a multisteps search in the conformational space that is driven by iteratively minimizing the error of fitting the given distance constraints and simultaneously enforcing the restraint of low elastic energy. At each step, an incremental structural displacement is computed as a linear combination of the lowest 10 normal modes derived from an elastic network model, whose eigenvectors are reorientated to correct for the distortions caused by the structural displacements in the previous steps. We test this method on a list of 16 pairs of protein structures for which relatively large conformational changes are observed (root mean square deviation >3 angstroms), using up to 10 pairwise distance constraints selected by a fluctuation analysis of the initial state structures. This method has achieved a near-optimal performance in almost all cases, and in many cases the final structural models lie within root mean square deviation of 1 approximately 2 angstroms from the native end state structures.

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.

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.

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.

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...

TH-E-BRF-09: Gaussian Mixture Model Analysis of Radiation-Induced Parotid-Gland Injury: An Ultrasound Study of Acute and Late Xerostomia in Head-And-Neck Radiotherapy

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

Liu, T; Yu, D; Beitler, J

Purpose: Xerostomia (dry mouth), secondary to parotid-gland injury, is a distressing side-effect in head-and-neck radiotherapy (RT). This study's purpose is to develop a novel ultrasound technique to quantitatively evaluate post-RT parotid-gland injury. Methods: Recent ultrasound studies have shown that healthy parotid glands exhibit homogeneous echotexture, whereas post-RT parotid glands are often heterogeneous, with multiple hypoechoic (inflammation) or hyperechoic (fibrosis) regions. We propose to use a Gaussian mixture model to analyze the ultrasonic echo-histogram of the parotid glands. An IRB-approved clinical study was conducted: (1) control-group: 13 healthy-volunteers, served as the control; (2) acutetoxicity group − 20 patients (mean age: 62.5more » ± 8.9 years, follow-up: 2.0±0.8 months); and (3) late-toxicity group − 18 patients (mean age: 60.7 ± 7.3 years, follow-up: 20.1±10.4 months). All patients experienced RTOG grade 1 or 2 salivary-gland toxicity. Each participant underwent an ultrasound scan (10 MHz) of the bilateral parotid glands. An echo-intensity histogram was derived for each parotid and a Gaussian mixture model was used to fit the histogram using expectation maximization (EM) algorithm. The quality of the fitting was evaluated with the R-squared value. Results: (1) Controlgroup: all parotid glands fitted well with one Gaussian component, with a mean intensity of 79.8±4.9 (R-squared>0.96). (2) Acute-toxicity group: 37 of the 40 post-RT parotid glands fitted well with two Gaussian components, with a mean intensity of 42.9±7.4, 73.3±12.2 (R-squared>0.95). (3) Latetoxicity group: 32 of the 36 post-RT parotid fitted well with 3 Gaussian components, with mean intensities of 49.7±7.6, 77.2±8.7, and 118.6±11.8 (R-squared>0.98). Conclusion: RT-associated parotid-gland injury is common in head-and-neck RT, but challenging to assess. This work has demonstrated that the Gaussian mixture model of the echo-histogram could quantify acute and late toxicity of the parotid glands. This study provides meaningful preliminary data from future observational and interventional clinical research.« less

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.

Improved Model Fitting for the Empirical Green's Function Approach Using Hierarchical Models

NASA Astrophysics Data System (ADS)

Van Houtte, Chris; Denolle, Marine

2018-04-01

Stress drops calculated from source spectral studies currently show larger variability than what is implied by empirical ground motion models. One of the potential origins of the inflated variability is the simplified model-fitting techniques used in most source spectral studies. This study examines a variety of model-fitting methods and shows that the choice of method can explain some of the discrepancy. The preferred method is Bayesian hierarchical modeling, which can reduce bias, better quantify uncertainties, and allow additional effects to be resolved. Two case study earthquakes are examined, the 2016 MW7.1 Kumamoto, Japan earthquake and a MW5.3 aftershock of the 2016 MW7.8 Kaikōura earthquake. By using hierarchical models, the variation of the corner frequency, fc, and the falloff rate, n, across the focal sphere can be retrieved without overfitting the data. Other methods commonly used to calculate corner frequencies may give substantial biases. In particular, if fc was calculated for the Kumamoto earthquake using an ω-square model, the obtained fc could be twice as large as a realistic value.

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…

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.

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.

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.

SU-E-I-07: Response Characteristics and Signal Conversion Modeling of KV Flat-Panel Detector in Cone Beam CT System

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

Wang, Yu; Cao, Ruifen; Pei, Xi

2015-06-15

Purpose: The flat-panel detector response characteristics are investigated to optimize the scanning parameter considering the image quality and less radiation dose. The signal conversion model is also established to predict the tumor shape and physical thickness changes. Methods: With the ELEKTA XVI system, the planar images of 10cm water phantom were obtained under different image acquisition conditions, including tube voltage, electric current, exposure time and frames. The averaged responses of square area in center were analyzed using Origin8.0. The response characteristics for each scanning parameter were depicted by different fitting types. The transmission measured for 10cm water was compared tomore » Monte Carlo simulation. Using the quadratic calibration method, a series of variable-thickness water phantoms images were acquired to derive the signal conversion model. A 20cm wedge water phantom with 2cm step thickness was used to verify the model. At last, the stability and reproducibility of the model were explored during a four week period. Results: The gray values of image center all decreased with the increase of different image acquisition parameter presets. The fitting types adopted were linear fitting, quadratic polynomial fitting, Gauss fitting and logarithmic fitting with the fitting R-Square 0.992, 0.995, 0.997 and 0.996 respectively. For 10cm water phantom, the transmission measured showed better uniformity than Monte Carlo simulation. The wedge phantom experiment show that the radiological thickness changes prediction error was in the range of (-4mm, 5mm). The signal conversion model remained consistent over a period of four weeks. Conclusion: The flat-panel response decrease with the increase of different scanning parameters. The preferred scanning parameter combination was 100kV, 10mA, 10ms, 15frames. It is suggested that the signal conversion model could effectively be used for tumor shape change and radiological thickness prediction. Supported by National Natural Science Foundation of China (81101132, 11305203) and Natural Science Foundation of Anhui Province (11040606Q55, 1308085QH138)« less

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.

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.

Assessing the fit of site-occupancy models

USGS Publications Warehouse

MacKenzie, D.I.; Bailey, L.L.

2004-01-01

Few species are likely to be so evident that they will always be detected at a site when present. Recently a model has been developed that enables estimation of the proportion of area occupied, when the target species is not detected with certainty. Here we apply this modeling approach to data collected on terrestrial salamanders in the Plethodon glutinosus complex in the Great Smoky Mountains National Park, USA, and wish to address the question 'how accurately does the fitted model represent the data?' The goodness-of-fit of the model needs to be assessed in order to make accurate inferences. This article presents a method where a simple Pearson chi-square statistic is calculated and a parametric bootstrap procedure is used to determine whether the observed statistic is unusually large. We found evidence that the most global model considered provides a poor fit to the data, hence estimated an overdispersion factor to adjust model selection procedures and inflate standard errors. Two hypothetical datasets with known assumption violations are also analyzed, illustrating that the method may be used to guide researchers to making appropriate inferences. The results of a simulation study are presented to provide a broader view of the methods properties.

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

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.

Functional Mixed Effects Model for Small Area Estimation.

PubMed

Maiti, Tapabrata; Sinha, Samiran; Zhong, Ping-Shou

2016-09-01

Functional data analysis has become an important area of research due to its ability of handling high dimensional and complex data structures. However, the development is limited in the context of linear mixed effect models, and in particular, for small area estimation. The linear mixed effect models are the backbone of small area estimation. In this article, we consider area level data, and fit a varying coefficient linear mixed effect model where the varying coefficients are semi-parametrically modeled via B-splines. We propose a method of estimating the fixed effect parameters and consider prediction of random effects that can be implemented using a standard software. For measuring prediction uncertainties, we derive an analytical expression for the mean squared errors, and propose a method of estimating the mean squared errors. The procedure is illustrated via a real data example, and operating characteristics of the method are judged using finite sample simulation studies.

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.

Students' motivational processes and their relationship to teacher ratings in school physical education: a self-determination theory approach.

PubMed

Standage, Martyn; Duda, Joan L; Ntoumanis, Nikos

2006-03-01

In the present study, we used a model of motivation grounded in self-determination theory (Deci & Ryan, 1985, 1991; Ryan & Deci, 2000a, 2000b, 2002) to examine the relationship between physical education (PE) students' motivational processes and ratings of their effort and persistence as provided by their PE teacher. Data were obtained from 394 British secondary school students (204 boys, 189 girls, 1 gender not specified; M age = 11.97 years; SD = .89; range = 11-14 years) who responded to a multisection inventory (tapping autonomy-support, autonomy, competence, relatedness, and self-determined motivation). The students' respective PE teachers subsequently provided ratings reflecting the effort and persistence each student exhibited in their PE classes. The hypothesized relationships among the study variables were examined via structural equation modeling analysis using latent factors. Results of maximum likelihood analysis using the bootstrapping method revealed the proposed model demonstrated a good fit to the data, chi-squared (292) = 632.68, p < .001; comparative fit index = .95; incremental fit index = .95, standardized root mean square residual = .077; root mean square error of approximation (RMSEA) = .054 (90% confidence interval of RMSEA = .049 -.060). Specifically, the model showed that students who perceived an autonomy supportive environment experienced greater levels of autonomy, competence, and relatedness and had higher scores on an index of self-determination. Student-reported levels of self-determined motivation positively predicted teacher ratings of effort and persistence in PE. The findings are discussed with regard to enhancing student motivation in PE settings.

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...

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

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.

Computing Robust, Bootstrap-Adjusted Fit Indices for Use with Nonnormal Data

ERIC Educational Resources Information Center

Walker, David A.; Smith, Thomas J.

2017-01-01

Nonnormality of data presents unique challenges for researchers who wish to carry out structural equation modeling. The subsequent SPSS syntax program computes bootstrap-adjusted fit indices (comparative fit index, Tucker-Lewis index, incremental fit index, and root mean square error of approximation) that adjust for nonnormality, along with the…

LC-PROM: Validation of a patient reported outcomes measure for liver cirrhosis patients.

PubMed

Zhang, Ying; Yang, Yuanyuan; Lv, Jing; Zhang, Yanbo

2016-05-10

The aim of the study is to develop a specific patient-reported scale of liver cirrhosis according to the Patient Reported Outcome guidelines of the Food and Drug Administration (FDA), and to examine its capacity to fill gaps in this field. A conceptual framework was developed and a preliminary item pool developed through literature review and interviews of 10 patients with liver cirrhosis. With the preliminary items, we performed a pilot survey that included a cognitive test with patients and interviews with experts; the focus was on content and language of the scale. In the item selection stage, seven statistical methods including discrete trends method, discrimination analysis, exploratory factor analysis, Cronbach's α coefficient, correlation coefficient, test-retest reliability, Item-Response Theory were applied to survey data from 200 subjects (150 liver cirrhosis patients and 50 controls). This produced the preliminary Liver Cirrhosis Patient-reported Outcome Measure (LC-PROM). In the next stage, we conducted the survey with 620 subjects (500 patients and 120 controls) to validate reliability, validity and acceptability of this scale. The 55 items and 13 dimensions addressed four domains: physical, psychological, social, and therapeutic. Cronbach's α coefficients were 0.921 for the total scale; the confirmatory factor analysis, t-tests and ANOVA supported scale validity; the model fit index as Root Mean Square Error of Approximation (RMSEA), Root Mean Square Residual (RMR), Normed Fit Index (NFI), Non-Normed Fit Index (NNFI), Comparative Fit Index (CFI) and Incremental Fit Index (IFI) met the criterion generally. The acceptance ratio and response rate indicated good feasibility. This study developed an accurate and stable patient-reported outcome scale of liver cirrhosis, which is able to evaluate clinical effects effectively, is helpful to patients in recognizing their health condition, and contributes to clinical decision making both for patients and physicians. Additionally, the LC-PROM can perform as an ultimate assessment of medical and health care effects and can inform clinical trials of new drugs for liver cirrhosis.

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

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.

ISOFIT - A PROGRAM FOR FITTING SORPTION ISOTHERMS TO EXPERIMENTAL DATA

EPA Science Inventory

Isotherm expressions are important for describing the partitioning of contaminants in environmental systems. ISOFIT (ISOtherm FItting Tool) is a software program that fits isotherm parameters to experimental data via the minimization of a weighted sum of squared error (WSSE) obje...

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.

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.

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.

Radar cross section models for limited aspect angle windows

NASA Astrophysics Data System (ADS)

Robinson, Mark C.

1992-12-01

This thesis presents a method for building Radar Cross Section (RCS) models of aircraft based on static data taken from limited aspect angle windows. These models statistically characterize static RCS. This is done to show that a limited number of samples can be used to effectively characterize static aircraft RCS. The optimum models are determined by performing both a Kolmogorov and a Chi-Square goodness-of-fit test comparing the static RCS data with a variety of probability density functions (pdf) that are known to be effective at approximating the static RCS of aircraft. The optimum parameter estimator is also determined by the goodness of-fit tests if there is a difference in pdf parameters obtained by the Maximum Likelihood Estimator (MLE) and the Method of Moments (MoM) estimators.

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.

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

75 FR 57456 - Light-Walled Rectangular Pipe and Tube from the People's Republic of China: Final Results of the...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-09-21

...'') U.S. affiliated importer FitMAX Inc. (``FitMAX'') on June 2, 2010 and June 16, 2010. FitMAX... carbon- quality light-walled steel pipe and tube, of rectangular (including square) cross section, having...

[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.

Reproducibility of isopach data and estimates of dispersal and eruption volumes

NASA Astrophysics Data System (ADS)

Klawonn, M.; Houghton, B. F.; Swanson, D.; Fagents, S. A.; Wessel, P.; Wolfe, C. J.

2012-12-01

Total erupted volume and deposit thinning relationships are key parameters in characterizing explosive eruptions and evaluating the potential risk from a volcano as well as inputs to volcanic plume models. Volcanologists most commonly estimate these parameters by hand-contouring deposit data, then representing these contours in thickness versus square root area plots, fitting empirical laws to the thinning relationships and integrating over the square root area to arrive at volume estimates. In this study we analyze the extent to which variability in hand-contouring thickness data for pyroclastic fall deposits influences the resulting estimates and investigate the effects of different fitting laws. 96 volcanologists (3% MA students, 19% PhD students, 20% postdocs, 27% professors, and 30% professional geologists) from 11 countries (Australia, Ecuador, France, Germany, Iceland, Italy, Japan, New Zealand, Switzerland, UK, USA) participated in our study and produced hand-contours on identical maps using our unpublished thickness measurements of the Kilauea Iki 1959 fall deposit. We computed volume estimates by (A) integrating over a surface fitted through the contour lines, as well as using the established methods of integrating over the thinning relationships of (B) an exponential fit with one to three segments, (C) a power law fit, and (D) a Weibull function fit. To focus on the differences from the hand-contours of the well constrained deposit and eliminate the effects of extrapolations to great but unmeasured thicknesses near the vent, we removed the volume contribution of the near vent deposit (defined as the deposit above 3.5 m) from the volume estimates. The remaining volume approximates to 1.76 *106 m3 (geometric mean for all methods) with maximum and minimum estimates of 2.5 *106 m3 and 1.1 *106 m3. Different integration methods of identical isopach maps result in volume estimate differences of up to 50% and, on average, maximum variation between integration methods of 14%. Volume estimates with methods (A), (C) and (D) show strong correlation (r = 0.8 to r = 0.9), while correlation of (B) with the other methods is weaker (r = 0.2 to r = 0.6) and correlation between (B) and (C) is not statistically significant. We find that the choice of larger maximum contours leads to smaller volume estimates due to method (C), but larger estimates with the other methods. We do not find statistically significant correlation between volume estimations and participants experience level, number of chosen contour levels, nor smoothness of contours. Overall, application of the different methods to the same maps leads to similar mean volume estimates, but the different methods show different dependencies and varying spread of volume estimates. The results indicate that these key parameters are less critically dependent on the operator and their choices of contour values, intervals etc., and more sensitive to the selection of technique to integrate these data.

A Graphic Chi-Square Test For Two-Class Genetic Segregation Ratios

Treesearch

A.E. Squillace; D.J. Squillace

1970-01-01

A chart is presented for testing the goodness of fit of observed two-class genetic segregation ratios against hypothetical ratios, eliminating the need of computing chi-square. Although designed mainly for genetic studies, the chart can also be used for other types of studies involving two-class chi-square tests.

46 CFR 193.15-15 - Piping.

Code of Federal Regulations, 2012 CFR

2012-10-01

... fittings shall have a bursting pressure of not less than 6,000 pounds per square inch. (b) All piping, in...,800 pounds per square inch shall be installed in the distribution manifold or such other location as... stop valves in the manifold shall be subjected to a pressure of 1,000 pounds per square inch. With no...

46 CFR 193.15-15 - Piping.

Code of Federal Regulations, 2013 CFR

2013-10-01

... fittings shall have a bursting pressure of not less than 6,000 pounds per square inch. (b) All piping, in...,800 pounds per square inch shall be installed in the distribution manifold or such other location as... stop valves in the manifold shall be subjected to a pressure of 1,000 pounds per square inch. With no...

46 CFR 193.15-15 - Piping.

Code of Federal Regulations, 2014 CFR

2014-10-01

... fittings shall have a bursting pressure of not less than 6,000 pounds per square inch. (b) All piping, in...,800 pounds per square inch shall be installed in the distribution manifold or such other location as... stop valves in the manifold shall be subjected to a pressure of 1,000 pounds per square inch. With no...

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.

Fitting a Point Cloud to a 3d Polyhedral Surface

NASA Astrophysics Data System (ADS)

Popov, E. V.; Rotkov, S. I.

2017-05-01

The ability to measure parameters of large-scale objects in a contactless fashion has a tremendous potential in a number of industrial applications. However, this problem is usually associated with an ambiguous task to compare two data sets specified in two different co-ordinate systems. This paper deals with the study of fitting a set of unorganized points to a polyhedral surface. The developed approach uses Principal Component Analysis (PCA) and Stretched grid method (SGM) to substitute a non-linear problem solution with several linear steps. The squared distance (SD) is a general criterion to control the process of convergence of a set of points to a target surface. The described numerical experiment concerns the remote measurement of a large-scale aerial in the form of a frame with a parabolic shape. The experiment shows that the fitting process of a point cloud to a target surface converges in several linear steps. The method is applicable to the geometry remote measurement of large-scale objects in a contactless fashion.

Fitting Multimeric Protein Complexes into Electron Microscopy Maps Using 3D Zernike Descriptors

PubMed Central

Esquivel-Rodríguez, Juan; Kihara, Daisuke

2012-01-01

A novel computational method for fitting high-resolution structures of multiple proteins into a cryoelectron microscopy map is presented. The method named EMLZerD generates a pool of candidate multiple protein docking conformations of component proteins, which are later compared with a provided electron microscopy (EM) density map to select the ones that fit well into the EM map. The comparison of docking conformations and the EM map is performed using the 3D Zernike descriptor (3DZD), a mathematical series expansion of three-dimensional functions. The 3DZD provides a unified representation of the surface shape of multimeric protein complex models and EM maps, which allows a convenient, fast quantitative comparison of the three dimensional structural data. Out of 19 multimeric complexes tested, near native complex structures with a root mean square deviation of less than 2.5 Å were obtained for 14 cases while medium range resolution structures with correct topology were computed for the additional 5 cases. PMID:22417139

Fitting multimeric protein complexes into electron microscopy maps using 3D Zernike descriptors.

PubMed

Esquivel-Rodríguez, Juan; Kihara, Daisuke

2012-06-14

A novel computational method for fitting high-resolution structures of multiple proteins into a cryoelectron microscopy map is presented. The method named EMLZerD generates a pool of candidate multiple protein docking conformations of component proteins, which are later compared with a provided electron microscopy (EM) density map to select the ones that fit well into the EM map. The comparison of docking conformations and the EM map is performed using the 3D Zernike descriptor (3DZD), a mathematical series expansion of three-dimensional functions. The 3DZD provides a unified representation of the surface shape of multimeric protein complex models and EM maps, which allows a convenient, fast quantitative comparison of the three-dimensional structural data. Out of 19 multimeric complexes tested, near native complex structures with a root-mean-square deviation of less than 2.5 Å were obtained for 14 cases while medium range resolution structures with correct topology were computed for the additional 5 cases.

Nonlinear method for including the mass uncertainty of standards and the system measurement errors in the fitting of calibration curves

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

Pickles, W.L.; McClure, J.W.; Howell, R.H.

1978-01-01

A sophisticated non-linear multiparameter fitting program has been used to produce a best fit calibration curve for the response of an x-ray fluorescence analyzer to uranium nitrate, freeze dried, 0.2% accurate, gravimetric standards. The program is based on unconstrained minimization subroutine, VA02A. The program considers the mass values of the gravimetric standards as parameters to be fit along with the normal calibration curve parameters. The fitting procedure weights with the system errors and the mass errors in a consistent way. The resulting best fit calibration curve parameters reflect the fact that the masses of the standard samples are measured quantitiesmore » with a known error. Error estimates for the calibration curve parameters can be obtined from the curvature of the Chi-Squared Matrix or from error relaxation techniques. It has been shown that non-dispersive x-ray fluorescence analysis of 0.1 to 1 mg freeze-dried UNO/sub 3/ can have an accuracy of 0.2% in 1000 sec.« less

Use of a non-linear method for including the mass uncertainty of gravimetric standards and system measurement errors in the fitting of calibration curves for XRFA freeze-dried UNO/sub 3/ standards

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

Pickles, W.L.; McClure, J.W.; Howell, R.H.

1978-05-01

A sophisticated nonlinear multiparameter fitting program was used to produce a best fit calibration curve for the response of an x-ray fluorescence analyzer to uranium nitrate, freeze dried, 0.2% accurate, gravimetric standards. The program is based on unconstrained minimization subroutine, VA02A. The program considers the mass values of the gravimetric standards as parameters to be fit along with the normal calibration curve parameters. The fitting procedure weights with the system errors and the mass errors in a consistent way. The resulting best fit calibration curve parameters reflect the fact that the masses of the standard samples are measured quantities withmore » a known error. Error estimates for the calibration curve parameters can be obtained from the curvature of the ''Chi-Squared Matrix'' or from error relaxation techniques. It was shown that nondispersive XRFA of 0.1 to 1 mg freeze-dried UNO/sub 3/ can have an accuracy of 0.2% in 1000 s.« less

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.

Transmissivity and storage coefficient estimates from slug tests, Naval Air Warfare Center, West Trenton, New Jersey

USGS Publications Warehouse

Fiore, Alex R.

2014-01-01

Slug tests were conducted on 56 observation wells open to bedrock at the former Naval Air Warfare Center (NAWC) in West Trenton, New Jersey. Aquifer transmissivity (T) and storage coefficient (S) values for most wells were estimated from slug-test data using the Cooper-Bredehoeft-Papadopulos method. Test data from three wells exhibited fast, underdamped water-level responses and were analyzed with the Butler high-K method. The range of T at NAWC was approximately 0.07 to 10,000 square feet per day. At 11 wells, water levels did not change measurably after 20 minutes following slug insertion; transmissivity at these 11 wells was estimated to be less than 0.07 square feet per day. The range of S was approximately 10-10 to 0.01, the mode being 10-10. Water-level responses for tests at three wells fit poorly to the type curves of both methods, indicating that these methods were not appropriate for adequately estimating T and S from those data.

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.

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.

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.

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.

Confirmatory Factor Analysis of the WHO Violence Against Women Instrument in Pregnant Women: Results from the BRISA Prenatal Cohort

PubMed Central

Ribeiro, Marizélia Rodrigues Costa; Alves, Maria Teresa Seabra Soares de Britto e.; Batista, Rosângela Fernandes Lucena; Ribeiro, Cecília Cláudia Costa; Schraiber, Lilia Blima; Barbieri, Marco Antônio; Bettiol, Heloisa; da Silva, Antônio Augusto Moura

2014-01-01

Background Screening for violence during pregnancy is one of the strategies for the prevention of abuse against women. Since violence is difficult to measure, it is necessary to validate questionnaires that can provide a good measure of the phenomenon. The present study analyzed the psychometric properties of the World Health Organization Violence Against Women (WHO VAW) instrument for the measurement of violence against pregnant women. Methods Data from the Brazilian Ribeirão Preto and São Luís birth cohort studies (BRISA) were used. The sample consisted of 1,446 pregnant women from São Luís and 1,378 from Ribeirão Preto, interviewed in 2010 and 2011. Thirteen variables were selected from a self-applied questionnaire. Confirmatory factor analysis was used to investigate whether violence is a uni-or-multidimensional construct consisting of psychological, physical and sexual dimensions. The mean-and-variance-adjusted weighted least squares estimator was used. Models were fitted separately for each city and a third model combining data from the two settings was also tested. Models suggested from modification indices were tested to determine whether changes in the WHO VAW model would produce a better fit. Results The unidimensional model did not show good fit (Root mean square error of approximation [RMSEA]  = 0.060, p<0.001 for the combined model). The multidimensional WHO VAW model showed good fit (RMSEA = 0.036, p = 0.999 for the combined model) and standardized factor loadings higher than 0.70, except for the sexual dimension for SL (0.65). The models suggested by the modification indices with cross loadings measuring simultaneously physical and psychological violence showed a significantly better fit compared to the original WHO model (p<0.001 for the difference between the model chi-squares). Conclusions Violence is a multidimensional second-order construct consisting of psychological, physical and sexual dimensions. The WHO VAW model and the modified models are suitable for measuring violence against pregnant women. PMID:25531654

Modelling Schumann resonances from ELF measurements using non-linear optimization methods

NASA Astrophysics Data System (ADS)

Castro, Francisco; Toledo-Redondo, Sergio; Fornieles, Jesús; Salinas, Alfonso; Portí, Jorge; Navarro, Enrique; Sierra, Pablo

2017-04-01

Schumann resonances (SR) can be found in planetary atmospheres, inside the cavity formed by the conducting surface of the planet and the lower ionosphere. They are a powerful tool to investigate both the electric processes that occur in the atmosphere and the characteristics of the surface and the lower ionosphere. In this study, the measurements are obtained in the ELF (Extremely Low Frequency) Juan Antonio Morente station located in the national park of Sierra Nevada. The three first modes, contained in the frequency band between 6 to 25 Hz, will be considered. For each time series recorded by the station, the amplitude spectrum was estimated by using Bartlett averaging. Then, the central frequencies and amplitudes of the SRs were obtained by fitting the spectrum with non-linear functions. In the poster, a study of nonlinear unconstrained optimization methods applied to the estimation of the Schumann Resonances will be presented. Non-linear fit, also known as optimization process, is the procedure followed in obtaining Schumann Resonances from the natural electromagnetic noise. The optimization methods that have been analysed are: Levenberg-Marquardt, Conjugate Gradient, Gradient, Newton and Quasi-Newton. The functions that the different methods fit to data are three lorentzian curves plus a straight line. Gaussian curves have also been considered. The conclusions of this study are outlined in the following paragraphs: i) Natural electromagnetic noise is better fitted using Lorentzian functions; ii) the measurement bandwidth can accelerate the convergence of the optimization method; iii) Gradient method has less convergence and has a highest mean squared error (MSE) between measurement and the fitted function, whereas Levenberg-Marquad, Gradient conjugate method and Cuasi-Newton method give similar results (Newton method presents higher MSE); v) There are differences in the MSE between the parameters that define the fit function, and an interval from 1% to 5% has been found.

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.

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.

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.

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.

Comparative analysis through probability distributions of a data set

NASA Astrophysics Data System (ADS)

Cristea, Gabriel; Constantinescu, Dan Mihai

2018-02-01

In practice, probability distributions are applied in such diverse fields as risk analysis, reliability engineering, chemical engineering, hydrology, image processing, physics, market research, business and economic research, customer support, medicine, sociology, demography etc. This article highlights important aspects of fitting probability distributions to data and applying the analysis results to make informed decisions. There are a number of statistical methods available which can help us to select the best fitting model. Some of the graphs display both input data and fitted distributions at the same time, as probability density and cumulative distribution. The goodness of fit tests can be used to determine whether a certain distribution is a good fit. The main used idea is to measure the "distance" between the data and the tested distribution, and compare that distance to some threshold values. Calculating the goodness of fit statistics also enables us to order the fitted distributions accordingly to how good they fit to data. This particular feature is very helpful for comparing the fitted models. The paper presents a comparison of most commonly used goodness of fit tests as: Kolmogorov-Smirnov, Anderson-Darling, and Chi-Squared. A large set of data is analyzed and conclusions are drawn by visualizing the data, comparing multiple fitted distributions and selecting the best model. These graphs should be viewed as an addition to the goodness of fit tests.

A Comparison of the One-and Three-Parameter Logistic Models on Measures of Test Efficiency.

ERIC Educational Resources Information Center

Benson, Jeri

Two methods of item selection were used to select sets of 40 items from a 50-item verbal analogies test, and the resulting item sets were compared for relative efficiency. The BICAL program was used to select the 40 items having the best mean square fit to the one parameter logistic (Rasch) model. The LOGIST program was used to select the 40 items…

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.

Sensitivity of Fit Indices to Misspecification in Growth Curve Models

ERIC Educational Resources Information Center

Wu, Wei; West, Stephen G.

2010-01-01

This study investigated the sensitivity of fit indices to model misspecification in within-individual covariance structure, between-individual covariance structure, and marginal mean structure in growth curve models. Five commonly used fit indices were examined, including the likelihood ratio test statistic, root mean square error of…

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.

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.

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.

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.

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.

Monte Carlo analysis for the determination of the conic constant of an aspheric micro lens based on a scanning white light interferometric measurement

NASA Astrophysics Data System (ADS)

Gugsa, Solomon A.; Davies, Angela

2005-08-01

Characterizing an aspheric micro lens is critical for understanding the performance and providing feedback to the manufacturing. We describe a method to find the best-fit conic of an aspheric micro lens using a least squares minimization and Monte Carlo analysis. Our analysis is based on scanning white light interferometry measurements, and we compare the standard rapid technique where a single measurement is taken of the apex of the lens to the more time-consuming stitching technique where more surface area is measured. Both are corrected for tip/tilt based on a planar fit to the substrate. Four major parameters and their uncertainties are estimated from the measurement and a chi-square minimization is carried out to determine the best-fit conic constant. The four parameters are the base radius of curvature, the aperture of the lens, the lens center, and the sag of the lens. A probability distribution is chosen for each of the four parameters based on the measurement uncertainties and a Monte Carlo process is used to iterate the minimization process. Eleven measurements were taken and data is also chosen randomly from the group during the Monte Carlo simulation to capture the measurement repeatability. A distribution of best-fit conic constants results, where the mean is a good estimate of the best-fit conic and the distribution width represents the combined measurement uncertainty. We also compare the Monte Carlo process for the stitched data and the not stitched data. Our analysis allows us to analyze the residual surface error in terms of Zernike polynomials and determine uncertainty estimates for each coefficient.

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.

[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.

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.

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.

Fitting Orbits to Jupiter's Moons with a Spreadsheet.

ERIC Educational Resources Information Center

Bridges, Richard

1995-01-01

Describes how a spreadsheet is used to fit a circular orbit model to observations of Jupiter's moons made with a small telescope. Kepler's Third Law and the inverse square law of gravity are observed. (AIM)

Profile of non-fatal injuries due to road traffic accidents from a industrial town in India

PubMed Central

Bayan, Pankaj; Bhawalkar, J. S.; Jadhav, S. L.; Banerjee, Amitav

2013-01-01

Background: India has one of the highest road traffic accident rates in the world. To lessen this burden, information on the contributing factors is necessary. Materials and Methods: We studied a series of cases of non-fatal road traffic accidents in two tertiary care hospitals in Pimpri, Pune, India. A total of 212 non-fatal road traffic accidents admitted over a period of one year in these two hospitals constituted the study sample. The study variables were, the gender of the accident victims, mode of accident, days of week on which the accident took place, time of day when the injury was sustained, part of the body injured, nature of injury, and self-reported reasons for the accident. Statistical Analysis: data were summarized using percentages. The Chi-square test for goodness of fit was applied, to see whether there was any association between the different weekdays or time of day and the accidents. Results: Male : female ratio was almost 5 : 1, which was statistically significant (Chi-Square for goodness of fit = 95.11, df = 1, P < 0.0001). The maximum accidents occurred on Sundays and Mondays and the least around midweek (Wednesday). This pattern was also statistically significant (Chi-square for goodness of fit = 30.09, df = 6, P < 0.001). Pedestrians were the most vulnerable group, followed by drivers and pillions of two wheelers. These categories of road users contributed to almost 80% of the cases of Road Traffic Injuries (RTIs). Accidents were more likely in the time zone of 8 pm to midnight, followed by 4 pm to 8 pm (Chi-square for goodness of fit = 89.58, df = 5, P < 0.0001). A majority of the patients sustained multiple injuries followed by injuries to the lower limbs. A majority reported impaired visibility and fatigue as the cause of accident. Almost half (46.22%) of the injured admitted to drinking alcohol on a regular basis. Conclusion: Wide pavements and safe zebra crossings should be provided for pedestrians, as the highest casualty in this study were pedestrians. More accidents occurred on Sundays and Mondays and in the late evenings. Extra supervision by traffic police may be considered on Sundays / Holidays and the day following. Roads should be well lit to improve visibility after sunset. PMID:23724378

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.

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.

Capacitive touch sensing : signal and image processing algorithms

NASA Astrophysics Data System (ADS)

Baharav, Zachi; Kakarala, Ramakrishna

2011-03-01

Capacitive touch sensors have been in use for many years, and recently gained center stage with the ubiquitous use in smart-phones. In this work we will analyze the most common method of projected capacitive sensing, that of absolute capacitive sensing, together with the most common sensing pattern, that of diamond-shaped sensors. After a brief introduction to the problem, and the reasons behind its popularity, we will formulate the problem as a reconstruction from projections. We derive analytic solutions for two simple cases: circular finger on a wire grid, and square finger on a square grid. The solutions give insight into the ambiguities of finding finger location from sensor readings. The main contribution of our paper is the discussion of interpolation algorithms including simple linear interpolation , curve fitting (parabolic and Gaussian), filtering, general look-up-table, and combinations thereof. We conclude with observations on the limits of the present algorithmic methods, and point to possible future research.

Four-Dimensional Golden Search

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

Fenimore, Edward E.

2015-02-25

The Golden search technique is a method to search a multiple-dimension space to find the minimum. It basically subdivides the possible ranges of parameters until it brackets, to within an arbitrarily small distance, the minimum. It has the advantages that (1) the function to be minimized can be non-linear, (2) it does not require derivatives of the function, (3) the convergence criterion does not depend on the magnitude of the function. Thus, if the function is a goodness of fit parameter such as chi-square, the convergence does not depend on the noise being correctly estimated or the function correctly followingmore » the chi-square statistic. And, (4) the convergence criterion does not depend on the shape of the function. Thus, long shallow surfaces can be searched without the problem of premature convergence. As with many methods, the Golden search technique can be confused by surfaces with multiple minima.« less

An Application of M[subscript 2] Statistic to Evaluate the Fit of Cognitive Diagnostic Models

ERIC Educational Resources Information Center

Liu, Yanlou; Tian, Wei; Xin, Tao

2016-01-01

The fit of cognitive diagnostic models (CDMs) to response data needs to be evaluated, since CDMs might yield misleading results when they do not fit the data well. Limited-information statistic M[subscript 2] and the associated root mean square error of approximation (RMSEA[subscript 2]) in item factor analysis were extended to evaluate the fit of…

How well will you FIT? Use of a modified MMI to assess applicants' compatibility with an emergency medicine residency program.

PubMed

Min, Alice A; Leetch, Aaron; Nuño, Tomas; Fiorello, Albert B

2016-01-01

Purpose Emergency medicine residency programs have evaluated the use of Multiple Mini Interviews (MMIs) for applicants. The authors developed an MMI-style method called the Fast Interview Track (FIT) to predict an applicant's 'fit' within an individual residency program. Methods Applicants meet with up to five residents and are asked one question by each. Residents score the applicant using a Likert scale from 1 to 5 on two questions: 'How well does the applicant think on his/her feet?' and 'How well do you think the applicant will fit in here?'. To assess how well these questions predicted a resident's 'fit', current residents scored fellow residents on these same questions. These scores were compared with the residents' interview FIT scores. A postmatch survey of applicants who did not match at this program solicited applicants' attitudes toward the FIT sessions. Results Among the junior class, the correlation between interview and current scores was significant for question 1 (rho=0.5192 [p=0.03]) and question 2 (rho=0.5753 [p=0.01]). Among seniors, Spearman's rho was statistically significant for question 2, though not statistically significant for question 1. The chi-square measure of high scores (4-5) versus low scores (1-3) found a statistically significant association between interview and current scores for interns and juniors. Of the 29 responses to the postmatch survey, 16 (55%) felt FIT sessions provided a good sense of the program's personality and only 6 (21%) disagreed. Nine (31%) felt FIT sessions positively impacted our program's ranking and 11 (38%) were 'Neutral'. Only two (7%) reported that FIT sessions negatively impacted their ranking of our program. Conclusions FIT provided program leadership with a sense of an applicant's 'fit' within this program. Interview day scores correlated with scores received during residency. Most applicants report a positive experience with FIT sessions. FIT provides a useful tool to recruit applicants who fit with the residency program.

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.

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.

SUPPLEMENTARY COMPARISON: EUROMET.L-S10 Comparison of squareness measurements

NASA Astrophysics Data System (ADS)

Mokros, Jiri

2005-01-01

The idea of performing a comparison of squareness resulted from the need to review the MRA Appendix C, Category 90° square. At its meeting in October 1999 (in Prague) it was decided upon a first comparison of squareness measurements in the framework of EUROMET, numbered #570, starting in 2000, with the Slovak Institute of Metrology (SMU) as the pilot laboratory. During the preparation stage of the project, it was agreed that it should be submitted as a EUROMET supplementary comparison in the framework of the Mutual Recognition Arrangement (MRA) of the Metre Convention and would boost confidence in calibration and measurement certificates issued by the participating national metrology institutes. The aim of the comparison of squareness measurement was to compare and verify the declared calibration measurement capabilities of participating laboratories and to investigate the effect of systematic influences in the measurement process and their elimination. Eleven NMIs from the EUROMET region carried out this project. Two standards were calibrated: granite squareness standard of rectangular shape, cylindrical squareness standard of steel with marked positions for the profile lines. The following parameters had to be calibrated: granite squareness standard: interior angle γB between two lines AB and AC (envelope - LS regression) fitted through the measured profiles, and/or granite squareness standard: interior angle γLS between two LS regression lines AB and AC fitted through the measured profiles, cylindrical squareness standard: interior angles γ0°, γ90°, γ180°, γ270° between the LS regression line fitted through the measurement profiles at 0°, 90°, 180°, 270° and the envelope plane of the basis (resting on a surface plate), local LS straightness deviation for all measured profiles (2 and 4) of both standards. The results of the comparison are the deviations of profiles and angles measured by the individual NMIs from the reference values. These resulted from the weighted mean of data from participating laboratories, while some of them were excluded on the basis of statistical evaluation. Graphical interpretations of all deviations are contained in the Final Report. In order to compare the individual deviations mutually (25 profiles for the granite square and 44 profiles for the cylinder), graphical illustrations of 'standard deviations' and both extreme values (max. and min.) of deviations were created. This regional supplementary comparison has provided independent information about the metrological properties of the measuring equipment and method used by the participating NMIs. The Final Report does not contain the En values. Participants could not estimate some contributions in the uncertainty budget on the basis of previous comparisons, since no comparison of this kind had ever been organized. Therefore the En value cannot reflect the actual state of the given NMI. Instead of En, an analysis has been performed by means of the Grubbs test according to ISO 5725-2. This comparison provided information about the state of provision of metrological services in the field of big squares measurement. Main text. To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/. The final report has been peer-reviewed and approved for publication by EUROMET, according to the provisions of the Mutual Recognition Arrangement (MRA).

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.

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.

Quantitative analysis of crystalline pharmaceuticals in powders and tablets by a pattern-fitting procedure using X-ray powder diffraction data.

PubMed

Yamamura, S; Momose, Y

2001-01-16

A pattern-fitting procedure for quantitative analysis of crystalline pharmaceuticals in solid dosage forms using X-ray powder diffraction data is described. This method is based on a procedure for pattern-fitting in crystal structure refinement, and observed X-ray scattering intensities were fitted to analytical expressions including some fitting parameters, i.e. scale factor, peak positions, peak widths and degree of preferred orientation of the crystallites. All fitting parameters were optimized by the non-linear least-squares procedure. Then the weight fraction of each component was determined from the optimized scale factors. In the present study, well-crystallized binary systems, zinc oxide-zinc sulfide (ZnO-ZnS) and salicylic acid-benzoic acid (SA-BA), were used as the samples. In analysis of the ZnO-ZnS system, the weight fraction of ZnO or ZnS could be determined quantitatively in the range of 5-95% in the case of both powders and tablets. In analysis of the SA-BA systems, the weight fraction of SA or BA could be determined quantitatively in the range of 20-80% in the case of both powders and tablets. Quantitative analysis applying this pattern-fitting procedure showed better reproducibility than other X-ray methods based on the linear or integral intensities of particular diffraction peaks. Analysis using this pattern-fitting procedure also has the advantage that the preferred orientation of the crystallites in solid dosage forms can be also determined in the course of quantitative analysis.

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.

Psychometric Properties and Correlates of the Beck Hopelessness Scale in Family Caregivers of Nigerian Patients with Psychiatric Disorders in Southwestern Nigeria

PubMed Central

Aloba, Olutayo; Ajao, Olayinka; Alimi, Taiwo; Esan, Olufemi

2016-01-01

Objectives: To examine the construct and correlates of hopelessness among family caregivers of Nigerian psychiatric patients. Materials and Methods: This is a cross-sectional, descriptive study involving 264 family caregiver-patients’ dyads recruited from two university teaching hospitals psychiatric clinics in Southwestern Nigeria. Results: Exploratory factor analysis revealed a two-factor 9-item model of the Beck Hopelessness Scale (BHS) among the family caregivers. Confirmatory factor analysis of the model revealed satisfactory indices of fitness (goodness of fit index = 0.97, comparative fit index = 0.96, Chi-square/degree of freedom (CMIN/DF) = 1.60, root mean square error of approximation = 0.048, expected cross-validation index = 0.307, and standardized root mean residual = 0.005). Reliability of the scale was modestly satisfactory (Cronbach's alpha 0.72). Construct validity of scale was supported by significant correlations with the family caregivers’ scores on the Zarit Burden Interview, mini international neuropsychiatric interview suicidality module, General Health Questionnaire-12 (GHQ-12), and Patient Health Questionnaire-9. The greatest variance in the family caregivers’ scores on the BHS was contributed by their scores on the psychological distress scale (GHQ-12). Conclusions: The BHS has adequate psychometric properties among Nigerian psychiatric patients’ family caregivers. There is the need to pay attention to the psychological well-being of the family caregivers of Nigerian psychiatric patients. PMID:28163498

2D Bayesian automated tilted-ring fitting of disc galaxies in large H I galaxy surveys: 2DBAT

NASA Astrophysics Data System (ADS)

Oh, Se-Heon; Staveley-Smith, Lister; Spekkens, Kristine; Kamphuis, Peter; Koribalski, Bärbel S.

2018-01-01

We present a novel algorithm based on a Bayesian method for 2D tilted-ring analysis of disc galaxy velocity fields. Compared to the conventional algorithms based on a chi-squared minimization procedure, this new Bayesian-based algorithm suffers less from local minima of the model parameters even with highly multimodal posterior distributions. Moreover, the Bayesian analysis, implemented via Markov Chain Monte Carlo sampling, only requires broad ranges of posterior distributions of the parameters, which makes the fitting procedure fully automated. This feature will be essential when performing kinematic analysis on the large number of resolved galaxies expected to be detected in neutral hydrogen (H I) surveys with the Square Kilometre Array and its pathfinders. The so-called 2D Bayesian Automated Tilted-ring fitter (2DBAT) implements Bayesian fits of 2D tilted-ring models in order to derive rotation curves of galaxies. We explore 2DBAT performance on (a) artificial H I data cubes built based on representative rotation curves of intermediate-mass and massive spiral galaxies, and (b) Australia Telescope Compact Array H I data from the Local Volume H I Survey. We find that 2DBAT works best for well-resolved galaxies with intermediate inclinations (20° < i < 70°), complementing 3D techniques better suited to modelling inclined galaxies.

Geostatistical interpolation of hourly precipitation from rain gauges and radar for a large-scale extreme rainfall event

NASA Astrophysics Data System (ADS)

Haberlandt, Uwe

2007-01-01

SummaryThe methods kriging with external drift (KED) and indicator kriging with external drift (IKED) are used for the spatial interpolation of hourly rainfall from rain gauges using additional information from radar, daily precipitation of a denser network, and elevation. The techniques are illustrated using data from the storm period of the 10th to the 13th of August 2002 that led to the extreme flood event in the Elbe river basin in Germany. Cross-validation is applied to compare the interpolation performance of the KED and IKED methods using different additional information with the univariate reference methods nearest neighbour (NN) or Thiessen polygons, inverse square distance weighting (IDW), ordinary kriging (OK) and ordinary indicator kriging (IK). Special attention is given to the analysis of the impact of the semivariogram estimation on the interpolation performance. Hourly and average semivariograms are inferred from daily, hourly and radar data considering either isotropic or anisotropic behaviour using automatic and manual fitting procedures. The multivariate methods KED and IKED clearly outperform the univariate ones with the most important additional information being radar, followed by precipitation from the daily network and elevation, which plays only a secondary role here. The best performance is achieved when all additional information are used simultaneously with KED. The indicator-based kriging methods provide, in some cases, smaller root mean square errors than the methods, which use the original data, but at the expense of a significant loss of variance. The impact of the semivariogram on interpolation performance is not very high. The best results are obtained using an automatic fitting procedure with isotropic variograms either from hourly or radar data.

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

Accuracy of Digital Impressions and Fitness of Single Crowns Based on Digital Impressions

PubMed Central

Yang, Xin; Lv, Pin; Liu, Yihong; Si, Wenjie; Feng, Hailan

2015-01-01

In this study, the accuracy (precision and trueness) of digital impressions and the fitness of single crowns manufactured based on digital impressions were evaluated. #14-17 epoxy resin dentitions were made, while full-crown preparations of extracted natural teeth were embedded at #16. (1) To assess precision, deviations among repeated scan models made by intraoral scanner TRIOS and MHT and model scanner D700 and inEos were calculated through best-fit algorithm and three-dimensional (3D) comparison. Root mean square (RMS) and color-coded difference images were offered. (2) To assess trueness, micro computed tomography (micro-CT) was used to get the reference model (REF). Deviations between REF and repeated scan models (from (1)) were calculated. (3) To assess fitness, single crowns were manufactured based on TRIOS, MHT, D700 and inEos scan models. The adhesive gaps were evaluated under stereomicroscope after cross-sectioned. Digital impressions showed lower precision and better trueness. Except for MHT, the means of RMS for precision were lower than 10 μm. Digital impressions showed better internal fitness. Fitness of single crowns based on digital impressions was up to clinical standard. Digital impressions could be an alternative method for single crowns manufacturing. PMID:28793417

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.

Surface Fitting Filtering of LIDAR Point Cloud with Waveform Information

NASA Astrophysics Data System (ADS)

Xing, S.; Li, P.; Xu, Q.; Wang, D.; Li, P.

2017-09-01

Full-waveform LiDAR is an active technology of photogrammetry and remote sensing. It provides more detailed information about objects along the path of a laser pulse than discrete-return topographic LiDAR. The point cloud and waveform information with high quality can be obtained by waveform decomposition, which could make contributions to accurate filtering. The surface fitting filtering method with waveform information is proposed to present such advantage. Firstly, discrete point cloud and waveform parameters are resolved by global convergent Levenberg Marquardt decomposition. Secondly, the ground seed points are selected, of which the abnormal ones are detected by waveform parameters and robust estimation. Thirdly, the terrain surface is fitted and the height difference threshold is determined in consideration of window size and mean square error. Finally, the points are classified gradually with the rising of window size. The filtering process is finished until window size is larger than threshold. The waveform data in urban, farmland and mountain areas from "WATER (Watershed Allied Telemetry Experimental Research)" are selected for experiments. Results prove that compared with traditional method, the accuracy of point cloud filtering is further improved and the proposed method has highly practical value.

Foveal Curvature and Asymmetry Assessed Using Optical Coherence Tomography.

PubMed

VanNasdale, Dean A; Eilerman, Amanda; Zimmerman, Aaron; Lai, Nicky; Ramsey, Keith; Sinnott, Loraine T

2017-06-01

The aims of this study were to use cross-sectional optical coherence tomography imaging and custom curve fitting software to evaluate and model the foveal curvature as a spherical surface and to compare the radius of curvature in the horizontal and vertical meridians and test the sensitivity of this technique to anticipated meridional differences. Six 30-degree foveal-centered radial optical coherence tomography cross-section scans were acquired in the right eye of 20 clinically normal subjects. Cross sections were manually segmented, and custom curve fitting software was used to determine foveal pit radius of curvature using the central 500, 1000, and 1500 μm of the foveal contour. Radius of curvature was compared across different fitting distances. Root mean square error was used to determine goodness of fit. The radius of curvature was compared between the horizontal and vertical meridians for each fitting distance. There radius of curvature was significantly different when comparing each of the three fitting distances (P < .01 for each comparison). The average radii of curvature were 970 μm (95% confidence interval [CI], 913 to 1028 μm), 1386 μm (95% CI, 1339 to 1439 μm), and 2121 μm (95% CI, 2066 to 2183) for the 500-, 1000-, and 1500-μm fitting distances, respectively. Root mean square error was also significantly different when comparing each fitting distance (P < .01 for each comparison). The average root mean square errors were 2.48 μm (95% CI, 2.41 to 2.53 μm), 6.22 μm (95% CI, 5.77 to 6.60 μm), and 13.82 μm (95% CI, 12.93 to 14.58 μm) for the 500-, 1000-, and 1500-μm fitting distances, respectively. The radius of curvature between the horizontal and vertical meridian radii was statistically different only in the 1000- and 1500-μm fitting distances (P < .01 for each), with the horizontal meridian being flatter than the vertical. The foveal contour can be modeled as a sphere with low curve fitting error over a limited distance and capable of detecting subtle foveal contour differences between meridians.

SU-F-T-408: On the Determination of Equivalent Squares for Rectangular Small MV Photon Fields

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

Sauer, OA; Wegener, S; Exner, F

Purpose: It is common practice to tabulate dosimetric data like output factors, scatter factors and detector signal correction factors for a set of square fields. In order to get the data for an arbitrary field, it is mapped to an equivalent square, having the same scatter as the field of interest. For rectangular fields both, tabulated data and empiric formula exist. We tested the applicability of such rules for very small fields. Methods: Using the Monte-Carlo method (EGSnrc-doseRZ), the dose to a point in 10cm depth in water was calculated for cylindrical impinging fluence distributions. Radii were from 0.5mm tomore » 11.5mm with 1mm thickness of the rings. Different photon energies were investigated. With these data a matrix was constructed assigning the amount of dose to the field center to each matrix element. By summing up the elements belonging to a certain field, the dose for an arbitrary point in 10cm depth could be determined. This was done for rectangles up to 21mm side length. Comparing the dose to square field results, equivalent squares could be assigned. The results were compared to using the geometrical mean and the 4Xperimeter/area rule. Results: For side length differences less than 2mm, the difference between all methods was in general less than 0.2mm. For more elongated fields, relevant differences of more than 1mm and up to 3mm for the fields investigated occurred. The mean square side length calculated from both empiric formulas fitted much better, deviating hardly more than 1mm and for the very elongated fields only. Conclusion: For small rectangular photon fields, deviating only moderately from square both investigated empiric methods are sufficiently accurate. As the deviations often differ regarding their sign, using the mean improves the accuracy and the useable elongation range. For ratios larger than 2, Monte-Carlo generated data are recommended. SW is funded by Deutsche Forschungsgemeinschaft (SA481/10-1)« less

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.

A quality control method for intensity-modulated radiation therapy planning based on generalized equivalent uniform dose.

PubMed

Pang, Haowen; Sun, Xiaoyang; Yang, Bo; Wu, Jingbo

2018-05-01

To ensure good quality intensity-modulated radiation therapy (IMRT) planning, we proposed the use of a quality control method based on generalized equivalent uniform dose (gEUD) that predicts absorbed radiation doses in organs at risk (OAR). We conducted a retrospective analysis of patients who underwent IMRT for the treatment of cervical carcinoma, nasopharyngeal carcinoma (NPC), or non-small cell lung cancer (NSCLC). IMRT plans were randomly divided into data acquisition and data verification groups. OAR in the data acquisition group for cervical carcinoma and NPC were further classified as sub-organs at risk (sOAR). The normalized volume of sOAR and normalized gEUD (a = 1) were analyzed using multiple linear regression to establish a fitting formula. For NSCLC, the normalized intersection volume of the planning target volume (PTV) and lung, the maximum diameter of the PTV (left-right, anterior-posterior, and superior-inferior), and the normalized gEUD (a = 1) were analyzed using multiple linear regression to establish a fitting formula for the lung gEUD (a = 1). The r-squared and P values indicated that the fitting formula was a good fit. In the data verification group, IMRT plans verified the accuracy of the fitting formula, and compared the gEUD (a = 1) for each OAR between the subjective method and the gEUD-based method. In conclusion, the gEUD-based method can be used effectively for quality control and can reduce the influence of subjective factors on IMRT planning optimization. © 2018 The Authors. Journal of Applied Clinical Medical Physics published by Wiley Periodicals, Inc. on behalf of American Association of Physicists in Medicine.

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.

Comparability of item quality indices from sparse data matrices with random and non-random missing data patterns.

PubMed

Wolfe, Edward W; McGill, Michael T

2011-01-01

This article summarizes a simulation study of the performance of five item quality indicators (the weighted and unweighted versions of the mean square and standardized mean square fit indices and the point-measure correlation) under conditions of relatively high and low amounts of missing data under both random and conditional patterns of missing data for testing contexts such as those encountered in operational administrations of a computerized adaptive certification or licensure examination. The results suggest that weighted fit indices, particularly the standardized mean square index, and the point-measure correlation provide the most consistent information between random and conditional missing data patterns and that these indices perform more comparably for items near the passing score than for items with extreme difficulty values.

Covariance Structure Model Fit Testing under Missing Data: An Application of the Supplemented EM Algorithm

ERIC Educational Resources Information Center

Cai, Li; Lee, Taehun

2009-01-01

We apply the Supplemented EM algorithm (Meng & Rubin, 1991) to address a chronic problem with the "two-stage" fitting of covariance structure models in the presence of ignorable missing data: the lack of an asymptotically chi-square distributed goodness-of-fit statistic. We show that the Supplemented EM algorithm provides a…

Residuals and the Residual-Based Statistic for Testing Goodness of Fit of Structural Equation Models

ERIC Educational Resources Information Center

Foldnes, Njal; Foss, Tron; Olsson, Ulf Henning

2012-01-01

The residuals obtained from fitting a structural equation model are crucial ingredients in obtaining chi-square goodness-of-fit statistics for the model. The authors present a didactic discussion of the residuals, obtaining a geometrical interpretation by recognizing the residuals as the result of oblique projections. This sheds light on the…

Does Breast Cancer Drive the Building of Survival Probability Models among States? An Assessment of Goodness of Fit for Patient Data from SEER Registries

PubMed

Khan, Hafiz; Saxena, Anshul; Perisetti, Abhilash; Rafiq, Aamrin; Gabbidon, Kemesha; Mende, Sarah; Lyuksyutova, Maria; Quesada, Kandi; Blakely, Summre; Torres, Tiffany; Afesse, Mahlet

2016-12-01

Background: Breast cancer is a worldwide public health concern and is the most prevalent type of cancer in women in the United States. This study concerned the best fit of statistical probability models on the basis of survival times for nine state cancer registries: California, Connecticut, Georgia, Hawaii, Iowa, Michigan, New Mexico, Utah, and Washington. Materials and Methods: A probability random sampling method was applied to select and extract records of 2,000 breast cancer patients from the Surveillance Epidemiology and End Results (SEER) database for each of the nine state cancer registries used in this study. EasyFit software was utilized to identify the best probability models by using goodness of fit tests, and to estimate parameters for various statistical probability distributions that fit survival data. Results: Statistical analysis for the summary of statistics is reported for each of the states for the years 1973 to 2012. Kolmogorov-Smirnov, Anderson-Darling, and Chi-squared goodness of fit test values were used for survival data, the highest values of goodness of fit statistics being considered indicative of the best fit survival model for each state. Conclusions: It was found that California, Connecticut, Georgia, Iowa, New Mexico, and Washington followed the Burr probability distribution, while the Dagum probability distribution gave the best fit for Michigan and Utah, and Hawaii followed the Gamma probability distribution. These findings highlight differences between states through selected sociodemographic variables and also demonstrate probability modeling differences in breast cancer survival times. The results of this study can be used to guide healthcare providers and researchers for further investigations into social and environmental factors in order to reduce the occurrence of and mortality due to breast cancer. Creative Commons Attribution License

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.

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.

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.

Comparison of Methods for Estimating Low Flow Characteristics of Streams

USGS Publications Warehouse

Tasker, Gary D.

1987-01-01

Four methods for estimating the 7-day, 10-year and 7-day, 20-year low flows for streams are compared by the bootstrap method. The bootstrap method is a Monte Carlo technique in which random samples are drawn from an unspecified sampling distribution defined from observed data. The nonparametric nature of the bootstrap makes it suitable for comparing methods based on a flow series for which the true distribution is unknown. Results show that the two methods based on hypothetical distribution (Log-Pearson III and Weibull) had lower mean square errors than did the G. E. P. Box-D. R. Cox transformation method or the Log-W. C. Boughton method which is based on a fit of plotting positions.

Calibration of the COBE FIRAS instrument

NASA Technical Reports Server (NTRS)

Fixsen, D. J.; Cheng, E. S.; Cottingham, D. A.; Eplee, R. E., Jr.; Hewagama, T.; Isaacman, R. B.; Jensen, K. A.; Mather, J. C.; Massa, D. L.; Meyer, S. S.

1994-01-01

The Far-Infrared Absolute Spectrophotometer (FIRAS) instrument on the Cosmic Background Explorer (COBE) satellite was designed to accurately measure the spectrum of the cosmic microwave background radiation (CMBR) in the frequency range 1-95/cm with an angular resolution of 7 deg. We describe the calibration of this instrument, including the method of obtaining calibration data, reduction of data, the instrument model, fitting the model to the calibration data, and application of the resulting model solution to sky observations. The instrument model fits well for calibration data that resemble sky condition. The method of propagating detector noise through the calibration process to yield a covariance matrix of the calibrated sky data is described. The final uncertainties are variable both in frequency and position, but for a typical calibrated sky 2.6 deg square pixel and 0.7/cm spectral element the random detector noise limit is of order of a few times 10(exp -7) ergs/sq cm/s/sr cm for 2-20/cm, and the difference between the sky and the best-fit cosmic blackbody can be measured with a gain uncertainty of less than 3%.

Pearson-type goodness-of-fit test with bootstrap maximum likelihood estimation.

PubMed

Yin, Guosheng; Ma, Yanyuan

2013-01-01

The Pearson test statistic is constructed by partitioning the data into bins and computing the difference between the observed and expected counts in these bins. If the maximum likelihood estimator (MLE) of the original data is used, the statistic generally does not follow a chi-squared distribution or any explicit distribution. We propose a bootstrap-based modification of the Pearson test statistic to recover the chi-squared distribution. We compute the observed and expected counts in the partitioned bins by using the MLE obtained from a bootstrap sample. This bootstrap-sample MLE adjusts exactly the right amount of randomness to the test statistic, and recovers the chi-squared distribution. The bootstrap chi-squared test is easy to implement, as it only requires fitting exactly the same model to the bootstrap data to obtain the corresponding MLE, and then constructs the bin counts based on the original data. We examine the test size and power of the new model diagnostic procedure using simulation studies and illustrate it with a real data set.

Non-overlap subaperture interferometric testing for large optics

NASA Astrophysics Data System (ADS)

Wu, Xin; Yu, Yingjie; Zeng, Wenhan; Qi, Te; Chen, Mingyi; Jiang, Xiangqian

2017-08-01

It has been shown that the number of subapertures and the amount of overlap has a significant influence on the stitching accuracy. In this paper, a non-overlap subaperture interferometric testing method (NOSAI) is proposed to inspect large optical components. This method would greatly reduce the number of subapertures and the influence of environmental interference while maintaining the accuracy of reconstruction. A general subaperture distribution pattern of NOSAI is also proposed for the large rectangle surface. The square Zernike polynomial is employed to fit such wavefront. The effect of the minimum fitting terms on the accuracy of NOSAI and the sensitivities of NOSAI to subaperture's alignment error, power systematic error, and random noise are discussed. Experimental results validate the feasibility and accuracy of the proposed NOSAI in comparison with wavefront obtained by a large aperture interferometer and stitching surface by multi-aperture overlap-scanning technique (MAOST).

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

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

Development and Validation of PRISM: A Survey Tool to Identify Diabetes Self-Management Barriers

PubMed Central

Cox, Elizabeth D.; Fritz, Katie A.; Hansen, Kristofer W.; Brown, Roger L.; Rajamanickam, Victoria; Wiles, Kaelyn E.; Fate, Bryan H.; Young, Henry N.; Moreno, Megan A.

2014-01-01

Aims Although most children with type 1 diabetes don’t achieve optimal glycemic control, no systematic method exists to identify and address self-management barriers. This study develops and validates PRISM (Problem Recognition in Illness Self-Management), a survey-based tool for efficiently identifying self-management barriers experienced by children/adolescents with diabetes and their parents. Methods Adolescents 13 years and older and parents of children 8 years and older visiting for routine diabetes management (n=425) were surveyed about self-management barriers. HbA1c was abstracted from the electronic health record. To develop PRISM, exploratory and confirmatory factor analyses were used. To assess validity, the association of PRISM scores with HbA1c was examined using linear regression. Results Factor analyses of adolescent and parent data yielded well-fitting models of self-management barriers, reflecting the following domains: 1) Understanding and Organizing Care, 2) Regimen Pain and Bother, 3) Denial of Disease and Consequences, and 4) Healthcare Team, 5) Family, or 6) Peer Interactions. All models exhibited good fit, with X2 ratios<2.21, root mean square errors of approximation<0.09, Confirmatory Fit Indices and Tucker-Lewis Indices both >0.92, and weighted root mean square residuals<1.71. Greater PRISM barrier scores were significantly associated with higher HbA1cs. Conclusions Our findings suggest at least six different domains exist within self-management barriers, nearly all of which are significantly related to HbA1c. PRISM could be used in clinical practice to identify each child and family’s unique self-management barriers, allowing existing self-management resources to be tailored to the family’s barriers, ultimately improving effectiveness of such services. PMID:24552680

Charactering baseline shift with 4th polynomial function for portable biomedical near-infrared spectroscopy device

NASA Astrophysics Data System (ADS)

Zhao, Ke; Ji, Yaoyao; Pan, Boan; Li, Ting

2018-02-01

The continuous-wave Near-infrared spectroscopy (NIRS) devices have been highlighted for its clinical and health care applications in noninvasive hemodynamic measurements. The baseline shift of the deviation measurement attracts lots of attentions for its clinical importance. Nonetheless current published methods have low reliability or high variability. In this study, we found a perfect polynomial fitting function for baseline removal, using NIRS. Unlike previous studies on baseline correction for near-infrared spectroscopy evaluation of non-hemodynamic particles, we focused on baseline fitting and corresponding correction method for NIRS and found that the polynomial fitting function at 4th order is greater than the function at 2nd order reported in previous research. Through experimental tests of hemodynamic parameters of the solid phantom, we compared the fitting effect between the 4th order polynomial and the 2nd order polynomial, by recording and analyzing the R values and the SSE (the sum of squares due to error) values. The R values of the 4th order polynomial function fitting are all higher than 0.99, which are significantly higher than the corresponding ones of 2nd order, while the SSE values of the 4th order are significantly smaller than the corresponding ones of the 2nd order. By using the high-reliable and low-variable 4th order polynomial fitting function, we are able to remove the baseline online to obtain more accurate NIRS measurements.

Deconvolution of Stark broadened spectra for multi-point density measurements in a flow Z-pinch

DOE PAGES

Vogman, G. V.; Shumlak, U.

2011-10-13

Stark broadened emission spectra, once separated from other broadening effects, provide a convenient non-perturbing means of making plasma density measurements. A deconvolution technique has been developed to measure plasma densities in the ZaP flow Z-pinch experiment. The ZaP experiment uses sheared flow to mitigate MHD instabilities. The pinches exhibit Stark broadened emission spectra, which are captured at 20 locations using a multi-chord spectroscopic system. Spectra that are time- and chord-integrated are well approximated by a Voigt function. The proposed method simultaneously resolves plasma electron density and ion temperature by deconvolving the spectral Voigt profile into constituent functions: a Gaussian functionmore » associated with instrument effects and Doppler broadening by temperature; and a Lorentzian function associated with Stark broadening by electron density. The method uses analytic Fourier transforms of the constituent functions to fit the Voigt profile in the Fourier domain. The method is discussed and compared to a basic least-squares fit. The Fourier transform fitting routine requires fewer fitting parameters and shows promise in being less susceptible to instrumental noise and to contamination from neighboring spectral lines. The method is evaluated and tested using simulated lines and is applied to experimental data for the 229.69 nm C III line from multiple chords to determine plasma density and temperature across the diameter of the pinch. As a result, these measurements are used to gain a better understanding of Z-pinch equilibria.« less

Deconvolution of Stark broadened spectra for multi-point density measurements in a flow Z-pinch

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

Vogman, G. V.; Shumlak, U.

2011-10-15

Stark broadened emission spectra, once separated from other broadening effects, provide a convenient non-perturbing means of making plasma density measurements. A deconvolution technique has been developed to measure plasma densities in the ZaP flow Z-pinch experiment. The ZaP experiment uses sheared flow to mitigate MHD instabilities. The pinches exhibit Stark broadened emission spectra, which are captured at 20 locations using a multi-chord spectroscopic system. Spectra that are time- and chord-integrated are well approximated by a Voigt function. The proposed method simultaneously resolves plasma electron density and ion temperature by deconvolving the spectral Voigt profile into constituent functions: a Gaussian functionmore » associated with instrument effects and Doppler broadening by temperature; and a Lorentzian function associated with Stark broadening by electron density. The method uses analytic Fourier transforms of the constituent functions to fit the Voigt profile in the Fourier domain. The method is discussed and compared to a basic least-squares fit. The Fourier transform fitting routine requires fewer fitting parameters and shows promise in being less susceptible to instrumental noise and to contamination from neighboring spectral lines. The method is evaluated and tested using simulated lines and is applied to experimental data for the 229.69 nm C III line from multiple chords to determine plasma density and temperature across the diameter of the pinch. These measurements are used to gain a better understanding of Z-pinch equilibria.« less

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.

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.

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.

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.

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

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.

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.

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.

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.

Health Promotion Behavior of Chinese International Students in Korea Including Acculturation Factors: A Structural Equation Model.

PubMed

Kim, Sun Jung; Yoo, Il Young

2016-03-01

The purpose of this study was to explain the health promotion behavior of Chinese international students in Korea using a structural equation model including acculturation factors. A survey using self-administered questionnaires was employed. Data were collected from 272 Chinese students who have resided in Korea for longer than 6 months. The data were analyzed using structural equation modeling. The p value of final model is .31. The fitness parameters of the final model such as goodness of fit index, adjusted goodness of fit index, normed fit index, non-normed fit index, and comparative fit index were more than .95. Root mean square of residual and root mean square error of approximation also met the criteria. Self-esteem, perceived health status, acculturative stress and acculturation level had direct effects on health promotion behavior of the participants and the model explained 30.0% of variance. The Chinese students in Korea with higher self-esteem, perceived health status, acculturation level, and lower acculturative stress reported higher health promotion behavior. The findings can be applied to develop health promotion strategies for this population. Copyright © 2016. Published by Elsevier B.V.

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

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.

Evaluation of the Edinburgh Post Natal Depression Scale using Rasch analysis

PubMed Central

Pallant, Julie F; Miller, Renée L; Tennant, Alan

2006-01-01

Background The Edinburgh Postnatal Depression Scale (EPDS) is a 10 item self-rating post-natal depression scale which has seen widespread use in epidemiological and clinical studies. Concern has been raised over the validity of the EPDS as a single summed scale, with suggestions that it measures two separate aspects, one of depressive feelings, the other of anxiety. Methods As part of a larger cross-sectional study conducted in Melbourne, Australia, a community sample (324 women, ranging in age from 18 to 44 years: mean = 32 yrs, SD = 4.6), was obtained by inviting primiparous women to participate voluntarily in this study. Data from the EPDS were fitted to the Rasch measurement model and tested for appropriate category ordering, for item bias through Differential Item Functioning (DIF) analysis, and for unidimensionality through tests of the assumption of local independence. Results Rasch analysis of the data from the ten item scale initially demonstrated a lack of fit to the model with a significant Item-Trait Interaction total chi-square (chi Square = 82.8, df = 40; p < .001). Removal of two items (items 7 and 8) resulted in a non-significant Item-Trait Interaction total chi-square with a residual mean value for items of -0.467 with a standard deviation of 0.850, showing fit to the model. No DIF existed in the final 8-item scale (EPDS-8) and all items showed fit to model expectations. Principal Components Analysis of the residuals supported the local independence assumption, and unidimensionality of the revised EPDS-8 scale. Revised cut points were identified for EPDS-8 to maintain the case identification of the original scale. Conclusion The results of this study suggest that EPDS, in its original 10 item form, is not a viable scale for the unidimensional measurement of depression. Rasch analysis suggests that a revised eight item version (EPDS-8) would provide a more psychometrically robust scale. The revised cut points of 7/8 and 9/10 for the EPDS-8 show high levels of agreement with the original case identification for the EPDS-10. PMID:16768803

A direct potential fitting RKR method: Semiclassical vs. quantal comparisons

NASA Astrophysics Data System (ADS)

Tellinghuisen, Joel

2016-12-01

Quantal and semiclassical (SC) eigenvalues are compared for three diatomic molecular potential curves: the X state of CO, the X state of Rb2, and the A state of I2. The comparisons show higher levels of agreement than generally recognized, when the SC calculations incorporate a quantum defect correction to the vibrational quantum number, in keeping with the Kaiser modification. One particular aspect of this is better agreement between quantal and SC estimates of the zero-point vibrational energy, supporting the need for the Y00 correction in this context. The pursuit of a direct-potential-fitting (DPF) RKR method is motivated by the notion that some of the limitations of RKR potentials may be innate, from their generation by an exact inversion of approximate quantities: the vibrational energy Gυ and rotational constant Bυ from least-squares analysis of spectroscopic data. In contrast, the DPF RKR method resembles the quantal DPF methods now increasingly used to analyze diatomic spectral data, but with the eigenvalues obtained from SC phase integrals. Application of this method to the analysis of 9500 assigned lines in the I2A ← X spectrum fails to alter the quantal-SC disparities found for the A-state RKR curve from a previous analysis. On the other hand, the SC method can be much faster than the quantal method in exploratory work with different potential functions, where it is convenient to use finite-difference methods to evaluate the partial derivatives required in nonlinear fitting.

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)

Psychometric Properties of the Heart Disease Knowledge Scale: Evidence from Item and Confirmatory Factor Analyses

PubMed Central

Lim, Bee Chiu; Kueh, Yee Cheng; Arifin, Wan Nor; Ng, Kok Huan

2016-01-01

Background Heart disease knowledge is an important concept for health education, yet there is lack of evidence on proper validated instruments used to measure levels of heart disease knowledge in the Malaysian context. Methods A cross-sectional, survey design was conducted to examine the psychometric properties of the adapted English version of the Heart Disease Knowledge Questionnaire (HDKQ). Using proportionate cluster sampling, 788 undergraduate students at Universiti Sains Malaysia, Malaysia, were recruited and completed the HDKQ. Item analysis and confirmatory factor analysis (CFA) were used for the psychometric evaluation. Construct validity of the measurement model was included. Results Most of the students were Malay (48%), female (71%), and from the field of science (51%). An acceptable range was obtained with respect to both the difficulty and discrimination indices in the item analysis results. The difficulty index ranged from 0.12–0.91 and a discrimination index of ≥ 0.20 were reported for the final retained 23 items. The final CFA model showed an adequate fit to the data, yielding a 23-item, one-factor model [weighted least squares mean and variance adjusted scaled chi-square difference = 1.22, degrees of freedom = 2, P-value = 0.544, the root mean square error of approximation = 0.03 (90% confidence interval = 0.03, 0.04); close-fit P-value = > 0.950]. Conclusion Adequate psychometric values were obtained for Malaysian undergraduate university students using the 23-item, one-factor model of the adapted HDKQ. PMID:27660543

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.)

Automatic Detection and Recognition of Craters Based on the Spectral Features of Lunar Rocks and Minerals

NASA Astrophysics Data System (ADS)

Ye, L.; Xu, X.; Luan, D.; Jiang, W.; Kang, Z.

2017-07-01

Crater-detection approaches can be divided into four categories: manual recognition, shape-profile fitting algorithms, machine-learning methods and geological information-based analysis using terrain and spectral data. The mainstream method is Shape-profile fitting algorithms. Many scholars throughout the world use the illumination gradient information to fit standard circles by least square method. Although this method has achieved good results, it is difficult to identify the craters with poor "visibility", complex structure and composition. Moreover, the accuracy of recognition is difficult to be improved due to the multiple solutions and noise interference. Aiming at the problem, we propose a method for the automatic extraction of impact craters based on spectral characteristics of the moon rocks and minerals: 1) Under the condition of sunlight, the impact craters are extracted from MI by condition matching and the positions as well as diameters of the craters are obtained. 2) Regolith is spilled while lunar is impacted and one of the elements of lunar regolith is iron. Therefore, incorrectly extracted impact craters can be removed by judging whether the crater contains "non iron" element. 3) Craters which are extracted correctly, are divided into two types: simple type and complex type according to their diameters. 4) Get the information of titanium and match the titanium distribution of the complex craters with normal distribution curve, then calculate the goodness of fit and set the threshold. The complex craters can be divided into two types: normal distribution curve type of titanium and non normal distribution curve type of titanium. We validated our proposed method with MI acquired by SELENE. Experimental results demonstrate that the proposed method has good performance in the test area.

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.

Development and assessment of the Quality of Life in Childhood Epilepsy Questionnaire (QOLCE-16).

PubMed

Goodwin, Shane W; Ferro, Mark A; Speechley, Kathy N

2018-03-01

The aim of this study was to develop and validate a brief version of the Quality of Life in Childhood Epilepsy Questionnaire (QOLCE). A secondary aim was to compare the results described in previously published studies using the QOLCE-55 with those obtained using the new brief version. Data come from 373 children involved in the Health-related Quality of Life in Children with Epilepsy Study, a multicenter prospective cohort study. Item response theory (IRT) methods were used to assess dimensionality and item properties and to guide the selection of items. Replication of results using the brief measure was conducted with multiple regression, multinomial regression, and latent mixture modeling techniques. IRT methods identified a bi-factor graded response model that best fits the data. Thirty-nine items were removed, resulting in a 16-item QOLCE (QOLCE-16) with an equal number of items in all 4 domains of functioning (Cognitive, Emotional, Social, and Physical). Model fit was excellent: Comparative Fit Index = 0.99; Tucker-Lewis Index = 0.99; root mean square error of approximation = 0.052 (90% confidence interval [CI] 0.041-0.064); weighted root mean square = 0.76. Results that were reported previously using the QOLCE-55 and QOLCE-76 were comparable to those generated using the QOLCE-16. The QOLCE-16 is a multidimensional measure of health-related quality of life (HRQoL) with good psychometric properties and a short-estimated completion time. It is notable that the items were calibrated using multidimensional IRT methods to create a measure that conforms to conventional definitions of HRQoL. The QOLCE-16 is an appropriate measure for both clinicians and researchers wanting to record HRQoL information in children with epilepsy. Wiley Periodicals, Inc. © 2018 International League Against Epilepsy.

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.

Phase-Based Adaptive Estimation of Magnitude-Squared Coherence Between Turbofan Internal Sensors and Far-Field Microphone Signals

NASA Technical Reports Server (NTRS)

Miles, Jeffrey Hilton

2015-01-01

A cross-power spectrum phase based adaptive technique is discussed which iteratively determines the time delay between two digitized signals that are coherent. The adaptive delay algorithm belongs to a class of algorithms that identifies a minimum of a pattern matching function. The algorithm uses a gradient technique to find the value of the adaptive delay that minimizes a cost function based in part on the slope of a linear function that fits the measured cross power spectrum phase and in part on the standard error of the curve fit. This procedure is applied to data from a Honeywell TECH977 static-engine test. Data was obtained using a combustor probe, two turbine exit probes, and far-field microphones. Signals from this instrumentation are used estimate the post-combustion residence time in the combustor. Comparison with previous studies of the post-combustion residence time validates this approach. In addition, the procedure removes the bias due to misalignment of signals in the calculation of coherence which is a first step in applying array processing methods to the magnitude squared coherence data. The procedure also provides an estimate of the cross-spectrum phase-offset.

FIREFLY (Fitting IteRativEly For Likelihood analYsis): a full spectral fitting code

NASA Astrophysics Data System (ADS)

Wilkinson, David M.; Maraston, Claudia; Goddard, Daniel; Thomas, Daniel; Parikh, Taniya

2017-12-01

We present a new spectral fitting code, FIREFLY, for deriving the stellar population properties of stellar systems. FIREFLY is a chi-squared minimization fitting code that fits combinations of single-burst stellar population models to spectroscopic data, following an iterative best-fitting process controlled by the Bayesian information criterion. No priors are applied, rather all solutions within a statistical cut are retained with their weight. Moreover, no additive or multiplicative polynomials are employed to adjust the spectral shape. This fitting freedom is envisaged in order to map out the effect of intrinsic spectral energy distribution degeneracies, such as age, metallicity, dust reddening on galaxy properties, and to quantify the effect of varying input model components on such properties. Dust attenuation is included using a new procedure, which was tested on Integral Field Spectroscopic data in a previous paper. The fitting method is extensively tested with a comprehensive suite of mock galaxies, real galaxies from the Sloan Digital Sky Survey and Milky Way globular clusters. We also assess the robustness of the derived properties as a function of signal-to-noise ratio (S/N) and adopted wavelength range. We show that FIREFLY is able to recover age, metallicity, stellar mass, and even the star formation history remarkably well down to an S/N ∼ 5, for moderately dusty systems. Code and results are publicly available.1

Establishment method of a mixture model and its practical application for transmission gears in an engineering vehicle

NASA Astrophysics Data System (ADS)

Wang, Jixin; Wang, Zhenyu; Yu, Xiangjun; Yao, Mingyao; Yao, Zongwei; Zhang, Erping

2012-09-01

Highly versatile machines, such as wheel loaders, forklifts, and mining haulers, are subject to many kinds of working conditions, as well as indefinite factors that lead to the complexity of the load. The load probability distribution function (PDF) of transmission gears has many distributions centers; thus, its PDF cannot be well represented by just a single-peak function. For the purpose of representing the distribution characteristics of the complicated phenomenon accurately, this paper proposes a novel method to establish a mixture model. Based on linear regression models and correlation coefficients, the proposed method can be used to automatically select the best-fitting function in the mixture model. Coefficient of determination, the mean square error, and the maximum deviation are chosen and then used as judging criteria to describe the fitting precision between the theoretical distribution and the corresponding histogram of the available load data. The applicability of this modeling method is illustrated by the field testing data of a wheel loader. Meanwhile, the load spectra based on the mixture model are compiled. The comparison results show that the mixture model is more suitable for the description of the load-distribution characteristics. The proposed research improves the flexibility and intelligence of modeling, reduces the statistical error and enhances the fitting accuracy, and the load spectra complied by this method can better reflect the actual load characteristic of the gear component.

Polyomino Problems to Confuse Computers

ERIC Educational Resources Information Center

Coffin, Stewart

2009-01-01

Computers are very good at solving certain types combinatorial problems, such as fitting sets of polyomino pieces into square or rectangular trays of a given size. However, most puzzle-solving programs now in use assume orthogonal arrangements. When one departs from the usual square grid layout, complications arise. The author--using a computer,…

Evaluating flow cytometer performance with weighted quadratic least squares analysis of LED and multi-level bead data

PubMed Central

Parks, David R.; Khettabi, Faysal El; Chase, Eric; Hoffman, Robert A.; Perfetto, Stephen P.; Spidlen, Josef; Wood, James C.S.; Moore, Wayne A.; Brinkman, Ryan R.

2017-01-01

We developed a fully automated procedure for analyzing data from LED pulses and multi-level bead sets to evaluate backgrounds and photoelectron scales of cytometer fluorescence channels. The method improves on previous formulations by fitting a full quadratic model with appropriate weighting and by providing standard errors and peak residuals as well as the fitted parameters themselves. Here we describe the details of the methods and procedures involved and present a set of illustrations and test cases that demonstrate the consistency and reliability of the results. The automated analysis and fitting procedure is generally quite successful in providing good estimates of the Spe (statistical photoelectron) scales and backgrounds for all of the fluorescence channels on instruments with good linearity. The precision of the results obtained from LED data is almost always better than for multi-level bead data, but the bead procedure is easy to carry out and provides results good enough for most purposes. Including standard errors on the fitted parameters is important for understanding the uncertainty in the values of interest. The weighted residuals give information about how well the data fits the model, and particularly high residuals indicate bad data points. Known photoelectron scales and measurement channel backgrounds make it possible to estimate the precision of measurements at different signal levels and the effects of compensated spectral overlap on measurement quality. Combining this information with measurements of standard samples carrying dyes of biological interest, we can make accurate comparisons of dye sensitivity among different instruments. Our method is freely available through the R/Bioconductor package flowQB. PMID:28160404

Understanding Scaling Relations in Fracture and Mechanical Deformation of Single Crystal and Polycrystalline Silicon by Performing Atomistic Simulations at Mesoscale

DTIC Science & Technology

2009-07-16

0.25 0.26 -0.85 1 SSR SSE R SSTO SSTO = = − 2 2 ˆ( ) : Regression sum of square, ˆwhere : mean value, : value from the fitted line ˆ...Error sum of square : Total sum of square i i i i SSR Y Y Y Y SSE Y Y SSTO SSE SSR = − = − = + ∑ ∑ Statistical analysis: Coefficient of correlation

Geostatistical methods in evaluating spatial variability of groundwater quality in Al-Kharj Region, Saudi Arabia

NASA Astrophysics Data System (ADS)

Al-Omran, Abdulrasoul M.; Aly, Anwar A.; Al-Wabel, Mohammad I.; Al-Shayaa, Mohammad S.; Sallam, Abdulazeam S.; Nadeem, Mahmoud E.

2017-11-01

The analyses of 180 groundwater samples of Al-Kharj, Saudi Arabia, recorded that most groundwaters are unsuitable for drinking uses due to high salinity; however, they can be used for irrigation with some restriction. The electric conductivity of studied groundwater ranged between 1.05 and 10.15 dS m-1 with an average of 3.0 dS m-1. Nitrate was also found in high concentration in some groundwater. Piper diagrams revealed that the majority of water samples are magnesium-calcium/sulfate-chloride water type. The Gibbs's diagram revealed that the chemical weathering of rock-forming minerals and evaporation are influencing the groundwater chemistry. A kriging method was used for predicting spatial distribution of salinity (EC dS m-1) and NO3 - (mg L-1) in Al-Kharj's groundwater using data of 180 different locations. After normalization of data, variogram was drawn, for selecting suitable model for fitness on experimental variogram, less residual sum of squares value was used. Then cross-validation and root mean square error were used to select the best method for interpolation. The kriging method was found suitable methods for groundwater interpolation and management using either GS+ or ArcGIS.

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.

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.)

Comparison of athletic training professional preparation to the prevalence of injury occurrence in the collegiate setting

NASA Astrophysics Data System (ADS)

Westerman, Beverly Jean

1999-10-01

This study investigated the relationship between the frequency of injuries that occur to certain body areas in National Collegiate Athletic Association (NCAA) athletes and the percentage of time teaching about the same subject areas in Athletic Training Education Programs (ATEP). Directors of Commission of Accreditation of Allied Health Education Programs (CAAHEP) accredited and National Athletic Trainers' Association (NATA) approved programs were surveyed. Randomly selected ATEP directors were interviewed by telephone to collect information on estimated teaching time, the strengths and weaknesses of their programs, and preferred teaching methods. Data were collected from the NCAA Injury Surveillance System to calculate the frequency of injury. Chi-square 'goodness-of-fit' tests were used to determine if a 'good fit' existed between injury frequency and teaching time in two categories: general body areas (head and face, upper extremity, lower extremity, spine, and abdomen and thorax) and specific body areas (head, face, upper arm and shoulder, elbow and forearm, wrist and hand, hip and pelvis, thigh, knee, lower leg, ankle and foot, cervical spine, thoracic spine, lumbar spine, abdomen, and thorax). Standardized residuals were used to assist in determining the location of statistical significance within the same two categories. The chi-square values calculated for both the general and specific body areas were greater than the critical value set at a significance level of .05 with 4 and 14 degrees of freedom respectively. Therefore, it was found that a 'good fit' does not exist between injury frequency and teaching time. The standardized residuals were calculated for each variable within the categories. One out of five general body areas and 10 out of 15 specific body areas were less than 2.00 in absolute value and were found not to contribute to the high chi-square value. Although the chi-square values showed a lack of fit between injury frequency and teaching time in the general and specific body areas, the standardized residuals indicated a relationship exists between some variables (body areas) within each category. In other words, the percentage of teaching time may correspond with injury frequency in some general and specific body areas. The responses from the program directors indicated they thought their academic programs were spending the appropriate amount of time teaching about the general and specific body areas. However, the percentages of teaching time reported for each of the body areas varied greatly among the responders. Further study is indicated to examine the relationship between teaching time/content and injury frequency.

Confirmatory factor analysis of the female sexual function index.

PubMed

Opperman, Emily A; Benson, Lindsay E; Milhausen, Robin R

2013-01-01

The Female Sexual Functioning Index (Rosen et al., 2000 ) was designed to assess the key dimensions of female sexual functioning using six domains: desire, arousal, lubrication, orgasm, satisfaction, and pain. A full-scale score was proposed to represent women's overall sexual function. The fifth revision to the Diagnostic and Statistical Manual (DSM) is currently underway and includes a proposal to combine desire and arousal problems. The objective of this article was to evaluate and compare four models of the Female Sexual Functioning Index: (a) single-factor model, (b) six-factor model, (c) second-order factor model, and (4) five-factor model combining the desire and arousal subscales. Cross-sectional and observational data from 85 women were used to conduct a confirmatory factor analysis on the Female Sexual Functioning Index. Local and global goodness-of-fit measures, the chi-square test of differences, squared multiple correlations, and regression weights were used. The single-factor model fit was not acceptable. The original six-factor model was confirmed, and good model fit was found for the second-order and five-factor models. Delta chi-square tests of differences supported best fit for the six-factor model validating usage of the six domains. However, when revisions are made to the DSM-5, the Female Sexual Functioning Index can adapt to reflect these changes and remain a valid assessment tool for women's sexual functioning, as the five-factor structure was also supported.

Distributions of the Kullback-Leibler divergence with applications.

PubMed

Belov, Dmitry I; Armstrong, Ronald D

2011-05-01

The Kullback-Leibler divergence (KLD) is a widely used method for measuring the fit of two distributions. In general, the distribution of the KLD is unknown. Under reasonable assumptions, common in psychometrics, the distribution of the KLD is shown to be asymptotically distributed as a scaled (non-central) chi-square with one degree of freedom or a scaled (doubly non-central) F. Applications of the KLD for detecting heterogeneous response data are discussed with particular emphasis on test security. © The British Psychological Society.

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.

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.

Closed-form solution for static pull-in voltage of electrostatically actuated clamped-clamped micro/nano beams under the effect of fringing field and van der Waals force

NASA Astrophysics Data System (ADS)

Bhojawala, V. M.; Vakharia, D. P.

2017-12-01

This investigation provides an accurate prediction of static pull-in voltage for clamped-clamped micro/nano beams based on distributed model. The Euler-Bernoulli beam theory is used adapting geometric non-linearity of beam, internal (residual) stress, van der Waals force, distributed electrostatic force and fringing field effects for deriving governing differential equation. The Galerkin discretisation method is used to make reduced-order model of the governing differential equation. A regime plot is presented in the current work for determining the number of modes required in reduced-order model to obtain completely converged pull-in voltage for micro/nano beams. A closed-form relation is developed based on the relationship obtained from curve fitting of pull-in instability plots and subsequent non-linear regression for the proposed relation. The output of regression analysis provides Chi-square (χ 2) tolerance value equals to 1  ×  10-9, adjusted R-square value equals to 0.999 29 and P-value equals to zero, these statistical parameters indicate the convergence of non-linear fit, accuracy of fitted data and significance of the proposed model respectively. The closed-form equation is validated using available data of experimental and numerical results. The relative maximum error of 4.08% in comparison to several available experimental and numerical data proves the reliability of the proposed closed-form equation.

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.

Angles-centroids fitting calibration and the centroid algorithm applied to reverse Hartmann test

NASA Astrophysics Data System (ADS)

Zhao, Zhu; Hui, Mei; Xia, Zhengzheng; Dong, Liquan; Liu, Ming; Liu, Xiaohua; Kong, Lingqin; Zhao, Yuejin

2017-02-01

In this paper, we develop an angles-centroids fitting (ACF) system and the centroid algorithm to calibrate the reverse Hartmann test (RHT) with sufficient precision. The essence of ACF calibration is to establish the relationship between ray angles and detector coordinates. Centroids computation is used to find correspondences between the rays of datum marks and detector pixels. Here, the point spread function of RHT is classified as circle of confusion (CoC), and the fitting of a CoC spot with 2D Gaussian profile to identify the centroid forms the basis of the centroid algorithm. Theoretical and experimental results of centroids computation demonstrate that the Gaussian fitting method has a less centroid shift or the shift grows at a slower pace when the quality of the image is reduced. In ACF tests, the optical instrumental alignments reach an overall accuracy of 0.1 pixel with the application of laser spot centroids tracking program. Locating the crystal at different positions, the feasibility and accuracy of ACF calibration are further validated to 10-6-10-4 rad root-mean-square error of the calibrations differences.

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

Quantified choice of root-mean-square errors of approximation for evaluation and power analysis of small differences between structural equation models.

PubMed

Li, Libo; Bentler, Peter M

2011-06-01

MacCallum, Browne, and Cai (2006) proposed a new framework for evaluation and power analysis of small differences between nested structural equation models (SEMs). In their framework, the null and alternative hypotheses for testing a small difference in fit and its related power analyses were defined by some chosen root-mean-square error of approximation (RMSEA) pairs. In this article, we develop a new method that quantifies those chosen RMSEA pairs and allows a quantitative comparison of them. Our method proposes the use of single RMSEA values to replace the choice of RMSEA pairs for model comparison and power analysis, thus avoiding the differential meaning of the chosen RMSEA pairs inherent in the approach of MacCallum et al. (2006). With this choice, the conventional cutoff values in model overall evaluation can directly be transferred and applied to the evaluation and power analysis of model differences. © 2011 American Psychological Association

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 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

The stress intensity factors for a periodic array of interacting coplanar penny-shaped cracks

PubMed Central

Lekesiz, Huseyin; Katsube, Noriko; Rokhlin, Stanislav I.; Seghi, Robert R.

2013-01-01

The effect of crack interactions on stress intensity factors is examined for a periodic array of coplanar penny-shaped cracks. Kachanov’s approximate method for crack interactions (Int. J. Solid. Struct. 1987; 23(1):23–43) is employed to analyze both hexagonal and square crack configurations. In approximating crack interactions, the solution converges when the total truncation number of the cracks is 109. As expected, due to high density packing crack interaction in the hexagonal configuration is stronger than that in the square configuration. Based on the numerical results, convenient fitting equations for quick evaluation of the mode I stress intensity factors are obtained as a function of crack density and angle around the crack edge for both crack configurations. Numerical results for the mode II and III stress intensity factors are presented in the form of contour lines for the case of Poisson’s ratio ν =0.3. Possible errors for these problems due to Kachanov’s approximate method are estimated. Good agreement is observed with the limited number of results available in the literature and obtained by different methods. PMID:27175035

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.

SU-F-T-125: Radial Dose Distributions From Carbon Ions of Therapeutic Energies Calculated with Geant4-DNA

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

Vassiliev, O

Purpose: Radial dose distribution D(r) is the dose as a function of lateral distance from the path of a heavy charged particle. Its main application is in modelling of biological effects of heavy ions, including applications to hadron therapy. It is the main physical parameter of a broad group of radiobiological models known as the amorphous track models. Our purpose was to calculate D(r) with Monte Carlo for carbon ions of therapeutic energies, find a simple formula for D(r) and fit it to the Monte Carlo data. Methods: All calculations were performed with Geant4-DNA code, for carbon ion energies frommore » 10 to 400 MeV/u (ranges in water: ∼ 0.4 mm to 27 cm). The spatial resolution of dose distribution in the lateral direction was 1 nm. Electron tracking cut off energy was 11 eV (ionization threshold). The maximum lateral distance considered was 10 µm. Over this distance, D(r) decreases with distance by eight orders of magnitude. Results: All calculated radial dose distributions had a similar shape dominated by the well-known inverse square dependence on the distance. Deviations from the inverse square law were observed close to the beam path (r<10 nm) and at large distances (r >1 µm). At small and large distances D(r) decreased, respectively, slower and faster than the inverse square of distance. A formula for D(r) consistent with this behavior was found and fitted to the Monte Carlo data. The accuracy of the fit was better than 10% for all distances considered. Conclusion: We have generated a set of radial dose distributions for carbon ions that covers the entire range of therapeutic energies, for distances from the ion path of up to 10 µm. The latter distance is sufficient for most applications because dose beyond 10 µm is extremely low.« less

Protofit: A program for determining surface protonation constants from titration data

NASA Astrophysics Data System (ADS)

Turner, Benjamin F.; Fein, Jeremy B.

2006-11-01

Determining the surface protonation behavior of natural adsorbents is essential to understand how they interact with their environments. ProtoFit is a tool for analysis of acid-base titration data and optimization of surface protonation models. The program offers a number of useful features including: (1) enables visualization of adsorbent buffering behavior; (2) uses an optimization approach independent of starting titration conditions or initial surface charge; (3) does not require an initial surface charge to be defined or to be treated as an optimizable parameter; (4) includes an error analysis intrinsically as part of the computational methods; and (5) generates simulated titration curves for comparison with observation. ProtoFit will typically be run through ProtoFit-GUI, a graphical user interface providing user-friendly control of model optimization, simulation, and data visualization. ProtoFit calculates an adsorbent proton buffering value as a function of pH from raw titration data (including pH and volume of acid or base added). The data is reduced to a form where the protons required to change the pH of the solution are subtracted out, leaving protons exchanged between solution and surface per unit mass of adsorbent as a function of pH. The buffering intensity function Qads* is calculated as the instantaneous slope of this reduced titration curve. Parameters for a surface complexation model are obtained by minimizing the sum of squares between the modeled (i.e. simulated) buffering intensity curve and the experimental data. The variance in the slope estimate, intrinsically produced as part of the Qads* calculation, can be used to weight the sum of squares calculation between the measured buffering intensity and a simulated curve. Effects of analytical error on data visualization and model optimization are discussed. Examples are provided of using ProtoFit for data visualization, model optimization, and model evaluation.

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

Zhou, S; Fan, Q; Lei, Y

Purpose: In-Water-Output-Ratio (IWOR) plays a significant role in linac-based radiotherapy treatment planning, linking MUs to delivered radiation dose. For an open rectangular field, IWOR depends on both its width and length, and changes rapidly when one of them becomes small. In this study, a universal functional form is proposed to fit the open field IWOR tables in Varian TrueBeam representative datasets for all photon energies. Methods: A novel Generalized Mean formula is first used to estimate the Equivalent Square (ES) for a rectangular field. The formula’s weighting factor and power index are determined by collapsing all data points as muchmore » as possible onto a single curve in IWOR vs. ES plot. The result is then fitted with a novel universal function IWOR=1+b*Log(ES/10cm)/(ES/10cm)^c via a least-square procedure to determine the optimal values for parameters b and c. The maximum relative residual error in IWOR over the entire two-dimensional measurement table with field sizes between 3cm and 40cm is used to evaluate the quality of fit for the function. Results: The two-step fitting strategy works very well in determining the optimal parameter values for open field IWOR of each photon energies in the Varian data-set. Relative residual error ≤0.71% is achieved for all photon energies (including Flattening-Filter-Free modes) with field sizes between 3cm and 40cm. The optimal parameter values change smoothly with regular photon beam quality. Conclusion: The universal functional form fits the Varian TrueBeam open field IWOR measurement tables accurately with small relative residual errors for all photon energies. Therefore, it can be an excellent choice to represent IWOR in absolute dose and MU calculations. The functional form can also be used as a QA/commissioning tool to verify the measured data quality and consistency by checking the IWOR data behavior against the function for new photon energies with arbitrary beam quality.« less

Impact of fitting algorithms on errors of parameter estimates in dynamic contrast-enhanced MRI

NASA Astrophysics Data System (ADS)

Debus, C.; Floca, R.; Nörenberg, D.; Abdollahi, A.; Ingrisch, M.

2017-12-01

Parameter estimation in dynamic contrast-enhanced MRI (DCE MRI) is usually performed by non-linear least square (NLLS) fitting of a pharmacokinetic model to a measured concentration-time curve. The two-compartment exchange model (2CXM) describes the compartments ‘plasma’ and ‘interstitial volume’ and their exchange in terms of plasma flow and capillary permeability. The model function can be defined by either a system of two coupled differential equations or a closed-form analytical solution. The aim of this study was to compare these two representations in terms of accuracy, robustness and computation speed, depending on parameter combination and temporal sampling. The impact on parameter estimation errors was investigated by fitting the 2CXM to simulated concentration-time curves. Parameter combinations representing five tissue types were used, together with two arterial input functions, a measured and a theoretical population based one, to generate 4D concentration images at three different temporal resolutions. Images were fitted by NLLS techniques, where the sum of squared residuals was calculated by either numeric integration with the Runge-Kutta method or convolution. Furthermore two example cases, a prostate carcinoma and a glioblastoma multiforme patient, were analyzed in order to investigate the validity of our findings in real patient data. The convolution approach yields improved results in precision and robustness of determined parameters. Precision and stability are limited in curves with low blood flow. The model parameter ve shows great instability and little reliability in all cases. Decreased temporal resolution results in significant errors for the differential equation approach in several curve types. The convolution excelled in computational speed by three orders of magnitude. Uncertainties in parameter estimation at low temporal resolution cannot be compensated by usage of the differential equations. Fitting with the convolution approach is superior in computational time, with better stability and accuracy at the same time.

Parameterizing sorption isotherms using a hybrid global-local fitting procedure.

PubMed

Matott, L Shawn; Singh, Anshuman; Rabideau, Alan J

2017-05-01

Predictive modeling of the transport and remediation of groundwater contaminants requires an accurate description of the sorption process, which is usually provided by fitting an isotherm model to site-specific laboratory data. Commonly used calibration procedures, listed in order of increasing sophistication, include: trial-and-error, linearization, non-linear regression, global search, and hybrid global-local search. Given the considerable variability in fitting procedures applied in published isotherm studies, we investigated the importance of algorithm selection through a series of numerical experiments involving 13 previously published sorption datasets. These datasets, considered representative of state-of-the-art for isotherm experiments, had been previously analyzed using trial-and-error, linearization, or non-linear regression methods. The isotherm expressions were re-fit using a 3-stage hybrid global-local search procedure (i.e. global search using particle swarm optimization followed by Powell's derivative free local search method and Gauss-Marquardt-Levenberg non-linear regression). The re-fitted expressions were then compared to previously published fits in terms of the optimized weighted sum of squared residuals (WSSR) fitness function, the final estimated parameters, and the influence on contaminant transport predictions - where easily computed concentration-dependent contaminant retardation factors served as a surrogate measure of likely transport behavior. Results suggest that many of the previously published calibrated isotherm parameter sets were local minima. In some cases, the updated hybrid global-local search yielded order-of-magnitude reductions in the fitness function. In particular, of the candidate isotherms, the Polanyi-type models were most likely to benefit from the use of the hybrid fitting procedure. In some cases, improvements in fitness function were associated with slight (<10%) changes in parameter values, but in other cases significant (>50%) changes in parameter values were noted. Despite these differences, the influence of isotherm misspecification on contaminant transport predictions was quite variable and difficult to predict from inspection of the isotherms. Copyright © 2017 Elsevier B.V. All rights reserved.

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.

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.

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.

[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.

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…

Technical player profiles related to the physical fitness of young female volleyball players predict team performance.

PubMed

Dávila-Romero, C; Hernández-Mocholí, M A; García-Hermoso, A

2015-03-01

This study is divided into three sequential stages: identification of fitness and game performance profiles (individual player performance), an assessment of the relationship between these profiles, and an assessment of the relationship between individual player profiles and team performance during play (in championship performance). The overall study sample comprised 525 (19 teams) female volleyball players aged 12-16 years and a subsample (N.=43) used to examine study aims one and two was selected from overall sample. Anthropometric, fitness and individual player performance (actual game) data were collected in the subsample. These data were analyzed through clustering methods, ANOVA and independence chi-square test. Then, we investigated whether the proportion of players with the highest individual player performance profile might predict a team's results in the championship. Cluster analysis identified three volleyball fitness profiles (high, medium, and low) and two individual player performance profiles (high and low). The results showed a relationship between both types of profile (fitness and individual player performance). Then, linear regression revealed a moderate relationship between the number of players with a high volleyball fitness profile and a team's results in the championship (R2=0.23). The current study findings may enable coaches and trainers to manage training programs more efficiently in order to obtain tailor-made training, identify volleyball-specific physical fitness training requirements and reach better results during competitions.

An automated approach to Litchfield and Wilcoxon's evaluation of dose–effect experiments using the R package LW1949

USGS Publications Warehouse

Adams, Jean V.; Slaght, Karen; Boogaard, Michael A.

2016-01-01

The authors developed a package, LW1949, for use with the statistical software R to automatically carry out the manual steps of Litchfield and Wilcoxon's method of evaluating dose–effect experiments. The LW1949 package consistently finds the best fitting dose–effect relation by minimizing the chi-squared statistic of the observed and expected number of affected individuals and substantially speeds up the line-fitting process and other calculations that Litchfield and Wilcoxon originally carried out by hand. Environ Toxicol Chem 2016;9999:1–4. Published 2016 Wiley Periodicals Inc. on behalf of SETAC. This article is a US Government work and, as such, is in the public domain in the United States of America.

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.

Material characterization in partially filled waveguides using inverse scattering and multiple sample orientations

NASA Astrophysics Data System (ADS)

Sjöberg, Daniel; Larsson, Christer

2015-06-01

We present a method aimed at reducing uncertainties and instabilities when characterizing materials in waveguide setups. The method is based on measuring the S parameters for three different orientations of a rectangular sample block in a rectangular waveguide. The corresponding geometries are modeled in a commercial full-wave simulation program, taking any material parameters as input. The material parameters of the sample are found by minimizing the squared distance between measured and calculated S parameters. The information added by the different sample orientations is quantified using the Cramér-Rao lower bound. The flexibility of the method allows the determination of material parameters of an arbitrarily shaped sample that fits in the waveguide.

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.

The Evaluation and Selection of Adequate Causal Models: A Compensatory Education Example.

ERIC Educational Resources Information Center

Tanaka, Jeffrey S.

1982-01-01

Implications of model evaluation (using traditional chi square goodness of fit statistics, incremental fit indices for covariance structure models, and latent variable coefficients of determination) on substantive conclusions are illustrated with an example examining the effects of participation in a compensatory education program on posttreatment…

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...

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

Long-term statistics of extreme tsunami height at Crescent City

NASA Astrophysics Data System (ADS)

Dong, Sheng; Zhai, Jinjin; Tao, Shanshan

2017-06-01

Historically, Crescent City is one of the most vulnerable communities impacted by tsunamis along the west coast of the United States, largely attributed to its offshore geography. Trans-ocean tsunamis usually produce large wave runup at Crescent Harbor resulting in catastrophic damages, property loss and human death. How to determine the return values of tsunami height using relatively short-term observation data is of great significance to assess the tsunami hazards and improve engineering design along the coast of Crescent City. In the present study, the extreme tsunami heights observed along the coast of Crescent City from 1938 to 2015 are fitted using six different probabilistic distributions, namely, the Gumbel distribution, the Weibull distribution, the maximum entropy distribution, the lognormal distribution, the generalized extreme value distribution and the generalized Pareto distribution. The maximum likelihood method is applied to estimate the parameters of all above distributions. Both Kolmogorov-Smirnov test and root mean square error method are utilized for goodness-of-fit test and the better fitting distribution is selected. Assuming that the occurrence frequency of tsunami in each year follows the Poisson distribution, the Poisson compound extreme value distribution can be used to fit the annual maximum tsunami amplitude, and then the point and interval estimations of return tsunami heights are calculated for structural design. The results show that the Poisson compound extreme value distribution fits tsunami heights very well and is suitable to determine the return tsunami heights for coastal disaster prevention.

A highly accurate dynamic contact angle algorithm for drops on inclined surface based on ellipse-fitting.

PubMed

Xu, Z N; Wang, S Y

2015-02-01

To improve the accuracy in the calculation of dynamic contact angle for drops on the inclined surface, a significant number of numerical drop profiles on the inclined surface with different inclination angles, drop volumes, and contact angles are generated based on the finite difference method, a least-squares ellipse-fitting algorithm is used to calculate the dynamic contact angle. The influences of the above three factors are systematically investigated. The results reveal that the dynamic contact angle errors, including the errors of the left and right contact angles, evaluated by the ellipse-fitting algorithm tend to increase with inclination angle/drop volume/contact angle. If the drop volume and the solid substrate are fixed, the errors of the left and right contact angles increase with inclination angle. After performing a tremendous amount of computation, the critical dimensionless drop volumes corresponding to the critical contact angle error are obtained. Based on the values of the critical volumes, a highly accurate dynamic contact angle algorithm is proposed and fully validated. Within nearly the whole hydrophobicity range, it can decrease the dynamic contact angle error in the inclined plane method to less than a certain value even for different types of liquids.

[Modification and evaluation of assessment of 
medication literacy].

PubMed

Zheng, Feng; Zhong, Zhuqing; Ding, Siqing; Luo, Aijing; Liu, Zina

2016-11-28

To translate and revise the Medication Literacy Assessment in English (MedLitRxSE-English) and evaluate its validity and reliability.
 Methods: We introduced MedLitRxSE-English from abroad. According to the principles of Brislin and culture adjustment, we revised it as a Chinese edition. Using random sampling method, from Oct, 2014 to Jan, 2015, 461 non-hospitalized patients from the outpatient departments of the top three hospitals in Changsha city were investigated. The reliability and validity of the scale was tested.
 Results: The test-retest reliability of the Chinese version for medication literacy scale was 0.885; the split reliability was 0.840; K-R was 0.820; the correlations between the assessment of medication literacy and the corresponding items were 0.427-0.587; the confirmatory factor analysis revealed overall good fit. Root mean square error of approximation (RMSEA), χ2/df, goodness of fit index (GFI) and comparative fit index (CFI) was 0.08, 3.06, 0.91 and 0.94, respectively. 
 Conclusion: The Chinese version for the assessment of medication literacy is in good reliability and validity, and it can be used to evaluate the medication literacy in our country.

Electrostatic and Small-Signal Analysis of CMUTs With Circular and Square Anisotropic Plates.

PubMed

Funding la Cour, Mette; Christiansen, Thomas Lehrmann; Jensen, Jørgen Arendt; Thomsen, Erik Vilain

2015-08-01

Traditionally, capacitive micromachined ultrasonic transducers (CMUTs) are modeled using the isotropic plate equation, and this leads to deviations between analytical calculations and finite element modeling (FEM). In this paper, the deflection is calculated for both circular and square plates using the full anisotropic plate equation. It is shown that the anisotropic calculations match excellently with FEM, whereas an isotropic approach causes up to 10% deviations in deflection. For circular plates, an exact solution can be found. For square plates using the Galerkin method, and utilizing the symmetry of the silicon crystal, a compact and accurate expression for the deflection can be obtained. The deviation from FEM in center deflection is <0.1%. The theory of multilayer plates is also applied to the CMUT. The deflection of a square plate was measured on fabricated CMUTs using a white light interferometer. Fitting the plate parameter for the anisotropic calculated deflection to the measurement, a deviation of 0.07% is seen. Electrostatic and small-signal dynamic analysis are performed using energy considerations including anisotropy. The stable position, effective spring constant, pullin distance, and pull-in voltage are found for both circular and square anisotropic plates, and the pressure dependence is included by comparison with the corresponding analysis for a parallel plate. Measurements on fabricated devices with both circular and square plates subjected to increasing bias voltage are performed, and it is observed that the models including anisotropic effects are within the uncertainty interval of the measurements. Finally, a lumped element small-signal model for both circular and square anisotropic plates is derived to describe the dynamics of the CMUT.

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.

A non-linear data mining parameter selection algorithm for continuous variables

PubMed Central

Razavi, Marianne; Brady, Sean

2017-01-01

In this article, we propose a new data mining algorithm, by which one can both capture the non-linearity in data and also find the best subset model. To produce an enhanced subset of the original variables, a preferred selection method should have the potential of adding a supplementary level of regression analysis that would capture complex relationships in the data via mathematical transformation of the predictors and exploration of synergistic effects of combined variables. The method that we present here has the potential to produce an optimal subset of variables, rendering the overall process of model selection more efficient. This algorithm introduces interpretable parameters by transforming the original inputs and also a faithful fit to the data. The core objective of this paper is to introduce a new estimation technique for the classical least square regression framework. This new automatic variable transformation and model selection method could offer an optimal and stable model that minimizes the mean square error and variability, while combining all possible subset selection methodology with the inclusion variable transformations and interactions. Moreover, this method controls multicollinearity, leading to an optimal set of explanatory variables. PMID:29131829

A three dimensional point cloud registration method based on rotation matrix eigenvalue

NASA Astrophysics Data System (ADS)

Wang, Chao; Zhou, Xiang; Fei, Zixuan; Gao, Xiaofei; Jin, Rui

2017-09-01

We usually need to measure an object at multiple angles in the traditional optical three-dimensional measurement method, due to the reasons for the block, and then use point cloud registration methods to obtain a complete threedimensional shape of the object. The point cloud registration based on a turntable is essential to calculate the coordinate transformation matrix between the camera coordinate system and the turntable coordinate system. We usually calculate the transformation matrix by fitting the rotation center and the rotation axis normal of the turntable in the traditional method, which is limited by measuring the field of view. The range of exact feature points used for fitting the rotation center and the rotation axis normal is approximately distributed within an arc less than 120 degrees, resulting in a low fit accuracy. In this paper, we proposes a better method, based on the invariant eigenvalue principle of rotation matrix in the turntable coordinate system and the coordinate transformation matrix of the corresponding coordinate points. First of all, we control the rotation angle of the calibration plate with the turntable to calibrate the coordinate transformation matrix of the corresponding coordinate points by using the least squares method. And then we use the feature decomposition to calculate the coordinate transformation matrix of the camera coordinate system and the turntable coordinate system. Compared with the traditional previous method, it has a higher accuracy, better robustness and it is not affected by the camera field of view. In this method, the coincidence error of the corresponding points on the calibration plate after registration is less than 0.1mm.

Predicting protein concentrations with ELISA microarray assays, monotonic splines and Monte Carlo simulation

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

Daly, Don S.; Anderson, Kevin K.; White, Amanda M.

Background: A microarray of enzyme-linked immunosorbent assays, or ELISA microarray, predicts simultaneously the concentrations of numerous proteins in a small sample. These predictions, however, are uncertain due to processing error and biological variability. Making sound biological inferences as well as improving the ELISA microarray process require require both concentration predictions and creditable estimates of their errors. Methods: We present a statistical method based on monotonic spline statistical models, penalized constrained least squares fitting (PCLS) and Monte Carlo simulation (MC) to predict concentrations and estimate prediction errors in ELISA microarray. PCLS restrains the flexible spline to a fit of assay intensitymore » that is a monotone function of protein concentration. With MC, both modeling and measurement errors are combined to estimate prediction error. The spline/PCLS/MC method is compared to a common method using simulated and real ELISA microarray data sets. Results: In contrast to the rigid logistic model, the flexible spline model gave credible fits in almost all test cases including troublesome cases with left and/or right censoring, or other asymmetries. For the real data sets, 61% of the spline predictions were more accurate than their comparable logistic predictions; especially the spline predictions at the extremes of the prediction curve. The relative errors of 50% of comparable spline and logistic predictions differed by less than 20%. Monte Carlo simulation rendered acceptable asymmetric prediction intervals for both spline and logistic models while propagation of error produced symmetric intervals that diverged unrealistically as the standard curves approached horizontal asymptotes. Conclusions: The spline/PCLS/MC method is a flexible, robust alternative to a logistic/NLS/propagation-of-error method to reliably predict protein concentrations and estimate their errors. The spline method simplifies model selection and fitting, and reliably estimates believable prediction errors. For the 50% of the real data sets fit well by both methods, spline and logistic predictions are practically indistinguishable, varying in accuracy by less than 15%. The spline method may be useful when automated prediction across simultaneous assays of numerous proteins must be applied routinely with minimal user intervention.« less

A Combined SRTM Digital Elevation Model for Zanjan State of Iran Based on the Corrective Surface Idea

NASA Astrophysics Data System (ADS)

Kiamehr, Ramin

2016-04-01

One arc-second high resolution version of the SRTM model recently published for the Iran by the US Geological Survey database. Digital Elevation Models (DEM) is widely used in different disciplines and applications by geoscientist. It is an essential data in geoid computation procedure, e.g., to determine the topographic, downward continuation (DWC) and atmospheric corrections. Also, it can be used in road location and design in civil engineering and hydrological analysis. However, a DEM is only a model of the elevation surface and it is subject to errors. The most important parts of errors could be comes from the bias in height datum. On the other hand, the accuracy of DEM is usually published in global sense and it is important to have estimation about the accuracy in the area of interest before using of it. One of the best methods to have a reasonable indication about the accuracy of DEM is obtained from the comparison of their height versus the precise national GPS/levelling data. It can be done by the determination of the Root-Mean-Square (RMS) of fitting between the DEM and leveling heights. The errors in the DEM can be approximated by different kinds of functions in order to fit the DEMs to a set of GPS/levelling data using the least squares adjustment. In the current study, several models ranging from a simple linear regression to seven parameter similarity transformation model are used in fitting procedure. However, the seven parameter model gives the best fitting with minimum standard division in all selected DEMs in the study area. Based on the 35 precise GPS/levelling data we obtain a RMS of 7 parameter fitting for SRTM DEM 5.5 m, The corrective surface model in generated based on the transformation parameters and included to the original SRTM model. The result of fitting in combined model is estimated again by independent GPS/leveling data. The result shows great improvement in absolute accuracy of the model with the standard deviation of 3.4 meter.

Machine learning-based kinetic modeling: a robust and reproducible solution for quantitative analysis of dynamic PET data

NASA Astrophysics Data System (ADS)

Pan, Leyun; Cheng, Caixia; Haberkorn, Uwe; Dimitrakopoulou-Strauss, Antonia

2017-05-01

A variety of compartment models are used for the quantitative analysis of dynamic positron emission tomography (PET) data. Traditionally, these models use an iterative fitting (IF) method to find the least squares between the measured and calculated values over time, which may encounter some problems such as the overfitting of model parameters and a lack of reproducibility, especially when handling noisy data or error data. In this paper, a machine learning (ML) based kinetic modeling method is introduced, which can fully utilize a historical reference database to build a moderate kinetic model directly dealing with noisy data but not trying to smooth the noise in the image. Also, due to the database, the presented method is capable of automatically adjusting the models using a multi-thread grid parameter searching technique. Furthermore, a candidate competition concept is proposed to combine the advantages of the ML and IF modeling methods, which could find a balance between fitting to historical data and to the unseen target curve. The machine learning based method provides a robust and reproducible solution that is user-independent for VOI-based and pixel-wise quantitative analysis of dynamic PET data.

Machine learning-based kinetic modeling: a robust and reproducible solution for quantitative analysis of dynamic PET data.

PubMed

Pan, Leyun; Cheng, Caixia; Haberkorn, Uwe; Dimitrakopoulou-Strauss, Antonia

2017-05-07

A variety of compartment models are used for the quantitative analysis of dynamic positron emission tomography (PET) data. Traditionally, these models use an iterative fitting (IF) method to find the least squares between the measured and calculated values over time, which may encounter some problems such as the overfitting of model parameters and a lack of reproducibility, especially when handling noisy data or error data. In this paper, a machine learning (ML) based kinetic modeling method is introduced, which can fully utilize a historical reference database to build a moderate kinetic model directly dealing with noisy data but not trying to smooth the noise in the image. Also, due to the database, the presented method is capable of automatically adjusting the models using a multi-thread grid parameter searching technique. Furthermore, a candidate competition concept is proposed to combine the advantages of the ML and IF modeling methods, which could find a balance between fitting to historical data and to the unseen target curve. The machine learning based method provides a robust and reproducible solution that is user-independent for VOI-based and pixel-wise quantitative analysis of dynamic PET data.

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

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

Health-related physical fitness and physical activity in elementary school students.

PubMed

Chen, Weiyun; Hammond-Bennett, Austin; Hypnar, Andrew; Mason, Steve

2018-01-30

This study examined associations between students' physical fitness and physical activity (PA), as well as what specific physical fitness components were more significant correlates to being physically active in different settings for boys and girls. A total of 265 fifth-grade students with an average age of 11 voluntarily participated in this study. The students' physical fitness was assessed using four FitnessGram tests, including Progressive Aerobic Cardiovascular Endurance Run (PACER), curl-up, push-up, and trunk lift tests. The students' daily PA was assessed in various settings using a daily PA log for 7 days. Data was analyzed with descriptive statistics, univariate analyses, and multiple R-squared liner regression methods. Performance on the four physical fitness tests was significantly associated with the PA minutes spent in physical education (PE) class and recess for the total sample and for girls, but not for boys. Performance on the four fitness tests was significantly linked to participation in sports/dances outside school and the total weekly PA minutes for the total sample, boys, and girls. Further, boys and girls who were the most physically fit spent significantly more time engaging in sports/dances and had greater total weekly PA than boys and girls who were not physically fit. In addition, the physically fit girls were more physically active in recess than girls who were not physically fit. Overall, students' performance on the four physical fitness tests was significantly associated with them being physically active during PE and in recess and engaging in sports/dances, as well as with their total weekly PA minutes, but not with their participation in non-organized physical play outside school. ClinicalTrials.gov ID: NCT03015337 , registered date: 1/09/2017, as "retrospectively registered".

The Relationship between Root Mean Square Error of Approximation and Model Misspecification in Confirmatory Factor Analysis Models

ERIC Educational Resources Information Center

Savalei, Victoria

2012-01-01

The fit index root mean square error of approximation (RMSEA) is extremely popular in structural equation modeling. However, its behavior under different scenarios remains poorly understood. The present study generates continuous curves where possible to capture the full relationship between RMSEA and various "incidental parameters," such as…

Evaluating flow cytometer performance with weighted quadratic least squares analysis of LED and multi-level bead data.

PubMed

Parks, David R; El Khettabi, Faysal; Chase, Eric; Hoffman, Robert A; Perfetto, Stephen P; Spidlen, Josef; Wood, James C S; Moore, Wayne A; Brinkman, Ryan R

2017-03-01

We developed a fully automated procedure for analyzing data from LED pulses and multilevel bead sets to evaluate backgrounds and photoelectron scales of cytometer fluorescence channels. The method improves on previous formulations by fitting a full quadratic model with appropriate weighting and by providing standard errors and peak residuals as well as the fitted parameters themselves. Here we describe the details of the methods and procedures involved and present a set of illustrations and test cases that demonstrate the consistency and reliability of the results. The automated analysis and fitting procedure is generally quite successful in providing good estimates of the Spe (statistical photoelectron) scales and backgrounds for all the fluorescence channels on instruments with good linearity. The precision of the results obtained from LED data is almost always better than that from multilevel bead data, but the bead procedure is easy to carry out and provides results good enough for most purposes. Including standard errors on the fitted parameters is important for understanding the uncertainty in the values of interest. The weighted residuals give information about how well the data fits the model, and particularly high residuals indicate bad data points. Known photoelectron scales and measurement channel backgrounds make it possible to estimate the precision of measurements at different signal levels and the effects of compensated spectral overlap on measurement quality. Combining this information with measurements of standard samples carrying dyes of biological interest, we can make accurate comparisons of dye sensitivity among different instruments. Our method is freely available through the R/Bioconductor package flowQB. © 2017 International Society for Advancement of Cytometry. © 2017 International Society for Advancement of Cytometry.

A comparison of small-field tissue phantom ratio data generation methods for an Elekta Agility 6 MV photon beam

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

Richmond, Neil, E-mail: neil.richmond@stees.nhs.uk; Brackenridge, Robert

2014-04-01

Tissue-phantom ratios (TPRs) are a common dosimetric quantity used to describe the change in dose with depth in tissue. These can be challenging and time consuming to measure. The conversion of percentage depth dose (PDD) data using standard formulae is widely employed as an alternative method in generating TPR. However, the applicability of these formulae for small fields has been questioned in the literature. Functional representation has also been proposed for small-field TPR production. This article compares measured TPR data for small 6 MV photon fields against that generated by conversion of PDD using standard formulae to assess the efficacymore » of the conversion data. By functionally fitting the measured TPR data for square fields greater than 4 cm in length, the TPR curves for smaller fields are generated and compared with measurements. TPRs and PDDs were measured in a water tank for a range of square field sizes. The PDDs were converted to TPRs using standard formulae. TPRs for fields of 4 × 4 cm{sup 2} and larger were used to create functional fits. The parameterization coefficients were used to construct extrapolated TPR curves for 1 × 1 cm{sup 2}, 2 × 2-cm{sup 2}, and 3 × 3-cm{sup 2} fields. The TPR data generated using standard formulae were in excellent agreement with direct TPR measurements. The TPR data for 1 × 1-cm{sup 2}, 2 × 2-cm{sup 2}, and 3 × 3-cm{sup 2} fields created by extrapolation of the larger field functional fits gave inaccurate initial results. The corresponding mean differences for the 3 fields were 4.0%, 2.0%, and 0.9%. Generation of TPR data using a standard PDD-conversion methodology has been shown to give good agreement with our directly measured data for small fields. However, extrapolation of TPR data using the functional fit to fields of 4 × 4 cm{sup 2} or larger resulted in generation of TPR curves that did not compare well with the measured data.« less

Measuring implementation behaviour of menu guidelines in the childcare setting: confirmatory factor analysis of a theoretical domains framework questionnaire (TDFQ).

PubMed

Seward, Kirsty; Wolfenden, Luke; Wiggers, John; Finch, Meghan; Wyse, Rebecca; Oldmeadow, Christopher; Presseau, Justin; Clinton-McHarg, Tara; Yoong, Sze Lin

2017-04-04

While there are number of frameworks which focus on supporting the implementation of evidence based approaches, few psychometrically valid measures exist to assess constructs within these frameworks. This study aimed to develop and psychometrically assess a scale measuring each domain of the Theoretical Domains Framework for use in assessing the implementation of dietary guidelines within a non-health care setting (childcare services). A 75 item 14-domain Theoretical Domains Framework Questionnaire (TDFQ) was developed and administered via telephone interview to 202 centre based childcare service cooks who had a role in planning the service menu. Confirmatory factor analysis (CFA) was undertaken to assess the reliability, discriminant validity and goodness of fit of the 14-domain theoretical domain framework measure. For the CFA, five iterative processes of adjustment were undertaken where 14 items were removed, resulting in a final measure consisting of 14 domains and 61 items. For the final measure: the Chi-Square goodness of fit statistic was 3447.19; the Standardized Root Mean Square Residual (SRMR) was 0.070; the Root Mean Square Error of Approximation (RMSEA) was 0.072; and the Comparative Fit Index (CFI) had a value of 0.78. While only one of the three indices support goodness of fit of the measurement model tested, a 14-domain model with 61 items showed good discriminant validity and internally consistent items. Future research should aim to assess the psychometric properties of the developed TDFQ in other community-based settings.

How well will you FIT? Use of a modified MMI to assess applicants’ compatibility with an emergency medicine residency program

PubMed Central

Min, Alice A.; Leetch, Aaron; Nuño, Tomas; Fiorello, Albert B.

2016-01-01

Purpose Emergency medicine residency programs have evaluated the use of Multiple Mini Interviews (MMIs) for applicants. The authors developed an MMI-style method called the Fast Interview Track (FIT) to predict an applicant's ‘fit’ within an individual residency program. Methods Applicants meet with up to five residents and are asked one question by each. Residents score the applicant using a Likert scale from 1 to 5 on two questions: ‘How well does the applicant think on his/her feet?’ and ‘How well do you think the applicant will fit in here?’. To assess how well these questions predicted a resident's ‘fit’, current residents scored fellow residents on these same questions. These scores were compared with the residents’ interview FIT scores. A postmatch survey of applicants who did not match at this program solicited applicants’ attitudes toward the FIT sessions. Results Among the junior class, the correlation between interview and current scores was significant for question 1 (rho=0.5192 [p=0.03]) and question 2 (rho=0.5753 [p=0.01]). Among seniors, Spearman's rho was statistically significant for question 2, though not statistically significant for question 1. The chi-square measure of high scores (4–5) versus low scores (1–3) found a statistically significant association between interview and current scores for interns and juniors. Of the 29 responses to the postmatch survey, 16 (55%) felt FIT sessions provided a good sense of the program's personality and only 6 (21%) disagreed. Nine (31%) felt FIT sessions positively impacted our program's ranking and 11 (38%) were ‘Neutral’. Only two (7%) reported that FIT sessions negatively impacted their ranking of our program. Conclusions FIT provided program leadership with a sense of an applicant's ‘fit’ within this program. Interview day scores correlated with scores received during residency. Most applicants report a positive experience with FIT sessions. FIT provides a useful tool to recruit applicants who fit with the residency program. PMID:26842824

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.

Fitting ordinary differential equations to short time course data.

PubMed

Brewer, Daniel; Barenco, Martino; Callard, Robin; Hubank, Michael; Stark, Jaroslav

2008-02-28

Ordinary differential equations (ODEs) are widely used to model many systems in physics, chemistry, engineering and biology. Often one wants to compare such equations with observed time course data, and use this to estimate parameters. Surprisingly, practical algorithms for doing this are relatively poorly developed, particularly in comparison with the sophistication of numerical methods for solving both initial and boundary value problems for differential equations, and for locating and analysing bifurcations. A lack of good numerical fitting methods is particularly problematic in the context of systems biology where only a handful of time points may be available. In this paper, we present a survey of existing algorithms and describe the main approaches. We also introduce and evaluate a new efficient technique for estimating ODEs linear in parameters particularly suited to situations where noise levels are high and the number of data points is low. It employs a spline-based collocation scheme and alternates linear least squares minimization steps with repeated estimates of the noise-free values of the variables. This is reminiscent of expectation-maximization methods widely used for problems with nuisance parameters or missing data.

A ground truth based comparative study on clustering of gene expression data.

PubMed

Zhu, Yitan; Wang, Zuyi; Miller, David J; Clarke, Robert; Xuan, Jianhua; Hoffman, Eric P; Wang, Yue

2008-05-01

Given the variety of available clustering methods for gene expression data analysis, it is important to develop an appropriate and rigorous validation scheme to assess the performance and limitations of the most widely used clustering algorithms. In this paper, we present a ground truth based comparative study on the functionality, accuracy, and stability of five data clustering methods, namely hierarchical clustering, K-means clustering, self-organizing maps, standard finite normal mixture fitting, and a caBIG toolkit (VIsual Statistical Data Analyzer--VISDA), tested on sample clustering of seven published microarray gene expression datasets and one synthetic dataset. We examined the performance of these algorithms in both data-sufficient and data-insufficient cases using quantitative performance measures, including cluster number detection accuracy and mean and standard deviation of partition accuracy. The experimental results showed that VISDA, an interactive coarse-to-fine maximum likelihood fitting algorithm, is a solid performer on most of the datasets, while K-means clustering and self-organizing maps optimized by the mean squared compactness criterion generally produce more stable solutions than the other methods.

Using Fit Indexes to Select a Covariance Model for Longitudinal Data

ERIC Educational Resources Information Center

Liu, Siwei; Rovine, Michael J.; Molenaar, Peter C. M.

2012-01-01

This study investigated the performance of fit indexes in selecting a covariance structure for longitudinal data. Data were simulated to follow a compound symmetry, first-order autoregressive, first-order moving average, or random-coefficients covariance structure. We examined the ability of the likelihood ratio test (LRT), root mean square error…

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 86.123-78 - Oxides of nitrogen analyzer calibration.

Code of Federal Regulations, 2012 CFR

2012-07-01

...-squares best-fit straight line is 2 percent or less of the value at each data point, concentration values... percent at any point, the best-fit non-linear equation which represents the data to within 2 percent of... may be necessary to clean the analyzer frequently to prevent interference with NOX measurements (see...

40 CFR 86.123-78 - Oxides of nitrogen analyzer calibration.

Code of Federal Regulations, 2014 CFR

2014-07-01

...-squares best-fit straight line is 2 percent or less of the value at each data point, concentration values... percent at any point, the best-fit non-linear equation which represents the data to within 2 percent of... may be necessary to clean the analyzer frequently to prevent interference with NOX measurements (see...

40 CFR 86.123-78 - Oxides of nitrogen analyzer calibration.

Code of Federal Regulations, 2013 CFR

2013-07-01

...-squares best-fit straight line is 2 percent or less of the value at each data point, concentration values... percent at any point, the best-fit non-linear equation which represents the data to within 2 percent of... may be necessary to clean the analyzer frequently to prevent interference with NOX measurements (see...

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 90.318 - Oxides of nitrogen analyzer calibration.

Code of Federal Regulations, 2012 CFR

2012-07-01

... chemiluminescent oxides of nitrogen analyzer as described in this section. (b) Initial and Periodic Interference...-squares best-fit straight line is two percent or less of the value at each data point, calculate... at any point, use the best-fit non-linear equation which represents the data to within two percent of...

40 CFR 91.318 - Oxides of nitrogen analyzer calibration.

Code of Federal Regulations, 2012 CFR

2012-07-01

... nitrogen analyzer as described in this section. (b) Initial and periodic interference. Prior to its...-squares best-fit straight line is two percent or less of the value at each data point, concentration... two percent at any point, use the best-fit non-linear equation which represents the data to within two...

40 CFR 90.318 - Oxides of nitrogen analyzer calibration.

Code of Federal Regulations, 2014 CFR

2014-07-01

... chemiluminescent oxides of nitrogen analyzer as described in this section. (b) Initial and Periodic Interference...-squares best-fit straight line is two percent or less of the value at each data point, calculate... at any point, use the best-fit non-linear equation which represents the data to within two percent of...

40 CFR 91.318 - Oxides of nitrogen analyzer calibration.

Code of Federal Regulations, 2014 CFR

2014-07-01

... nitrogen analyzer as described in this section. (b) Initial and periodic interference. Prior to its...-squares best-fit straight line is two percent or less of the value at each data point, concentration... two percent at any point, use the best-fit non-linear equation which represents the data to within two...

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.

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

GOSSIP: SED fitting code

NASA Astrophysics Data System (ADS)

Franzetti, Paolo; Scodeggio, Marco

2012-10-01

GOSSIP fits the electro-magnetic emission of an object (the SED, Spectral Energy Distribution) against synthetic models to find the simulated one that best reproduces the observed data. It builds-up the observed SED of an object (or a large sample of objects) combining magnitudes in different bands and eventually a spectrum; then it performs a chi-square minimization fitting procedure versus a set of synthetic models. The fitting results are used to estimate a number of physical parameters like the Star Formation History, absolute magnitudes, stellar mass and their Probability Distribution Functions.

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

Effect of noise on defect chaos in a reaction-diffusion model.

PubMed

Wang, Hongli; Ouyang, Qi

2005-06-01

The influence of noise on defect chaos due to breakup of spiral waves through Doppler and Eckhaus instabilities is investigated numerically with a modified Fitzhugh-Nagumo model. By numerical simulations we show that the noise can drastically enhance the creation and annihilation rates of topological defects. The noise-free probability distribution function for defects in this model is found not to fit with the previously reported squared-Poisson distribution. Under the influence of noise, the distributions are flattened, and can fit with the squared-Poisson or the modified-Poisson distribution. The defect lifetime and diffusive property of defects under the influence of noise are also checked in this model.

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.

Unsteady convection in tin in a Bridgman configuration

NASA Technical Reports Server (NTRS)

Knuteson, David J.; Fripp, Archibald L.; Woodell, Glenn A.; Debnam, William J., Jr.; Narayanan, Ranga

1991-01-01

When a quiescent fluid is heated sufficiently from below, steady convection will begin. Further heating will cause oscillatory and then turbulent flow. Theoretical results predict that the frequency of oscillation will depend on the square root of the Rayleigh number in the fluid. In the current work, liquid tin was heated from below for three aspect ratios, h/R = 3.4, 5.3, and 7.0. The experimental results are curve-fit for the square-root relation and also for a linear relation. The fit of the expression is evaluated using a correlation coefficient. An estimate for the first critical Rayleigh number (onset of steady convection) is obtained for both expressions. These values are compared to previous 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.

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.

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)

An ab initio potential energy surface for the formic acid dimer: zero-point energy, selected anharmonic fundamental energies, and ground-state tunneling splitting calculated in relaxed 1-4-mode subspaces.

PubMed

Qu, Chen; Bowman, Joel M

2016-09-14

We report a full-dimensional, permutationally invariant potential energy surface (PES) for the cyclic formic acid dimer. This PES is a least-squares fit to 13475 CCSD(T)-F12a/haTZ (VTZ for H and aVTZ for C and O) energies. The energy-weighted, root-mean-square fitting error is 11 cm -1 and the barrier for the double-proton transfer on the PES is 2848 cm -1 , in good agreement with the directly-calculated ab initio value of 2853 cm -1 . The zero-point vibrational energy of 15 337 ± 7 cm -1 is obtained from diffusion Monte Carlo calculations. Energies of fundamentals of fifteen modes are calculated using the vibrational self-consistent field and virtual-state configuration interaction method. The ground-state tunneling splitting is computed using a reduced-dimensional Hamiltonian with relaxed potentials. The highest-level, four-mode coupled calculation gives a tunneling splitting of 0.037 cm -1 , which is roughly twice the experimental value. The tunneling splittings of (DCOOH) 2 and (DCOOD) 2 from one to three mode calculations are, as expected, smaller than that for (HCOOH) 2 and consistent with experiment.

Validation of the Malay Version of the Inventory of Functional Status after Childbirth Questionnaire

PubMed Central

Noor, Norhayati Mohd; Aziz, Aniza Abd.; Mostapa, Mohd Rosmizaki; Awang, Zainudin

2015-01-01

Objective. This study was designed to examine the psychometric properties of Malay version of the Inventory of Functional Status after Childbirth (IFSAC). Design. A cross-sectional study. Materials and Methods. A total of 108 postpartum mothers attending Obstetrics and Gynaecology Clinic, in a tertiary teaching hospital in Malaysia, were involved. Construct validity and internal consistency were performed after the translation, content validity, and face validity process. The data were analyzed using Analysis of Moment Structure version 18 and Statistical Packages for the Social Sciences version 20. Results. The final model consists of four constructs, namely, infant care, personal care, household activities, and social and community activities, with 18 items demonstrating acceptable factor loadings, domain to domain correlation, and best fit (Chi-squared/degree of freedom = 1.678; Tucker-Lewis index = 0.923; comparative fit index = 0.936; and root mean square error of approximation = 0.080). Composite reliability and average variance extracted of the domains ranged from 0.659 to 0.921 and from 0.499 to 0.628, respectively. Conclusion. The study suggested that the four-factor model with 18 items of the Malay version of IFSAC was acceptable to be used to measure functional status after childbirth because it is valid, reliable, and simple. PMID:25667932

Spline-Based Smoothing of Airfoil Curvatures

NASA Technical Reports Server (NTRS)

Li, W.; Krist, S.

2008-01-01

Constrained fitting for airfoil curvature smoothing (CFACS) is a splinebased method of interpolating airfoil surface coordinates (and, concomitantly, airfoil thicknesses) between specified discrete design points so as to obtain smoothing of surface-curvature profiles in addition to basic smoothing of surfaces. CFACS was developed in recognition of the fact that the performance of a transonic airfoil is directly related to both the curvature profile and the smoothness of the airfoil surface. Older methods of interpolation of airfoil surfaces involve various compromises between smoothing of surfaces and exact fitting of surfaces to specified discrete design points. While some of the older methods take curvature profiles into account, they nevertheless sometimes yield unfavorable results, including curvature oscillations near end points and substantial deviations from desired leading-edge shapes. In CFACS as in most of the older methods, one seeks a compromise between smoothing and exact fitting. Unlike in the older methods, the airfoil surface is modified as little as possible from its original specified form and, instead, is smoothed in such a way that the curvature profile becomes a smooth fit of the curvature profile of the original airfoil specification. CFACS involves a combination of rigorous mathematical modeling and knowledge-based heuristics. Rigorous mathematical formulation provides assurance of removal of undesirable curvature oscillations with minimum modification of the airfoil geometry. Knowledge-based heuristics bridge the gap between theory and designers best practices. In CFACS, one of the measures of the deviation of an airfoil surface from smoothness is the sum of squares of the jumps in the third derivatives of a cubicspline interpolation of the airfoil data. This measure is incorporated into a formulation for minimizing an overall deviation- from-smoothness measure of the airfoil data within a specified fitting error tolerance. CFACS has been extensively tested on a number of supercritical airfoil data sets generated by inverse design and optimization computer programs. All of the smoothing results show that CFACS is able to generate unbiased smooth fits of curvature profiles, trading small modifications of geometry for increasing curvature smoothness by eliminating curvature oscillations and bumps (see figure).

Fourier-domain Mobility Spectrum Analysis (FMSA) for Characterizing Semiconductors with Multi-Electron/Hole Species

NASA Astrophysics Data System (ADS)

Cui, Boya; Kielb, Edward; Luo, Jiajun; Tang, Yang; Grayson, Matthew

Superlattices and narrow gap semiconductors often host multiple conducting species, such as electrons and holes, requiring a mobility spectral analysis (MSA) method to separate contributions to the conductivity. Here, a least-squares MSA method is introduced: the QR-algorithm Fourier-domain MSA (FMSA). Like other MSA methods, the FMSA sorts the conductivity contributions of different carrier species from magnetotransport measurements, arriving at a best fit to the experimentally measured longitudinal and Hall conductivities σxx and σxy, respectively. This method distinguishes itself from other methods by using the so-called QR-algorithm of linear algebra to achieve rapid convergence of the mobility spectrum as the solution to an eigenvalue problem, and by alternately solving this problem in both the mobility domain and its Fourier reciprocal-space. The result accurately fits a mobility range spanning nearly four orders of magnitude (μ = 300 to 1,000,000 cm2/V .s). This method resolves the mobility spectra as well as, or better than, competing MSA methods while also achieving high computational efficiency, requiring less than 30 second on average to converge to a solution on a standard desktop computer. Acknowledgement: Funded by AFOSR FA9550-15-1-0377 and AFOSR FA9550-15-1-0247.

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

Testing a healthcare provider-patient communicative relationship quality model of pharmaceutical care in hospitals.

PubMed

Wang, Dan; Liu, Chenxi; Zhang, Zinan; Ye, Liping; Zhang, Xinping

2018-06-01

Background Patient-centeredness and participatory care is increasingly regarded as a proxy for high-quality interpersonal care. Considering the development of patient-centeredness and participatory care relationship model in pharmacist-patient domain, it is of great significance to explore the mechanism of how pharmacist and patient participative behaviors influence relationship quality and patient outcomes. Objective To validate pharmacist-patient relationship quality model in Chinese hospitals. Four tertiary hospitals in 2017. Methods The provision of pharmaceutical care was investigated. A cross-sectional questionnaire survey covering different constructs of communicative relationship quality model was conducted and the associations among pairs of the study constructs were explored. Based on the results of confirmatory factor analysis, path analysis was conducted to validate the proposed communicative relationship quality model. Main outcome measure Model fit indicators including Tucker-Lewis index (TLI), comparative fit index (CFI), root mean square error of approximation (RMSEA) and weighted root mean square residual(WRMR). Results There were 589 patients included in our study. The final path model had an excellent fit (TLI = 0.98, CFI = 0.98, RMSEA = 0.05; WRMR = 1.06). HCP participative behavior/patient-centeredness (β = 0.79, p < 0.001) and interpersonal communication (β = 0.13, p < 0.001) directly impact the communicative relationship quality. But patient participative behavior was not a predictor of either communicative relationship quality or patient satisfaction. Conclusion HCP participative behavior/patient-centeredness and interpersonal communication are positively related to relationship quality, and relationship quality is mediator between HCP participative behavior and interpersonal communication with patient satisfaction.

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.

Measuring the Processes of Change From the Transtheoretical Model for Physical Activity and Exercise in Overweight and Obese Adults.

PubMed

Romain, Ahmed Jerôme; Bernard, Paquito; Hokayem, Marie; Gernigon, Christophe; Avignon, Antoine

2016-03-01

This study aimed to test three factorial structures conceptualizing the processes of change (POC) from the transtheoretical model and to examine the relationships between the POC and stages of change (SOC) among overweight and obese adults. Cross-sectional study. This study was conducted at the University Hospital of Montpellier, France. A sample of 289 overweight or obese participants (199 women) was enrolled in the study. Participants completed the POC and SOC questionnaires during a 5-day hospitalization for weight management. Structural equation modeling was used to compare the different factorial structures. The unweighted least-squares method was used to identify the best-fit indices for the five fully correlated model (goodness-of-fit statistic = .96; adjusted goodness-of-fit statistic = .95; standardized root mean residual = .062; normed-fit index = .95; parsimonious normed-fit index = .83; parsimonious goodness-of-fit statistic = .78). The multivariate analysis of variance was significant (p < .001). A post hoc test showed that individuals in advanced SOC used more of both experiential and behavioral POC than those in preaction stages, with effect sizes ranging from .06 to .29. This study supports the validity of the factorial structure of POC concerning physical activity and confirms the assumption that, in this context, people with excess weight use both experiential and behavioral processes. These preliminary results should be confirmed in a longitudinal study. © The Author(s) 2016.

A Numerical Fit of Analytical to Simulated Density Profiles in Dark Matter Haloes

NASA Astrophysics Data System (ADS)

Caimmi, R.; Marmo, C.; Valentinuzzi, T.

2005-06-01

Analytical and geometrical properties of generalized power-law (GPL) density profiles are investigated in detail. In particular, a one-to-one correspondence is found between mathematical parameters (a scaling radius, r_0, a scaling density, rho_0, and three exponents, alpha, beta, gamma), and geometrical parameters (the coordinates of the intersection of the asymptotes, x_C, y_C, and three vertical intercepts, b, b_beta, b_gamma, related to the curve and the asymptotes, respectively): (r_0,rho_0,alpha,beta,gamma) <--> (x_C,y_C,b,b_beta,b_gamma). Then GPL density profiles are compared with simulated dark haloes (SDH) density profiles, and nonlinear least-absolute values and least-squares fits involving the above mentioned five parameters (RFSM5 method) are prescribed. More specifically, the sum of absolute values or squares of absolute logarithmic residuals, R_i= log rhoSDH(r_i)-log rhoGPL(r_i), is evaluated on 10^5 points making a 5- dimension hypergrid, through a few iterations. The size is progressively reduced around a fiducial minimum, and superpositions on nodes of earlier hypergrids are avoided. An application is made to a sample of 17 SDHs on the scale of cluster of galaxies, within a flat LambdaCDM cosmological model (Rasia et al. 2004). In dealing with the mean SDH density profile, a virial radius, rvir, averaged over the whole sample, is assigned, which allows the calculation of the remaining parameters. Using a RFSM5 method provides a better fit with respect to other methods. The geometrical parameters, averaged over the whole sample of best fitting GPL density profiles, yield (alpha,beta,gamma) approx(0.6,3.1,1.0), to be compared with (alpha,beta,gamma)=(1,3,1), i.e. the NFW density profile (Navarro et al. 1995, 1996, 1997), (alpha,beta,gamma)=(1.5,3,1.5) (Moore et al. 1998, 1999), (alpha,beta,gamma)=(1,2.5,1) (Rasia et al. 2004); and, in addition, gamma approx 1.5 (Hiotelis 2003), deduced from the application of a RFSM5 method, but using a different definition of scaled radius, or concentration; and gamma approx 1.2-1.3 deduced from more recent high-resolution simulations (Diemand et al. 2004, Reed et al. 2005). No evident correlation is found between SDH dynamical state (relaxed or merging) and asymptotic inner slope of the fitting logarithmic density profile or (for SDH comparable virial masses) scaled radius. Mean values and standard deviations of some parameters are calculated, and in particular the decimal logarithm of the scaled radius, xivir, reads < log xivir >=0.74 and sigma_s log xivir=0.15-0.17, consistent with previous results related to NFW density profiles. It provides additional support to the idea, that NFW density profiles may be considered as a convenient way to parametrize SDH density profiles, without implying that it necessarily produces the best possible fit (Bullock et al. 2001). A certain degree of degeneracy is found in fitting GPL to SDH density profiles. If it is intrinsic to the RFSM5 method or it could be reduced by the next generation of high-resolution simulations, still remains an open question.

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.

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.

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.

The self-transcendence scale: an investigation of the factor structure among nursing home patients.

PubMed

Haugan, Gørill; Rannestad, Toril; Garåsen, Helge; Hammervold, Randi; Espnes, Geir Arild

2012-09-01

Self-transcendence, the ability to expand personal boundaries in multiple ways, has been found to provide well-being. The purpose of this study was to examine the dimensionality of the Norwegian version of the Self-Transcendence Scale, which comprises 15 items. Reed's empirical nursing theory of self-transcendence provided the theoretical framework; self-transcendence includes an interpersonal, intrapersonal, transpersonal, and temporal dimension. Cross-sectional data were obtained from a sample of 202 cognitively intact elderly patients in 44 Norwegian nursing homes. Exploratory factor analysis revealed two and four internally consistent dimensions of self-transcendence, explaining 35.3% (two factors) and 50.7% (four factors) of the variance, respectively. Confirmatory factor analysis indicated that the hypothesized two- and four-factor models fitted better than the one-factor model (cx (2), root mean square error of approximation, standardized root mean square residual, normed fit index, nonnormed fit index, comparative fit index, goodness-of-fit index, and adjusted goodness-of-fit index). The findings indicate self-transcendence as a multifactorial construct; at present, we conclude that the two-factor model might be the most accurate and reasonable measure of self-transcendence. This research generates insights in the application of the widely used Self-Transcendence Scale by investigating its psychometric properties by applying a confirmatory factor analysis. It also generates new research-questions on the associations between self-transcendence and well-being.