Solving the Inverse-Square Problem with Complex Variables

ERIC Educational Resources Information Center

Gauthier, N.

2005-01-01

The equation of motion for a mass that moves under the influence of a central, inverse-square force is formulated and solved as a problem in complex variables. To find the solution, the constancy of angular momentum is first established using complex variables. Next, the complex position coordinate and complex velocity of the particle are assumed…

Linear Least Squares for Correlated Data

NASA Technical Reports Server (NTRS)

Dean, Edwin B.

1988-01-01

Throughout the literature authors have consistently discussed the suspicion that regression results were less than satisfactory when the independent variables were correlated. Camm, Gulledge, and Womer, and Womer and Marcotte provide excellent applied examples of these concerns. Many authors have obtained partial solutions for this problem as discussed by Womer and Marcotte and Wonnacott and Wonnacott, which result in generalized least squares algorithms to solve restrictive cases. This paper presents a simple but relatively general multivariate method for obtaining linear least squares coefficients which are free of the statistical distortion created by correlated independent variables.

An Efficient Estimator for Moving Target Localization Using Multi-Station Dual-Frequency Radars.

PubMed

Huang, Jiyan; Zhang, Ying; Luo, Shan

2017-12-15

Localization of a moving target in a dual-frequency radars system has now gained considerable attention. The noncoherent localization approach based on a least squares (LS) estimator has been addressed in the literature. Compared with the LS method, a novel localization method based on a two-step weighted least squares estimator is proposed to increase positioning accuracy for a multi-station dual-frequency radars system in this paper. The effects of signal noise ratio and the number of samples on the performance of range estimation are also analyzed in the paper. Furthermore, both the theoretical variance and Cramer-Rao lower bound (CRLB) are derived. The simulation results verified the proposed method.

An Efficient Estimator for Moving Target Localization Using Multi-Station Dual-Frequency Radars

PubMed Central

Zhang, Ying; Luo, Shan

2017-01-01

Localization of a moving target in a dual-frequency radars system has now gained considerable attention. The noncoherent localization approach based on a least squares (LS) estimator has been addressed in the literature. Compared with the LS method, a novel localization method based on a two-step weighted least squares estimator is proposed to increase positioning accuracy for a multi-station dual-frequency radars system in this paper. The effects of signal noise ratio and the number of samples on the performance of range estimation are also analyzed in the paper. Furthermore, both the theoretical variance and Cramer–Rao lower bound (CRLB) are derived. The simulation results verified the proposed method. PMID:29244727

Temporal analysis of the frequency and duration of low and high streamflow: Years of record needed to characterize streamflow variability

USGS Publications Warehouse

Huh, S.; Dickey, D.A.; Meador, M.R.; Ruhl, K.E.

2005-01-01

A temporal analysis of the number and duration of exceedences of high- and low-flow thresholds was conducted to determine the number of years required to detect a level shift using data from Virginia, North Carolina, and South Carolina. Two methods were used - ordinary least squares assuming a known error variance and generalized least squares without a known error variance. Using ordinary least squares, the mean number of years required to detect a one standard deviation level shift in measures of low-flow variability was 57.2 (28.6 on either side of the break), compared to 40.0 years for measures of high-flow variability. These means become 57.6 and 41.6 when generalized least squares is used. No significant relations between years and elevation or drainage area were detected (P>0.05). Cluster analysis did not suggest geographic patterns in years related to physiography or major hydrologic regions. Referring to the number of observations required to detect a one standard deviation shift as 'characterizing' the variability, it appears that at least 20 years of record on either side of a shift may be necessary to adequately characterize high-flow variability. A longer streamflow record (about 30 years on either side) may be required to characterize low-flow variability. ?? 2005 Elsevier B.V. All rights reserved.

Multivariate fault isolation of batch processes via variable selection in partial least squares discriminant analysis.

PubMed

Yan, Zhengbing; Kuang, Te-Hui; Yao, Yuan

2017-09-01

In recent years, multivariate statistical monitoring of batch processes has become a popular research topic, wherein multivariate fault isolation is an important step aiming at the identification of the faulty variables contributing most to the detected process abnormality. Although contribution plots have been commonly used in statistical fault isolation, such methods suffer from the smearing effect between correlated variables. In particular, in batch process monitoring, the high autocorrelations and cross-correlations that exist in variable trajectories make the smearing effect unavoidable. To address such a problem, a variable selection-based fault isolation method is proposed in this research, which transforms the fault isolation problem into a variable selection problem in partial least squares discriminant analysis and solves it by calculating a sparse partial least squares model. As different from the traditional methods, the proposed method emphasizes the relative importance of each process variable. Such information may help process engineers in conducting root-cause diagnosis. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

An Alternative Two Stage Least Squares (2SLS) Estimator for Latent Variable Equations.

ERIC Educational Resources Information Center

Bollen, Kenneth A.

1996-01-01

An alternative two-stage least squares (2SLS) estimator of the parameters in LISREL type models is proposed and contrasted with existing estimators. The new 2SLS estimator allows observed and latent variables to originate from nonnormal distributions, is consistent, has a known asymptotic covariance matrix, and can be estimated with standard…

The crux of the method: assumptions in ordinary least squares and logistic regression.

PubMed

Long, Rebecca G

2008-10-01

Logistic regression has increasingly become the tool of choice when analyzing data with a binary dependent variable. While resources relating to the technique are widely available, clear discussions of why logistic regression should be used in place of ordinary least squares regression are difficult to find. The current paper compares and contrasts the assumptions of ordinary least squares with those of logistic regression and explains why logistic regression's looser assumptions make it adept at handling violations of the more important assumptions in ordinary least squares.

Identification of multivariable nonlinear systems in the presence of colored noises using iterative hierarchical least squares algorithm.

PubMed

Jafari, Masoumeh; Salimifard, Maryam; Dehghani, Maryam

2014-07-01

This paper presents an efficient method for identification of nonlinear Multi-Input Multi-Output (MIMO) systems in the presence of colored noises. The method studies the multivariable nonlinear Hammerstein and Wiener models, in which, the nonlinear memory-less block is approximated based on arbitrary vector-based basis functions. The linear time-invariant (LTI) block is modeled by an autoregressive moving average with exogenous (ARMAX) model which can effectively describe the moving average noises as well as the autoregressive and the exogenous dynamics. According to the multivariable nature of the system, a pseudo-linear-in-the-parameter model is obtained which includes two different kinds of unknown parameters, a vector and a matrix. Therefore, the standard least squares algorithm cannot be applied directly. To overcome this problem, a Hierarchical Least Squares Iterative (HLSI) algorithm is used to simultaneously estimate the vector and the matrix of unknown parameters as well as the noises. The efficiency of the proposed identification approaches are investigated through three nonlinear MIMO case studies. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Variable selection based on clustering analysis for improvement of polyphenols prediction in green tea using synchronous fluorescence spectra

NASA Astrophysics Data System (ADS)

Shan, Jiajia; Wang, Xue; Zhou, Hao; Han, Shuqing; Riza, Dimas Firmanda Al; Kondo, Naoshi

2018-04-01

Synchronous fluorescence spectra, combined with multivariate analysis were used to predict flavonoids content in green tea rapidly and nondestructively. This paper presented a new and efficient spectral intervals selection method called clustering based partial least square (CL-PLS), which selected informative wavelengths by combining clustering concept and partial least square (PLS) methods to improve models’ performance by synchronous fluorescence spectra. The fluorescence spectra of tea samples were obtained and k-means and kohonen-self organizing map clustering algorithms were carried out to cluster full spectra into several clusters, and sub-PLS regression model was developed on each cluster. Finally, CL-PLS models consisting of gradually selected clusters were built. Correlation coefficient (R) was used to evaluate the effect on prediction performance of PLS models. In addition, variable influence on projection partial least square (VIP-PLS), selectivity ratio partial least square (SR-PLS), interval partial least square (iPLS) models and full spectra PLS model were investigated and the results were compared. The results showed that CL-PLS presented the best result for flavonoids prediction using synchronous fluorescence spectra.

Variable selection based on clustering analysis for improvement of polyphenols prediction in green tea using synchronous fluorescence spectra.

PubMed

Shan, Jiajia; Wang, Xue; Zhou, Hao; Han, Shuqing; Riza, Dimas Firmanda Al; Kondo, Naoshi

2018-03-13

Synchronous fluorescence spectra, combined with multivariate analysis were used to predict flavonoids content in green tea rapidly and nondestructively. This paper presented a new and efficient spectral intervals selection method called clustering based partial least square (CL-PLS), which selected informative wavelengths by combining clustering concept and partial least square (PLS) methods to improve models' performance by synchronous fluorescence spectra. The fluorescence spectra of tea samples were obtained and k-means and kohonen-self organizing map clustering algorithms were carried out to cluster full spectra into several clusters, and sub-PLS regression model was developed on each cluster. Finally, CL-PLS models consisting of gradually selected clusters were built. Correlation coefficient (R) was used to evaluate the effect on prediction performance of PLS models. In addition, variable influence on projection partial least square (VIP-PLS), selectivity ratio partial least square (SR-PLS), interval partial least square (iPLS) models and full spectra PLS model were investigated and the results were compared. The results showed that CL-PLS presented the best result for flavonoids prediction using synchronous fluorescence spectra.

[Formula: see text]-regularized recursive total least squares based sparse system identification for the error-in-variables.

PubMed

Lim, Jun-Seok; Pang, Hee-Suk

2016-01-01

In this paper an [Formula: see text]-regularized recursive total least squares (RTLS) algorithm is considered for the sparse system identification. Although recursive least squares (RLS) has been successfully applied in sparse system identification, the estimation performance in RLS based algorithms becomes worse, when both input and output are contaminated by noise (the error-in-variables problem). We proposed an algorithm to handle the error-in-variables problem. The proposed [Formula: see text]-RTLS algorithm is an RLS like iteration using the [Formula: see text] regularization. The proposed algorithm not only gives excellent performance but also reduces the required complexity through the effective inversion matrix handling. Simulations demonstrate the superiority of the proposed [Formula: see text]-regularized RTLS for the sparse system identification setting.

Petroleomics by electrospray ionization FT-ICR mass spectrometry coupled to partial least squares with variable selection methods: prediction of the total acid number of crude oils.

PubMed

Terra, Luciana A; Filgueiras, Paulo R; Tose, Lílian V; Romão, Wanderson; de Souza, Douglas D; de Castro, Eustáquio V R; de Oliveira, Mirela S L; Dias, Júlio C M; Poppi, Ronei J

2014-10-07

Negative-ion mode electrospray ionization, ESI(-), with Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) was coupled to a Partial Least Squares (PLS) regression and variable selection methods to estimate the total acid number (TAN) of Brazilian crude oil samples. Generally, ESI(-)-FT-ICR mass spectra present a power of resolution of ca. 500,000 and a mass accuracy less than 1 ppm, producing a data matrix containing over 5700 variables per sample. These variables correspond to heteroatom-containing species detected as deprotonated molecules, [M - H](-) ions, which are identified primarily as naphthenic acids, phenols and carbazole analog species. The TAN values for all samples ranged from 0.06 to 3.61 mg of KOH g(-1). To facilitate the spectral interpretation, three methods of variable selection were studied: variable importance in the projection (VIP), interval partial least squares (iPLS) and elimination of uninformative variables (UVE). The UVE method seems to be more appropriate for selecting important variables, reducing the dimension of the variables to 183 and producing a root mean square error of prediction of 0.32 mg of KOH g(-1). By reducing the size of the data, it was possible to relate the selected variables with their corresponding molecular formulas, thus identifying the main chemical species responsible for the TAN values.

First-Order System Least-Squares for Second-Order Elliptic Problems with Discontinuous Coefficients

NASA Technical Reports Server (NTRS)

Manteuffel, Thomas A.; McCormick, Stephen F.; Starke, Gerhard

1996-01-01

The first-order system least-squares methodology represents an alternative to standard mixed finite element methods. Among its advantages is the fact that the finite element spaces approximating the pressure and flux variables are not restricted by the inf-sup condition and that the least-squares functional itself serves as an appropriate error measure. This paper studies the first-order system least-squares approach for scalar second-order elliptic boundary value problems with discontinuous coefficients. Ellipticity of an appropriately scaled least-squares bilinear form of the size of the jumps in the coefficients leading to adequate finite element approximation results. The occurrence of singularities at interface corners and cross-points is discussed. and a weighted least-squares functional is introduced to handle such cases. Numerical experiments are presented for two test problems to illustrate the performance of this approach.

Coupled Research in Ocean Acoustics and Signal Processing for the Next Generation of Underwater Acoustic Communication Systems

DTIC Science & Technology

2016-08-05

technique which used unobserved ”intermediate” variables to break a high-dimensional estimation problem such as least- squares (LS) optimization of a large...Least Squares (GEM-LS). The estimator is iterative and the work in this time period focused on characterizing the convergence properties of this...ap- proach by relaxing the statistical assumptions which is termed the Relaxed Approximate Graph-Structured Recursive Least Squares (RAGS-RLS). This

Generalized Structured Component Analysis

ERIC Educational Resources Information Center

Hwang, Heungsun; Takane, Yoshio

2004-01-01

We propose an alternative method to partial least squares for path analysis with components, called generalized structured component analysis. The proposed method replaces factors by exact linear combinations of observed variables. It employs a well-defined least squares criterion to estimate model parameters. As a result, the proposed method…

Effect of genetic algorithm as a variable selection method on different chemometric models applied for the analysis of binary mixture of amoxicillin and flucloxacillin: A comparative study

NASA Astrophysics Data System (ADS)

Attia, Khalid A. M.; Nassar, Mohammed W. I.; El-Zeiny, Mohamed B.; Serag, Ahmed

2016-03-01

Different chemometric models were applied for the quantitative analysis of amoxicillin (AMX), and flucloxacillin (FLX) in their binary mixtures, namely, partial least squares (PLS), spectral residual augmented classical least squares (SRACLS), concentration residual augmented classical least squares (CRACLS) and artificial neural networks (ANNs). All methods were applied with and without variable selection procedure (genetic algorithm GA). The methods were used for the quantitative analysis of the drugs in laboratory prepared mixtures and real market sample via handling the UV spectral data. Robust and simpler models were obtained by applying GA. The proposed methods were found to be rapid, simple and required no preliminary separation steps.

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.

Partial least squares correspondence analysis: A framework to simultaneously analyze behavioral and genetic data.

PubMed

Beaton, Derek; Dunlop, Joseph; Abdi, Hervé

2016-12-01

For nearly a century, detecting the genetic contributions to cognitive and behavioral phenomena has been a core interest for psychological research. Recently, this interest has been reinvigorated by the availability of genotyping technologies (e.g., microarrays) that provide new genetic data, such as single nucleotide polymorphisms (SNPs). These SNPs-which represent pairs of nucleotide letters (e.g., AA, AG, or GG) found at specific positions on human chromosomes-are best considered as categorical variables, but this coding scheme can make difficult the multivariate analysis of their relationships with behavioral measurements, because most multivariate techniques developed for the analysis between sets of variables are designed for quantitative variables. To palliate this problem, we present a generalization of partial least squares-a technique used to extract the information common to 2 different data tables measured on the same observations-called partial least squares correspondence analysis-that is specifically tailored for the analysis of categorical and mixed ("heterogeneous") data types. Here, we formally define and illustrate-in a tutorial format-how partial least squares correspondence analysis extends to various types of data and design problems that are particularly relevant for psychological research that include genetic data. We illustrate partial least squares correspondence analysis with genetic, behavioral, and neuroimaging data from the Alzheimer's Disease Neuroimaging Initiative. R code is available on the Comprehensive R Archive Network and via the authors' websites. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

A spectral mimetic least-squares method

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

Bochev, Pavel; Gerritsma, Marc

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

A spectral mimetic least-squares method

DOE PAGES

Bochev, Pavel; Gerritsma, Marc

2014-09-01

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

Variable forgetting factor mechanisms for diffusion recursive least squares algorithm in sensor networks

NASA Astrophysics Data System (ADS)

Zhang, Ling; Cai, Yunlong; Li, Chunguang; de Lamare, Rodrigo C.

2017-12-01

In this work, we present low-complexity variable forgetting factor (VFF) techniques for diffusion recursive least squares (DRLS) algorithms. Particularly, we propose low-complexity VFF-DRLS algorithms for distributed parameter and spectrum estimation in sensor networks. For the proposed algorithms, they can adjust the forgetting factor automatically according to the posteriori error signal. We develop detailed analyses in terms of mean and mean square performance for the proposed algorithms and derive mathematical expressions for the mean square deviation (MSD) and the excess mean square error (EMSE). The simulation results show that the proposed low-complexity VFF-DRLS algorithms achieve superior performance to the existing DRLS algorithm with fixed forgetting factor when applied to scenarios of distributed parameter and spectrum estimation. Besides, the simulation results also demonstrate a good match for our proposed analytical expressions.

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.

A note on implementation of decaying product correlation structures for quasi-least squares.

PubMed

Shults, Justine; Guerra, Matthew W

2014-08-30

This note implements an unstructured decaying product matrix via the quasi-least squares approach for estimation of the correlation parameters in the framework of generalized estimating equations. The structure we consider is fairly general without requiring the large number of parameters that are involved in a fully unstructured matrix. It is straightforward to show that the quasi-least squares estimators of the correlation parameters yield feasible values for the unstructured decaying product structure. Furthermore, subject to conditions that are easily checked, the quasi-least squares estimators are valid for longitudinal Bernoulli data. We demonstrate implementation of the structure in a longitudinal clinical trial with both a continuous and binary outcome variable. Copyright © 2014 John Wiley & Sons, Ltd.

On Using the Average Intercorrelation Among Predictor Variables and Eigenvector Orientation to Choose a Regression Solution.

ERIC Educational Resources Information Center

Mugrage, Beverly; And Others

Three ridge regression solutions are compared with ordinary least squares regression and with principal components regression using all components. Ridge regression, particularly the Lawless-Wang solution, out-performed ordinary least squares regression and the principal components solution on the criteria of stability of coefficient and closeness…

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

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

Mu, Lin; Wang, Junping; Ye, Xiu

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore » the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.« less

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu

2017-08-17

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore » the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.« less

A numerical scheme based on radial basis function finite difference (RBF-FD) technique for solving the high-dimensional nonlinear Schrödinger equations using an explicit time discretization: Runge-Kutta method

NASA Astrophysics Data System (ADS)

Dehghan, Mehdi; Mohammadi, Vahid

2017-08-01

In this research, we investigate the numerical solution of nonlinear Schrödinger equations in two and three dimensions. The numerical meshless method which will be used here is RBF-FD technique. The main advantage of this method is the approximation of the required derivatives based on finite difference technique at each local-support domain as Ωi. At each Ωi, we require to solve a small linear system of algebraic equations with a conditionally positive definite matrix of order 1 (interpolation matrix). This scheme is efficient and its computational cost is same as the moving least squares (MLS) approximation. A challengeable issue is choosing suitable shape parameter for interpolation matrix in this way. In order to overcome this matter, an algorithm which was established by Sarra (2012), will be applied. This algorithm computes the condition number of the local interpolation matrix using the singular value decomposition (SVD) for obtaining the smallest and largest singular values of that matrix. Moreover, an explicit method based on Runge-Kutta formula of fourth-order accuracy will be applied for approximating the time variable. It also decreases the computational costs at each time step since we will not solve a nonlinear system. On the other hand, to compare RBF-FD method with another meshless technique, the moving kriging least squares (MKLS) approximation is considered for the studied model. Our results demonstrate the ability of the present approach for solving the applicable model which is investigated in the current research work.

Classification and quantitation of milk powder by near-infrared spectroscopy and mutual information-based variable selection and partial least squares

NASA Astrophysics Data System (ADS)

Chen, Hui; Tan, Chao; Lin, Zan; Wu, Tong

2018-01-01

Milk is among the most popular nutrient source worldwide, which is of great interest due to its beneficial medicinal properties. The feasibility of the classification of milk powder samples with respect to their brands and the determination of protein concentration is investigated by NIR spectroscopy along with chemometrics. Two datasets were prepared for experiment. One contains 179 samples of four brands for classification and the other contains 30 samples for quantitative analysis. Principal component analysis (PCA) was used for exploratory analysis. Based on an effective model-independent variable selection method, i.e., minimal-redundancy maximal-relevance (MRMR), only 18 variables were selected to construct a partial least-square discriminant analysis (PLS-DA) model. On the test set, the PLS-DA model based on the selected variable set was compared with the full-spectrum PLS-DA model, both of which achieved 100% accuracy. In quantitative analysis, the partial least-square regression (PLSR) model constructed by the selected subset of 260 variables outperforms significantly the full-spectrum model. It seems that the combination of NIR spectroscopy, MRMR and PLS-DA or PLSR is a powerful tool for classifying different brands of milk and determining the protein content.

Hybrid robust model based on an improved functional link neural network integrating with partial least square (IFLNN-PLS) and its application to predicting key process variables.

PubMed

He, Yan-Lin; Xu, Yuan; Geng, Zhi-Qiang; Zhu, Qun-Xiong

2016-03-01

In this paper, a hybrid robust model based on an improved functional link neural network integrating with partial least square (IFLNN-PLS) is proposed. Firstly, an improved functional link neural network with small norm of expanded weights and high input-output correlation (SNEWHIOC-FLNN) was proposed for enhancing the generalization performance of FLNN. Unlike the traditional FLNN, the expanded variables of the original inputs are not directly used as the inputs in the proposed SNEWHIOC-FLNN model. The original inputs are attached to some small norm of expanded weights. As a result, the correlation coefficient between some of the expanded variables and the outputs is enhanced. The larger the correlation coefficient is, the more relevant the expanded variables tend to be. In the end, the expanded variables with larger correlation coefficient are selected as the inputs to improve the performance of the traditional FLNN. In order to test the proposed SNEWHIOC-FLNN model, three UCI (University of California, Irvine) regression datasets named Housing, Concrete Compressive Strength (CCS), and Yacht Hydro Dynamics (YHD) are selected. Then a hybrid model based on the improved FLNN integrating with partial least square (IFLNN-PLS) was built. In IFLNN-PLS model, the connection weights are calculated using the partial least square method but not the error back propagation algorithm. Lastly, IFLNN-PLS was developed as an intelligent measurement model for accurately predicting the key variables in the Purified Terephthalic Acid (PTA) process and the High Density Polyethylene (HDPE) process. Simulation results illustrated that the IFLNN-PLS could significant improve the prediction performance. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

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.

Multi-objective aerodynamic shape optimization of small livestock trailers

NASA Astrophysics Data System (ADS)

Gilkeson, C. A.; Toropov, V. V.; Thompson, H. M.; Wilson, M. C. T.; Foxley, N. A.; Gaskell, P. H.

2013-11-01

This article presents a formal optimization study of the design of small livestock trailers, within which the majority of animals are transported to market in the UK. The benefits of employing a headboard fairing to reduce aerodynamic drag without compromising the ventilation of the animals' microclimate are investigated using a multi-stage process involving computational fluid dynamics (CFD), optimal Latin hypercube (OLH) design of experiments (DoE) and moving least squares (MLS) metamodels. Fairings are parameterized in terms of three design variables and CFD solutions are obtained at 50 permutations of design variables. Both global and local search methods are employed to locate the global minimum from metamodels of the objective functions and a Pareto front is generated. The importance of carefully selecting an objective function is demonstrated and optimal fairing designs, offering drag reductions in excess of 5% without compromising animal ventilation, are presented.

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.

Optimal moving grids for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Wathen, A. J.

1989-01-01

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of partial differential equation solutions in the least squares norm.

Optimal moving grids for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Wathen, A. J.

1992-01-01

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.

Credit Risk Evaluation Using a C-Variable Least Squares Support Vector Classification Model

NASA Astrophysics Data System (ADS)

Yu, Lean; Wang, Shouyang; Lai, K. K.

Credit risk evaluation is one of the most important issues in financial risk management. In this paper, a C-variable least squares support vector classification (C-VLSSVC) model is proposed for credit risk analysis. The main idea of this model is based on the prior knowledge that different classes may have different importance for modeling and more weights should be given to those classes with more importance. The C-VLSSVC model can be constructed by a simple modification of the regularization parameter in LSSVC, whereby more weights are given to the lease squares classification errors with important classes than the lease squares classification errors with unimportant classes while keeping the regularized terms in its original form. For illustration purpose, a real-world credit dataset is used to test the effectiveness of the C-VLSSVC model.

Dynamic least-squares kernel density modeling of Fokker-Planck equations with application to neural population.

PubMed

Shotorban, Babak

2010-04-01

The dynamic least-squares kernel density (LSQKD) model [C. Pantano and B. Shotorban, Phys. Rev. E 76, 066705 (2007)] is used to solve the Fokker-Planck equations. In this model the probability density function (PDF) is approximated by a linear combination of basis functions with unknown parameters whose governing equations are determined by a global least-squares approximation of the PDF in the phase space. In this work basis functions are set to be Gaussian for which the mean, variance, and covariances are governed by a set of partial differential equations (PDEs) or ordinary differential equations (ODEs) depending on what phase-space variables are approximated by Gaussian functions. Three sample problems of univariate double-well potential, bivariate bistable neurodynamical system [G. Deco and D. Martí, Phys. Rev. E 75, 031913 (2007)], and bivariate Brownian particles in a nonuniform gas are studied. The LSQKD is verified for these problems as its results are compared against the results of the method of characteristics in nondiffusive cases and the stochastic particle method in diffusive cases. For the double-well potential problem it is observed that for low to moderate diffusivity the dynamic LSQKD well predicts the stationary PDF for which there is an exact solution. A similar observation is made for the bistable neurodynamical system. In both these problems least-squares approximation is made on all phase-space variables resulting in a set of ODEs with time as the independent variable for the Gaussian function parameters. In the problem of Brownian particles in a nonuniform gas, this approximation is made only for the particle velocity variable leading to a set of PDEs with time and particle position as independent variables. Solving these PDEs, a very good performance by LSQKD is observed for a wide range of diffusivities.

A Partial Least-Squares Analysis of Health-Related Quality-of-Life Outcomes After Aneurysmal Subarachnoid Hemorrhage.

PubMed

Young, Julia M; Morgan, Benjamin R; Mišić, Bratislav; Schweizer, Tom A; Ibrahim, George M; Macdonald, R Loch

2015-12-01

Individuals who have aneurysmal subarachnoid hemorrhages (SAHs) experience decreased health-related qualities of life (HRQoLs) that persist after the primary insult. To identify clinical variables that concurrently associate with HRQoL outcomes by using a partial least-squares approach, which has the distinct advantage of explaining multidimensional variance where predictor variables may be highly collinear. Data collected from the CONSCIOUS-1 trial was used to extract 29 clinical variables including SAH presentation, hospital procedures, and demographic information in addition to 5 HRQoL outcome variables for 256 individuals. A partial least-squares analysis was performed by calculating a heterogeneous correlation matrix and applying singular value decomposition to determine components that best represent the correlations between the 2 sets of variables. Bootstrapping was used to estimate statistical significance. The first 2 components accounting for 81.6% and 7.8% of the total variance revealed significant associations between clinical predictors and HRQoL outcomes. The first component identified associations between disability in self-care with longer durations of critical care stay, invasive intracranial monitoring, ventricular drain time, poorer clinical grade on presentation, greater amounts of cerebral spinal fluid drainage, and a history of hypertension. The second component identified associations between disability due to pain and discomfort as well as anxiety and depression with greater body mass index, abnormal heart rate, longer durations of deep sedation and critical care, and higher World Federation of Neurosurgical Societies and Hijdra scores. By applying a data-driven, multivariate approach, we identified robust associations between SAH clinical presentations and HRQoL outcomes. EQ-VAS, EuroQoL visual analog scaleHRQoL, health-related quality of lifeICU, intensive care unitIVH, intraventricular hemorrhagePLS, partial least squaresSAH, subarachnoid hemorrhageSVD, singular value decompositionWFNS, World Federation of Neurosurgical Societies.

Space-Time Joint Interference Cancellation Using Fuzzy-Inference-Based Adaptive Filtering Techniques in Frequency-Selective Multipath Channels

NASA Astrophysics Data System (ADS)

Hu, Chia-Chang; Lin, Hsuan-Yu; Chen, Yu-Fan; Wen, Jyh-Horng

2006-12-01

An adaptive minimum mean-square error (MMSE) array receiver based on the fuzzy-logic recursive least-squares (RLS) algorithm is developed for asynchronous DS-CDMA interference suppression in the presence of frequency-selective multipath fading. This receiver employs a fuzzy-logic control mechanism to perform the nonlinear mapping of the squared error and squared error variation, denoted by ([InlineEquation not available: see fulltext.],[InlineEquation not available: see fulltext.]), into a forgetting factor[InlineEquation not available: see fulltext.]. For the real-time applicability, a computationally efficient version of the proposed receiver is derived based on the least-mean-square (LMS) algorithm using the fuzzy-inference-controlled step-size[InlineEquation not available: see fulltext.]. This receiver is capable of providing both fast convergence/tracking capability as well as small steady-state misadjustment as compared with conventional LMS- and RLS-based MMSE DS-CDMA receivers. Simulations show that the fuzzy-logic LMS and RLS algorithms outperform, respectively, other variable step-size LMS (VSS-LMS) and variable forgetting factor RLS (VFF-RLS) algorithms at least 3 dB and 1.5 dB in bit-error-rate (BER) for multipath fading channels.

Determination of main fruits in adulterated nectars by ATR-FTIR spectroscopy combined with multivariate calibration and variable selection methods.

PubMed

Miaw, Carolina Sheng Whei; Assis, Camila; Silva, Alessandro Rangel Carolino Sales; Cunha, Maria Luísa; Sena, Marcelo Martins; de Souza, Scheilla Vitorino Carvalho

2018-07-15

Grape, orange, peach and passion fruit nectars were formulated and adulterated by dilution with syrup, apple and cashew juices at 10 levels for each adulterant. Attenuated total reflectance Fourier transform mid infrared (ATR-FTIR) spectra were obtained. Partial least squares (PLS) multivariate calibration models allied to different variable selection methods, such as interval partial least squares (iPLS), ordered predictors selection (OPS) and genetic algorithm (GA), were used to quantify the main fruits. PLS improved by iPLS-OPS variable selection showed the highest predictive capacity to quantify the main fruit contents. The selected variables in the final models varied from 72 to 100; the root mean square errors of prediction were estimated from 0.5 to 2.6%; the correlation coefficients of prediction ranged from 0.948 to 0.990; and, the mean relative errors of prediction varied from 3.0 to 6.7%. All of the developed models were validated. Copyright © 2018 Elsevier Ltd. All rights reserved.

Interpreting the Results of Weighted Least-Squares Regression: Caveats for the Statistical Consumer.

ERIC Educational Resources Information Center

Willett, John B.; Singer, Judith D.

In research, data sets often occur in which the variance of the distribution of the dependent variable at given levels of the predictors is a function of the values of the predictors. In this situation, the use of weighted least-squares (WLS) or techniques is required. Weights suitable for use in a WLS regression analysis must be estimated. A…

49 CFR 375.213 - What information must I provide to a prospective individual shipper?

Code of Federal Regulations, 2010 CFR

2010-10-01

... type font size is 10 points or larger and the size of the booklet is at least as large as 36 square... cover in 12-point or larger bold or full-faced type: “Your Rights and Responsibilities When You Move...

Random Initialisation of the Spectral Variables: an Alternate Approach for Initiating Multivariate Curve Resolution Alternating Least Square (MCR-ALS) Analysis.

PubMed

Kumar, Keshav

2017-11-01

Multivariate curve resolution alternating least square (MCR-ALS) analysis is the most commonly used curve resolution technique. The MCR-ALS model is fitted using the alternate least square (ALS) algorithm that needs initialisation of either contribution profiles or spectral profiles of each of the factor. The contribution profiles can be initialised using the evolve factor analysis; however, in principle, this approach requires that data must belong to the sequential process. The initialisation of the spectral profiles are usually carried out using the pure variable approach such as SIMPLISMA algorithm, this approach demands that each factor must have the pure variables in the data sets. Despite these limitations, the existing approaches have been quite a successful for initiating the MCR-ALS analysis. However, the present work proposes an alternate approach for the initialisation of the spectral variables by generating the random variables in the limits spanned by the maxima and minima of each spectral variable of the data set. The proposed approach does not require that there must be pure variables for each component of the multicomponent system or the concentration direction must follow the sequential process. The proposed approach is successfully validated using the excitation-emission matrix fluorescence data sets acquired for certain fluorophores with significant spectral overlap. The calculated contribution and spectral profiles of these fluorophores are found to correlate well with the experimental results. In summary, the present work proposes an alternate way to initiate the MCR-ALS analysis.

Comparison between results of solution of Burgers' equation and Laplace's equation by Galerkin and least-square finite element methods

NASA Astrophysics Data System (ADS)

Adib, Arash; Poorveis, Davood; Mehraban, Farid

2018-03-01

In this research, two equations are considered as examples of hyperbolic and elliptic equations. In addition, two finite element methods are applied for solving of these equations. The purpose of this research is the selection of suitable method for solving each of two equations. Burgers' equation is a hyperbolic equation. This equation is a pure advection (without diffusion) equation. This equation is one-dimensional and unsteady. A sudden shock wave is introduced to the model. This wave moves without deformation. In addition, Laplace's equation is an elliptical equation. This equation is steady and two-dimensional. The solution of Laplace's equation in an earth dam is considered. By solution of Laplace's equation, head pressure and the value of seepage in the directions X and Y are calculated in different points of earth dam. At the end, water table is shown in the earth dam. For Burgers' equation, least-square method can show movement of wave with oscillation but Galerkin method can not show it correctly (the best method for solving of the Burgers' equation is discrete space by least-square finite element method and discrete time by forward difference.). For Laplace's equation, Galerkin and least square methods can show water table correctly in earth dam.

Application of the Galerkin/least-squares formulation to the analysis of hypersonic flows. II - Flow past a double ellipse

NASA Technical Reports Server (NTRS)

Chalot, F.; Hughes, T. J. R.; Johan, Z.; Shakib, F.

1991-01-01

A finite element method for the compressible Navier-Stokes equations is introduced. The discretization is based on entropy variables. The methodology is developed within the framework of a Galerkin/least-squares formulation to which a discontinuity-capturing operator is added. Results for four test cases selected among those of the Workshop on Hypersonic Flows for Reentry Problems are presented.

Application of the Galerkin/least-squares formulation to the analysis of hypersonic flows. I - Flow over a two-dimensional ramp

NASA Technical Reports Server (NTRS)

Chalot, F.; Hughes, T. J. R.; Johan, Z.; Shakib, F.

1991-01-01

An FEM for the compressible Navier-Stokes equations is introduced. The discretization is based on entropy variables. The methodology is developed within the framework of a Galerkin/least-squares formulation to which a discontinuity-capturing operator is added. Results for three test cases selected among those of the Workshop on Hypersonic Flows for Reentry Problems are presented.

An Analysis of Factor Extraction Strategies: A Comparison of the Relative Strengths of Principal Axis, Ordinary Least Squares, and Maximum Likelihood in Research Contexts That Include Both Categorical and Continuous Variables

ERIC Educational Resources Information Center

Coughlin, Kevin B.

2013-01-01

This study is intended to provide researchers with empirically derived guidelines for conducting factor analytic studies in research contexts that include dichotomous and continuous levels of measurement. This study is based on the hypotheses that ordinary least squares (OLS) factor analysis will yield more accurate parameter estimates than…

On the Performance of Maximum Likelihood versus Means and Variance Adjusted Weighted Least Squares Estimation in CFA

ERIC Educational Resources Information Center

Beauducel, Andre; Herzberg, Philipp Yorck

2006-01-01

This simulation study compared maximum likelihood (ML) estimation with weighted least squares means and variance adjusted (WLSMV) estimation. The study was based on confirmatory factor analyses with 1, 2, 4, and 8 factors, based on 250, 500, 750, and 1,000 cases, and on 5, 10, 20, and 40 variables with 2, 3, 4, 5, and 6 categories. There was no…

More efficient parameter estimates for factor analysis of ordinal variables by ridge generalized least squares.

PubMed

Yuan, Ke-Hai; Jiang, Ge; Cheng, Ying

2017-11-01

Data in psychology are often collected using Likert-type scales, and it has been shown that factor analysis of Likert-type data is better performed on the polychoric correlation matrix than on the product-moment covariance matrix, especially when the distributions of the observed variables are skewed. In theory, factor analysis of the polychoric correlation matrix is best conducted using generalized least squares with an asymptotically correct weight matrix (AGLS). However, simulation studies showed that both least squares (LS) and diagonally weighted least squares (DWLS) perform better than AGLS, and thus LS or DWLS is routinely used in practice. In either LS or DWLS, the associations among the polychoric correlation coefficients are completely ignored. To mend such a gap between statistical theory and empirical work, this paper proposes new methods, called ridge GLS, for factor analysis of ordinal data. Monte Carlo results show that, for a wide range of sample sizes, ridge GLS methods yield uniformly more accurate parameter estimates than existing methods (LS, DWLS, AGLS). A real-data example indicates that estimates by ridge GLS are 9-20% more efficient than those by existing methods. Rescaled and adjusted test statistics as well as sandwich-type standard errors following the ridge GLS methods also perform reasonably well. © 2017 The British Psychological Society.

Robust analysis of trends in noisy tokamak confinement data using geodesic least squares regression

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

Verdoolaege, G., E-mail: geert.verdoolaege@ugent.be; Laboratory for Plasma Physics, Royal Military Academy, B-1000 Brussels; Shabbir, A.

Regression analysis is a very common activity in fusion science for unveiling trends and parametric dependencies, but it can be a difficult matter. We have recently developed the method of geodesic least squares (GLS) regression that is able to handle errors in all variables, is robust against data outliers and uncertainty in the regression model, and can be used with arbitrary distribution models and regression functions. We here report on first results of application of GLS to estimation of the multi-machine scaling law for the energy confinement time in tokamaks, demonstrating improved consistency of the GLS results compared to standardmore » least squares.« less

Prediction model of sinoatrial node field potential using high order partial least squares.

PubMed

Feng, Yu; Cao, Hui; Zhang, Yanbin

2015-01-01

High order partial least squares (HOPLS) is a novel data processing method. It is highly suitable for building prediction model which has tensor input and output. The objective of this study is to build a prediction model of the relationship between sinoatrial node field potential and high glucose using HOPLS. The three sub-signals of the sinoatrial node field potential made up the model's input. The concentration and the actuation duration of high glucose made up the model's output. The results showed that on the premise of predicting two dimensional variables, HOPLS had the same predictive ability and a lower dispersion degree compared with partial least squares (PLS).

Weighted partial least squares based on the error and variance of the recovery rate in calibration set.

PubMed

Yu, Shaohui; Xiao, Xue; Ding, Hong; Xu, Ge; Li, Haixia; Liu, Jing

2017-08-05

The quantitative analysis is very difficult for the emission-excitation fluorescence spectroscopy of multi-component mixtures whose fluorescence peaks are serious overlapping. As an effective method for the quantitative analysis, partial least squares can extract the latent variables from both the independent variables and the dependent variables, so it can model for multiple correlations between variables. However, there are some factors that usually affect the prediction results of partial least squares, such as the noise, the distribution and amount of the samples in calibration set etc. This work focuses on the problems in the calibration set that are mentioned above. Firstly, the outliers in the calibration set are removed by leave-one-out cross-validation. Then, according to two different prediction requirements, the EWPLS method and the VWPLS method are proposed. The independent variables and dependent variables are weighted in the EWPLS method by the maximum error of the recovery rate and weighted in the VWPLS method by the maximum variance of the recovery rate. Three organic matters with serious overlapping excitation-emission fluorescence spectroscopy are selected for the experiments. The step adjustment parameter, the iteration number and the sample amount in the calibration set are discussed. The results show the EWPLS method and the VWPLS method are superior to the PLS method especially for the case of small samples in the calibration set. Copyright © 2017 Elsevier B.V. All rights reserved.

Application of copulas to improve covariance estimation for partial least squares.

PubMed

D'Angelo, Gina M; Weissfeld, Lisa A

2013-02-20

Dimension reduction techniques, such as partial least squares, are useful for computing summary measures and examining relationships in complex settings. Partial least squares requires an estimate of the covariance matrix as a first step in the analysis, making this estimate critical to the results. In addition, the covariance matrix also forms the basis for other techniques in multivariate analysis, such as principal component analysis and independent component analysis. This paper has been motivated by an example from an imaging study in Alzheimer's disease where there is complete separation between Alzheimer's and control subjects for one of the imaging modalities. This separation occurs in one block of variables and does not occur with the second block of variables resulting in inaccurate estimates of the covariance. We propose the use of a copula to obtain estimates of the covariance in this setting, where one set of variables comes from a mixture distribution. Simulation studies show that the proposed estimator is an improvement over the standard estimators of covariance. We illustrate the methods from the motivating example from a study in the area of Alzheimer's disease. Copyright © 2012 John Wiley & Sons, Ltd.

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.

Local food prices and their associations with children's weight and food security.

PubMed

Morrissey, Taryn W; Jacknowitz, Alison; Vinopal, Katie

2014-03-01

Both obesity and food insecurity are important public health problems facing young children in the United States. A lack of affordable, healthy foods is one of the neighborhood factors presumed to underlie both food insecurity and obesity among children. We examine associations between local food prices and children's BMI, weight, and food security outcomes. We linked data from the Early Childhood Longitudinal Study-Birth Cohort, a nationally representative study of children from infancy to age 5, to local food price data from the Council for Community and Economic Research (C2ER) Cost-of-Living Index (n = 11,700 observations). Using ordinary least squares (OLS), linear probability, and within-child fixed effects (FE) models, we exploit the variability in food price data over time and among children who move residences focusing on a subsample of households under 300% of the Federal Poverty Level. Results from ordinary least squares and FE models indicate that higher-priced fruits and vegetables are associated with higher child BMI, and this relationship is driven by the prices of fresh (versus frozen or canned) fruits and vegetables. In the FE models, higher-priced soft drinks are associated with a lower likelihood of being overweight, and surprisingly, higher fast food prices are associated with a greater likelihood of being overweight. Policies that reduce the costs of fresh fruits and vegetables may be effective in promoting healthy weight outcomes among young children.

An immersed boundary formulation for simulating high-speed compressible viscous flows with moving solids

NASA Astrophysics Data System (ADS)

Qu, Yegao; Shi, Ruchao; Batra, Romesh C.

2018-02-01

We present a robust sharp-interface immersed boundary method for numerically studying high speed flows of compressible and viscous fluids interacting with arbitrarily shaped either stationary or moving rigid solids. The Navier-Stokes equations are discretized on a rectangular Cartesian grid based on a low-diffusion flux splitting method for inviscid fluxes and conservative high-order central-difference schemes for the viscous components. Discontinuities such as those introduced by shock waves and contact surfaces are captured by using a high-resolution weighted essentially non-oscillatory (WENO) scheme. Ghost cells in the vicinity of the fluid-solid interface are introduced to satisfy boundary conditions on the interface. Values of variables in the ghost cells are found by using a constrained moving least squares method (CMLS) that eliminates numerical instabilities encountered in the conventional MLS formulation. The solution of the fluid flow and the solid motion equations is advanced in time by using the third-order Runge-Kutta and the implicit Newmark integration schemes, respectively. The performance of the proposed method has been assessed by computing results for the following four problems: shock-boundary layer interaction, supersonic viscous flows past a rigid cylinder, moving piston in a shock tube and lifting off from a flat surface of circular, rectangular and elliptic cylinders triggered by shock waves, and comparing computed results with those available in the literature.

Online Least Squares One-Class Support Vector Machines-Based Abnormal Visual Event Detection

PubMed Central

Wang, Tian; Chen, Jie; Zhou, Yi; Snoussi, Hichem

2013-01-01

The abnormal event detection problem is an important subject in real-time video surveillance. In this paper, we propose a novel online one-class classification algorithm, online least squares one-class support vector machine (online LS-OC-SVM), combined with its sparsified version (sparse online LS-OC-SVM). LS-OC-SVM extracts a hyperplane as an optimal description of training objects in a regularized least squares sense. The online LS-OC-SVM learns a training set with a limited number of samples to provide a basic normal model, then updates the model through remaining data. In the sparse online scheme, the model complexity is controlled by the coherence criterion. The online LS-OC-SVM is adopted to handle the abnormal event detection problem. Each frame of the video is characterized by the covariance matrix descriptor encoding the moving information, then is classified into a normal or an abnormal frame. Experiments are conducted, on a two-dimensional synthetic distribution dataset and a benchmark video surveillance dataset, to demonstrate the promising results of the proposed online LS-OC-SVM method. PMID:24351629

Online least squares one-class support vector machines-based abnormal visual event detection.

PubMed

Wang, Tian; Chen, Jie; Zhou, Yi; Snoussi, Hichem

2013-12-12

The abnormal event detection problem is an important subject in real-time video surveillance. In this paper, we propose a novel online one-class classification algorithm, online least squares one-class support vector machine (online LS-OC-SVM), combined with its sparsified version (sparse online LS-OC-SVM). LS-OC-SVM extracts a hyperplane as an optimal description of training objects in a regularized least squares sense. The online LS-OC-SVM learns a training set with a limited number of samples to provide a basic normal model, then updates the model through remaining data. In the sparse online scheme, the model complexity is controlled by the coherence criterion. The online LS-OC-SVM is adopted to handle the abnormal event detection problem. Each frame of the video is characterized by the covariance matrix descriptor encoding the moving information, then is classified into a normal or an abnormal frame. Experiments are conducted, on a two-dimensional synthetic distribution dataset and a benchmark video surveillance dataset, to demonstrate the promising results of the proposed online LS-OC-SVM method.

Particle-based solid for nonsmooth multidomain dynamics

NASA Astrophysics Data System (ADS)

Nordberg, John; Servin, Martin

2018-04-01

A method for simulation of elastoplastic solids in multibody systems with nonsmooth and multidomain dynamics is developed. The solid is discretised into pseudo-particles using the meshfree moving least squares method for computing the strain tensor. The particle's strain and stress tensor variables are mapped to a compliant deformation constraint. The discretised solid model thus fit a unified framework for nonsmooth multidomain dynamics simulations including rigid multibodies with complex kinematic constraints such as articulation joints, unilateral contacts with dry friction, drivelines, and hydraulics. The nonsmooth formulation allows for impact impulses to propagate instantly between the rigid multibody and the solid. Plasticity is introduced through an associative perfectly plastic modified Drucker-Prager model. The elastic and plastic dynamics are verified for simple test systems, and the capability of simulating tracked terrain vehicles driving on a deformable terrain is demonstrated.

Peak flow regression equations For small, ungaged streams in Maine: Comparing map-based to field-based variables

USGS Publications Warehouse

Lombard, Pamela J.; Hodgkins, Glenn A.

2015-01-01

Regression equations to estimate peak streamflows with 1- to 500-year recurrence intervals (annual exceedance probabilities from 99 to 0.2 percent, respectively) were developed for small, ungaged streams in Maine. Equations presented here are the best available equations for estimating peak flows at ungaged basins in Maine with drainage areas from 0.3 to 12 square miles (mi2). Previously developed equations continue to be the best available equations for estimating peak flows for basin areas greater than 12 mi2. New equations presented here are based on streamflow records at 40 U.S. Geological Survey streamgages with a minimum of 10 years of recorded peak flows between 1963 and 2012. Ordinary least-squares regression techniques were used to determine the best explanatory variables for the regression equations. Traditional map-based explanatory variables were compared to variables requiring field measurements. Two field-based variables—culvert rust lines and bankfull channel widths—either were not commonly found or did not explain enough of the variability in the peak flows to warrant inclusion in the equations. The best explanatory variables were drainage area and percent basin wetlands; values for these variables were determined with a geographic information system. Generalized least-squares regression was used with these two variables to determine the equation coefficients and estimates of accuracy for the final equations.

Partial Least Squares Regression Models for the Analysis of Kinase Signaling.

PubMed

Bourgeois, Danielle L; Kreeger, Pamela K

2017-01-01

Partial least squares regression (PLSR) is a data-driven modeling approach that can be used to analyze multivariate relationships between kinase networks and cellular decisions or patient outcomes. In PLSR, a linear model relating an X matrix of dependent variables and a Y matrix of independent variables is generated by extracting the factors with the strongest covariation. While the identified relationship is correlative, PLSR models can be used to generate quantitative predictions for new conditions or perturbations to the network, allowing for mechanisms to be identified. This chapter will provide a brief explanation of PLSR and provide an instructive example to demonstrate the use of PLSR to analyze kinase signaling.

An improved partial least-squares regression method for Raman spectroscopy

NASA Astrophysics Data System (ADS)

Momenpour Tehran Monfared, Ali; Anis, Hanan

2017-10-01

It is known that the performance of partial least-squares (PLS) regression analysis can be improved using the backward variable selection method (BVSPLS). In this paper, we further improve the BVSPLS based on a novel selection mechanism. The proposed method is based on sorting the weighted regression coefficients, and then the importance of each variable of the sorted list is evaluated using root mean square errors of prediction (RMSEP) criterion in each iteration step. Our Improved BVSPLS (IBVSPLS) method has been applied to leukemia and heparin data sets and led to an improvement in limit of detection of Raman biosensing ranged from 10% to 43% compared to PLS. Our IBVSPLS was also compared to the jack-knifing (simpler) and Genetic Algorithm (more complex) methods. Our method was consistently better than the jack-knifing method and showed either a similar or a better performance compared to the genetic algorithm.

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.

Multivariate statistical analysis of a high rate biofilm process treating kraft mill bleach plant effluent.

PubMed

Goode, C; LeRoy, J; Allen, D G

2007-01-01

This study reports on a multivariate analysis of the moving bed biofilm reactor (MBBR) wastewater treatment system at a Canadian pulp mill. The modelling approach involved a data overview by principal component analysis (PCA) followed by partial least squares (PLS) modelling with the objective of explaining and predicting changes in the BOD output of the reactor. Over two years of data with 87 process measurements were used to build the models. Variables were collected from the MBBR control scheme as well as upstream in the bleach plant and in digestion. To account for process dynamics, a variable lagging approach was used for variables with significant temporal correlations. It was found that wood type pulped at the mill was a significant variable governing reactor performance. Other important variables included flow parameters, faults in the temperature or pH control of the reactor, and some potential indirect indicators of biomass activity (residual nitrogen and pH out). The most predictive model was found to have an RMSEP value of 606 kgBOD/d, representing a 14.5% average error. This was a good fit, given the measurement error of the BOD test. Overall, the statistical approach was effective in describing and predicting MBBR treatment performance.

A KPI-based process monitoring and fault detection framework for large-scale processes.

PubMed

Zhang, Kai; Shardt, Yuri A W; Chen, Zhiwen; Yang, Xu; Ding, Steven X; Peng, Kaixiang

2017-05-01

Large-scale processes, consisting of multiple interconnected subprocesses, are commonly encountered in industrial systems, whose performance needs to be determined. A common approach to this problem is to use a key performance indicator (KPI)-based approach. However, the different KPI-based approaches are not developed with a coherent and consistent framework. Thus, this paper proposes a framework for KPI-based process monitoring and fault detection (PM-FD) for large-scale industrial processes, which considers the static and dynamic relationships between process and KPI variables. For the static case, a least squares-based approach is developed that provides an explicit link with least-squares regression, which gives better performance than partial least squares. For the dynamic case, using the kernel representation of each subprocess, an instrument variable is used to reduce the dynamic case to the static case. This framework is applied to the TE benchmark process and the hot strip mill rolling process. The results show that the proposed method can detect faults better than previous methods. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Partial Least Squares for Discrimination in fMRI Data

PubMed Central

Andersen, Anders H.; Rayens, William S.; Liu, Yushu; Smith, Charles D.

2011-01-01

Multivariate methods for discrimination were used in the comparison of brain activation patterns between groups of cognitively normal women who are at either high or low Alzheimer's disease risk based on family history and apolipoprotein-E4 status. Linear discriminant analysis (LDA) was preceded by dimension reduction using either principal component analysis (PCA), partial least squares (PLS), or a new oriented partial least squares (OrPLS) method. The aim was to identify a spatial pattern of functionally connected brain regions that was differentially expressed by the risk groups and yielded optimal classification accuracy. Multivariate dimension reduction is required prior to LDA when the data contains more feature variables than there are observations on individual subjects. Whereas PCA has been commonly used to identify covariance patterns in neuroimaging data, this approach only identifies gross variability and is not capable of distinguishing among-groups from within-groups variability. PLS and OrPLS provide a more focused dimension reduction by incorporating information on class structure and therefore lead to more parsimonious models for discrimination. Performance was evaluated in terms of the cross-validated misclassification rates. The results support the potential of using fMRI as an imaging biomarker or diagnostic tool to discriminate individuals with disease or high risk. PMID:22227352

The Robustness of LISREL Estimates in Structural Equation Models with Categorical Variables.

ERIC Educational Resources Information Center

Ethington, Corinna A.

1987-01-01

This study examined the effect of type of correlation matrix on the robustness of LISREL maximum likelihood and unweighted least squares structural parameter estimates for models with categorical variables. The analysis of mixed matrices produced estimates that closely approximated the model parameters except where dichotomous variables were…

Accuracy of least-squares methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Bochev, Pavel B.; Gunzburger, Max D.

1993-01-01

Recently there has been substantial interest in least-squares finite element methods for velocity-vorticity-pressure formulations of the incompressible Navier-Stokes equations. The main cause for this interest is the fact that algorithms for the resulting discrete equations can be devised which require the solution of only symmetric, positive definite systems of algebraic equations. On the other hand, it is well-documented that methods using the vorticity as a primary variable often yield very poor approximations. Thus, here we study the accuracy of these methods through a series of computational experiments, and also comment on theoretical error estimates. It is found, despite the failure of standard methods for deriving error estimates, that computational evidence suggests that these methods are, at the least, nearly optimally accurate. Thus, in addition to the desirable matrix properties yielded by least-squares methods, one also obtains accurate approximations.

Influence of variable selection on partial least squares discriminant analysis models for explosive residue classification

NASA Astrophysics Data System (ADS)

De Lucia, Frank C., Jr.; Gottfried, Jennifer L.

2011-02-01

Using a series of thirteen organic materials that includes novel high-nitrogen energetic materials, conventional organic military explosives, and benign organic materials, we have demonstrated the importance of variable selection for maximizing residue discrimination with partial least squares discriminant analysis (PLS-DA). We built several PLS-DA models using different variable sets based on laser induced breakdown spectroscopy (LIBS) spectra of the organic residues on an aluminum substrate under an argon atmosphere. The model classification results for each sample are presented and the influence of the variables on these results is discussed. We found that using the whole spectra as the data input for the PLS-DA model gave the best results. However, variables due to the surrounding atmosphere and the substrate contribute to discrimination when the whole spectra are used, indicating this may not be the most robust model. Further iterative testing with additional validation data sets is necessary to determine the most robust model.

Real-Time Adaptive Least-Squares Drag Minimization for Performance Adaptive Aeroelastic Wing

NASA Technical Reports Server (NTRS)

Ferrier, Yvonne L.; Nguyen, Nhan T.; Ting, Eric

2016-01-01

This paper contains a simulation study of a real-time adaptive least-squares drag minimization algorithm for an aeroelastic model of a flexible wing aircraft. The aircraft model is based on the NASA Generic Transport Model (GTM). The wing structures incorporate a novel aerodynamic control surface known as the Variable Camber Continuous Trailing Edge Flap (VCCTEF). The drag minimization algorithm uses the Newton-Raphson method to find the optimal VCCTEF deflections for minimum drag in the context of an altitude-hold flight control mode at cruise conditions. The aerodynamic coefficient parameters used in this optimization method are identified in real-time using Recursive Least Squares (RLS). The results demonstrate the potential of the VCCTEF to improve aerodynamic efficiency for drag minimization for transport aircraft.

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.

Total sulfur determination in residues of crude oil distillation using FT-IR/ATR and variable selection methods

NASA Astrophysics Data System (ADS)

Müller, Aline Lima Hermes; Picoloto, Rochele Sogari; Mello, Paola de Azevedo; Ferrão, Marco Flores; dos Santos, Maria de Fátima Pereira; Guimarães, Regina Célia Lourenço; Müller, Edson Irineu; Flores, Erico Marlon Moraes

2012-04-01

Total sulfur concentration was determined in atmospheric residue (AR) and vacuum residue (VR) samples obtained from petroleum distillation process by Fourier transform infrared spectroscopy with attenuated total reflectance (FT-IR/ATR) in association with chemometric methods. Calibration and prediction set consisted of 40 and 20 samples, respectively. Calibration models were developed using two variable selection models: interval partial least squares (iPLS) and synergy interval partial least squares (siPLS). Different treatments and pre-processing steps were also evaluated for the development of models. The pre-treatment based on multiplicative scatter correction (MSC) and the mean centered data were selected for models construction. The use of siPLS as variable selection method provided a model with root mean square error of prediction (RMSEP) values significantly better than those obtained by PLS model using all variables. The best model was obtained using siPLS algorithm with spectra divided in 20 intervals and combinations of 3 intervals (911-824, 823-736 and 737-650 cm-1). This model produced a RMSECV of 400 mg kg-1 S and RMSEP of 420 mg kg-1 S, showing a correlation coefficient of 0.990.

Three Least-Squares Minimization Approaches to Interpret Gravity Data Due to Dipping Faults

NASA Astrophysics Data System (ADS)

Abdelrahman, E. M.; Essa, K. S.

2015-02-01

We have developed three different least-squares minimization approaches to determine, successively, the depth, dip angle, and amplitude coefficient related to the thickness and density contrast of a buried dipping fault from first moving average residual gravity anomalies. By defining the zero-anomaly distance and the anomaly value at the origin of the moving average residual profile, the problem of depth determination is transformed into a constrained nonlinear gravity inversion. After estimating the depth of the fault, the dip angle is estimated by solving a nonlinear inverse problem. Finally, after estimating the depth and dip angle, the amplitude coefficient is determined using a linear equation. This method can be applied to residuals as well as to measured gravity data because it uses the moving average residual gravity anomalies to estimate the model parameters of the faulted structure. The proposed method was tested on noise-corrupted synthetic and real gravity data. In the case of the synthetic data, good results are obtained when errors are given in the zero-anomaly distance and the anomaly value at the origin, and even when the origin is determined approximately. In the case of practical data (Bouguer anomaly over Gazal fault, south Aswan, Egypt), the fault parameters obtained are in good agreement with the actual ones and with those given in the published literature.

Effect of trial-to-trial variability on optimal event-related fMRI design: Implications for Beta-series correlation and multi-voxel pattern analysis

PubMed Central

Abdulrahman, Hunar; Henson, Richard N.

2016-01-01

Functional magnetic resonance imaging (fMRI) studies typically employ rapid, event-related designs for behavioral reasons and for reasons associated with statistical efficiency. Efficiency is calculated from the precision of the parameters (Betas) estimated from a General Linear Model (GLM) in which trial onsets are convolved with a Hemodynamic Response Function (HRF). However, previous calculations of efficiency have ignored likely variability in the neural response from trial to trial, for example due to attentional fluctuations, or different stimuli across trials. Here we compare three GLMs in their efficiency for estimating average and individual Betas across trials as a function of trial variability, scan noise and Stimulus Onset Asynchrony (SOA): “Least Squares All” (LSA), “Least Squares Separate” (LSS) and “Least Squares Unitary” (LSU). Estimation of responses to individual trials in particular is important for both functional connectivity using “Beta-series correlation” and “multi-voxel pattern analysis” (MVPA). Our simulations show that the ratio of trial-to-trial variability to scan noise impacts both the optimal SOA and optimal GLM, especially for short SOAs < 5 s: LSA is better when this ratio is high, whereas LSS and LSU are better when the ratio is low. For MVPA, the consistency across voxels of trial variability and of scan noise is also critical. These findings not only have important implications for design of experiments using Beta-series regression and MVPA, but also statistical parametric mapping studies that seek only efficient estimation of the mean response across trials. PMID:26549299

Tutorial on Using Regression Models with Count Outcomes Using R

ERIC Educational Resources Information Center

Beaujean, A. Alexander; Morgan, Grant B.

2016-01-01

Education researchers often study count variables, such as times a student reached a goal, discipline referrals, and absences. Most researchers that study these variables use typical regression methods (i.e., ordinary least-squares) either with or without transforming the count variables. In either case, using typical regression for count data can…

Causal Models with Unmeasured Variables: An Introduction to LISREL.

ERIC Educational Resources Information Center

Wolfle, Lee M.

Whenever one uses ordinary least squares regression, one is making an implicit assumption that all of the independent variables have been measured without error. Such an assumption is obviously unrealistic for most social data. One approach for estimating such regression models is to measure implied coefficients between latent variables for which…

The application of the mesh-free method in the numerical simulations of the higher-order continuum structures

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

Sun, Yuzhou, E-mail: yuzhousun@126.com; Chen, Gensheng; Li, Dongxia

2016-06-08

This paper attempts to study the application of mesh-free method in the numerical simulations of the higher-order continuum structures. A high-order bending beam considers the effect of the third-order derivative of deflections, and can be viewed as a one-dimensional higher-order continuum structure. The moving least-squares method is used to construct the shape function with the high-order continuum property, the curvature and the third-order derivative of deflections are directly interpolated with nodal variables and the second- and third-order derivative of the shape function, and the mesh-free computational scheme is establish for beams. The coupled stress theory is introduced to describe themore » special constitutive response of the layered rock mass in which the bending effect of thin layer is considered. The strain and the curvature are directly interpolated with the nodal variables, and the mesh-free method is established for the layered rock mass. The good computational efficiency is achieved based on the developed mesh-free method, and some key issues are discussed.« less

ASSOCIATION OF LANDSCAPE METRICS TO SURFACE WATER BIOLOGY IN THE SAVANNAH RIVER BASIN

EPA Science Inventory

Surface water quality for the Savannah River basin was assessed using water biology and landscape metrics. Two multivariate analyses, partial least square and cannonical correlation, were used to describe how the structural variation in landscape variable(s) that contribute the ...

Avoiding and Correcting Bias in Score-Based Latent Variable Regression with Discrete Manifest Items

ERIC Educational Resources Information Center

Lu, Irene R. R.; Thomas, D. Roland

2008-01-01

This article considers models involving a single structural equation with latent explanatory and/or latent dependent variables where discrete items are used to measure the latent variables. Our primary focus is the use of scores as proxies for the latent variables and carrying out ordinary least squares (OLS) regression on such scores to estimate…

Rapid Detection of Volatile Oil in Mentha haplocalyx by Near-Infrared Spectroscopy and Chemometrics.

PubMed

Yan, Hui; Guo, Cheng; Shao, Yang; Ouyang, Zhen

2017-01-01

Near-infrared spectroscopy combined with partial least squares regression (PLSR) and support vector machine (SVM) was applied for the rapid determination of chemical component of volatile oil content in Mentha haplocalyx . The effects of data pre-processing methods on the accuracy of the PLSR calibration models were investigated. The performance of the final model was evaluated according to the correlation coefficient ( R ) and root mean square error of prediction (RMSEP). For PLSR model, the best preprocessing method combination was first-order derivative, standard normal variate transformation (SNV), and mean centering, which had of 0.8805, of 0.8719, RMSEC of 0.091, and RMSEP of 0.097, respectively. The wave number variables linking to volatile oil are from 5500 to 4000 cm-1 by analyzing the loading weights and variable importance in projection (VIP) scores. For SVM model, six LVs (less than seven LVs in PLSR model) were adopted in model, and the result was better than PLSR model. The and were 0.9232 and 0.9202, respectively, with RMSEC and RMSEP of 0.084 and 0.082, respectively, which indicated that the predicted values were accurate and reliable. This work demonstrated that near infrared reflectance spectroscopy with chemometrics could be used to rapidly detect the main content volatile oil in M. haplocalyx . The quality of medicine directly links to clinical efficacy, thus, it is important to control the quality of Mentha haplocalyx . Near-infrared spectroscopy combined with partial least squares regression (PLSR) and support vector machine (SVM) was applied for the rapid determination of chemical component of volatile oil content in Mentha haplocalyx . For SVM model, 6 LVs (less than 7 LVs in PLSR model) were adopted in model, and the result was better than PLSR model. It demonstrated that near infrared reflectance spectroscopy with chemometrics could be used to rapidly detect the main content volatile oil in Mentha haplocalyx . Abbreviations used: 1 st der: First-order derivative; 2 nd der: Second-order derivative; LOO: Leave-one-out; LVs: Latent variables; MC: Mean centering, NIR: Near-infrared; NIRS: Near infrared spectroscopy; PCR: Principal component regression, PLSR: Partial least squares regression; RBF: Radial basis function; RMSEC: Root mean square error of cross validation, RMSEC: Root mean square error of calibration; RMSEP: Root mean square error of prediction; SNV: Standard normal variate transformation; SVM: Support vector machine; VIP: Variable Importance in projection.

Gap Acceptance During Lane Changes by Large-Truck Drivers—An Image-Based Analysis

PubMed Central

Nobukawa, Kazutoshi; Bao, Shan; LeBlanc, David J.; Zhao, Ding; Peng, Huei; Pan, Christopher S.

2016-01-01

This paper presents an analysis of rearward gap acceptance characteristics of drivers of large trucks in highway lane change scenarios. The range between the vehicles was inferred from camera images using the estimated lane width obtained from the lane tracking camera as the reference. Six-hundred lane change events were acquired from a large-scale naturalistic driving data set. The kinematic variables from the image-based gap analysis were filtered by the weighted linear least squares in order to extrapolate them at the lane change time. In addition, the time-to-collision and required deceleration were computed, and potential safety threshold values are provided. The resulting range and range rate distributions showed directional discrepancies, i.e., in left lane changes, large trucks are often slower than other vehicles in the target lane, whereas they are usually faster in right lane changes. Video observations have confirmed that major motivations for changing lanes are different depending on the direction of move, i.e., moving to the left (faster) lane occurs due to a slower vehicle ahead or a merging vehicle on the right-hand side, whereas right lane changes are frequently made to return to the original lane after passing. PMID:26924947

Gap Acceptance During Lane Changes by Large-Truck Drivers-An Image-Based Analysis.

PubMed

Nobukawa, Kazutoshi; Bao, Shan; LeBlanc, David J; Zhao, Ding; Peng, Huei; Pan, Christopher S

2016-03-01

This paper presents an analysis of rearward gap acceptance characteristics of drivers of large trucks in highway lane change scenarios. The range between the vehicles was inferred from camera images using the estimated lane width obtained from the lane tracking camera as the reference. Six-hundred lane change events were acquired from a large-scale naturalistic driving data set. The kinematic variables from the image-based gap analysis were filtered by the weighted linear least squares in order to extrapolate them at the lane change time. In addition, the time-to-collision and required deceleration were computed, and potential safety threshold values are provided. The resulting range and range rate distributions showed directional discrepancies, i.e., in left lane changes, large trucks are often slower than other vehicles in the target lane, whereas they are usually faster in right lane changes. Video observations have confirmed that major motivations for changing lanes are different depending on the direction of move, i.e., moving to the left (faster) lane occurs due to a slower vehicle ahead or a merging vehicle on the right-hand side, whereas right lane changes are frequently made to return to the original lane after passing.

Optimization of seasonal ARIMA models using differential evolution - simulated annealing (DESA) algorithm in forecasting dengue cases in Baguio City

NASA Astrophysics Data System (ADS)

Addawe, Rizavel C.; Addawe, Joel M.; Magadia, Joselito C.

2016-10-01

Accurate forecasting of dengue cases would significantly improve epidemic prevention and control capabilities. This paper attempts to provide useful models in forecasting dengue epidemic specific to the young and adult population of Baguio City. To capture the seasonal variations in dengue incidence, this paper develops a robust modeling approach to identify and estimate seasonal autoregressive integrated moving average (SARIMA) models in the presence of additive outliers. Since the least squares estimators are not robust in the presence of outliers, we suggest a robust estimation based on winsorized and reweighted least squares estimators. A hybrid algorithm, Differential Evolution - Simulated Annealing (DESA), is used to identify and estimate the parameters of the optimal SARIMA model. The method is applied to the monthly reported dengue cases in Baguio City, Philippines.

Application of partial least squares near-infrared spectral classification in diabetic identification

NASA Astrophysics Data System (ADS)

Yan, Wen-juan; Yang, Ming; He, Guo-quan; Qin, Lin; Li, Gang

2014-11-01

In order to identify the diabetic patients by using tongue near-infrared (NIR) spectrum - a spectral classification model of the NIR reflectivity of the tongue tip is proposed, based on the partial least square (PLS) method. 39sample data of tongue tip's NIR spectra are harvested from healthy people and diabetic patients , respectively. After pretreatment of the reflectivity, the spectral data are set as the independent variable matrix, and information of classification as the dependent variables matrix, Samples were divided into two groups - i.e. 53 samples as calibration set and 25 as prediction set - then the PLS is used to build the classification model The constructed modelfrom the 53 samples has the correlation of 0.9614 and the root mean square error of cross-validation (RMSECV) of 0.1387.The predictions for the 25 samples have the correlation of 0.9146 and the RMSECV of 0.2122.The experimental result shows that the PLS method can achieve good classification on features of healthy people and diabetic patients.

Migration plans and hours of work in Malaysia.

PubMed

Gillin, E D; Sumner, D A

1985-01-01

"This article describes characteristics of prospective migrants in the Malaysian Family Life Survey and investigates how planning to move affects hours of work. [The authors] use ideas about intertemporal substitution...to discuss the response to temporary and permanent wage expectations on the part of potential migrants. [An] econometric section presents reduced-form estimates for wage rates and planned migration equations and two-stage least squares estimates for hours of work. Men currently planning a move were found to work fewer hours. Those originally planning only a temporary stay at their current location work more hours." excerpt

Functional Relationships and Regression Analysis.

ERIC Educational Resources Information Center

Preece, Peter F. W.

1978-01-01

Using a degenerate multivariate normal model for the distribution of organismic variables, the form of least-squares regression analysis required to estimate a linear functional relationship between variables is derived. It is suggested that the two conventional regression lines may be considered to describe functional, not merely statistical,…

Ordinary Least Squares Estimation of Parameters in Exploratory Factor Analysis with Ordinal Data

ERIC Educational Resources Information Center

Lee, Chun-Ting; Zhang, Guangjian; Edwards, Michael C.

2012-01-01

Exploratory factor analysis (EFA) is often conducted with ordinal data (e.g., items with 5-point responses) in the social and behavioral sciences. These ordinal variables are often treated as if they were continuous in practice. An alternative strategy is to assume that a normally distributed continuous variable underlies each ordinal variable.…

Total sulfur determination in residues of crude oil distillation using FT-IR/ATR and variable selection methods.

PubMed

Müller, Aline Lima Hermes; Picoloto, Rochele Sogari; de Azevedo Mello, Paola; Ferrão, Marco Flores; de Fátima Pereira dos Santos, Maria; Guimarães, Regina Célia Lourenço; Müller, Edson Irineu; Flores, Erico Marlon Moraes

2012-04-01

Total sulfur concentration was determined in atmospheric residue (AR) and vacuum residue (VR) samples obtained from petroleum distillation process by Fourier transform infrared spectroscopy with attenuated total reflectance (FT-IR/ATR) in association with chemometric methods. Calibration and prediction set consisted of 40 and 20 samples, respectively. Calibration models were developed using two variable selection models: interval partial least squares (iPLS) and synergy interval partial least squares (siPLS). Different treatments and pre-processing steps were also evaluated for the development of models. The pre-treatment based on multiplicative scatter correction (MSC) and the mean centered data were selected for models construction. The use of siPLS as variable selection method provided a model with root mean square error of prediction (RMSEP) values significantly better than those obtained by PLS model using all variables. The best model was obtained using siPLS algorithm with spectra divided in 20 intervals and combinations of 3 intervals (911-824, 823-736 and 737-650 cm(-1)). This model produced a RMSECV of 400 mg kg(-1) S and RMSEP of 420 mg kg(-1) S, showing a correlation coefficient of 0.990. Copyright © 2011 Elsevier B.V. All rights reserved.

Vis-NIR spectrometric determination of Brix and sucrose in sugar production samples using kernel partial least squares with interval selection based on the successive projections algorithm.

PubMed

de Almeida, Valber Elias; de Araújo Gomes, Adriano; de Sousa Fernandes, David Douglas; Goicoechea, Héctor Casimiro; Galvão, Roberto Kawakami Harrop; Araújo, Mario Cesar Ugulino

2018-05-01

This paper proposes a new variable selection method for nonlinear multivariate calibration, combining the Successive Projections Algorithm for interval selection (iSPA) with the Kernel Partial Least Squares (Kernel-PLS) modelling technique. The proposed iSPA-Kernel-PLS algorithm is employed in a case study involving a Vis-NIR spectrometric dataset with complex nonlinear features. The analytical problem consists of determining Brix and sucrose content in samples from a sugar production system, on the basis of transflectance spectra. As compared to full-spectrum Kernel-PLS, the iSPA-Kernel-PLS models involve a smaller number of variables and display statistically significant superiority in terms of accuracy and/or bias in the predictions. Published by Elsevier B.V.

Segmented Polynomial Models in Quasi-Experimental Research.

ERIC Educational Resources Information Center

Wasik, John L.

1981-01-01

The use of segmented polynomial models is explained. Examples of design matrices of dummy variables are given for the least squares analyses of time series and discontinuity quasi-experimental research designs. Linear combinations of dummy variable vectors appear to provide tests of effects in the two quasi-experimental designs. (Author/BW)

A comparison between the use of Cox regression and the use of partial least squares-Cox regression to predict the survival of kidney-transplant patients

NASA Astrophysics Data System (ADS)

Solimun

2017-05-01

The aim of this research is to model survival data from kidney-transplant patients using the partial least squares (PLS)-Cox regression, which can both meet and not meet the no-multicollinearity assumption. The secondary data were obtained from research entitled "Factors affecting the survival of kidney-transplant patients". The research subjects comprised 250 patients. The predictor variables consisted of: age (X1), sex (X2); two categories, prior hemodialysis duration (X3), diabetes (X4); two categories, prior transplantation number (X5), number of blood transfusions (X6), discrepancy score (X7), use of antilymphocyte globulin(ALG) (X8); two categories, while the response variable was patient survival time (in months). Partial least squares regression is a model that connects the predictor variables X and the response variable y and it initially aims to determine the relationship between them. Results of the above analyses suggest that the survival of kidney transplant recipients ranged from 0 to 55 months, with 62% of the patients surviving until they received treatment that lasted for 55 months. The PLS-Cox regression analysis results revealed that patients' age and the use of ALG significantly affected the survival time of patients. The factor of patients' age (X1) in the PLS-Cox regression model merely affected the failure probability by 1.201. This indicates that the probability of dying for elderly patients with a kidney transplant is 1.152 times higher than that for younger patients.

Lameness detection challenges in automated milking systems addressed with partial least squares discriminant analysis.

PubMed

Garcia, E; Klaas, I; Amigo, J M; Bro, R; Enevoldsen, C

2014-12-01

Lameness causes decreased animal welfare and leads to higher production costs. This study explored data from an automatic milking system (AMS) to model on-farm gait scoring from a commercial farm. A total of 88 cows were gait scored once per week, for 2 5-wk periods. Eighty variables retrieved from AMS were summarized week-wise and used to predict 2 defined classes: nonlame and clinically lame cows. Variables were represented with 2 transformations of the week summarized variables, using 2-wk data blocks before gait scoring, totaling 320 variables (2 × 2 × 80). The reference gait scoring error was estimated in the first week of the study and was, on average, 15%. Two partial least squares discriminant analysis models were fitted to parity 1 and parity 2 groups, respectively, to assign the lameness class according to the predicted probability of being lame (score 3 or 4/4) or not lame (score 1/4). Both models achieved sensitivity and specificity values around 80%, both in calibration and cross-validation. At the optimum values in the receiver operating characteristic curve, the false-positive rate was 28% in the parity 1 model, whereas in the parity 2 model it was about half (16%), which makes it more suitable for practical application; the model error rates were, 23 and 19%, respectively. Based on data registered automatically from one AMS farm, we were able to discriminate nonlame and lame cows, where partial least squares discriminant analysis achieved similar performance to the reference method. Copyright © 2014 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

[Spectral quantitative analysis by nonlinear partial least squares based on neural network internal model for flue gas of thermal power plant].

PubMed

Cao, Hui; Li, Yao-Jiang; Zhou, Yan; Wang, Yan-Xia

2014-11-01

To deal with nonlinear characteristics of spectra data for the thermal power plant flue, a nonlinear partial least square (PLS) analysis method with internal model based on neural network is adopted in the paper. The latent variables of the independent variables and the dependent variables are extracted by PLS regression firstly, and then they are used as the inputs and outputs of neural network respectively to build the nonlinear internal model by train process. For spectra data of flue gases of the thermal power plant, PLS, the nonlinear PLS with the internal model of back propagation neural network (BP-NPLS), the non-linear PLS with the internal model of radial basis function neural network (RBF-NPLS) and the nonlinear PLS with the internal model of adaptive fuzzy inference system (ANFIS-NPLS) are compared. The root mean square error of prediction (RMSEP) of sulfur dioxide of BP-NPLS, RBF-NPLS and ANFIS-NPLS are reduced by 16.96%, 16.60% and 19.55% than that of PLS, respectively. The RMSEP of nitric oxide of BP-NPLS, RBF-NPLS and ANFIS-NPLS are reduced by 8.60%, 8.47% and 10.09% than that of PLS, respectively. The RMSEP of nitrogen dioxide of BP-NPLS, RBF-NPLS and ANFIS-NPLS are reduced by 2.11%, 3.91% and 3.97% than that of PLS, respectively. Experimental results show that the nonlinear PLS is more suitable for the quantitative analysis of glue gas than PLS. Moreover, by using neural network function which can realize high approximation of nonlinear characteristics, the nonlinear partial least squares method with internal model mentioned in this paper have well predictive capabilities and robustness, and could deal with the limitations of nonlinear partial least squares method with other internal model such as polynomial and spline functions themselves under a certain extent. ANFIS-NPLS has the best performance with the internal model of adaptive fuzzy inference system having ability to learn more and reduce the residuals effectively. Hence, ANFIS-NPLS is an accurate and useful quantitative thermal power plant flue gas analysis method.

Modeling Hurricane Katrina's merchantable timber and wood damage in south Mississippi using remotely sensed and field-measured data

NASA Astrophysics Data System (ADS)

Collins, Curtis Andrew

Ordinary and weighted least squares multiple linear regression techniques were used to derive 720 models predicting Katrina-induced storm damage in cubic foot volume (outside bark) and green weight tons (outside bark). The large number of models was dictated by the use of three damage classes, three product types, and four forest type model strata. These 36 models were then fit and reported across 10 variable sets and variable set combinations for volume and ton units. Along with large model counts, potential independent variables were created using power transforms and interactions. The basis of these variables was field measured plot data, satellite (Landsat TM and ETM+) imagery, and NOAA HWIND wind data variable types. As part of the modeling process, lone variable types as well as two-type and three-type combinations were examined. By deriving models with these varying inputs, model utility is flexible as all independent variable data are not needed in future applications. The large number of potential variables led to the use of forward, sequential, and exhaustive independent variable selection techniques. After variable selection, weighted least squares techniques were often employed using weights of one over the square root of the pre-storm volume or weight of interest. This was generally successful in improving residual variance homogeneity. Finished model fits, as represented by coefficient of determination (R2), surpassed 0.5 in numerous models with values over 0.6 noted in a few cases. Given these models, an analyst is provided with a toolset to aid in risk assessment and disaster recovery should Katrina-like weather events reoccur.

VizieR Online Data Catalog: Variable Stars in the Galactic Center (Dong+, 2017)

NASA Astrophysics Data System (ADS)

Dong, H.; Schodel, R.; William, B. F.; Nogueras-Lara, F.; Gallego-Cano, E.; Gallego-Calvente, T.; Wang, Q. D.; Morris, R. M.; Do, T.; Ghez, A.

2017-06-01

We use the 'DOLPHOT' to detect sources and extract photometry from the HST WFC3/IR observations at the F127M and F135M bands of the Galactic Centre from 2010 to 2014. The F153M observations, which are used to identify variable stars, include 290 dithered exposures from six HST programs. The detailed description of the HST dataset are given in Table 1 of the paper. We identified 33070 sources. Their F127M and F153M magnitudes, as well as their uncertainties, are given in Table 3. For each star, we used the least chi square method to identify whether it is variable or not. The output from the least chi square method are chi2y and chi2d, which are calculated from all the 290 dithered exposures and the exposures in March and April, 2014, respectively, to examine whether the star varies among years and/or days. In order to reduce the potential variation among dithered exposures, which could be potentially introduced by instrument effects, we also bin the dithered exposures and use the least chi square method to calculate chi2y,b and chi2{d,b}. We classify stars with chi2y>3 and chi2y,b>2 are variables among years and stars with chi2d>3 and chi2d,b>2 are variables among days. The detailed description about the data analysis is given in the paper. In Table 4, we gives the magnitudes of sources in individual dithered exposures, as well as the photometric uncertainties and the quality control parameters provided by 'DOLPHOT', such as signal-to-noise ratio, sharpness^2, crowd and flag. We also cross-correlated our variables with previous variable studies taken by ground-based telescopes in Table 8 and spectroscopic observations in Table 9. (4 data files).

Eddy current nondestructive testing device for measuring variable characteristics of a sample utilizing Walsh functions

DOEpatents

Libby, Hugo L.; Hildebrand, Bernard P.

1978-01-01

An eddy current testing device for measuring variable characteristics of a sample generates a signal which varies with variations in such characteristics. A signal expander samples at least a portion of this generated signal and expands the sampled signal on a selected basis of square waves or Walsh functions to produce a plurality of signal components representative of the sampled signal. A network combines these components to provide a display of at least one of the characteristics of the sample.

Stability indicating methods for the analysis of cefprozil in the presence of its alkaline induced degradation product

NASA Astrophysics Data System (ADS)

Attia, Khalid A. M.; Nassar, Mohammed W. I.; El-Zeiny, Mohamed B.; Serag, Ahmed

2016-04-01

Three simple, specific, accurate and precise spectrophotometric methods were developed for the determination of cefprozil (CZ) in the presence of its alkaline induced degradation product (DCZ). The first method was the bivariate method, while the two other multivariate methods were partial least squares (PLS) and spectral residual augmented classical least squares (SRACLS). The multivariate methods were applied with and without variable selection procedure (genetic algorithm GA). These methods were tested by analyzing laboratory prepared mixtures of the above drug with its alkaline induced degradation product and they were applied to its commercial pharmaceutical products.

Identification of Medicinal Mugua Origin by Near Infrared Spectroscopy Combined with Partial Least-squares Discriminant Analysis.

PubMed

Han, Bangxing; Peng, Huasheng; Yan, Hui

2016-01-01

Mugua is a common Chinese herbal medicine. There are three main medicinal origin places in China, Xuancheng City Anhui Province, Qijiang District Chongqing City, Yichang City, Hubei Province, and suitable for food origin places Linyi City Shandong Province. To construct a qualitative analytical method to identify the origin of medicinal Mugua by near infrared spectroscopy (NIRS). Partial least squares discriminant analysis (PLSDA) model was established after the Mugua derived from five different origins were preprocessed by the original spectrum. Moreover, the hierarchical cluster analysis was performed. The result showed that PLSDA model was established. According to the relationship of the origins-related important score and wavenumber, and K-mean cluster analysis, the Muguas derived from different origins were effectively identified. NIRS technology can quickly and accurately identify the origin of Mugua, provide a new method and technology for the identification of Chinese medicinal materials. After preprocessed by D1+autoscale, more peaks were increased in the preprocessed Mugua in the near infrared spectrumFive latent variable scores could reflect the information related to the origin place of MuguaOrigins of Mugua were well-distinguished according to K. mean value clustering analysis. Abbreviations used: TCM: Traditional Chinese Medicine, NIRS: Near infrared spectroscopy, SG: Savitzky-Golay smoothness, D1: First derivative, D2: Second derivative, SNV: Standard normal variable transformation, MSC: Multiplicative scatter correction, PLSDA: Partial least squares discriminant analysis, LV: Latent variable, VIP scores: Important score.

Taper equation and volume tables for plantation-grown red alder.

Treesearch

Andrew A. Bluhm; Sean M. Garber; David E. Hibbs

2007-01-01

A taper equation and associated tables are presented for red alder (Alnus rubra Bong.) trees grown in plantations. The data were gathered from variable-density experimental plantations throughout the Pacific Northwest. Diameter inside bark along the stem was fitted to a variable exponent model form by using generalized nonlinear least squares and a...

The Robustness of LISREL Estimates in Structural Equation Models with Categorical Variables.

ERIC Educational Resources Information Center

Ethington, Corinna A.

This study examined the effect of type of correlation matrix on the robustness of LISREL maximum likelihood and unweighted least squares structural parameter estimates for models with categorical manifest variables. Two types of correlation matrices were analyzed; one containing Pearson product-moment correlations and one containing tetrachoric,…

Use of Partial Least Squares improves the efficacy of removing unwanted variability in differential expression analyses based on RNA-Seq data.

PubMed

Chakraborty, Sutirtha

2018-05-26

RNA-Seq technology has revolutionized the face of gene expression profiling by generating read count data measuring the transcript abundances for each queried gene on multiple experimental subjects. But on the downside, the underlying technical artefacts and hidden biological profiles of the samples generate a wide variety of latent effects that may potentially distort the actual transcript/gene expression signals. Standard normalization techniques fail to correct for these hidden variables and lead to flawed downstream analyses. In this work I demonstrate the use of Partial Least Squares (built as an R package 'SVAPLSseq') to correct for the traces of extraneous variability in RNA-Seq data. A novel and thorough comparative analysis of the PLS based method is presented along with some of the other popularly used approaches for latent variable correction in RNA-Seq. Overall, the method is found to achieve a substantially improved estimation of the hidden effect signatures in the RNA-Seq transcriptome expression landscape compared to other available techniques. Copyright © 2017. Published by Elsevier Inc.

Durbin-Watson partial least-squares regression applied to MIR data on adulteration with edible oils of different origins.

PubMed

Jović, Ozren

2016-12-15

A novel method for quantitative prediction and variable-selection on spectroscopic data, called Durbin-Watson partial least-squares regression (dwPLS), is proposed in this paper. The idea is to inspect serial correlation in infrared data that is known to consist of highly correlated neighbouring variables. The method selects only those variables whose intervals have a lower Durbin-Watson statistic (dw) than a certain optimal cutoff. For each interval, dw is calculated on a vector of regression coefficients. Adulteration of cold-pressed linseed oil (L), a well-known nutrient beneficial to health, is studied in this work by its being mixed with cheaper oils: rapeseed oil (R), sesame oil (Se) and sunflower oil (Su). The samples for each botanical origin of oil vary with respect to producer, content and geographic origin. The results obtained indicate that MIR-ATR, combined with dwPLS could be implemented to quantitative determination of edible-oil adulteration. Copyright © 2016 Elsevier Ltd. All rights reserved.

Direct Regularized Estimation of Retinal Vascular Oxygen Tension Based on an Experimental Model

PubMed Central

Yildirim, Isa; Ansari, Rashid; Yetik, I. Samil; Shahidi, Mahnaz

2014-01-01

Phosphorescence lifetime imaging is commonly used to generate oxygen tension maps of retinal blood vessels by classical least squares (LS) estimation method. A spatial regularization method was later proposed and provided improved results. However, both methods obtain oxygen tension values from the estimates of intermediate variables, and do not yield an optimum estimate of oxygen tension values, due to their nonlinear dependence on the ratio of intermediate variables. In this paper, we provide an improved solution by devising a regularized direct least squares (RDLS) method that exploits available knowledge in studies that provide models of oxygen tension in retinal arteries and veins, unlike the earlier regularized LS approach where knowledge about intermediate variables is limited. The performance of the proposed RDLS method is evaluated by investigating and comparing the bias, variance, oxygen tension maps, 1-D profiles of arterial oxygen tension, and mean absolute error with those of earlier methods, and its superior performance both quantitatively and qualitatively is demonstrated. PMID:23732915

Novel near-infrared spectrum analysis tool: Synergy adaptive moving window model based on immune clone algorithm.

PubMed

Wang, Shenghao; Zhang, Yuyan; Cao, Fuyi; Pei, Zhenying; Gao, Xuewei; Zhang, Xu; Zhao, Yong

2018-02-13

This paper presents a novel spectrum analysis tool named synergy adaptive moving window modeling based on immune clone algorithm (SA-MWM-ICA) considering the tedious and inconvenient labor involved in the selection of pre-processing methods and spectral variables by prior experience. In this work, immune clone algorithm is first introduced into the spectrum analysis field as a new optimization strategy, covering the shortage of the relative traditional methods. Based on the working principle of the human immune system, the performance of the quantitative model is regarded as antigen, and a special vector corresponding to the above mentioned antigen is regarded as antibody. The antibody contains a pre-processing method optimization region which is created by 11 decimal digits, and a spectrum variable optimization region which is formed by some moving windows with changeable width and position. A set of original antibodies are created by modeling with this algorithm. After calculating the affinity of these antibodies, those with high affinity will be selected to clone. The regulation for cloning is that the higher the affinity, the more copies will be. In the next step, another import operation named hyper-mutation is applied to the antibodies after cloning. Moreover, the regulation for hyper-mutation is that the lower the affinity, the more possibility will be. Several antibodies with high affinity will be created on the basis of these steps. Groups of simulated dataset, gasoline near-infrared spectra dataset, and soil near-infrared spectra dataset are employed to verify and illustrate the performance of SA-MWM-ICA. Analysis results show that the performance of the quantitative models adopted by SA-MWM-ICA are better especially for structures with relatively complex spectra than traditional models such as partial least squares (PLS), moving window PLS (MWPLS), genetic algorithm PLS (GAPLS), and pretreatment method classification and adjustable parameter changeable size moving window PLS (CA-CSMWPLS). The selected pre-processing methods and spectrum variables are easily explained. The proposed method will converge in few generations and can be used not only for near-infrared spectroscopy analysis but also for other similar spectral analysis, such as infrared spectroscopy. Copyright © 2017 Elsevier B.V. All rights reserved.

A novel approach to the experimental study on methane/steam reforming kinetics using the Orthogonal Least Squares method

NASA Astrophysics Data System (ADS)

Sciazko, Anna; Komatsu, Yosuke; Brus, Grzegorz; Kimijima, Shinji; Szmyd, Janusz S.

2014-09-01

For a mathematical model based on the result of physical measurements, it becomes possible to determine their influence on the final solution and its accuracy. However, in classical approaches, the influence of different model simplifications on the reliability of the obtained results are usually not comprehensively discussed. This paper presents a novel approach to the study of methane/steam reforming kinetics based on an advanced methodology called the Orthogonal Least Squares method. The kinetics of the reforming process published earlier are divergent among themselves. To obtain the most probable values of kinetic parameters and enable direct and objective model verification, an appropriate calculation procedure needs to be proposed. The applied Generalized Least Squares (GLS) method includes all the experimental results into the mathematical model which becomes internally contradicted, as the number of equations is greater than number of unknown variables. The GLS method is adopted to select the most probable values of results and simultaneously determine the uncertainty coupled with all the variables in the system. In this paper, the evaluation of the reaction rate after the pre-determination of the reaction rate, which was made by preliminary calculation based on the obtained experimental results over a Nickel/Yttria-stabilized Zirconia catalyst, was performed.

Spectroscopic Determination of Aboveground Biomass in Grasslands Using Spectral Transformations, Support Vector Machine and Partial Least Squares Regression

PubMed Central

Marabel, Miguel; Alvarez-Taboada, Flor

2013-01-01

Aboveground biomass (AGB) is one of the strategic biophysical variables of interest in vegetation studies. The main objective of this study was to evaluate the Support Vector Machine (SVM) and Partial Least Squares Regression (PLSR) for estimating the AGB of grasslands from field spectrometer data and to find out which data pre-processing approach was the most suitable. The most accurate model to predict the total AGB involved PLSR and the Maximum Band Depth index derived from the continuum removed reflectance in the absorption features between 916–1,120 nm and 1,079–1,297 nm (R2 = 0.939, RMSE = 7.120 g/m2). Regarding the green fraction of the AGB, the Area Over the Minimum index derived from the continuum removed spectra provided the most accurate model overall (R2 = 0.939, RMSE = 3.172 g/m2). Identifying the appropriate absorption features was proved to be crucial to improve the performance of PLSR to estimate the total and green aboveground biomass, by using the indices derived from those spectral regions. Ordinary Least Square Regression could be used as a surrogate for the PLSR approach with the Area Over the Minimum index as the independent variable, although the resulting model would not be as accurate. PMID:23925082

On Some Separated Algorithms for Separable Nonlinear Least Squares Problems.

PubMed

Gan, Min; Chen, C L Philip; Chen, Guang-Yong; Chen, Long

2017-10-03

For a class of nonlinear least squares problems, it is usually very beneficial to separate the variables into a linear and a nonlinear part and take full advantage of reliable linear least squares techniques. Consequently, the original problem is turned into a reduced problem which involves only nonlinear parameters. We consider in this paper four separated algorithms for such problems. The first one is the variable projection (VP) algorithm with full Jacobian matrix of Golub and Pereyra. The second and third ones are VP algorithms with simplified Jacobian matrices proposed by Kaufman and Ruano et al. respectively. The fourth one only uses the gradient of the reduced problem. Monte Carlo experiments are conducted to compare the performance of these four algorithms. From the results of the experiments, we find that: 1) the simplified Jacobian proposed by Ruano et al. is not a good choice for the VP algorithm; moreover, it may render the algorithm hard to converge; 2) the fourth algorithm perform moderately among these four algorithms; 3) the VP algorithm with the full Jacobian matrix perform more stable than that of the VP algorithm with Kuafman's simplified one; and 4) the combination of VP algorithm and Levenberg-Marquardt method is more effective than the combination of VP algorithm and Gauss-Newton method.

Evaluation of the Bitterness of Traditional Chinese Medicines using an E-Tongue Coupled with a Robust Partial Least Squares Regression Method.

PubMed

Lin, Zhaozhou; Zhang, Qiao; Liu, Ruixin; Gao, Xiaojie; Zhang, Lu; Kang, Bingya; Shi, Junhan; Wu, Zidan; Gui, Xinjing; Li, Xuelin

2016-01-25

To accurately, safely, and efficiently evaluate the bitterness of Traditional Chinese Medicines (TCMs), a robust predictor was developed using robust partial least squares (RPLS) regression method based on data obtained from an electronic tongue (e-tongue) system. The data quality was verified by the Grubb's test. Moreover, potential outliers were detected based on both the standardized residual and score distance calculated for each sample. The performance of RPLS on the dataset before and after outlier detection was compared to other state-of-the-art methods including multivariate linear regression, least squares support vector machine, and the plain partial least squares regression. Both R² and root-mean-squares error (RMSE) of cross-validation (CV) were recorded for each model. With four latent variables, a robust RMSECV value of 0.3916 with bitterness values ranging from 0.63 to 4.78 were obtained for the RPLS model that was constructed based on the dataset including outliers. Meanwhile, the RMSECV, which was calculated using the models constructed by other methods, was larger than that of the RPLS model. After six outliers were excluded, the performance of all benchmark methods markedly improved, but the difference between the RPLS model constructed before and after outlier exclusion was negligible. In conclusion, the bitterness of TCM decoctions can be accurately evaluated with the RPLS model constructed using e-tongue data.

Structural Equation Modelling with Three Schemes Estimation of Score Factors on Partial Least Square (Case Study: The Quality Of Education Level SMA/MA in Sumenep Regency)

NASA Astrophysics Data System (ADS)

Anekawati, Anik; Widjanarko Otok, Bambang; Purhadi; Sutikno

2017-06-01

Research in education often involves a latent variable. Statistical analysis technique that has the ability to analyze the pattern of relationship among latent variables as well as between latent variables and their indicators is Structural Equation Modeling (SEM). SEM partial least square (PLS) was developed as an alternative if these conditions are met: the theory that underlying the design of the model is weak, does not assume a certain scale measurement, the sample size should not be large and the data does not have the multivariate normal distribution. The purpose of this paper is to compare the results of modeling of the educational quality in high school level (SMA/MA) in Sumenep Regency with structural equation modeling approach partial least square with three schemes estimation of score factors. This paper is a result of explanatory research using secondary data from Sumenep Education Department and Badan Pusat Statistik (BPS) Sumenep which was data of Sumenep in the Figures and the District of Sumenep in the Figures for the year 2015. The unit of observation in this study were districts in Sumenep that consists of 18 districts on the mainland and 9 districts in the islands. There were two endogenous variables and one exogenous variable. Endogenous variables are the quality of education level of SMA/MA (Y1) and school infrastructure (Y2), whereas exogenous variable is socio-economic condition (X1). In this study, There is one improved model which represented by model from path scheme because this model is a consistent, all of its indicators are valid and its the value of R-square increased which is: Y1=0.651Y2. In this model, the quality of education influenced only by the school infrastructure (0.651). The socio-economic condition did not affect neither the school infrastructure nor the quality of education. If the school infrastructure increased 1 point, then the quality of education increased 0.651 point. The quality of education had an R2 of 0.418, which indicates that 41.8 percent of variance in the quality of education is explained by the school infrastructure, the remaining 58.2% is explained by the other factors which were not investigated in this work.

Firmness prediction in Prunus persica 'Calrico' peaches by visible/short-wave near infrared spectroscopy and acoustic measurements using optimised linear and non-linear chemometric models.

PubMed

Lafuente, Victoria; Herrera, Luis J; Pérez, María del Mar; Val, Jesús; Negueruela, Ignacio

2015-08-15

In this work, near infrared spectroscopy (NIR) and an acoustic measure (AWETA) (two non-destructive methods) were applied in Prunus persica fruit 'Calrico' (n = 260) to predict Magness-Taylor (MT) firmness. Separate and combined use of these measures was evaluated and compared using partial least squares (PLS) and least squares support vector machine (LS-SVM) regression methods. Also, a mutual-information-based variable selection method, seeking to find the most significant variables to produce optimal accuracy of the regression models, was applied to a joint set of variables (NIR wavelengths and AWETA measure). The newly proposed combined NIR-AWETA model gave good values of the determination coefficient (R(2)) for PLS and LS-SVM methods (0.77 and 0.78, respectively), improving the reliability of MT firmness prediction in comparison with separate NIR and AWETA predictions. The three variables selected by the variable selection method (AWETA measure plus NIR wavelengths 675 and 697 nm) achieved R(2) values 0.76 and 0.77, PLS and LS-SVM. These results indicated that the proposed mutual-information-based variable selection algorithm was a powerful tool for the selection of the most relevant variables. © 2014 Society of Chemical Industry.

Variable selection based near infrared spectroscopy quantitative and qualitative analysis on wheat wet gluten

NASA Astrophysics Data System (ADS)

Lü, Chengxu; Jiang, Xunpeng; Zhou, Xingfan; Zhang, Yinqiao; Zhang, Naiqian; Wei, Chongfeng; Mao, Wenhua

2017-10-01

Wet gluten is a useful quality indicator for wheat, and short wave near infrared spectroscopy (NIRS) is a high performance technique with the advantage of economic rapid and nondestructive test. To study the feasibility of short wave NIRS analyzing wet gluten directly from wheat seed, 54 representative wheat seed samples were collected and scanned by spectrometer. 8 spectral pretreatment method and genetic algorithm (GA) variable selection method were used to optimize analysis. Both quantitative and qualitative model of wet gluten were built by partial least squares regression and discriminate analysis. For quantitative analysis, normalization is the optimized pretreatment method, 17 wet gluten sensitive variables are selected by GA, and GA model performs a better result than that of all variable model, with R2V=0.88, and RMSEV=1.47. For qualitative analysis, automatic weighted least squares baseline is the optimized pretreatment method, all variable models perform better results than those of GA models. The correct classification rates of 3 class of <24%, 24-30%, >30% wet gluten content are 95.45, 84.52, and 90.00%, respectively. The short wave NIRS technique shows potential for both quantitative and qualitative analysis of wet gluten for wheat seed.

Calibration method for video and radiation imagers

DOEpatents

Cunningham, Mark F [Oak Ridge, TN; Fabris, Lorenzo [Knoxville, TN; Gee, Timothy F [Oak Ridge, TN; Goddard, Jr., James S.; Karnowski, Thomas P [Knoxville, TN; Ziock, Klaus-peter [Clinton, TN

2011-07-05

The relationship between the high energy radiation imager pixel (HERIP) coordinate and real-world x-coordinate is determined by a least square fit between the HERIP x-coordinate and the measured real-world x-coordinates of calibration markers that emit high energy radiation imager and reflect visible light. Upon calibration, a high energy radiation imager pixel position may be determined based on a real-world coordinate of a moving vehicle. Further, a scale parameter for said high energy radiation imager may be determined based on the real-world coordinate. The scale parameter depends on the y-coordinate of the moving vehicle as provided by a visible light camera. The high energy radiation imager may be employed to detect radiation from moving vehicles in multiple lanes, which correspondingly have different distances to the high energy radiation imager.

Discrete variable representation in electronic structure theory: quadrature grids for least-squares tensor hypercontraction.

PubMed

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

2013-05-21

We investigate the application of molecular quadratures obtained from either standard Becke-type grids or discrete variable representation (DVR) techniques to the recently developed least-squares tensor hypercontraction (LS-THC) representation of the electron repulsion integral (ERI) tensor. LS-THC uses least-squares fitting to renormalize a two-sided pseudospectral decomposition of the ERI, over a physical-space quadrature grid. While this procedure is technically applicable with any choice of grid, the best efficiency is obtained when the quadrature is tuned to accurately reproduce the overlap metric for quadratic products of the primary orbital basis. Properly selected Becke DFT grids can roughly attain this property. Additionally, we provide algorithms for adopting the DVR techniques of the dynamics community to produce two different classes of grids which approximately attain this property. The simplest algorithm is radial discrete variable representation (R-DVR), which diagonalizes the finite auxiliary-basis representation of the radial coordinate for each atom, and then combines Lebedev-Laikov spherical quadratures and Becke atomic partitioning to produce the full molecular quadrature grid. The other algorithm is full discrete variable representation (F-DVR), which uses approximate simultaneous diagonalization of the finite auxiliary-basis representation of the full position operator to produce non-direct-product quadrature grids. The qualitative features of all three grid classes are discussed, and then the relative efficiencies of these grids are compared in the context of LS-THC-DF-MP2. Coarse Becke grids are found to give essentially the same accuracy and efficiency as R-DVR grids; however, the latter are built from explicit knowledge of the basis set and may guide future development of atom-centered grids. F-DVR is found to provide reasonable accuracy with markedly fewer points than either Becke or R-DVR schemes.

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.

Career Technical Education Adjunct Faculty Teacher Readiness: An Investigation of Teacher Excellence and Variables of Preparedness

ERIC Educational Resources Information Center

Guerra, Jorge

2012-01-01

The purpose of this research was to examine the relationship between teaching readiness and teaching excellence with three variables of preparedness of adjunct professors teaching career technical education courses through student surveys using a correlational design of two statistical techniques; least-squares regression and one-way analysis of…

A spectral mimetic least-squares method for the Stokes equations with no-slip boundary condition

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

Gerritsma, Marc; Bochev, Pavel

Formulation of locally conservative least-squares finite element methods (LSFEMs) for the Stokes equations with the no-slip boundary condition has been a long standing problem. Existing LSFEMs that yield exactly divergence free velocities require non-standard boundary conditions (Bochev and Gunzburger, 2009 [3]), while methods that admit the no-slip condition satisfy the incompressibility equation only approximately (Bochev and Gunzburger, 2009 [4, Chapter 7]). Here we address this problem by proving a new non-standard stability bound for the velocity–vorticity–pressure Stokes system augmented with a no-slip boundary condition. This bound gives rise to a norm-equivalent least-squares functional in which the velocity can be approximatedmore » by div-conforming finite element spaces, thereby enabling a locally-conservative approximations of this variable. Here, we also provide a practical realization of the new LSFEM using high-order spectral mimetic finite element spaces (Kreeft et al., 2011) and report several numerical tests, which confirm its mimetic properties.« less

A spectral mimetic least-squares method for the Stokes equations with no-slip boundary condition

DOE PAGES

Gerritsma, Marc; Bochev, Pavel

2016-03-22

Formulation of locally conservative least-squares finite element methods (LSFEMs) for the Stokes equations with the no-slip boundary condition has been a long standing problem. Existing LSFEMs that yield exactly divergence free velocities require non-standard boundary conditions (Bochev and Gunzburger, 2009 [3]), while methods that admit the no-slip condition satisfy the incompressibility equation only approximately (Bochev and Gunzburger, 2009 [4, Chapter 7]). Here we address this problem by proving a new non-standard stability bound for the velocity–vorticity–pressure Stokes system augmented with a no-slip boundary condition. This bound gives rise to a norm-equivalent least-squares functional in which the velocity can be approximatedmore » by div-conforming finite element spaces, thereby enabling a locally-conservative approximations of this variable. Here, we also provide a practical realization of the new LSFEM using high-order spectral mimetic finite element spaces (Kreeft et al., 2011) and report several numerical tests, which confirm its mimetic properties.« less

Ultra-Short-Term Wind Power Prediction Using a Hybrid Model

NASA Astrophysics Data System (ADS)

Mohammed, E.; Wang, S.; Yu, J.

2017-05-01

This paper aims to develop and apply a hybrid model of two data analytical methods, multiple linear regressions and least square (MLR&LS), for ultra-short-term wind power prediction (WPP), for example taking, Northeast China electricity demand. The data was obtained from the historical records of wind power from an offshore region, and from a wind farm of the wind power plant in the areas. The WPP achieved in two stages: first, the ratios of wind power were forecasted using the proposed hybrid method, and then the transformation of these ratios of wind power to obtain forecasted values. The hybrid model combines the persistence methods, MLR and LS. The proposed method included two prediction types, multi-point prediction and single-point prediction. WPP is tested by applying different models such as autoregressive moving average (ARMA), autoregressive integrated moving average (ARIMA) and artificial neural network (ANN). By comparing results of the above models, the validity of the proposed hybrid model is confirmed in terms of error and correlation coefficient. Comparison of results confirmed that the proposed method works effectively. Additional, forecasting errors were also computed and compared, to improve understanding of how to depict highly variable WPP and the correlations between actual and predicted wind power.

A nonlinear quality-related fault detection approach based on modified kernel partial least squares.

PubMed

Jiao, Jianfang; Zhao, Ning; Wang, Guang; Yin, Shen

2017-01-01

In this paper, a new nonlinear quality-related fault detection method is proposed based on kernel partial least squares (KPLS) model. To deal with the nonlinear characteristics among process variables, the proposed method maps these original variables into feature space in which the linear relationship between kernel matrix and output matrix is realized by means of KPLS. Then the kernel matrix is decomposed into two orthogonal parts by singular value decomposition (SVD) and the statistics for each part are determined appropriately for the purpose of quality-related fault detection. Compared with relevant existing nonlinear approaches, the proposed method has the advantages of simple diagnosis logic and stable performance. A widely used literature example and an industrial process are used for the performance evaluation for the proposed method. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

A comparison of different strategies in multivariate regression models for the direct determination of Mn, Cr, and Ni in steel samples using laser-induced breakdown spectroscopy

NASA Astrophysics Data System (ADS)

Luna, Aderval S.; Gonzaga, Fabiano B.; da Rocha, Werickson F. C.; Lima, Igor C. A.

2018-01-01

Laser-induced breakdown spectroscopy (LIBS) analysis was carried out on eleven steel samples to quantify the concentrations of chromium, nickel, and manganese. LIBS spectral data were correlated to known concentrations of the samples using different strategies in partial least squares (PLS) regression models. For the PLS analysis, one predictive model was separately generated for each element, while different approaches were used for the selection of variables (VIP: variable importance in projection and iPLS: interval partial least squares) in the PLS model to quantify the contents of the elements. The comparison of the performance of the models showed that there was no significant statistical difference using the Wilcoxon signed rank test. The elliptical joint confidence region (EJCR) did not detect systematic errors in these proposed methodologies for each metal.

Automatic load forecasting. Final report

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

Nelson, D.J.; Vemuri, S.

A method which lends itself to on-line forecasting of hourly electric loads is presented and the results of its use are compared to models developed using the Box-Jenkins method. The method consists of processing the historical hourly loads with a sequential least-squares estimator to identify a finite order autoregressive model which in turn is used to obtain a parsimonious autoregressive-moving average model. A procedure is also defined for incorporating temperature as a variable to improve forecasts where loads are temperature dependent. The method presented has several advantages in comparison to the Box-Jenkins method including much less human intervention and improvedmore » model identification. The method has been tested using three-hourly data from the Lincoln Electric System, Lincoln, Nebraska. In the exhaustive analyses performed on this data base this method produced significantly better results than the Box-Jenkins method. The method also proved to be more robust in that greater confidence could be placed in the accuracy of models based upon the various measures available at the identification stage.« less

A weighted least squares estimation of the polynomial regression model on paddy production in the area of Kedah and Perlis

NASA Astrophysics Data System (ADS)

Musa, Rosliza; Ali, Zalila; Baharum, Adam; Nor, Norlida Mohd

2017-08-01

The linear regression model assumes that all random error components are identically and independently distributed with constant variance. Hence, each data point provides equally precise information about the deterministic part of the total variation. In other words, the standard deviations of the error terms are constant over all values of the predictor variables. When the assumption of constant variance is violated, the ordinary least squares estimator of regression coefficient lost its property of minimum variance in the class of linear and unbiased estimators. Weighted least squares estimation are often used to maximize the efficiency of parameter estimation. A procedure that treats all of the data equally would give less precisely measured points more influence than they should have and would give highly precise points too little influence. Optimizing the weighted fitting criterion to find the parameter estimates allows the weights to determine the contribution of each observation to the final parameter estimates. This study used polynomial model with weighted least squares estimation to investigate paddy production of different paddy lots based on paddy cultivation characteristics and environmental characteristics in the area of Kedah and Perlis. The results indicated that factors affecting paddy production are mixture fertilizer application cycle, average temperature, the squared effect of average rainfall, the squared effect of pest and disease, the interaction between acreage with amount of mixture fertilizer, the interaction between paddy variety and NPK fertilizer application cycle and the interaction between pest and disease and NPK fertilizer application cycle.

Hypoglycemia early alarm systems based on recursive autoregressive partial least squares models.

PubMed

Bayrak, Elif Seyma; Turksoy, Kamuran; Cinar, Ali; Quinn, Lauretta; Littlejohn, Elizabeth; Rollins, Derrick

2013-01-01

Hypoglycemia caused by intensive insulin therapy is a major challenge for artificial pancreas systems. Early detection and prevention of potential hypoglycemia are essential for the acceptance of fully automated artificial pancreas systems. Many of the proposed alarm systems are based on interpretation of recent values or trends in glucose values. In the present study, subject-specific linear models are introduced to capture glucose variations and predict future blood glucose concentrations. These models can be used in early alarm systems of potential hypoglycemia. A recursive autoregressive partial least squares (RARPLS) algorithm is used to model the continuous glucose monitoring sensor data and predict future glucose concentrations for use in hypoglycemia alarm systems. The partial least squares models constructed are updated recursively at each sampling step with a moving window. An early hypoglycemia alarm algorithm using these models is proposed and evaluated. Glucose prediction models based on real-time filtered data has a root mean squared error of 7.79 and a sum of squares of glucose prediction error of 7.35% for six-step-ahead (30 min) glucose predictions. The early alarm systems based on RARPLS shows good performance. A sensitivity of 86% and a false alarm rate of 0.42 false positive/day are obtained for the early alarm system based on six-step-ahead predicted glucose values with an average early detection time of 25.25 min. The RARPLS models developed provide satisfactory glucose prediction with relatively smaller error than other proposed algorithms and are good candidates to forecast and warn about potential hypoglycemia unless preventive action is taken far in advance. © 2012 Diabetes Technology Society.

Hypoglycemia Early Alarm Systems Based on Recursive Autoregressive Partial Least Squares Models

PubMed Central

Bayrak, Elif Seyma; Turksoy, Kamuran; Cinar, Ali; Quinn, Lauretta; Littlejohn, Elizabeth; Rollins, Derrick

2013-01-01

Background Hypoglycemia caused by intensive insulin therapy is a major challenge for artificial pancreas systems. Early detection and prevention of potential hypoglycemia are essential for the acceptance of fully automated artificial pancreas systems. Many of the proposed alarm systems are based on interpretation of recent values or trends in glucose values. In the present study, subject-specific linear models are introduced to capture glucose variations and predict future blood glucose concentrations. These models can be used in early alarm systems of potential hypoglycemia. Methods A recursive autoregressive partial least squares (RARPLS) algorithm is used to model the continuous glucose monitoring sensor data and predict future glucose concentrations for use in hypoglycemia alarm systems. The partial least squares models constructed are updated recursively at each sampling step with a moving window. An early hypoglycemia alarm algorithm using these models is proposed and evaluated. Results Glucose prediction models based on real-time filtered data has a root mean squared error of 7.79 and a sum of squares of glucose prediction error of 7.35% for six-step-ahead (30 min) glucose predictions. The early alarm systems based on RARPLS shows good performance. A sensitivity of 86% and a false alarm rate of 0.42 false positive/day are obtained for the early alarm system based on six-step-ahead predicted glucose values with an average early detection time of 25.25 min. Conclusions The RARPLS models developed provide satisfactory glucose prediction with relatively smaller error than other proposed algorithms and are good candidates to forecast and warn about potential hypoglycemia unless preventive action is taken far in advance. PMID:23439179

Recursive least squares estimation and its application to shallow trench isolation

NASA Astrophysics Data System (ADS)

Wang, Jin; Qin, S. Joe; Bode, Christopher A.; Purdy, Matthew A.

2003-06-01

In recent years, run-to-run (R2R) control technology has received tremendous interest in semiconductor manufacturing. One class of widely used run-to-run controllers is based on the exponentially weighted moving average (EWMA) statistics to estimate process deviations. Using an EWMA filter to smooth the control action on a linear process has been shown to provide good results in a number of applications. However, for a process with severe drifts, the EWMA controller is insufficient even when large weights are used. This problem becomes more severe when there is measurement delay, which is almost inevitable in semiconductor industry. In order to control drifting processes, a predictor-corrector controller (PCC) and a double EWMA controller have been developed. Chen and Guo (2001) show that both PCC and double-EWMA controller are in effect Integral-double-Integral (I-II) controllers, which are able to control drifting processes. However, since offset is often within the noise of the process, the second integrator can actually cause jittering. Besides, tuning the second filter is not as intuitive as a single EWMA filter. In this work, we look at an alternative way Recursive Least Squares (RLS), to estimate and control the drifting process. EWMA and double-EWMA are shown to be the least squares estimate for locally constant mean model and locally constant linear trend model. Then the recursive least squares with exponential factor is applied to shallow trench isolation etch process to predict the future etch rate. The etch process, which is a critical process in the flash memory manufacturing, is known to suffer from significant etch rate drift due to chamber seasoning. In order to handle the metrology delay, we propose a new time update scheme. RLS with the new time update method gives very good result. The estimate error variance is smaller than that from EWMA, and mean square error decrease more than 10% compared to that from EWMA.

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

PubMed

Kochiya, Yuko; Hirabayashi, Akari; Ichimaru, Yuhei

2017-09-16

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

Methods for estimating annual exceedance probability discharges for streams in Arkansas, based on data through water year 2013

USGS Publications Warehouse

Wagner, Daniel M.; Krieger, Joshua D.; Veilleux, Andrea G.

2016-08-04

In 2013, the U.S. Geological Survey initiated a study to update regional skew, annual exceedance probability discharges, and regional regression equations used to estimate annual exceedance probability discharges for ungaged locations on streams in the study area with the use of recent geospatial data, new analytical methods, and available annual peak-discharge data through the 2013 water year. An analysis of regional skew using Bayesian weighted least-squares/Bayesian generalized-least squares regression was performed for Arkansas, Louisiana, and parts of Missouri and Oklahoma. The newly developed constant regional skew of -0.17 was used in the computation of annual exceedance probability discharges for 281 streamgages used in the regional regression analysis. Based on analysis of covariance, four flood regions were identified for use in the generation of regional regression models. Thirty-nine basin characteristics were considered as potential explanatory variables, and ordinary least-squares regression techniques were used to determine the optimum combinations of basin characteristics for each of the four regions. Basin characteristics in candidate models were evaluated based on multicollinearity with other basin characteristics (variance inflation factor < 2.5) and statistical significance at the 95-percent confidence level (p ≤ 0.05). Generalized least-squares regression was used to develop the final regression models for each flood region. Average standard errors of prediction of the generalized least-squares models ranged from 32.76 to 59.53 percent, with the largest range in flood region D. Pseudo coefficients of determination of the generalized least-squares models ranged from 90.29 to 97.28 percent, with the largest range also in flood region D. The regional regression equations apply only to locations on streams in Arkansas where annual peak discharges are not substantially affected by regulation, diversion, channelization, backwater, or urbanization. The applicability and accuracy of the regional regression equations depend on the basin characteristics measured for an ungaged location on a stream being within range of those used to develop the equations.

Evaluation of the Bitterness of Traditional Chinese Medicines using an E-Tongue Coupled with a Robust Partial Least Squares Regression Method

PubMed Central

Lin, Zhaozhou; Zhang, Qiao; Liu, Ruixin; Gao, Xiaojie; Zhang, Lu; Kang, Bingya; Shi, Junhan; Wu, Zidan; Gui, Xinjing; Li, Xuelin

2016-01-01

To accurately, safely, and efficiently evaluate the bitterness of Traditional Chinese Medicines (TCMs), a robust predictor was developed using robust partial least squares (RPLS) regression method based on data obtained from an electronic tongue (e-tongue) system. The data quality was verified by the Grubb’s test. Moreover, potential outliers were detected based on both the standardized residual and score distance calculated for each sample. The performance of RPLS on the dataset before and after outlier detection was compared to other state-of-the-art methods including multivariate linear regression, least squares support vector machine, and the plain partial least squares regression. Both R2 and root-mean-squares error (RMSE) of cross-validation (CV) were recorded for each model. With four latent variables, a robust RMSECV value of 0.3916 with bitterness values ranging from 0.63 to 4.78 were obtained for the RPLS model that was constructed based on the dataset including outliers. Meanwhile, the RMSECV, which was calculated using the models constructed by other methods, was larger than that of the RPLS model. After six outliers were excluded, the performance of all benchmark methods markedly improved, but the difference between the RPLS model constructed before and after outlier exclusion was negligible. In conclusion, the bitterness of TCM decoctions can be accurately evaluated with the RPLS model constructed using e-tongue data. PMID:26821026

Spectral distance decay: Assessing species beta-diversity by quantile regression

USGS Publications Warehouse

Rocchinl, D.; Nagendra, H.; Ghate, R.; Cade, B.S.

2009-01-01

Remotely sensed data represents key information for characterizing and estimating biodiversity. Spectral distance among sites has proven to be a powerful approach for detecting species composition variability. Regression analysis of species similarity versus spectral distance may allow us to quantitatively estimate how beta-diversity in species changes with respect to spectral and ecological variability. In classical regression analysis, the residual sum of squares is minimized for the mean of the dependent variable distribution. However, many ecological datasets are characterized by a high number of zeroes that can add noise to the regression model. Quantile regression can be used to evaluate trend in the upper quantiles rather than a mean trend across the whole distribution of the dependent variable. In this paper, we used ordinary least square (ols) and quantile regression to estimate the decay of species similarity versus spectral distance. The achieved decay rates were statistically nonzero (p < 0.05) considering both ols and quantile regression. Nonetheless, ols regression estimate of mean decay rate was only half the decay rate indicated by the upper quantiles. Moreover, the intercept value, representing the similarity reached when spectral distance approaches zero, was very low compared with the intercepts of upper quantiles, which detected high species similarity when habitats are more similar. In this paper we demonstrated the power of using quantile regressions applied to spectral distance decay in order to reveal species diversity patterns otherwise lost or underestimated by ordinary least square regression. ?? 2009 American Society for Photogrammetry and Remote Sensing.

Hyperspectral Imaging for Predicting the Internal Quality of Kiwifruits Based on Variable Selection Algorithms and Chemometric Models.

PubMed

Zhu, Hongyan; Chu, Bingquan; Fan, Yangyang; Tao, Xiaoya; Yin, Wenxin; He, Yong

2017-08-10

We investigated the feasibility and potentiality of determining firmness, soluble solids content (SSC), and pH in kiwifruits using hyperspectral imaging, combined with variable selection methods and calibration models. The images were acquired by a push-broom hyperspectral reflectance imaging system covering two spectral ranges. Weighted regression coefficients (BW), successive projections algorithm (SPA) and genetic algorithm-partial least square (GAPLS) were compared and evaluated for the selection of effective wavelengths. Moreover, multiple linear regression (MLR), partial least squares regression and least squares support vector machine (LS-SVM) were developed to predict quality attributes quantitatively using effective wavelengths. The established models, particularly SPA-MLR, SPA-LS-SVM and GAPLS-LS-SVM, performed well. The SPA-MLR models for firmness (R pre  = 0.9812, RPD = 5.17) and SSC (R pre  = 0.9523, RPD = 3.26) at 380-1023 nm showed excellent performance, whereas GAPLS-LS-SVM was the optimal model at 874-1734 nm for predicting pH (R pre  = 0.9070, RPD = 2.60). Image processing algorithms were developed to transfer the predictive model in every pixel to generate prediction maps that visualize the spatial distribution of firmness and SSC. Hence, the results clearly demonstrated that hyperspectral imaging has the potential as a fast and non-invasive method to predict the quality attributes of kiwifruits.

Equations for Estimating Biomass of Herbaceous and Woody Vegetation in Early-Successional Southern Appalachian Pine-Hardwood Forests

Treesearch

Katherine J. Elliott; Barton D. Clinton

1993-01-01

Allometric equations were developed to predict aboveground dry weight of herbaceous and woody species on prescribe-burned sites in the Southern Appalachians. Best-fit least-square regression models were developed using diamet,er, height, or both, as the independent variables and dry weight as the dependent variable. Coefficients of determination for the selected total...

A Hedonic Approach to Estimating Software Cost Using Ordinary Least Squares Regression and Nominal Attribute Variables

DTIC Science & Technology

2006-03-01

included zero, there is insufficient evidence to indicate that the error mean is 35 not zero. The Breusch - Pagan test was used to test the constant...Multicollinearity .............................................................................. 33 Testing OLS Assumptions...programming styles used by developers (Stamelos and others, 2003:733). Kemerer tested to see how models utilizing SLOC as an independent variable

MULTIVARIATE ANALYSES (CONONICAL CORRELATION AND PARTIAL LEAST SQUARE, PLS) TO MODEL AND ASSESS THE ASSOCIATION OF LANDSCAPE METRICS TO SURFACE WATER CHEMICAL AND BIOLOGICAL PROPERTIES USING SAVANNAH RIVER BASIN DATA.

EPA Science Inventory

Many multivariate methods are used in describing and predicting relation; each has its unique usage of categorical and non-categorical data. In multivariate analysis of variance (MANOVA), many response variables (y's) are related to many independent variables that are categorical...

Unified Least Squares Methods for the Evaluation of Diagnostic Tests With the Gold Standard

PubMed Central

Tang, Liansheng Larry; Yuan, Ao; Collins, John; Che, Xuan; Chan, Leighton

2017-01-01

The article proposes a unified least squares method to estimate the receiver operating characteristic (ROC) parameters for continuous and ordinal diagnostic tests, such as cancer biomarkers. The method is based on a linear model framework using the empirically estimated sensitivities and specificities as input “data.” It gives consistent estimates for regression and accuracy parameters when the underlying continuous test results are normally distributed after some monotonic transformation. The key difference between the proposed method and the method of Tang and Zhou lies in the response variable. The response variable in the latter is transformed empirical ROC curves at different thresholds. It takes on many values for continuous test results, but few values for ordinal test results. The limited number of values for the response variable makes it impractical for ordinal data. However, the response variable in the proposed method takes on many more distinct values so that the method yields valid estimates for ordinal data. Extensive simulation studies are conducted to investigate and compare the finite sample performance of the proposed method with an existing method, and the method is then used to analyze 2 real cancer diagnostic example as an illustration. PMID:28469385

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

A Cubic Radial Basis Function in the MLPG Method for Beam Problems

NASA Technical Reports Server (NTRS)

Raju, I. S.; Phillips, D. R.

2002-01-01

A non-compactly supported cubic radial basis function implementation of the MLPG method for beam problems is presented. The evaluation of the derivatives of the shape functions obtained from the radial basis function interpolation is much simpler than the evaluation of the moving least squares shape function derivatives. The radial basis MLPG yields results as accurate or better than those obtained by the conventional MLPG method for problems with discontinuous and other complex loading conditions.

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.

Water Quality Variable Estimation using Partial Least Squares Regression and Multi-Scale Remote Sensing.

NASA Astrophysics Data System (ADS)

Peterson, K. T.; Wulamu, A.

2017-12-01

Water, essential to all living organisms, is one of the Earth's most precious resources. Remote sensing offers an ideal approach to monitor water quality over traditional in-situ techniques that are highly time and resource consuming. Utilizing a multi-scale approach, incorporating data from handheld spectroscopy, UAS based hyperspectal, and satellite multispectral images were collected in coordination with in-situ water quality samples for the two midwestern watersheds. The remote sensing data was modeled and correlated to the in-situ water quality variables including chlorophyll content (Chl), turbidity, and total dissolved solids (TDS) using Normalized Difference Spectral Indices (NDSI) and Partial Least Squares Regression (PLSR). The results of the study supported the original hypothesis that correlating water quality variables with remotely sensed data benefits greatly from the use of more complex modeling and regression techniques such as PLSR. The final results generated from the PLSR analysis resulted in much higher R2 values for all variables when compared to NDSI. The combination of NDSI and PLSR analysis also identified key wavelengths for identification that aligned with previous study's findings. This research displays the advantages and future for complex modeling and machine learning techniques to improve water quality variable estimation from spectral data.

Testing concordance of instrumental variable effects in generalized linear models with application to Mendelian randomization

PubMed Central

Dai, James Y.; Chan, Kwun Chuen Gary; Hsu, Li

2014-01-01

Instrumental variable regression is one way to overcome unmeasured confounding and estimate causal effect in observational studies. Built on structural mean models, there has been considerale work recently developed for consistent estimation of causal relative risk and causal odds ratio. Such models can sometimes suffer from identification issues for weak instruments. This hampered the applicability of Mendelian randomization analysis in genetic epidemiology. When there are multiple genetic variants available as instrumental variables, and causal effect is defined in a generalized linear model in the presence of unmeasured confounders, we propose to test concordance between instrumental variable effects on the intermediate exposure and instrumental variable effects on the disease outcome, as a means to test the causal effect. We show that a class of generalized least squares estimators provide valid and consistent tests of causality. For causal effect of a continuous exposure on a dichotomous outcome in logistic models, the proposed estimators are shown to be asymptotically conservative. When the disease outcome is rare, such estimators are consistent due to the log-linear approximation of the logistic function. Optimality of such estimators relative to the well-known two-stage least squares estimator and the double-logistic structural mean model is further discussed. PMID:24863158

Discriminative least squares regression for multiclass classification and feature selection.

PubMed

Xiang, Shiming; Nie, Feiping; Meng, Gaofeng; Pan, Chunhong; Zhang, Changshui

2012-11-01

This paper presents a framework of discriminative least squares regression (LSR) for multiclass classification and feature selection. The core idea is to enlarge the distance between different classes under the conceptual framework of LSR. First, a technique called ε-dragging is introduced to force the regression targets of different classes moving along opposite directions such that the distances between classes can be enlarged. Then, the ε-draggings are integrated into the LSR model for multiclass classification. Our learning framework, referred to as discriminative LSR, has a compact model form, where there is no need to train two-class machines that are independent of each other. With its compact form, this model can be naturally extended for feature selection. This goal is achieved in terms of L2,1 norm of matrix, generating a sparse learning model for feature selection. The model for multiclass classification and its extension for feature selection are finally solved elegantly and efficiently. Experimental evaluation over a range of benchmark datasets indicates the validity of our method.

Calibration of Lévy Processes with American Options

NASA Astrophysics Data System (ADS)

Achdou, Yves

We study options on financial assets whose discounted prices are exponential of Lévy processes. The price of an American vanilla option as a function of the maturity and the strike satisfies a linear complementarity problem involving a non-local partial integro-differential operator. It leads to a variational inequality in a suitable weighted Sobolev space. Calibrating the Lévy process may be done by solving an inverse least square problem where the state variable satisfies the previously mentioned variational inequality. We first assume that the volatility is positive: after carefully studying the direct problem, we propose necessary optimality conditions for the least square inverse problem. We also consider the direct problem when the volatility is zero.

Does Mother Know Best? Treatment Adherence as a Function of Anticipated Treatment Benefit

PubMed Central

Glymour, M. Maria; Nguyen, Quynh; Matsouaka, Roland; Tchetgen Tchetgen, Eric J.; Schmidt, Nicole M.; Osypuk, Theresa L.

2016-01-01

Background We describe bias resulting from individualized treatment selection, which occurs when treatment has heterogeneous effects and individuals selectively choose treatments of greatest benefit to themselves. This pernicious bias may confound estimates from observational studies and lead to important misinterpretation of intent-to-treat analyses of randomized trials. Despite the potentially serious threat to inferences, individualized treatment selection has rarely been formally described or assessed. Methods The Moving to Opportunity (MTO) trial randomly assigned subsidized rental vouchers to low-income families in high-poverty public housing. We assessed the Kessler-6 psychological distress and Behavior Problems Index outcomes for 2,829 adolescents 4–7 years after randomization. Among families randomly assigned to receive vouchers, we estimated probability of moving (treatment), predicted by pre-randomization characteristics (c-statistic=0.63). We categorized families into tertiles of this estimated probability of moving, and compared instrumental variable effect estimates for moving on Behavior Problems Index and Kessler-6 across tertiles. Results Instrumental variable estimated effects of moving on behavioral problems index were most adverse for boys least likely to move (b=0.93; 95% CI: 0.33, 1.53) compared to boys most likely to move (b=0.14; 95% CI: −0.15, 0.44; p=.02 for treatment*tertile interaction). Effects on Kessler-6 were more beneficial for girls least likely to move compared to girls most likely to move (−0.62 vs. 0.02; interaction p=.03). Conclusions Evidence of Individualized treatment selection differed by child gender and outcome and should be evaluated in randomized trial reports, especially when heterogeneous treatment effects are likely and non-adherence is common. PMID:26628424

Theoretical study of the incompressible Navier-Stokes equations by the least-squares method

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Loh, Ching Y.; Povinelli, Louis A.

1994-01-01

Usually the theoretical analysis of the Navier-Stokes equations is conducted via the Galerkin method which leads to difficult saddle-point problems. This paper demonstrates that the least-squares method is a useful alternative tool for the theoretical study of partial differential equations since it leads to minimization problems which can often be treated by an elementary technique. The principal part of the Navier-Stokes equations in the first-order velocity-pressure-vorticity formulation consists of two div-curl systems, so the three-dimensional div-curl system is thoroughly studied at first. By introducing a dummy variable and by using the least-squares method, this paper shows that the div-curl system is properly determined and elliptic, and has a unique solution. The same technique then is employed to prove that the Stokes equations are properly determined and elliptic, and that four boundary conditions on a fixed boundary are required for three-dimensional problems. This paper also shows that under four combinations of non-standard boundary conditions the solution of the Stokes equations is unique. This paper emphasizes the application of the least-squares method and the div-curl method to derive a high-order version of differential equations and additional boundary conditions. In this paper, an elementary method (integration by parts) is used to prove Friedrichs' inequalities related to the div and curl operators which play an essential role in the analysis.

Modelling by partial least squares the relationship between the HPLC mobile phases and analytes on phenyl column.

PubMed

Markopoulou, Catherine K; Kouskoura, Maria G; Koundourellis, John E

2011-06-01

Twenty-five descriptors and 61 structurally different analytes have been used on a partial least squares (PLS) to latent structure technique in order to study chromatographically their interaction mechanism on a phenyl column. According to the model, 240 different retention times of the analytes, expressed as Y variable (log k), at different % MeOH mobile-phase concentrations have been correlated with their theoretical most important structural or molecular descriptors. The goodness-of-fit was estimated by the coefficient of multiple determinations r(2) (0.919), and the root mean square error of estimation (RMSEE=0.1283) values with a predictive ability (Q(2)) of 0.901. The model was further validated using cross-validation (CV), validated by 20 response permutations r(2) (0.0, 0.0146), Q(2) (0.0, -0.136) and validated by external prediction. The contribution of certain mechanism interactions between the analytes, the mobile phase and the column, proportional or counterbalancing is also studied. Trying to evaluate the influence on Y of every variable in a PLS model, VIP (variables importance in the projection) plot provides evidence that lipophilicity (expressed as Log D, Log P), polarizability, refractivity and the eluting power of the mobile phase are dominant in the retention mechanism on a phenyl column. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

A meshless method for solving two-dimensional variable-order time fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Tayebi, A.; Shekari, Y.; Heydari, M. H.

2017-07-01

Several physical phenomena such as transformation of pollutants, energy, particles and many others can be described by the well-known convection-diffusion equation which is a combination of the diffusion and advection equations. In this paper, this equation is generalized with the concept of variable-order fractional derivatives. The generalized equation is called variable-order time fractional advection-diffusion equation (V-OTFA-DE). An accurate and robust meshless method based on the moving least squares (MLS) approximation and the finite difference scheme is proposed for its numerical solution on two-dimensional (2-D) arbitrary domains. In the time domain, the finite difference technique with a θ-weighted scheme and in the space domain, the MLS approximation are employed to obtain appropriate semi-discrete solutions. Since the newly developed method is a meshless approach, it does not require any background mesh structure to obtain semi-discrete solutions of the problem under consideration, and the numerical solutions are constructed entirely based on a set of scattered nodes. The proposed method is validated in solving three different examples including two benchmark problems and an applied problem of pollutant distribution in the atmosphere. In all such cases, the obtained results show that the proposed method is very accurate and robust. Moreover, a remarkable property so-called positive scheme for the proposed method is observed in solving concentration transport phenomena.

What Determines Alumni Generosity?

ERIC Educational Resources Information Center

Baade, Robert A.; Sundberg, Jeffrey O.

1996-01-01

College alumni giving is correlated with institutional characteristics (quality and development efforts) and student characteristics (quality and wealth). This paper uses a two-step least-squares approach with data and quality/wealth variables to explore the "rich-student, quality-school" alumni generosity phenomenon. Alumni giving is…

When Can Categorical Variables Be Treated as Continuous? A Comparison of Robust Continuous and Categorical SEM Estimation Methods under Suboptimal Conditions

ERIC Educational Resources Information Center

Rhemtulla, Mijke; Brosseau-Liard, Patricia E.; Savalei, Victoria

2012-01-01

A simulation study compared the performance of robust normal theory maximum likelihood (ML) and robust categorical least squares (cat-LS) methodology for estimating confirmatory factor analysis models with ordinal variables. Data were generated from 2 models with 2-7 categories, 4 sample sizes, 2 latent distributions, and 5 patterns of category…

Spatial Autocorrelation Approaches to Testing Residuals from Least Squares Regression.

PubMed

Chen, Yanguang

2016-01-01

In geo-statistics, the Durbin-Watson test is frequently employed to detect the presence of residual serial correlation from least squares regression analyses. However, the Durbin-Watson statistic is only suitable for ordered time or spatial series. If the variables comprise cross-sectional data coming from spatial random sampling, the test will be ineffectual because the value of Durbin-Watson's statistic depends on the sequence of data points. This paper develops two new statistics for testing serial correlation of residuals from least squares regression based on spatial samples. By analogy with the new form of Moran's index, an autocorrelation coefficient is defined with a standardized residual vector and a normalized spatial weight matrix. Then by analogy with the Durbin-Watson statistic, two types of new serial correlation indices are constructed. As a case study, the two newly presented statistics are applied to a spatial sample of 29 China's regions. These results show that the new spatial autocorrelation models can be used to test the serial correlation of residuals from regression analysis. In practice, the new statistics can make up for the deficiencies of the Durbin-Watson test.

The relationship between air pollution, fossil fuel energy consumption, and water resources in the panel of selected Asia-Pacific countries.

PubMed

Rafindadi, Abdulkadir Abdulrashid; Yusof, Zarinah; Zaman, Khalid; Kyophilavong, Phouphet; Akhmat, Ghulam

2014-10-01

The objective of the study is to examine the relationship between air pollution, fossil fuel energy consumption, water resources, and natural resource rents in the panel of selected Asia-Pacific countries, over a period of 1975-2012. The study includes number of variables in the model for robust analysis. The results of cross-sectional analysis show that there is a significant relationship between air pollution, energy consumption, and water productivity in the individual countries of Asia-Pacific. However, the results of each country vary according to the time invariant shocks. For this purpose, the study employed the panel least square technique which includes the panel least square regression, panel fixed effect regression, and panel two-stage least square regression. In general, all the panel tests indicate that there is a significant and positive relationship between air pollution, energy consumption, and water resources in the region. The fossil fuel energy consumption has a major dominating impact on the changes in the air pollution in the region.

Partial least squares density modeling (PLS-DM) - a new class-modeling strategy applied to the authentication of olives in brine by near-infrared spectroscopy.

PubMed

Oliveri, Paolo; López, M Isabel; Casolino, M Chiara; Ruisánchez, Itziar; Callao, M Pilar; Medini, Luca; Lanteri, Silvia

2014-12-03

A new class-modeling method, referred to as partial least squares density modeling (PLS-DM), is presented. The method is based on partial least squares (PLS), using a distance-based sample density measurement as the response variable. Potential function probability density is subsequently calculated on PLS scores and used, jointly with residual Q statistics, to develop efficient class models. The influence of adjustable model parameters on the resulting performances has been critically studied by means of cross-validation and application of the Pareto optimality criterion. The method has been applied to verify the authenticity of olives in brine from cultivar Taggiasca, based on near-infrared (NIR) spectra recorded on homogenized solid samples. Two independent test sets were used for model validation. The final optimal model was characterized by high efficiency and equilibrate balance between sensitivity and specificity values, if compared with those obtained by application of well-established class-modeling methods, such as soft independent modeling of class analogy (SIMCA) and unequal dispersed classes (UNEQ). Copyright © 2014 Elsevier B.V. All rights reserved.

The emotional effects of violations of causality, or How to make a square amusing

PubMed Central

Bressanelli, Daniela; Parovel, Giulia

2012-01-01

In Michotte's launching paradigm a square moves up to and makes contact with another square, which then moves off more slowly. In the triggering effect, the second square moves much faster than the first, eliciting an amusing impression. We generated 13 experimental displays in which there was always incongruity between cause and effect. We hypothesized that the comic impression would be stronger when objects are perceived as living agents and weaker when objects are perceived as mechanically non-animated. General findings support our hypothesis. PMID:23145274

Clinical Trials With Large Numbers of Variables: Important Advantages of Canonical Analysis.

PubMed

Cleophas, Ton J

2016-01-01

Canonical analysis assesses the combined effects of a set of predictor variables on a set of outcome variables, but it is little used in clinical trials despite the omnipresence of multiple variables. The aim of this study was to assess the performance of canonical analysis as compared with traditional multivariate methods using multivariate analysis of covariance (MANCOVA). As an example, a simulated data file with 12 gene expression levels and 4 drug efficacy scores was used. The correlation coefficient between the 12 predictor and 4 outcome variables was 0.87 (P = 0.0001) meaning that 76% of the variability in the outcome variables was explained by the 12 covariates. Repeated testing after the removal of 5 unimportant predictor and 1 outcome variable produced virtually the same overall result. The MANCOVA identified identical unimportant variables, but it was unable to provide overall statistics. (1) Canonical analysis is remarkable, because it can handle many more variables than traditional multivariate methods such as MANCOVA can. (2) At the same time, it accounts for the relative importance of the separate variables, their interactions and differences in units. (3) Canonical analysis provides overall statistics of the effects of sets of variables, whereas traditional multivariate methods only provide the statistics of the separate variables. (4) Unlike other methods for combining the effects of multiple variables such as factor analysis/partial least squares, canonical analysis is scientifically entirely rigorous. (5) Limitations include that it is less flexible than factor analysis/partial least squares, because only 2 sets of variables are used and because multiple solutions instead of one is offered. We do hope that this article will stimulate clinical investigators to start using this remarkable method.

The Impact of Moisture on Mountain Waves During T-REX

DTIC Science & Technology

2009-11-01

sensitivity to the upstream wind speed. After re- moving these three outliers, the linear least squares re- gression using the other 21 points yields W( U c )5...The wave amplitudes for the 24 flights normalized by the reference wave amplitude are plotted versus the upstream RH maxima in Fig. 3b. There are four...mountaintop level de- rived from the upwind sondes for 24 UWKA flights. The filled circles represent moist cases as defined in the text. The bold line

Orthogonalizing EM: A design-based least squares algorithm.

PubMed

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

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

Estimating magnitude and frequency of peak discharges for rural, unregulated, streams in West Virginia

USGS Publications Warehouse

Wiley, J.B.; Atkins, John T.; Tasker, Gary D.

2000-01-01

Multiple and simple least-squares regression models for the log10-transformed 100-year discharge with independent variables describing the basin characteristics (log10-transformed and untransformed) for 267 streamflow-gaging stations were evaluated, and the regression residuals were plotted as areal distributions that defined three regions of the State, designated East, North, and South. Exploratory data analysis procedures identified 31 gaging stations at which discharges are different than would be expected for West Virginia. Regional equations for the 2-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-year peak discharges were determined by generalized least-squares regression using data from 236 gaging stations. Log10-transformed drainage area was the most significant independent variable for all regions.Equations developed in this study are applicable only to rural, unregulated, streams within the boundaries of West Virginia. The accuracy of estimating equations is quantified by measuring the average prediction error (from 27.7 to 44.7 percent) and equivalent years of record (from 1.6 to 20.0 years).

Exact and Approximate Statistical Inference for Nonlinear Regression and the Estimating Equation Approach.

PubMed

Demidenko, Eugene

2017-09-01

The exact density distribution of the nonlinear least squares estimator in the one-parameter regression model is derived in closed form and expressed through the cumulative distribution function of the standard normal variable. Several proposals to generalize this result are discussed. The exact density is extended to the estimating equation (EE) approach and the nonlinear regression with an arbitrary number of linear parameters and one intrinsically nonlinear parameter. For a very special nonlinear regression model, the derived density coincides with the distribution of the ratio of two normally distributed random variables previously obtained by Fieller (1932), unlike other approximations previously suggested by other authors. Approximations to the density of the EE estimators are discussed in the multivariate case. Numerical complications associated with the nonlinear least squares are illustrated, such as nonexistence and/or multiple solutions, as major factors contributing to poor density approximation. The nonlinear Markov-Gauss theorem is formulated based on the near exact EE density approximation.

Space-time least-squares finite element method for convection-reaction system with transformed variables

PubMed Central

Nam, Jaewook

2011-01-01

We present a method to solve a convection-reaction system based on a least-squares finite element method (LSFEM). For steady-state computations, issues related to recirculation flow are stated and demonstrated with a simple example. The method can compute concentration profiles in open flow even when the generation term is small. This is the case for estimating hemolysis in blood. Time-dependent flows are computed with the space-time LSFEM discretization. We observe that the computed hemoglobin concentration can become negative in certain regions of the flow; it is a physically unacceptable result. To prevent this, we propose a quadratic transformation of variables. The transformed governing equation can be solved in a straightforward way by LSFEM with no sign of unphysical behavior. The effect of localized high shear on blood damage is shown in a circular Couette-flow-with-blade configuration, and a physiological condition is tested in an arterial graft flow. PMID:21709752

Modelling daily dissolved oxygen concentration using least square support vector machine, multivariate adaptive regression splines and M5 model tree

NASA Astrophysics Data System (ADS)

Heddam, Salim; Kisi, Ozgur

2018-04-01

In the present study, three types of artificial intelligence techniques, least square support vector machine (LSSVM), multivariate adaptive regression splines (MARS) and M5 model tree (M5T) are applied for modeling daily dissolved oxygen (DO) concentration using several water quality variables as inputs. The DO concentration and water quality variables data from three stations operated by the United States Geological Survey (USGS) were used for developing the three models. The water quality data selected consisted of daily measured of water temperature (TE, °C), pH (std. unit), specific conductance (SC, μS/cm) and discharge (DI cfs), are used as inputs to the LSSVM, MARS and M5T models. The three models were applied for each station separately and compared to each other. According to the results obtained, it was found that: (i) the DO concentration could be successfully estimated using the three models and (ii) the best model among all others differs from one station to another.

Deep sea tides determination from GEOS-3

NASA Technical Reports Server (NTRS)

Maul, G. A.; Yanaway, A.

1978-01-01

GEOS 3 altimeter data in a 5 degree X 5 degree square centered at 30 deg N, 70 deg W were analyzed to evaluate deep sea tide determination from a spacecraft. The signal to noise ratio of known tidal variability to altimeter measurement of sea level above the ellipsoid was 0.1. A sample was obtained in a 5 deg x 5 deg area approximately once every four days. The randomly spaced time series was analyzed using two independent least squares techniques.

Psychosocial factors and financial literacy.

PubMed

Murphy, John L

2013-01-01

This study uses data from the Health and Retirement Study (HRS) to analyze the psychological and social variables associated with financial literacy. The HRS is a nationally representative longitudinal survey of individuals older than age 50 and their spouses. An ordinary least squares linear regression analysis explores the relationship between financial literacy and several economic and psychosocial variables. After controlling for earnings, level of education, and other socioeconomic variables in this exploratory study, I find that financial satisfaction and religiosity are correlated with financial literacy.

Estimating the magnitude and frequency of floods in urban basins in Missouri

USGS Publications Warehouse

Southard, Rodney E.

2010-01-01

Streamgage flood-frequency analyses were done for 35 streamgages on urban streams in and adjacent to Missouri for estimation of the magnitude and frequency of floods in urban areas of Missouri. A log-Pearson Type-III distribution was fitted to the annual series of peak flow data retrieved from the U.S. Geological Survey National Water Information System. For this report, the flood frequency estimates are expressed in terms of percent annual exceedance probabilities of 50, 20, 10, 4, 2, 1, and 0.2. Of the 35 streamgages, 30 are located in Missouri. The remaining five non-Missouri streamgages were added to the dataset to improve the range and applicability of the regression analyses from the streamgage frequency analyses. Ordinary least-squares was used to determine the best set of independent variables for the regression equations. Basin characteristics selected for independent variables into the ordinary least-squares regression analyses were based on theoretical relation to flood flows, literature review of possible basin characteristics, and the ability to measure the basin characteristics using digital datasets and geographic information system technology. Results of the ordinary least-squares were evaluated on the basis of Mallow's Cp statistic, the adjusted coefficient of determination, and the statistical significance of the independent variables. The independent variables of drainage area and percent impervious area were determined to be statistically significant and readily determined from existing digital datasets. The drainage area variable was computed using the best elevation data available, either from a statewide 10-meter grid or high-resolution elevation data from urban areas. The impervious area variable was computed from the National Land Cover Dataset 2001 impervious area dataset. The National Land Cover Dataset 2001 impervious area data for each basin was compared to historical imagery and 7.5-minute topographic maps to verify the national dataset represented the urbanization of the basin at the time streamgage data were collected. Eight streamgages had less urbanization during the period of time streamflow data were collected than was shown on the 2001 dataset. The impervious area values for these eight urban basins were adjusted downward as much as 23 percent to account for the additional urbanization since the streamflow data were collected. Weighted least-squares regression techniques were used to determine the final regression equations for the statewide urban flood-frequency equations. Weighted least-squares techniques improve regression equations by adjusting for different and varying lengths in streamflow records. The final flood-frequency equations for the 50-, 20-, 10-, 4-, 2-, 1-, and 0.2-percent annual exceedance probability floods for Missouri provide a technique for estimating peak flows on urban streams at gaged and ungaged sites. The applicability of the equations is limited by the range in basin characteristics used to develop the regression equations. The range in drainage area is 0.28 to 189 square miles; range in impervious area is 2.3 to 46.0 percent. Seven of the 35 selected streamgages were used to compare the results of the existing rural and urban equations to the urban equations presented in this report for the 1-percent annual exceedance probability. Results of the comparison indicate that the estimated peak flows for the urban equation in this report ranged from 3 to 52 percent higher than the results from the rural equations. Comparing the estimated urban peak flows from this report to the existing urban equation developed in 1986 indicated the range was 255 percent lower to 10 percent higher. The overall comparison between the current (2010) and 1986 urban equations indicates a reduction in estimated peak flow values for the 1-percent annual exceedance probability flood.

Independent contrasts and PGLS regression estimators are equivalent.

PubMed

Blomberg, Simon P; Lefevre, James G; Wells, Jessie A; Waterhouse, Mary

2012-05-01

We prove that the slope parameter of the ordinary least squares regression of phylogenetically independent contrasts (PICs) conducted through the origin is identical to the slope parameter of the method of generalized least squares (GLSs) regression under a Brownian motion model of evolution. This equivalence has several implications: 1. Understanding the structure of the linear model for GLS regression provides insight into when and why phylogeny is important in comparative studies. 2. The limitations of the PIC regression analysis are the same as the limitations of the GLS model. In particular, phylogenetic covariance applies only to the response variable in the regression and the explanatory variable should be regarded as fixed. Calculation of PICs for explanatory variables should be treated as a mathematical idiosyncrasy of the PIC regression algorithm. 3. Since the GLS estimator is the best linear unbiased estimator (BLUE), the slope parameter estimated using PICs is also BLUE. 4. If the slope is estimated using different branch lengths for the explanatory and response variables in the PIC algorithm, the estimator is no longer the BLUE, so this is not recommended. Finally, we discuss whether or not and how to accommodate phylogenetic covariance in regression analyses, particularly in relation to the problem of phylogenetic uncertainty. This discussion is from both frequentist and Bayesian perspectives.

An improved method to estimate reflectance parameters for high dynamic range imaging

NASA Astrophysics Data System (ADS)

Li, Shiying; Deguchi, Koichiro; Li, Renfa; Manabe, Yoshitsugu; Chihara, Kunihiro

2008-01-01

Two methods are described to accurately estimate diffuse and specular reflectance parameters for colors, gloss intensity and surface roughness, over the dynamic range of the camera used to capture input images. Neither method needs to segment color areas on an image, or to reconstruct a high dynamic range (HDR) image. The second method improves on the first, bypassing the requirement for specific separation of diffuse and specular reflection components. For the latter method, diffuse and specular reflectance parameters are estimated separately, using the least squares method. Reflection values are initially assumed to be diffuse-only reflection components, and are subjected to the least squares method to estimate diffuse reflectance parameters. Specular reflection components, obtained by subtracting the computed diffuse reflection components from reflection values, are then subjected to a logarithmically transformed equation of the Torrance-Sparrow reflection model, and specular reflectance parameters for gloss intensity and surface roughness are finally estimated using the least squares method. Experiments were carried out using both methods, with simulation data at different saturation levels, generated according to the Lambert and Torrance-Sparrow reflection models, and the second method, with spectral images captured by an imaging spectrograph and a moving light source. Our results show that the second method can estimate the diffuse and specular reflectance parameters for colors, gloss intensity and surface roughness more accurately and faster than the first one, so that colors and gloss can be reproduced more efficiently for HDR imaging.

Partial Least Square Analyses of Landscape and Surface Water Biota Associations in the Savannah River Basin

EPA Science Inventory

Ecologists are often faced with problem of small sample size, correlated and large number of predictors, and high noise-to-signal relationships. This necessitates excluding important variables from the model when applying standard multiple or multivariate regression analyses. In ...

Ridge: a computer program for calculating ridge regression estimates

Treesearch

Donald E. Hilt; Donald W. Seegrist

1977-01-01

Least-squares coefficients for multiple-regression models may be unstable when the independent variables are highly correlated. Ridge regression is a biased estimation procedure that produces stable estimates of the coefficients. Ridge regression is discussed, and a computer program for calculating the ridge coefficients is presented.

Orthogonalizing EM: A design-based least squares algorithm

PubMed Central

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

2016-01-01

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

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.

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.

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

Slattery, Stuart R.

In this study we analyze and extend mesh-free algorithms for three-dimensional data transfer problems in partitioned multiphysics simulations. We first provide a direct comparison between a mesh-based weighted residual method using the common-refinement scheme and two mesh-free algorithms leveraging compactly supported radial basis functions: one using a spline interpolation and one using a moving least square reconstruction. Through the comparison we assess both the conservation and accuracy of the data transfer obtained from each of the methods. We do so for a varying set of geometries with and without curvature and sharp features and for functions with and without smoothnessmore » and with varying gradients. Our results show that the mesh-based and mesh-free algorithms are complementary with cases where each was demonstrated to perform better than the other. We then focus on the mesh-free methods by developing a set of algorithms to parallelize them based on sparse linear algebra techniques. This includes a discussion of fast parallel radius searching in point clouds and restructuring the interpolation algorithms to leverage data structures and linear algebra services designed for large distributed computing environments. The scalability of our new algorithms is demonstrated on a leadership class computing facility using a set of basic scaling studies. Finally, these scaling studies show that for problems with reasonable load balance, our new algorithms for both spline interpolation and moving least square reconstruction demonstrate both strong and weak scalability using more than 100,000 MPI processes with billions of degrees of freedom in the data transfer operation.« less

Automatic variable selection method and a comparison for quantitative analysis in laser-induced breakdown spectroscopy

NASA Astrophysics Data System (ADS)

Duan, Fajie; Fu, Xiao; Jiang, Jiajia; Huang, Tingting; Ma, Ling; Zhang, Cong

2018-05-01

In this work, an automatic variable selection method for quantitative analysis of soil samples using laser-induced breakdown spectroscopy (LIBS) is proposed, which is based on full spectrum correction (FSC) and modified iterative predictor weighting-partial least squares (mIPW-PLS). The method features automatic selection without artificial processes. To illustrate the feasibility and effectiveness of the method, a comparison with genetic algorithm (GA) and successive projections algorithm (SPA) for different elements (copper, barium and chromium) detection in soil was implemented. The experimental results showed that all the three methods could accomplish variable selection effectively, among which FSC-mIPW-PLS required significantly shorter computation time (12 s approximately for 40,000 initial variables) than the others. Moreover, improved quantification models were got with variable selection approaches. The root mean square errors of prediction (RMSEP) of models utilizing the new method were 27.47 (copper), 37.15 (barium) and 39.70 (chromium) mg/kg, which showed comparable prediction effect with GA and SPA.

Simplified Discontinuous Galerkin Methods for Systems of Conservation Laws with Convex Extension

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

1999-01-01

Simplified forms of the space-time discontinuous Galerkin (DG) and discontinuous Galerkin least-squares (DGLS) finite element method are developed and analyzed. The new formulations exploit simplifying properties of entropy endowed conservation law systems while retaining the favorable energy properties associated with symmetric variable formulations.

PARTIAL LEAST SQUARE ANALYSES FOR ASSOCIATION OF LANDSCAPE METRICS WITH WATER BIOLOGICAL AND CHEMICAL PROPERTIES IN THE SAVANNAH RIVER BASIN

EPA Science Inventory

Surface water quality is related to conditions in the surrounding geophysical environment, including soils, landcover, and anthropogenic activities. A number of statistical methods may be used to analyze and explore relationships among variables. Single-, multiple- and multivaria...

College Quality and Early Adult Outcomes

ERIC Educational Resources Information Center

Long, Mark C.

2008-01-01

This paper estimates the effects of various college qualities on several early adult outcomes, using panel data from the National Education Longitudinal Study. I compare the results using ordinary least squares with three alternative methods of estimation, including instrumental variables, and the methods used by Dale and Krueger [(2002).…

Correlation of ERTS MSS data and earth coordinate systems

NASA Technical Reports Server (NTRS)

Malila, W. A. (Principal Investigator); Hieber, R. H.; Mccleer, A. P.

1973-01-01

The author has identified the following significant results. Experience has revealed a problem in the analysis and interpretation of ERTS-1 multispectral scanner (MSS) data. The problem is one of accurately correlating ERTS-1 MSS pixels with analysis areas specified on aerial photographs or topographic maps for training recognition computers and/or evaluating recognition results. It is difficult for an analyst to accurately identify which ERTS-1 pixels on a digital image display belong to specific areas and test plots, especially when they are small. A computer-aided procedure to correlate coordinates from topographic maps and/or aerial photographs with ERTS-1 data coordinates has been developed. In the procedure, a map transformation from earth coordinates to ERTS-1 scan line and point numbers is calculated using selected ground control points nad the method of least squares. The map transformation is then applied to the earth coordinates of selected areas to obtain the corresponding ERTS-1 point and line numbers. An optional provision allows moving the boundaries of the plots inward by variable distances so the selected pixels will not overlap adjacent features.

Sampling characteristics of satellite orbits

NASA Technical Reports Server (NTRS)

Wunsch, Carl

1989-01-01

The irregular space-time sampling of any finite region by an orbiting satellite raises difficult questions as to which frequencies and wavenumbers can be determined and which will alias into others. Conventional sampling theorems must be extended to account for both irregular data distributions and observational noise - the sampling irregularity making the system much more susceptible to noise than in regularly sampled cases. The problem is formulated here in terms of least-squares and applied to spacecraft in 10-day and 17-day repeating orbits. The 'diamond-pattern' laid down spatially in such repeating orbits means that either repeat period adequately samples the spatial variables, but the slow overall temporal coverage in the 17-day pattern leads to much greater uncertainty than in the shorter repeat cycle. The result is not definitive and it is not concluded that a 10-day orbit repeat is the most appropriate one. A major conclusion, however, is that different orbital choices have potentially quite different sampling characteristics which need to be analyzed in terms of the spectral characteristics of the moving sea surface.

Mapping health outcome measures from a stroke registry to EQ-5D weights.

PubMed

Ghatnekar, Ola; Eriksson, Marie; Glader, Eva-Lotta

2013-03-07

To map health outcome related variables from a national register, not part of any validated instrument, with EQ-5D weights among stroke patients. We used two cross-sectional data sets including patient characteristics, outcome variables and EQ-5D weights from the national Swedish stroke register. Three regression techniques were used on the estimation set (n=272): ordinary least squares (OLS), Tobit, and censored least absolute deviation (CLAD). The regression coefficients for "dressing", "toileting", "mobility", "mood", "general health" and "proxy-responders" were applied to the validation set (n=272), and the performance was analysed with mean absolute error (MAE) and mean square error (MSE). The number of statistically significant coefficients varied by model, but all models generated consistent coefficients in terms of sign. Mean utility was underestimated in all models (least in OLS) and with lower variation (least in OLS) compared to the observed. The maximum attainable EQ-5D weight ranged from 0.90 (OLS) to 1.00 (Tobit and CLAD). Health states with utility weights <0.5 had greater errors than those with weights ≥ 0.5 (P<0.01). This study indicates that it is possible to map non-validated health outcome measures from a stroke register into preference-based utilities to study the development of stroke care over time, and to compare with other conditions in terms of utility.

Year-class formation of upper St. Lawrence River northern pike

USGS Publications Warehouse

Smith, B.M.; Farrell, J.M.; Underwood, H.B.; Smith, S.J.

2007-01-01

Variables associated with year-class formation in upper St. Lawrence River northern pike Esox lucius were examined to explore population trends. A partial least-squares (PLS) regression model (PLS 1) was used to relate a year-class strength index (YCSI; 1974-1997) to explanatory variables associated with spawning and nursery areas (seasonal water level and temperature and their variability, number of ice days, and last day of ice presence). A second model (PLS 2) incorporated four additional ecological variables: potential predators (abundance of double-crested cormorants Phalacrocorax auritus and yellow perch Perca flavescens), female northern pike biomass (as a measure of stock-recruitment effects), and total phosphorus (productivity). Trends in adult northern pike catch revealed a decline (1981-2005), and year-class strength was positively related to catch per unit effort (CPUE; R2 = 0.58). The YCSI exceeded the 23-year mean in only 2 of the last 10 years. Cyclic patterns in the YCSI time series (along with strong year-classes every 4-6 years) were apparent, as was a dampening effect of amplitude beginning around 1990. The PLS 1 model explained over 50% of variation in both explanatory variables and the dependent variable, YCSI first-order moving-average residuals. Variables retained (N = 10; Wold's statistic ??? 0.8) included negative YCSI associations with high summer water levels, high variability in spring and fall water levels, and variability in fall water temperature. The YCSI exhibited positive associations with high spring, summer, and fall water temperature, variability in spring temperature, and high winter and spring water level. The PLS 2 model led to positive YCSI associations with phosphorus and yellow perch CPUE and a negative correlation with double-crested cormorant abundance. Environmental variables (water level and temperature) are hypothesized to regulate northern pike YCSI cycles, and dampening in YCSI magnitude may be related to a combination of factors, including wetland habitat changes, reduced nutrient loading, and increased predation by double-crested cormorants. ?? Copyright by the American Fisheries Society 2007.

Non-parametric and least squares Langley plot methods

NASA Astrophysics Data System (ADS)

Kiedron, P. W.; Michalsky, J. J.

2016-01-01

Langley plots are used to calibrate sun radiometers primarily for the measurement of the aerosol component of the atmosphere that attenuates (scatters and absorbs) incoming direct solar radiation. In principle, the calibration of a sun radiometer is a straightforward application of the Bouguer-Lambert-Beer law V = V0e-τ ṡ m, where a plot of ln(V) voltage vs. m air mass yields a straight line with intercept ln(V0). This ln(V0) subsequently can be used to solve for τ for any measurement of V and calculation of m. This calibration works well on some high mountain sites, but the application of the Langley plot calibration technique is more complicated at other, more interesting, locales. This paper is concerned with ferreting out calibrations at difficult sites and examining and comparing a number of conventional and non-conventional methods for obtaining successful Langley plots. The 11 techniques discussed indicate that both least squares and various non-parametric techniques produce satisfactory calibrations with no significant differences among them when the time series of ln(V0)'s are smoothed and interpolated with median and mean moving window filters.

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.

Spatial Autocorrelation Approaches to Testing Residuals from Least Squares Regression

PubMed Central

Chen, Yanguang

2016-01-01

In geo-statistics, the Durbin-Watson test is frequently employed to detect the presence of residual serial correlation from least squares regression analyses. However, the Durbin-Watson statistic is only suitable for ordered time or spatial series. If the variables comprise cross-sectional data coming from spatial random sampling, the test will be ineffectual because the value of Durbin-Watson’s statistic depends on the sequence of data points. This paper develops two new statistics for testing serial correlation of residuals from least squares regression based on spatial samples. By analogy with the new form of Moran’s index, an autocorrelation coefficient is defined with a standardized residual vector and a normalized spatial weight matrix. Then by analogy with the Durbin-Watson statistic, two types of new serial correlation indices are constructed. As a case study, the two newly presented statistics are applied to a spatial sample of 29 China’s regions. These results show that the new spatial autocorrelation models can be used to test the serial correlation of residuals from regression analysis. In practice, the new statistics can make up for the deficiencies of the Durbin-Watson test. PMID:26800271

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.

Expert system for generating initial layouts of zoom systems with multiple moving lens groups

NASA Astrophysics Data System (ADS)

Cheng, Xuemin; Wang, Yongtian; Hao, Qun; Sasián, José M.

2005-01-01

An expert system is developed for the automatic generation of initial layouts for the design of zoom systems with multiple moving lens groups. The Gaussian parameters of the zoom system are optimized using the damped-least-squares method to achieve smooth zoom cam curves, with the f-number of each lens group in the zoom system constrained to a rational value. Then each lens group is selected automatically from a database according to its range of f-number, field of view, and magnification ratio as it is used in the zoom system. The lens group database is established from the results of analyzing thousands of zoom lens patents. Design examples are given, which show that the scheme is a practical approach to generate starting points for zoom lens design.

Efficient Levenberg-Marquardt minimization of the maximum likelihood estimator for Poisson deviates

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

Laurence, T; Chromy, B

2009-11-10

Histograms of counted events are Poisson distributed, but are typically fitted without justification using nonlinear least squares fitting. The more appropriate maximum likelihood estimator (MLE) for Poisson distributed data is seldom used. We extend the use of the Levenberg-Marquardt algorithm commonly used for nonlinear least squares minimization for use with the MLE for Poisson distributed data. In so doing, we remove any excuse for not using this more appropriate MLE. We demonstrate the use of the algorithm and the superior performance of the MLE using simulations and experiments in the context of fluorescence lifetime imaging. Scientists commonly form histograms ofmore » counted events from their data, and extract parameters by fitting to a specified model. Assuming that the probability of occurrence for each bin is small, event counts in the histogram bins will be distributed according to the Poisson distribution. We develop here an efficient algorithm for fitting event counting histograms using the maximum likelihood estimator (MLE) for Poisson distributed data, rather than the non-linear least squares measure. This algorithm is a simple extension of the common Levenberg-Marquardt (L-M) algorithm, is simple to implement, quick and robust. Fitting using a least squares measure is most common, but it is the maximum likelihood estimator only for Gaussian-distributed data. Non-linear least squares methods may be applied to event counting histograms in cases where the number of events is very large, so that the Poisson distribution is well approximated by a Gaussian. However, it is not easy to satisfy this criterion in practice - which requires a large number of events. It has been well-known for years that least squares procedures lead to biased results when applied to Poisson-distributed data; a recent paper providing extensive characterization of these biases in exponential fitting is given. The more appropriate measure based on the maximum likelihood estimator (MLE) for the Poisson distribution is also well known, but has not become generally used. This is primarily because, in contrast to non-linear least squares fitting, there has been no quick, robust, and general fitting method. In the field of fluorescence lifetime spectroscopy and imaging, there have been some efforts to use this estimator through minimization routines such as Nelder-Mead optimization, exhaustive line searches, and Gauss-Newton minimization. Minimization based on specific one- or multi-exponential models has been used to obtain quick results, but this procedure does not allow the incorporation of the instrument response, and is not generally applicable to models found in other fields. Methods for using the MLE for Poisson-distributed data have been published by the wider spectroscopic community, including iterative minimization schemes based on Gauss-Newton minimization. The slow acceptance of these procedures for fitting event counting histograms may also be explained by the use of the ubiquitous, fast Levenberg-Marquardt (L-M) fitting procedure for fitting non-linear models using least squares fitting (simple searches obtain {approx}10000 references - this doesn't include those who use it, but don't know they are using it). The benefits of L-M include a seamless transition between Gauss-Newton minimization and downward gradient minimization through the use of a regularization parameter. This transition is desirable because Gauss-Newton methods converge quickly, but only within a limited domain of convergence; on the other hand the downward gradient methods have a much wider domain of convergence, but converge extremely slowly nearer the minimum. L-M has the advantages of both procedures: relative insensitivity to initial parameters and rapid convergence. Scientists, when wanting an answer quickly, will fit data using L-M, get an answer, and move on. Only those that are aware of the bias issues will bother to fit using the more appropriate MLE for Poisson deviates. However, since there is a simple, analytical formula for the appropriate MLE measure for Poisson deviates, it is inexcusable that least squares estimators are used almost exclusively when fitting event counting histograms. There have been ways found to use successive non-linear least squares fitting to obtain similarly unbiased results, but this procedure is justified by simulation, must be re-tested when conditions change significantly, and requires two successive fits. There is a great need for a fitting routine for the MLE estimator for Poisson deviates that has convergence domains and rates comparable to the non-linear least squares L-M fitting. We show in this report that a simple way to achieve that goal is to use the L-M fitting procedure not to minimize the least squares measure, but the MLE for Poisson deviates.« less

Development of variable pathlength UV-vis spectroscopy combined with partial-least-squares regression for wastewater chemical oxygen demand (COD) monitoring.

PubMed

Chen, Baisheng; Wu, Huanan; Li, Sam Fong Yau

2014-03-01

To overcome the challenging task to select an appropriate pathlength for wastewater chemical oxygen demand (COD) monitoring with high accuracy by UV-vis spectroscopy in wastewater treatment process, a variable pathlength approach combined with partial-least squares regression (PLSR) was developed in this study. Two new strategies were proposed to extract relevant information of UV-vis spectral data from variable pathlength measurements. The first strategy was by data fusion with two data fusion levels: low-level data fusion (LLDF) and mid-level data fusion (MLDF). Predictive accuracy was found to improve, indicated by the lower root-mean-square errors of prediction (RMSEP) compared with those obtained for single pathlength measurements. Both fusion levels were found to deliver very robust PLSR models with residual predictive deviations (RPD) greater than 3 (i.e. 3.22 and 3.29, respectively). The second strategy involved calculating the slopes of absorbance against pathlength at each wavelength to generate slope-derived spectra. Without the requirement to select the optimal pathlength, the predictive accuracy (RMSEP) was improved by 20-43% as compared to single pathlength spectroscopy. Comparing to nine-factor models from fusion strategy, the PLSR model from slope-derived spectroscopy was found to be more parsimonious with only five factors and more robust with residual predictive deviation (RPD) of 3.72. It also offered excellent correlation of predicted and measured COD values with R(2) of 0.936. In sum, variable pathlength spectroscopy with the two proposed data analysis strategies proved to be successful in enhancing prediction performance of COD in wastewater and showed high potential to be applied in on-line water quality monitoring. Copyright © 2013 Elsevier B.V. All rights reserved.

GSTAR-SUR Modeling With Calendar Variations And Intervention To Forecast Outflow Of Currencies In Java Indonesia

NASA Astrophysics Data System (ADS)

Akbar, M. S.; Setiawan; Suhartono; Ruchjana, B. N.; Riyadi, M. A. A.

2018-03-01

Ordinary Least Squares (OLS) is general method to estimates Generalized Space Time Autoregressive (GSTAR) parameters. But in some cases, the residuals of GSTAR are correlated between location. If OLS is applied to this case, then the estimators are inefficient. Generalized Least Squares (GLS) is a method used in Seemingly Unrelated Regression (SUR) model. This method estimated parameters of some models with residuals between equations are correlated. Simulation study shows that GSTAR with GLS method for estimating parameters (GSTAR-SUR) is more efficient than GSTAR-OLS method. The purpose of this research is to apply GSTAR-SUR with calendar variation and intervention as exogenous variable (GSTARX-SUR) for forecast outflow of currency in Java, Indonesia. As a result, GSTARX-SUR provides better performance than GSTARX-OLS.

Concerning an application of the method of least squares with a variable weight matrix

NASA Technical Reports Server (NTRS)

Sukhanov, A. A.

1979-01-01

An estimate of a state vector for a physical system when the weight matrix in the method of least squares is a function of this vector is considered. An iterative procedure is proposed for calculating the desired estimate. Conditions for the existence and uniqueness of the limit of this procedure are obtained, and a domain is found which contains the limit estimate. A second method for calculating the desired estimate which reduces to the solution of a system of algebraic equations is proposed. The question of applying Newton's method of tangents to solving the given system of algebraic equations is considered and conditions for the convergence of the modified Newton's method are obtained. Certain properties of the estimate obtained are presented together with an example.

On estimating gravity anomalies: A comparison of least squares collocation with least squares techniques

NASA Technical Reports Server (NTRS)

Argentiero, P.; Lowrey, B.

1976-01-01

The least squares collocation algorithm for estimating gravity anomalies from geodetic data is shown to be an application of the well known regression equations which provide the mean and covariance of a random vector (gravity anomalies) given a realization of a correlated random vector (geodetic data). It is also shown that the collocation solution for gravity anomalies is equivalent to the conventional least-squares-Stokes' function solution when the conventional solution utilizes properly weighted zero a priori estimates. The mathematical and physical assumptions underlying the least squares collocation estimator are described, and its numerical properties are compared with the numerical properties of the conventional least squares estimator.

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.

Multivariate Approaches for Simultaneous Determination of Avanafil and Dapoxetine by UV Chemometrics and HPLC-QbD in Binary Mixtures and Pharmaceutical Product.

PubMed

2016-04-07

Multivariate UV-spectrophotometric methods and Quality by Design (QbD) HPLC are described for concurrent estimation of avanafil (AV) and dapoxetine (DP) in the binary mixture and in the dosage form. Chemometric methods have been developed, including classical least-squares, principal component regression, partial least-squares, and multiway partial least-squares. Analytical figures of merit, such as sensitivity, selectivity, analytical sensitivity, LOD, and LOQ were determined. QbD consists of three steps, starting with the screening approach to determine the critical process parameter and response variables. This is followed by understanding of factors and levels, and lastly the application of a Box-Behnken design containing four critical factors that affect the method. From an Ishikawa diagram and a risk assessment tool, four main factors were selected for optimization. Design optimization, statistical calculation, and final-condition optimization of all the reactions were Carried out. Twenty-five experiments were done, and a quadratic model was used for all response variables. Desirability plot, surface plot, design space, and three-dimensional plots were calculated. In the optimized condition, HPLC separation was achieved on Phenomenex Gemini C18 column (250 × 4.6 mm, 5 μm) using acetonitrile-buffer (ammonium acetate buffer at pH 3.7 with acetic acid) as a mobile phase at flow rate of 0.7 mL/min. Quantification was done at 239 nm, and temperature was set at 20°C. The developed methods were validated and successfully applied for simultaneous determination of AV and DP in the dosage form.

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)

Least-Squares Models to Correct for Rater Effects in Performance Assessment.

ERIC Educational Resources Information Center

Raymond, Mark R.; Viswesvaran, Chockalingam

This study illustrates the use of three least-squares models to control for rater effects in performance evaluation: (1) ordinary least squares (OLS); (2) weighted least squares (WLS); and (3) OLS subsequent to applying a logistic transformation to observed ratings (LOG-OLS). The three models were applied to ratings obtained from four…

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.

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.

Prediction of BP reactivity to talking using hybrid soft computing approaches.

PubMed

Kaur, Gurmanik; Arora, Ajat Shatru; Jain, Vijender Kumar

2014-01-01

High blood pressure (BP) is associated with an increased risk of cardiovascular diseases. Therefore, optimal precision in measurement of BP is appropriate in clinical and research studies. In this work, anthropometric characteristics including age, height, weight, body mass index (BMI), and arm circumference (AC) were used as independent predictor variables for the prediction of BP reactivity to talking. Principal component analysis (PCA) was fused with artificial neural network (ANN), adaptive neurofuzzy inference system (ANFIS), and least square-support vector machine (LS-SVM) model to remove the multicollinearity effect among anthropometric predictor variables. The statistical tests in terms of coefficient of determination (R (2)), root mean square error (RMSE), and mean absolute percentage error (MAPE) revealed that PCA based LS-SVM (PCA-LS-SVM) model produced a more efficient prediction of BP reactivity as compared to other models. This assessment presents the importance and advantages posed by PCA fused prediction models for prediction of biological variables.

Determining Home Range and Preferred Habitat of Feral Horses on the Nevada National Security Site Using Geographic Information Systems

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

Burns, Ashley V.

2014-05-30

Feral horses (Equus caballus) are free-roaming descendants of domesticated horses and legally protected by the Wild and Free-Roaming Horses and Burros Act of 1971, which mandates how feral horses and burros should be managed and protected on federal lands. Using a geographic information system to determine the home range and suitable habitat of feral horses on the federally managed Nevada National Security Site can enable wildlife biologists in making best management practice recommendations. Home range was estimated at 88.1 square kilometers. Site suitability was calculated for elevation, forage, slope, water presence and horse observations. These variables were combined in successivemore » iterations into one polygon. Suitability rankings established that 85 square kilometers are most suitable habitat, with 2,052 square kilometers of good habitat 1,252 square kilometers of fair habitat and 122 square kilometers of least suitable habitat.« less

Wage Determinants among Medical Doctors and Nurses in Spain

ERIC Educational Resources Information Center

Salas-Velasco, Manuel

2010-01-01

This paper examines the determination of wage rates for health professionals using three well known, and commonly used, econometric techniques: ordinary least squares, instrumental variables, and Heckman's method. The data come from a graduate survey and the analysis focuses on a regional labor market, due to nationwide information on salaries is…

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…

Private Schooling Promotes Political and Economic Freedom? An International Fixed Effects Instrumental Variables Analysis

ERIC Educational Resources Information Center

DeAngelis, Corey A.; Shakeel, M. Danish

2018-01-01

Specialised learning environments provided through private schooling may increase educational quality, which may increase the likelihood that citizens will pursue human rights through civic engagement. We employed 2-stage least squares year and country-level fixed effects and examined how private schooling could affect political rights, civil…

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

Rapid determination of major bioactive isoflavonoid compounds during the extraction process of kudzu (Pueraria lobata) by near-infrared transmission spectroscopy.

PubMed

Wang, Pei; Zhang, Hui; Yang, Hailong; Nie, Lei; Zang, Hengchang

2015-02-25

Near-infrared (NIR) spectroscopy has been developed into an indispensable tool for both academic research and industrial quality control in a wide field of applications. The feasibility of NIR spectroscopy to monitor the concentration of puerarin, daidzin, daidzein and total isoflavonoid (TIF) during the extraction process of kudzu (Pueraria lobata) was verified in this work. NIR spectra were collected in transmission mode and pretreated with smoothing and derivative. Partial least square regression (PLSR) was used to establish calibration models. Three different variable selection methods, including correlation coefficient method, interval partial least squares (iPLS), and successive projections algorithm (SPA) were performed and compared with models based on all of the variables. The results showed that the approach was very efficient and environmentally friendly for rapid determination of the four quality indices (QIs) in the kudzu extraction process. This method established may have the potential to be used as a process analytical technological (PAT) tool in the future. Copyright © 2014 Elsevier B.V. All rights reserved.

Hysteresis modeling of magnetic shape memory alloy actuator based on Krasnosel'skii-Pokrovskii model.

PubMed

Zhou, Miaolei; Wang, Shoubin; Gao, Wei

2013-01-01

As a new type of intelligent material, magnetically shape memory alloy (MSMA) has a good performance in its applications in the actuator manufacturing. Compared with traditional actuators, MSMA actuator has the advantages as fast response and large deformation; however, the hysteresis nonlinearity of the MSMA actuator restricts its further improving of control precision. In this paper, an improved Krasnosel'skii-Pokrovskii (KP) model is used to establish the hysteresis model of MSMA actuator. To identify the weighting parameters of the KP operators, an improved gradient correction algorithm and a variable step-size recursive least square estimation algorithm are proposed in this paper. In order to demonstrate the validity of the proposed modeling approach, simulation experiments are performed, simulations with improved gradient correction algorithm and variable step-size recursive least square estimation algorithm are studied, respectively. Simulation results of both identification algorithms demonstrate that the proposed modeling approach in this paper can establish an effective and accurate hysteresis model for MSMA actuator, and it provides a foundation for improving the control precision of MSMA actuator.

Estimating the magnitude of annual peak discharges with recurrence intervals between 1.1 and 3.0 years for rural, unregulated streams in West Virginia

USGS Publications Warehouse

Wiley, Jeffrey B.; Atkins, John T.; Newell, Dawn A.

2002-01-01

Multiple and simple least-squares regression models for the log10-transformed 1.5- and 2-year recurrence intervals of peak discharges with independent variables describing the basin characteristics (log10-transformed and untransformed) for 236 streamflow-gaging stations were evaluated, and the regression residuals were plotted as areal distributions that defined three regions in West Virginia designated as East, North, and South. Regional equations for the 1.1-, 1.2-, 1.3-, 1.4-, 1.5-, 1.6-, 1.7-, 1.8-, 1.9-, 2.0-, 2.5-, and 3-year recurrence intervals of peak discharges were determined by generalized least-squares regression. Log10-transformed drainage area was the most significant independent variable for all regions. Equations developed in this study are applicable only to rural, unregulated streams within the boundaries of West Virginia. The accuracies of estimating equations are quantified by measuring the average prediction error (from 27.4 to 52.4 percent) and equivalent years of record (from 1.1 to 3.4 years).

Hysteresis Modeling of Magnetic Shape Memory Alloy Actuator Based on Krasnosel'skii-Pokrovskii Model

PubMed Central

Wang, Shoubin; Gao, Wei

2013-01-01

As a new type of intelligent material, magnetically shape memory alloy (MSMA) has a good performance in its applications in the actuator manufacturing. Compared with traditional actuators, MSMA actuator has the advantages as fast response and large deformation; however, the hysteresis nonlinearity of the MSMA actuator restricts its further improving of control precision. In this paper, an improved Krasnosel'skii-Pokrovskii (KP) model is used to establish the hysteresis model of MSMA actuator. To identify the weighting parameters of the KP operators, an improved gradient correction algorithm and a variable step-size recursive least square estimation algorithm are proposed in this paper. In order to demonstrate the validity of the proposed modeling approach, simulation experiments are performed, simulations with improved gradient correction algorithm and variable step-size recursive least square estimation algorithm are studied, respectively. Simulation results of both identification algorithms demonstrate that the proposed modeling approach in this paper can establish an effective and accurate hysteresis model for MSMA actuator, and it provides a foundation for improving the control precision of MSMA actuator. PMID:23737730

Optimal least-squares finite element method for elliptic problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Povinelli, Louis A.

1991-01-01

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

The effects of spatial autoregressive dependencies on inference in ordinary least squares: a geometric approach

NASA Astrophysics Data System (ADS)

Smith, Tony E.; Lee, Ka Lok

2012-01-01

There is a common belief that the presence of residual spatial autocorrelation in ordinary least squares (OLS) regression leads to inflated significance levels in beta coefficients and, in particular, inflated levels relative to the more efficient spatial error model (SEM). However, our simulations show that this is not always the case. Hence, the purpose of this paper is to examine this question from a geometric viewpoint. The key idea is to characterize the OLS test statistic in terms of angle cosines and examine the geometric implications of this characterization. Our first result is to show that if the explanatory variables in the regression exhibit no spatial autocorrelation, then the distribution of test statistics for individual beta coefficients in OLS is independent of any spatial autocorrelation in the error term. Hence, inferences about betas exhibit all the optimality properties of the classic uncorrelated error case. However, a second more important series of results show that if spatial autocorrelation is present in both the dependent and explanatory variables, then the conventional wisdom is correct. In particular, even when an explanatory variable is statistically independent of the dependent variable, such joint spatial dependencies tend to produce "spurious correlation" that results in over-rejection of the null hypothesis. The underlying geometric nature of this problem is clarified by illustrative examples. The paper concludes with a brief discussion of some possible remedies for this problem.

Multivariate Regression Analysis of Winter Ozone Events in the Uinta Basin of Eastern Utah, USA

NASA Astrophysics Data System (ADS)

Mansfield, M. L.

2012-12-01

I report on a regression analysis of a number of variables that are involved in the formation of winter ozone in the Uinta Basin of Eastern Utah. One goal of the analysis is to develop a mathematical model capable of predicting the daily maximum ozone concentration from values of a number of independent variables. The dependent variable is the daily maximum ozone concentration at a particular site in the basin. Independent variables are (1) daily lapse rate, (2) daily "basin temperature" (defined below), (3) snow cover, (4) midday solar zenith angle, (5) monthly oil production, (6) monthly gas production, and (7) the number of days since the beginning of a multi-day inversion event. Daily maximum temperature and daily snow cover data are available at ten or fifteen different sites throughout the basin. The daily lapse rate is defined operationally as the slope of the linear least-squares fit to the temperature-altitude plot, and the "basin temperature" is defined as the value assumed by the same least-squares line at an altitude of 1400 m. A multi-day inversion event is defined as a set of consecutive days for which the lapse rate remains positive. The standard deviation in the accuracy of the model is about 10 ppb. The model has been combined with historical climate and oil & gas production data to estimate historical ozone levels.

Signal-to-noise ratio enhancement on SEM images using a cubic spline interpolation with Savitzky-Golay filters and weighted least squares error.

PubMed

Kiani, M A; Sim, K S; Nia, M E; Tso, C P

2015-05-01

A new technique based on cubic spline interpolation with Savitzky-Golay smoothing using weighted least squares error filter is enhanced for scanning electron microscope (SEM) images. A diversity of sample images is captured and the performance is found to be better when compared with the moving average and the standard median filters, with respect to eliminating noise. This technique can be implemented efficiently on real-time SEM images, with all mandatory data for processing obtained from a single image. Noise in images, and particularly in SEM images, are undesirable. A new noise reduction technique, based on cubic spline interpolation with Savitzky-Golay and weighted least squares error method, is developed. We apply the combined technique to single image signal-to-noise ratio estimation and noise reduction for SEM imaging system. This autocorrelation-based technique requires image details to be correlated over a few pixels, whereas the noise is assumed to be uncorrelated from pixel to pixel. The noise component is derived from the difference between the image autocorrelation at zero offset, and the estimation of the corresponding original autocorrelation. In the few test cases involving different images, the efficiency of the developed noise reduction filter is proved to be significantly better than those obtained from the other methods. Noise can be reduced efficiently with appropriate choice of scan rate from real-time SEM images, without generating corruption or increasing scanning time. © 2015 The Authors Journal of Microscopy © 2015 Royal Microscopical Society.

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

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

PubMed

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

2013-11-01

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

Streamflow record extension using power transformations and application to sediment transport

NASA Astrophysics Data System (ADS)

Moog, Douglas B.; Whiting, Peter J.; Thomas, Robert B.

1999-01-01

To obtain a representative set of flow rates for a stream, it is often desirable to fill in missing data or extend measurements to a longer time period by correlation to a nearby gage with a longer record. Linear least squares regression of the logarithms of the flows is a traditional and still common technique. However, its purpose is to generate optimal estimates of each day's discharge, rather than the population of discharges, for which it tends to underestimate variance. Maintenance-of-variance-extension (MOVE) equations [Hirsch, 1982] were developed to correct this bias. This study replaces the logarithmic transformation by the more general Box-Cox scaled power transformation, generating a more linear, constant-variance relationship for the MOVE extension. Combining the Box-Cox transformation with the MOVE extension is shown to improve accuracy in estimating order statistics of flow rate, particularly for the nonextreme discharges which generally govern cumulative transport over time. This advantage is illustrated by prediction of cumulative fractions of total bed load transport.

Validation of Spacecraft Active Cavity Radiometer Total Solar Irradiance (TSI) Long Term Measurement Trends Using Proxy TSI Least Squares Analyses

NASA Technical Reports Server (NTRS)

Lee, Robert Benjamin, III; Wilson, Robert S.

2003-01-01

Long-term, incoming total solar irradiance (TSI) measurement trends were validated using proxy TSI values, derived from indices of solar magnetic activity. Spacecraft active cavity radiometers (ACR) are being used to measure longterm TSI variability, which may trigger global climate changes. The TSI, typically referred to as the solar constant, was normalized to the mean earth-sun distance. Studies of spacecraft TSI data sets confirmed the existence of a 0.1 %, long-term TSI variability component within a 10-year period. The 0.1% TSI variability component is clearly present in the spacecraft data sets from the 1984-2004 time frame. Typically, three overlapping spacecraft data sets were used to validate long-term TSI variability trends. However, during the years of 1978-1984, 1989-1991, and 1993-1996, three overlapping spacecraft data sets were not available in order to validate TSI trends. The TSI was found to vary with indices of solar magnetic activity associated with recent 10-year sunspot cycles. Proxy TSI values were derived from least squares analyses of the measured TSI variability with the solar indices of 10.7-cm solar fluxes, and with limb-darked sunspot fluxes. The resulting proxy TSI values were compared to the spacecraft ACR measurements of TSI variability to detect ACR instrument degradation, which may be interpreted as TSI variability. Analyses of ACR measurements and TSI proxies are presented primarily for the 1984-2004, Earth Radiation Budget Experiment (ERBE) ACR solar monitor data set. Differences in proxy and spacecraft measurement data sets suggest the existence of another TSI variability component with an amplitude greater than or equal to 0.5 Wm-2 (0.04%), and with a cycle of 20 years or more.

Post-processing through linear regression

NASA Astrophysics Data System (ADS)

van Schaeybroeck, B.; Vannitsem, S.

2011-03-01

Various post-processing techniques are compared for both deterministic and ensemble forecasts, all based on linear regression between forecast data and observations. In order to evaluate the quality of the regression methods, three criteria are proposed, related to the effective correction of forecast error, the optimal variability of the corrected forecast and multicollinearity. The regression schemes under consideration include the ordinary least-square (OLS) method, a new time-dependent Tikhonov regularization (TDTR) method, the total least-square method, a new geometric-mean regression (GM), a recently introduced error-in-variables (EVMOS) method and, finally, a "best member" OLS method. The advantages and drawbacks of each method are clarified. These techniques are applied in the context of the 63 Lorenz system, whose model version is affected by both initial condition and model errors. For short forecast lead times, the number and choice of predictors plays an important role. Contrarily to the other techniques, GM degrades when the number of predictors increases. At intermediate lead times, linear regression is unable to provide corrections to the forecast and can sometimes degrade the performance (GM and the best member OLS with noise). At long lead times the regression schemes (EVMOS, TDTR) which yield the correct variability and the largest correlation between ensemble error and spread, should be preferred.

Fast Algorithms for Structured Least Squares and Total Least Squares Problems

PubMed Central

Kalsi, Anoop; O’Leary, Dianne P.

2006-01-01

We consider the problem of solving least squares problems involving a matrix M of small displacement rank with respect to two matrices Z1 and Z2. We develop formulas for the generators of the matrix M HM in terms of the generators of M and show that the Cholesky factorization of the matrix M HM can be computed quickly if Z1 is close to unitary and Z2 is triangular and nilpotent. These conditions are satisfied for several classes of matrices, including Toeplitz, block Toeplitz, Hankel, and block Hankel, and for matrices whose blocks have such structure. Fast Cholesky factorization enables fast solution of least squares problems, total least squares problems, and regularized total least squares problems involving these classes of matrices. PMID:27274922

Fast Algorithms for Structured Least Squares and Total Least Squares Problems.

PubMed

Kalsi, Anoop; O'Leary, Dianne P

2006-01-01

We consider the problem of solving least squares problems involving a matrix M of small displacement rank with respect to two matrices Z 1 and Z 2. We develop formulas for the generators of the matrix M (H) M in terms of the generators of M and show that the Cholesky factorization of the matrix M (H) M can be computed quickly if Z 1 is close to unitary and Z 2 is triangular and nilpotent. These conditions are satisfied for several classes of matrices, including Toeplitz, block Toeplitz, Hankel, and block Hankel, and for matrices whose blocks have such structure. Fast Cholesky factorization enables fast solution of least squares problems, total least squares problems, and regularized total least squares problems involving these classes of matrices.

A variant of sparse partial least squares for variable selection and data exploration.

PubMed

Olson Hunt, Megan J; Weissfeld, Lisa; Boudreau, Robert M; Aizenstein, Howard; Newman, Anne B; Simonsick, Eleanor M; Van Domelen, Dane R; Thomas, Fridtjof; Yaffe, Kristine; Rosano, Caterina

2014-01-01

When data are sparse and/or predictors multicollinear, current implementation of sparse partial least squares (SPLS) does not give estimates for non-selected predictors nor provide a measure of inference. In response, an approach termed "all-possible" SPLS is proposed, which fits a SPLS model for all tuning parameter values across a set grid. Noted is the percentage of time a given predictor is chosen, as well as the average non-zero parameter estimate. Using a "large" number of multicollinear predictors, simulation confirmed variables not associated with the outcome were least likely to be chosen as sparsity increased across the grid of tuning parameters, while the opposite was true for those strongly associated. Lastly, variables with a weak association were chosen more often than those with no association, but less often than those with a strong relationship to the outcome. Similarly, predictors most strongly related to the outcome had the largest average parameter estimate magnitude, followed by those with a weak relationship, followed by those with no relationship. Across two independent studies regarding the relationship between volumetric MRI measures and a cognitive test score, this method confirmed a priori hypotheses about which brain regions would be selected most often and have the largest average parameter estimates. In conclusion, the percentage of time a predictor is chosen is a useful measure for ordering the strength of the relationship between the independent and dependent variables, serving as a form of inference. The average parameter estimates give further insight regarding the direction and strength of association. As a result, all-possible SPLS gives more information than the dichotomous output of traditional SPLS, making it useful when undertaking data exploration and hypothesis generation for a large number of potential predictors.

On estimating gravity anomalies - A comparison of least squares collocation with conventional least squares techniques

NASA Technical Reports Server (NTRS)

Argentiero, P.; Lowrey, B.

1977-01-01

The least squares collocation algorithm for estimating gravity anomalies from geodetic data is shown to be an application of the well known regression equations which provide the mean and covariance of a random vector (gravity anomalies) given a realization of a correlated random vector (geodetic data). It is also shown that the collocation solution for gravity anomalies is equivalent to the conventional least-squares-Stokes' function solution when the conventional solution utilizes properly weighted zero a priori estimates. The mathematical and physical assumptions underlying the least squares collocation estimator are described.

Mesh-free data transfer algorithms for partitioned multiphysics problems: Conservation, accuracy, and parallelism

DOE PAGES

Slattery, Stuart R.

2015-12-02

In this study we analyze and extend mesh-free algorithms for three-dimensional data transfer problems in partitioned multiphysics simulations. We first provide a direct comparison between a mesh-based weighted residual method using the common-refinement scheme and two mesh-free algorithms leveraging compactly supported radial basis functions: one using a spline interpolation and one using a moving least square reconstruction. Through the comparison we assess both the conservation and accuracy of the data transfer obtained from each of the methods. We do so for a varying set of geometries with and without curvature and sharp features and for functions with and without smoothnessmore » and with varying gradients. Our results show that the mesh-based and mesh-free algorithms are complementary with cases where each was demonstrated to perform better than the other. We then focus on the mesh-free methods by developing a set of algorithms to parallelize them based on sparse linear algebra techniques. This includes a discussion of fast parallel radius searching in point clouds and restructuring the interpolation algorithms to leverage data structures and linear algebra services designed for large distributed computing environments. The scalability of our new algorithms is demonstrated on a leadership class computing facility using a set of basic scaling studies. Finally, these scaling studies show that for problems with reasonable load balance, our new algorithms for both spline interpolation and moving least square reconstruction demonstrate both strong and weak scalability using more than 100,000 MPI processes with billions of degrees of freedom in the data transfer operation.« less

Method and apparatus for calibrating a linear variable differential transformer

DOEpatents

Pokrywka, Robert J [North Huntingdon, PA

2005-01-18

A calibration apparatus for calibrating a linear variable differential transformer (LVDT) having an armature positioned in au LVDT armature orifice, and the armature able to move along an axis of movement. The calibration apparatus includes a heating mechanism with an internal chamber, a temperature measuring mechanism for measuring the temperature of the LVDT, a fixture mechanism with an internal chamber for at least partially accepting the LVDT and for securing the LVDT within the heating mechanism internal chamber, a moving mechanism for moving the armature, a position measurement mechanism for measuring the position of the armature, and an output voltage measurement mechanism. A method for calibrating an LVDT, including the steps of: powering the LVDT; heating the LVDT to a desired temperature; measuring the position of the armature with respect to the armature orifice; and measuring the output voltage of the LVDT.

Mapping health outcome measures from a stroke registry to EQ-5D weights

PubMed Central

2013-01-01

Purpose To map health outcome related variables from a national register, not part of any validated instrument, with EQ-5D weights among stroke patients. Methods We used two cross-sectional data sets including patient characteristics, outcome variables and EQ-5D weights from the national Swedish stroke register. Three regression techniques were used on the estimation set (n = 272): ordinary least squares (OLS), Tobit, and censored least absolute deviation (CLAD). The regression coefficients for “dressing“, “toileting“, “mobility”, “mood”, “general health” and “proxy-responders” were applied to the validation set (n = 272), and the performance was analysed with mean absolute error (MAE) and mean square error (MSE). Results The number of statistically significant coefficients varied by model, but all models generated consistent coefficients in terms of sign. Mean utility was underestimated in all models (least in OLS) and with lower variation (least in OLS) compared to the observed. The maximum attainable EQ-5D weight ranged from 0.90 (OLS) to 1.00 (Tobit and CLAD). Health states with utility weights <0.5 had greater errors than those with weights ≥0.5 (P < 0.01). Conclusion This study indicates that it is possible to map non-validated health outcome measures from a stroke register into preference-based utilities to study the development of stroke care over time, and to compare with other conditions in terms of utility. PMID:23496957

Generalized adjustment by least squares ( GALS).

USGS Publications Warehouse

Elassal, A.A.

1983-01-01

The least-squares principle is universally accepted as the basis for adjustment procedures in the allied fields of geodesy, photogrammetry and surveying. A prototype software package for Generalized Adjustment by Least Squares (GALS) is described. The package is designed to perform all least-squares-related functions in a typical adjustment program. GALS is capable of supporting development of adjustment programs of any size or degree of complexity. -Author

A fast least-squares algorithm for population inference

PubMed Central

2013-01-01

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

A fast least-squares algorithm for population inference.

PubMed

Parry, R Mitchell; Wang, May D

2013-01-23

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

A comparative simulation study of AR(1) estimators in short time series.

PubMed

Krone, Tanja; Albers, Casper J; Timmerman, Marieke E

2017-01-01

Various estimators of the autoregressive model exist. We compare their performance in estimating the autocorrelation in short time series. In Study 1, under correct model specification, we compare the frequentist r 1 estimator, C-statistic, ordinary least squares estimator (OLS) and maximum likelihood estimator (MLE), and a Bayesian method, considering flat (B f ) and symmetrized reference (B sr ) priors. In a completely crossed experimental design we vary lengths of time series (i.e., T = 10, 25, 40, 50 and 100) and autocorrelation (from -0.90 to 0.90 with steps of 0.10). The results show a lowest bias for the B sr , and a lowest variability for r 1 . The power in different conditions is highest for B sr and OLS. For T = 10, the absolute performance of all measurements is poor, as expected. In Study 2, we study robustness of the methods through misspecification by generating the data according to an ARMA(1,1) model, but still analysing the data with an AR(1) model. We use the two methods with the lowest bias for this study, i.e., B sr and MLE. The bias gets larger when the non-modelled moving average parameter becomes larger. Both the variability and power show dependency on the non-modelled parameter. The differences between the two estimation methods are negligible for all measurements.

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.

Effect Sizes and their Intervals: The Two-Level Repeated Measures Case

ERIC Educational Resources Information Center

Algina, James; Keselman, H. J.; Penfield, Randall D.

2005-01-01

Probability coverage for eight different confidence intervals (CIs) of measures of effect size (ES) in a two-level repeated measures design was investigated. The CIs and measures of ES differed with regard to whether they used least squares or robust estimates of central tendency and variability, whether the end critical points of the interval…

The Collinearity Free and Bias Reduced Regression Estimation Project: The Theory of Normalization Ridge Regression. Report No. 2.

ERIC Educational Resources Information Center

Bulcock, J. W.; And Others

Multicollinearity refers to the presence of highly intercorrelated independent variables in structural equation models, that is, models estimated by using techniques such as least squares regression and maximum likelihood. There is a problem of multicollinearity in both the natural and social sciences where theory formulation and estimation is in…

Determinants of Students' Academic Performance in Four Selected Accounting Courses at University of Zimbabwe

ERIC Educational Resources Information Center

Nyikahadzoi, Loveness; Matamande, Wilson; Taderera, Ever; Mandimika, Elinah

2013-01-01

The study seeks to establish scientific evidence of the factors affecting academic performance for first year accounting students using four selected courses at the University of Zimbabwe. It uses Ordinary Least Squares method to analyse the influence of personal and family background on performance. The findings show that variables age gender,…

CONTRIBUTION OF NUTRIENTS AND E. COLI TO SURFACE WATER CONDITION IN THE OZARKS I. USING PARTIAL LEAST SQUARES PREDICTIONS WHEN STANDARD REGRESSION ASSUMPTIONS ARE VIOLATED

EPA Science Inventory

We present here the application of PLS regression to predicting surface water total phosphorous, total ammonia and Escherichia coli from landscape metrics. The amount of variability in surface water constituents explained by each model reflects the composition of the contributi...

Application of multivariate analysis and mass transfer principles for refinement of a 3-L bioreactor scale-down model--when shake flasks mimic 15,000-L bioreactors better.

PubMed

Ahuja, Sanjeev; Jain, Shilpa; Ram, Kripa

2015-01-01

Characterization of manufacturing processes is key to understanding the effects of process parameters on process performance and product quality. These studies are generally conducted using small-scale model systems. Because of the importance of the results derived from these studies, the small-scale model should be predictive of large scale. Typically, small-scale bioreactors, which are considered superior to shake flasks in simulating large-scale bioreactors, are used as the scale-down models for characterizing mammalian cell culture processes. In this article, we describe a case study where a cell culture unit operation in bioreactors using one-sided pH control and their satellites (small-scale runs conducted using the same post-inoculation cultures and nutrient feeds) in 3-L bioreactors and shake flasks indicated that shake flasks mimicked the large-scale performance better than 3-L bioreactors. We detail here how multivariate analysis was used to make the pertinent assessment and to generate the hypothesis for refining the existing 3-L scale-down model. Relevant statistical techniques such as principal component analysis, partial least square, orthogonal partial least square, and discriminant analysis were used to identify the outliers and to determine the discriminatory variables responsible for performance differences at different scales. The resulting analysis, in combination with mass transfer principles, led to the hypothesis that observed similarities between 15,000-L and shake flask runs, and differences between 15,000-L and 3-L runs, were due to pCO2 and pH values. This hypothesis was confirmed by changing the aeration strategy at 3-L scale. By reducing the initial sparge rate in 3-L bioreactor, process performance and product quality data moved closer to that of large scale. © 2015 American Institute of Chemical Engineers.

Lipidomics study of plasma phospholipid metabolism in early type 2 diabetes rats with ancient prescription Huang-Qi-San intervention by UPLC/Q-TOF-MS and correlation coefficient.

PubMed

Wu, Xia; Zhu, Jian-Cheng; Zhang, Yu; Li, Wei-Min; Rong, Xiang-Lu; Feng, Yi-Fan

2016-08-25

Potential impact of lipid research has been increasingly realized both in disease treatment and prevention. An effective metabolomics approach based on ultra-performance liquid chromatography/quadrupole-time-of-flight mass spectrometry (UPLC/Q-TOF-MS) along with multivariate statistic analysis has been applied for investigating the dynamic change of plasma phospholipids compositions in early type 2 diabetic rats after the treatment of an ancient prescription of Chinese Medicine Huang-Qi-San. The exported UPLC/Q-TOF-MS data of plasma samples were subjected to SIMCA-P and processed by bioMark, mixOmics, Rcomdr packages with R software. A clear score plots of plasma sample groups, including normal control group (NC), model group (MC), positive medicine control group (Flu) and Huang-Qi-San group (HQS), were achieved by principal-components analysis (PCA), partial least-squares discriminant analysis (PLS-DA) and orthogonal partial least-squares discriminant analysis (OPLS-DA). Biomarkers were screened out using student T test, principal component regression (PCR), partial least-squares regression (PLS) and important variable method (variable influence on projection, VIP). Structures of metabolites were identified and metabolic pathways were deduced by correlation coefficient. The relationship between compounds was explained by the correlation coefficient diagram, and the metabolic differences between similar compounds were illustrated. Based on KEGG database, the biological significances of identified biomarkers were described. The correlation coefficient was firstly applied to identify the structure and deduce the metabolic pathways of phospholipids metabolites, and the study provided a new methodological cue for further understanding the molecular mechanisms of metabolites in the process of regulating Huang-Qi-San for treating early type 2 diabetes. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Using Remote Sensing Data to Evaluate Surface Soil Properties in Alabama Ultisols

NASA Technical Reports Server (NTRS)

Sullivan, Dana G.; Shaw, Joey N.; Rickman, Doug; Mask, Paul L.; Luvall, Jeff

2005-01-01

Evaluation of surface soil properties via remote sensing could facilitate soil survey mapping, erosion prediction and allocation of agrochemicals for precision management. The objective of this study was to evaluate the relationship between soil spectral signature and surface soil properties in conventionally managed row crop systems. High-resolution RS data were acquired over bare fields in the Coastal Plain, Appalachian Plateau, and Ridge and Valley provinces of Alabama using the Airborne Terrestrial Applications Sensor multispectral scanner. Soils ranged from sandy Kandiudults to fine textured Rhodudults. Surface soil samples (0-1 cm) were collected from 163 sampling points for soil organic carbon, particle size distribution, and citrate dithionite extractable iron content. Surface roughness, soil water content, and crusting were also measured during sampling. Two methods of analysis were evaluated: 1) multiple linear regression using common spectral band ratios, and 2) partial least squares regression. Our data show that thermal infrared spectra are highly, linearly related to soil organic carbon, sand and clay content. Soil organic carbon content was the most difficult to quantify in these highly weathered systems, where soil organic carbon was generally less than 1.2%. Estimates of sand and clay content were best using partial least squares regression at the Valley site, explaining 42-59% of the variability. In the Coastal Plain, sandy surfaces prone to crusting limited estimates of sand and clay content via partial least squares and regression with common band ratios. Estimates of iron oxide content were a function of mineralogy and best accomplished using specific band ratios, with regression explaining 36-65% of the variability at the Valley and Coastal Plain sites, respectively.

[Based on the LS-SVM modeling method determination of soil available N and available K by using near-infrared spectroscopy].

PubMed

Liu, Xue-Mei; Liu, Jian-She

2012-11-01

Visible infrared spectroscopy (Vis/SW-NIRS) was investigated in the present study for measurement accuracy of soil properties,namely, available nitrogen(N) and available potassium(K). Three types of pretreatments including standard normal variate (SNV), multiplicative scattering correction (MSC) and Savitzky-Golay smoothing+first derivative were adopted to eliminate the system noises and external disturbances. Then partial least squares (PLS) and least squares-support vector machine (LS-SVM) models analysis were implemented for calibration models. Simultaneously, the performance of least squares-support vector machine (LS-SVM) models was compared with three kinds of inputs, including PCA(PCs), latent variables (LVs), and effective wavelengths (EWs). The results indicated that all LS-SVM models outperformed PLS models. The performance of the model was evaluated by the correlation coefficient (r2) and RMSEP. The optimal EWs-LS-SVM models were achieved, and the correlation coefficient (r2) and RMSEP were 0.82 and 17.2 for N and 0.72 and 15.0 for K, respectively. The results indicated that visible and short wave-near infrared spectroscopy (Vis/SW-NIRS)(325-1 075 nm) combined with LS-SVM could be utilized as a precision method for the determination of soil properties.

[Variable selection methods combined with local linear embedding theory used for optimization of near infrared spectral quantitative models].

PubMed

Hao, Yong; Sun, Xu-Dong; Yang, Qiang

2012-12-01

Variables selection strategy combined with local linear embedding (LLE) was introduced for the analysis of complex samples by using near infrared spectroscopy (NIRS). Three methods include Monte Carlo uninformation variable elimination (MCUVE), successive projections algorithm (SPA) and MCUVE connected with SPA were used for eliminating redundancy spectral variables. Partial least squares regression (PLSR) and LLE-PLSR were used for modeling complex samples. The results shown that MCUVE can both extract effective informative variables and improve the precision of models. Compared with PLSR models, LLE-PLSR models can achieve more accurate analysis results. MCUVE combined with LLE-PLSR is an effective modeling method for NIRS quantitative analysis.

Identifying maternal and infant factors associated with newborn size in rural Bangladesh by partial least squares (PLS) regression analysis

PubMed Central

Rahman, Md. Jahanur; Shamim, Abu Ahmed; Klemm, Rolf D. W.; Labrique, Alain B.; Rashid, Mahbubur; Christian, Parul; West, Keith P.

2017-01-01

Birth weight, length and circumferences of the head, chest and arm are key measures of newborn size and health in developing countries. We assessed maternal socio-demographic factors associated with multiple measures of newborn size in a large rural population in Bangladesh using partial least squares (PLS) regression method. PLS regression, combining features from principal component analysis and multiple linear regression, is a multivariate technique with an ability to handle multicollinearity while simultaneously handling multiple dependent variables. We analyzed maternal and infant data from singletons (n = 14,506) born during a double-masked, cluster-randomized, placebo-controlled maternal vitamin A or β-carotene supplementation trial in rural northwest Bangladesh. PLS regression results identified numerous maternal factors (parity, age, early pregnancy MUAC, living standard index, years of education, number of antenatal care visits, preterm delivery and infant sex) significantly (p<0.001) associated with newborn size. Among them, preterm delivery had the largest negative influence on newborn size (Standardized β = -0.29 − -0.19; p<0.001). Scatter plots of the scores of first two PLS components also revealed an interaction between newborn sex and preterm delivery on birth size. PLS regression was found to be more parsimonious than both ordinary least squares regression and principal component regression. It also provided more stable estimates than the ordinary least squares regression and provided the effect measure of the covariates with greater accuracy as it accounts for the correlation among the covariates and outcomes. Therefore, PLS regression is recommended when either there are multiple outcome measurements in the same study, or the covariates are correlated, or both situations exist in a dataset. PMID:29261760

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.

Identifying maternal and infant factors associated with newborn size in rural Bangladesh by partial least squares (PLS) regression analysis.

PubMed

Kabir, Alamgir; Rahman, Md Jahanur; Shamim, Abu Ahmed; Klemm, Rolf D W; Labrique, Alain B; Rashid, Mahbubur; Christian, Parul; West, Keith P

2017-01-01

Birth weight, length and circumferences of the head, chest and arm are key measures of newborn size and health in developing countries. We assessed maternal socio-demographic factors associated with multiple measures of newborn size in a large rural population in Bangladesh using partial least squares (PLS) regression method. PLS regression, combining features from principal component analysis and multiple linear regression, is a multivariate technique with an ability to handle multicollinearity while simultaneously handling multiple dependent variables. We analyzed maternal and infant data from singletons (n = 14,506) born during a double-masked, cluster-randomized, placebo-controlled maternal vitamin A or β-carotene supplementation trial in rural northwest Bangladesh. PLS regression results identified numerous maternal factors (parity, age, early pregnancy MUAC, living standard index, years of education, number of antenatal care visits, preterm delivery and infant sex) significantly (p<0.001) associated with newborn size. Among them, preterm delivery had the largest negative influence on newborn size (Standardized β = -0.29 - -0.19; p<0.001). Scatter plots of the scores of first two PLS components also revealed an interaction between newborn sex and preterm delivery on birth size. PLS regression was found to be more parsimonious than both ordinary least squares regression and principal component regression. It also provided more stable estimates than the ordinary least squares regression and provided the effect measure of the covariates with greater accuracy as it accounts for the correlation among the covariates and outcomes. Therefore, PLS regression is recommended when either there are multiple outcome measurements in the same study, or the covariates are correlated, or both situations exist in a dataset.

Understanding Least Squares through Monte Carlo Calculations

ERIC Educational Resources Information Center

Tellinghuisen, Joel

2005-01-01

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

2-D weighted least-squares phase unwrapping

DOEpatents

Ghiglia, Dennis C.; Romero, Louis A.

1995-01-01

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

2-D weighted least-squares phase unwrapping

DOEpatents

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

1995-06-13

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

Determination of propranolol hydrochloride in pharmaceutical preparations using near infrared spectrometry with fiber optic probe and multivariate calibration methods.

PubMed

Marques Junior, Jucelino Medeiros; Muller, Aline Lima Hermes; Foletto, Edson Luiz; da Costa, Adilson Ben; Bizzi, Cezar Augusto; Irineu Muller, Edson

2015-01-01

A method for determination of propranolol hydrochloride in pharmaceutical preparation using near infrared spectrometry with fiber optic probe (FTNIR/PROBE) and combined with chemometric methods was developed. Calibration models were developed using two variable selection models: interval partial least squares (iPLS) and synergy interval partial least squares (siPLS). The treatments based on the mean centered data and multiplicative scatter correction (MSC) were selected for models construction. A root mean square error of prediction (RMSEP) of 8.2 mg g(-1) was achieved using siPLS (s2i20PLS) algorithm with spectra divided into 20 intervals and combination of 2 intervals (8501 to 8801 and 5201 to 5501 cm(-1)). Results obtained by the proposed method were compared with those using the pharmacopoeia reference method and significant difference was not observed. Therefore, proposed method allowed a fast, precise, and accurate determination of propranolol hydrochloride in pharmaceutical preparations. Furthermore, it is possible to carry out on-line analysis of this active principle in pharmaceutical formulations with use of fiber optic probe.

Smoothed low rank and sparse matrix recovery by iteratively reweighted least squares minimization.

PubMed

Lu, Canyi; Lin, Zhouchen; Yan, Shuicheng

2015-02-01

This paper presents a general framework for solving the low-rank and/or sparse matrix minimization problems, which may involve multiple nonsmooth terms. The iteratively reweighted least squares (IRLSs) method is a fast solver, which smooths the objective function and minimizes it by alternately updating the variables and their weights. However, the traditional IRLS can only solve a sparse only or low rank only minimization problem with squared loss or an affine constraint. This paper generalizes IRLS to solve joint/mixed low-rank and sparse minimization problems, which are essential formulations for many tasks. As a concrete example, we solve the Schatten-p norm and l2,q-norm regularized low-rank representation problem by IRLS, and theoretically prove that the derived solution is a stationary point (globally optimal if p,q ≥ 1). Our convergence proof of IRLS is more general than previous one that depends on the special properties of the Schatten-p norm and l2,q-norm. Extensive experiments on both synthetic and real data sets demonstrate that our IRLS is much more efficient.

A Stochastic Total Least Squares Solution of Adaptive Filtering Problem

PubMed Central

Ahmad, Noor Atinah

2014-01-01

An efficient and computationally linear algorithm is derived for total least squares solution of adaptive filtering problem, when both input and output signals are contaminated by noise. The proposed total least mean squares (TLMS) algorithm is designed by recursively computing an optimal solution of adaptive TLS problem by minimizing instantaneous value of weighted cost function. Convergence analysis of the algorithm is given to show the global convergence of the proposed algorithm, provided that the stepsize parameter is appropriately chosen. The TLMS algorithm is computationally simpler than the other TLS algorithms and demonstrates a better performance as compared with the least mean square (LMS) and normalized least mean square (NLMS) algorithms. It provides minimum mean square deviation by exhibiting better convergence in misalignment for unknown system identification under noisy inputs. PMID:24688412

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…

Advances in data processing for open-path Fourier transform infrared spectrometry of greenhouse gases.

PubMed

Shao, Limin; Griffiths, Peter R; Leytem, April B

2010-10-01

The automated quantification of three greenhouse gases, ammonia, methane, and nitrous oxide, in the vicinity of a large dairy farm by open-path Fourier transform infrared (OP/FT-IR) spectrometry at intervals of 5 min is demonstrated. Spectral pretreatment, including the automated detection and correction of the effect of interrupting the infrared beam, is by a moving object, and the automated correction for the nonlinear detector response is applied to the measured interferograms. Two ways of obtaining quantitative data from OP/FT-IR data are described. The first, which is installed in a recently acquired commercial OP/FT-IR spectrometer, is based on classical least-squares (CLS) regression, and the second is based on partial least-squares (PLS) regression. It is shown that CLS regression only gives accurate results if the absorption features of the analytes are located in very short spectral intervals where lines due to atmospheric water vapor are absent or very weak; of the three analytes examined, only ammonia fell into this category. On the other hand, PLS regression works allowed what appeared to be accurate results to be obtained for all three analytes.

Phasing via pure crystallographic least squares: an unexpected feature.

PubMed

Burla, Maria Cristina; Carrozzini, Benedetta; Cascarano, Giovanni Luca; Giacovazzo, Carmelo; Polidori, Giampiero

2018-03-01

Crystallographic least-squares techniques, the main tool for crystal structure refinement of small and medium-size molecules, are for the first time used for ab initio phasing. It is shown that the chief obstacle to such use, the least-squares severe convergence limits, may be overcome by a multi-solution procedure able to progressively recognize and discard model atoms in false positions and to include in the current model new atoms sufficiently close to correct positions. The applications show that the least-squares procedure is able to solve many small structures without the use of important ancillary tools: e.g. no electron-density map is calculated as a support for the least-squares procedure.

Regional regression equations for estimation of natural streamflow statistics in Colorado

USGS Publications Warehouse

Capesius, Joseph P.; Stephens, Verlin C.

2009-01-01

The U.S. Geological Survey (USGS), in cooperation with the Colorado Water Conservation Board and the Colorado Department of Transportation, developed regional regression equations for estimation of various streamflow statistics that are representative of natural streamflow conditions at ungaged sites in Colorado. The equations define the statistical relations between streamflow statistics (response variables) and basin and climatic characteristics (predictor variables). The equations were developed using generalized least-squares and weighted least-squares multilinear regression reliant on logarithmic variable transformation. Streamflow statistics were derived from at least 10 years of streamflow data through about 2007 from selected USGS streamflow-gaging stations in the study area that are representative of natural-flow conditions. Basin and climatic characteristics used for equation development are drainage area, mean watershed elevation, mean watershed slope, percentage of drainage area above 7,500 feet of elevation, mean annual precipitation, and 6-hour, 100-year precipitation. For each of five hydrologic regions in Colorado, peak-streamflow equations that are based on peak-streamflow data from selected stations are presented for the 2-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-year instantaneous-peak streamflows. For four of the five hydrologic regions, equations based on daily-mean streamflow data from selected stations are presented for 7-day minimum 2-, 10-, and 50-year streamflows and for 7-day maximum 2-, 10-, and 50-year streamflows. Other equations presented for the same four hydrologic regions include those for estimation of annual- and monthly-mean streamflow and streamflow-duration statistics for exceedances of 10, 25, 50, 75, and 90 percent. All equations are reported along with salient diagnostic statistics, ranges of basin and climatic characteristics on which each equation is based, and commentary of potential bias, which is not otherwise removed by log-transformation of the variables of the equations from interpretation of residual plots. The predictor-variable ranges can be used to assess equation applicability for ungaged sites in Colorado.

Analysis to determine the maximum dimensions of flexible apertures in sensored security netting products.

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

Murton, Mark; Bouchier, Francis A.; vanDongen, Dale T.

2013-08-01

Although technological advances provide new capabilities to increase the robustness of security systems, they also potentially introduce new vulnerabilities. New capability sometimes requires new performance requirements. This paper outlines an approach to establishing a key performance requirement for an emerging intrusion detection sensor: the sensored net. Throughout the security industry, the commonly adopted standard for maximum opening size through barriers is a requirement based on square inchestypically 96 square inches. Unlike standard rigid opening, the dimensions of a flexible aperture are not fixed, but variable and conformable. It is demonstrably simple for a human intruder to move through a 96-square-inchmore » opening that is conformable to the human body. The longstanding 96-square-inch requirement itself, though firmly embedded in policy and best practice, lacks a documented empirical basis. This analysis concluded that the traditional 96-square-inch standard for openings is insufficient for flexible openings that are conformable to the human body. Instead, a circumference standard is recommended for these newer types of sensored barriers. The recommended maximum circumference for a flexible opening should be no more than 26 inches, as measured on the inside of the netting material.« less

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

NASA Technical Reports Server (NTRS)

Lawson, C. L.

1976-01-01

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

Measurement of human pilot dynamic characteristics in flight simulation

NASA Technical Reports Server (NTRS)

Reedy, James T.

1987-01-01

Fast Fourier Transform (FFT) and Least Square Error (LSE) estimation techniques were applied to the problem of identifying pilot-vehicle dynamic characteristics in flight simulation. A brief investigation of the effects of noise, input bandwidth and system delay upon the FFT and LSE techniques was undertaken using synthetic data. Data from a piloted simulation conducted at NASA Ames Research Center was then analyzed. The simulation was performed in the NASA Ames Research Center Variable Stability CH-47B helicopter operating in fixed-basis simulator mode. The piloting task consisted of maintaining the simulated vehicle over a moving hover pad whose motion was described by a random-appearing sum of sinusoids. The two test subjects used a head-down, color cathode ray tube (CRT) display for guidance and control information. Test configurations differed in the number of axes being controlled by the pilot (longitudinal only versus longitudinal and lateral), and in the presence or absence of an important display indicator called an 'acceleration ball'. A number of different pilot-vehicle transfer functions were measured, and where appropriate, qualitatively compared with theoretical pilot- vehicle models. Some indirect evidence suggesting pursuit behavior on the part of the test subjects is discussed.

First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity

NASA Technical Reports Server (NTRS)

Cai, Z.; Manteuffel, T. A.; McCormick, S. F.

1996-01-01

Following our earlier work on general second-order scalar equations, here we develop a least-squares functional for the two- and three-dimensional Stokes equations, generalized slightly by allowing a pressure term in the continuity equation. By introducing a velocity flux variable and associated curl and trace equations, we are able to establish ellipticity in an H(exp 1) product norm appropriately weighted by the Reynolds number. This immediately yields optimal discretization error estimates for finite element spaces in this norm and optimal algebraic convergence estimates for multiplicative and additive multigrid methods applied to the resulting discrete systems. Both estimates are uniform in the Reynolds number. Moreover, our pressure-perturbed form of the generalized Stokes equations allows us to develop an analogous result for the Dirichlet problem for linear elasticity with estimates that are uniform in the Lame constants.

SOM-based nonlinear least squares twin SVM via active contours for noisy image segmentation

NASA Astrophysics Data System (ADS)

Xie, Xiaomin; Wang, Tingting

2017-02-01

In this paper, a nonlinear least square twin support vector machine (NLSTSVM) with the integration of active contour model (ACM) is proposed for noisy image segmentation. Efforts have been made to seek the kernel-generated surfaces instead of hyper-planes for the pixels belonging to the foreground and background, respectively, using the kernel trick to enhance the performance. The concurrent self organizing maps (SOMs) are applied to approximate the intensity distributions in a supervised way, so as to establish the original training sets for the NLSTSVM. Further, the two sets are updated by adding the global region average intensities at each iteration. Moreover, a local variable regional term rather than edge stop function is adopted in the energy function to ameliorate the noise robustness. Experiment results demonstrate that our model holds the higher segmentation accuracy and more noise robustness.

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.

Linear regression in astronomy. II

NASA Technical Reports Server (NTRS)

Feigelson, Eric D.; Babu, Gutti J.

1992-01-01

A wide variety of least-squares linear regression procedures used in observational astronomy, particularly investigations of the cosmic distance scale, are presented and discussed. The classes of linear models considered are (1) unweighted regression lines, with bootstrap and jackknife resampling; (2) regression solutions when measurement error, in one or both variables, dominates the scatter; (3) methods to apply a calibration line to new data; (4) truncated regression models, which apply to flux-limited data sets; and (5) censored regression models, which apply when nondetections are present. For the calibration problem we develop two new procedures: a formula for the intercept offset between two parallel data sets, which propagates slope errors from one regression to the other; and a generalization of the Working-Hotelling confidence bands to nonstandard least-squares lines. They can provide improved error analysis for Faber-Jackson, Tully-Fisher, and similar cosmic distance scale relations.

Consistent Partial Least Squares Path Modeling via Regularization.

PubMed

Jung, Sunho; Park, JaeHong

2018-01-01

Partial least squares (PLS) path modeling is a component-based structural equation modeling that has been adopted in social and psychological research due to its data-analytic capability and flexibility. A recent methodological advance is consistent PLS (PLSc), designed to produce consistent estimates of path coefficients in structural models involving common factors. In practice, however, PLSc may frequently encounter multicollinearity in part because it takes a strategy of estimating path coefficients based on consistent correlations among independent latent variables. PLSc has yet no remedy for this multicollinearity problem, which can cause loss of statistical power and accuracy in parameter estimation. Thus, a ridge type of regularization is incorporated into PLSc, creating a new technique called regularized PLSc. A comprehensive simulation study is conducted to evaluate the performance of regularized PLSc as compared to its non-regularized counterpart in terms of power and accuracy. The results show that our regularized PLSc is recommended for use when serious multicollinearity is present.

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

PubMed Central

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

2017-01-01

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

Does finance affect environmental degradation: evidence from One Belt and One Road Initiative region?

PubMed

Hafeez, Muhammad; Chunhui, Yuan; Strohmaier, David; Ahmed, Manzoor; Jie, Liu

2018-04-01

This paper explores the effects of finance on environmental degradation and investigates environmental Kuznets curve (EKC) of each country among 52 that participate in the One Belt and One Road Initiative (OBORI) using the latest long panel data span (1980-2016). We utilized panel long run econometric models (fully modified ordinary least square and dynamic ordinary least square) to explore the long-run estimates in full panel and country level. Moreover, the Dumitrescu and Hurlin (2012) causality test is applied to examine the short-run causalities among our considered variables. The empirical findings validate the EKC hypothesis; the long-run estimates point out that finance significantly enhances the environmental degradation (negatively in few cases). The short-run heterogeneous causality confirms the bi-directional causality between finance and environmental degradation. The empirical outcomes suggest that policymakers should consider the environmental degradation issue caused by financial development in the One Belt and One Road region.

[The effect of tobacco prices on consumption: a time series data analysis for Mexico].

PubMed

Olivera-Chávez, Rosa Itandehui; Cermeño-Bazán, Rodolfo; de Miera-Juárez, Belén Sáenz; Jiménez-Ruiz, Jorge Alberto; Reynales-Shigematsu, Luz Myriam

2010-01-01

To estimate the price elasticity of the demand for cigarettes in Mexico based on data sources and a methodology different from the ones used in previous studies on the topic. Quarterly time series of consumption, income and price for the time period 1994 to 2005 were used. A long-run demand model was estimated using Ordinary Least Squares (OLS) and the existence of a cointegration relationship was investigated. Also, a model using Dinamic Ordinary Least Squares (DOLS) was estimated to correct for potential endogeneity of independent variables and autocorrelation of the residuals. DOLS estimates showed that a 10% increase in cigarette prices could reduce consumption in 2.5% (p<0.05) and increase government revenue in 16.11%. The results confirmed the effectiveness of taxes as an instrument for tobacco control in Mexico. An increase in taxes can be used to increase cigarette prices and therefore to reduce consumption and increase government revenue.

Buying a Better Air Force

DTIC Science & Technology

2006-03-01

identify if an explanatory variable may have been omitted due to model misspecification ( Ramsey , 1979). The RESET test resulted in failure to...Prob > F 0.0094 This model was also regressed using Huber-White estimators. Again, the Ramsey RESET test was done to ensure relevant...Aircraft. Annapolis, MD: Naval Institute Press, 2004. Ramsey , J. B. “ Tests for Specification Errors in Classical Least-Squares Regression Analysis

Emerging Perception of Causality in Action-and-Reaction Sequences from 4 to 6 Months of Age: Is It Domain-Specific?

ERIC Educational Resources Information Center

Schlottmann, Anne; Ray, Elizabeth D.; Surian, Luca

2012-01-01

Two experiments (N=136) studied how 4- to 6-month-olds perceive a simple schematic event, seen as goal-directed action and reaction from 3 years of age. In our causal reaction event, a red square moved toward a blue square, stopping prior to contact. Blue began to move away before red stopped, so that both briefly moved simultaneously at a…

Application of different spectrophotometric methods for simultaneous determination of elbasvir and grazoprevir in pharmaceutical preparation

NASA Astrophysics Data System (ADS)

Attia, Khalid A. M.; El-Abasawi, Nasr M.; El-Olemy, Ahmed; Abdelazim, Ahmed H.

2018-01-01

The first three UV spectrophotometric methods have been developed of simultaneous determination of two new FDA approved drugs namely; elbasvir and grazoprevir in their combined pharmaceutical dosage form. These methods include simultaneous equation, partial least squares with and without variable selection procedure (genetic algorithm). For simultaneous equation method, the absorbance values at 369 (λmax of elbasvir) and 253 nm (λmax of grazoprevir) have been selected for the formation of two simultaneous equations required for the mathematical processing and quantitative analysis of the studied drugs. Alternatively, the partial least squares with and without variable selection procedure (genetic algorithm) have been applied in the spectra analysis because the synchronous inclusion of many unreal wavelengths rather than by using a single or dual wavelength which greatly increases the precision and predictive ability of the methods. Successfully assay of the drugs in their pharmaceutical formulation has been done by the proposed methods. Statistically comparative analysis for the obtained results with the manufacturing methods has been performed. It is noteworthy to mention that there was no significant difference between the proposed methods and the manufacturing one with respect to the validation parameters.

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.

Weighted linear least squares estimation of diffusion MRI parameters: strengths, limitations, and pitfalls.

PubMed

Veraart, Jelle; Sijbers, Jan; Sunaert, Stefan; Leemans, Alexander; Jeurissen, Ben

2013-11-01

Linear least squares estimators are widely used in diffusion MRI for the estimation of diffusion parameters. Although adding proper weights is necessary to increase the precision of these linear estimators, there is no consensus on how to practically define them. In this study, the impact of the commonly used weighting strategies on the accuracy and precision of linear diffusion parameter estimators is evaluated and compared with the nonlinear least squares estimation approach. Simulation and real data experiments were done to study the performance of the weighted linear least squares estimators with weights defined by (a) the squares of the respective noisy diffusion-weighted signals; and (b) the squares of the predicted signals, which are reconstructed from a previous estimate of the diffusion model parameters. The negative effect of weighting strategy (a) on the accuracy of the estimator was surprisingly high. Multi-step weighting strategies yield better performance and, in some cases, even outperformed the nonlinear least squares estimator. If proper weighting strategies are applied, the weighted linear least squares approach shows high performance characteristics in terms of accuracy/precision and may even be preferred over nonlinear estimation methods. Copyright © 2013 Elsevier Inc. All rights reserved.

Least Squares Procedures.

ERIC Educational Resources Information Center

Hester, Yvette

Least squares methods are sophisticated mathematical curve fitting procedures used in all classical parametric methods. The linear least squares approximation is most often associated with finding the "line of best fit" or the regression line. Since all statistical analyses are correlational and all classical parametric methods are least…

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

NASA Astrophysics Data System (ADS)

Cheng, Jian; Zhang, Fan; Liu, Tiegang

2018-06-01

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

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.

Estimation of Flood-Frequency Discharges for Rural, Unregulated Streams in West Virginia

USGS Publications Warehouse

Wiley, Jeffrey B.; Atkins, John T.

2010-01-01

Flood-frequency discharges were determined for 290 streamgage stations having a minimum of 9 years of record in West Virginia and surrounding states through the 2006 or 2007 water year. No trend was determined in the annual peaks used to calculate the flood-frequency discharges. Multiple and simple least-squares regression equations for the 100-year (1-percent annual-occurrence probability) flood discharge with independent variables that describe the basin characteristics were developed for 290 streamgage stations in West Virginia and adjacent states. The regression residuals for the models were evaluated and used to define three regions of the State, designated as Eastern Panhandle, Central Mountains, and Western Plateaus. Exploratory data analysis procedures identified 44 streamgage stations that were excluded from the development of regression equations representative of rural, unregulated streams in West Virginia. Regional equations for the 1.1-, 1.5-, 2-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-year flood discharges were determined by generalized least-squares regression using data from the remaining 246 streamgage stations. Drainage area was the only significant independent variable determined for all equations in all regions. Procedures developed to estimate flood-frequency discharges on ungaged streams were based on (1) regional equations and (2) drainage-area ratios between gaged and ungaged locations on the same stream. The procedures are applicable only to rural, unregulated streams within the boundaries of West Virginia that have drainage areas within the limits of the stations used to develop the regional equations (from 0.21 to 1,461 square miles in the Eastern Panhandle, from 0.10 to 1,619 square miles in the Central Mountains, and from 0.13 to 1,516 square miles in the Western Plateaus). The accuracy of the equations is quantified by measuring the average prediction error (from 21.7 to 56.3 percent) and equivalent years of record (from 2.0 to 70.9 years).

Quantitative structure-retention relationship studies with immobilized artificial membrane chromatography II: partial least squares regression.

PubMed

Li, Jie; Sun, Jin; He, Zhonggui

2007-01-26

We aimed to establish quantitative structure-retention relationship (QSRR) with immobilized artificial membrane (IAM) chromatography using easily understood and obtained physicochemical molecular descriptors and to elucidate which descriptors are critical to affect the interaction process between solutes and immobilized phospholipid membranes. The retention indices (logk(IAM)) of 55 structurally diverse drugs were determined on an immobilized artificial membrane column (IAM.PC.DD2) directly or obtained by extrapolation method for highly hydrophobic compounds. Ten simple physicochemical property descriptors (clogP, rings, rotatory bond, hydro-bond counting, etc.) of these drugs were collected and used to establish QSRR and predict the retention data by partial least squares regression (PLSR). Five descriptors, clogP, rotatory bond (RotB), rings, molecular weight (MW) and total surface area (TSA), were reserved by using the Variable Importance for Projection (VIP) values as criterion to build the final PLSR model. An external test set was employed to verify the QSRR based on the training set with the five variables, and QSRR by PLSR exhibited a satisfying predictive ability with R(p)=0.902 and RMSE(p)=0.400. Comparison of coefficients of centered and scaled variables by PLSR demonstrated that, for the descriptors studied, clogP and TSA have the most significant positive effect but the rotatable bond has significant negative effect on drug IAM chromatographic retention.

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.

Statistical modeling methods to analyze the impacts of multiunit process variability on critical quality attributes of Chinese herbal medicine tablets.

PubMed

Sun, Fei; Xu, Bing; Zhang, Yi; Dai, Shengyun; Yang, Chan; Cui, Xianglong; Shi, Xinyuan; Qiao, Yanjiang

2016-01-01

The quality of Chinese herbal medicine tablets suffers from batch-to-batch variability due to a lack of manufacturing process understanding. In this paper, the Panax notoginseng saponins (PNS) immediate release tablet was taken as the research subject. By defining the dissolution of five active pharmaceutical ingredients and the tablet tensile strength as critical quality attributes (CQAs), influences of both the manipulated process parameters introduced by an orthogonal experiment design and the intermediate granules' properties on the CQAs were fully investigated by different chemometric methods, such as the partial least squares, the orthogonal projection to latent structures, and the multiblock partial least squares (MBPLS). By analyzing the loadings plots and variable importance in the projection indexes, the granule particle sizes and the minimal punch tip separation distance in tableting were identified as critical process parameters. Additionally, the MBPLS model suggested that the lubrication time in the final blending was also important in predicting tablet quality attributes. From the calculated block importance in the projection indexes, the tableting unit was confirmed to be the critical process unit of the manufacturing line. The results demonstrated that the combinatorial use of different multivariate modeling methods could help in understanding the complex process relationships as a whole. The output of this study can then be used to define a control strategy to improve the quality of the PNS immediate release tablet.

Activation of the Human MT Complex by Motion in Depth Induced by a Moving Cast Shadow

PubMed Central

Katsuyama, Narumi; Usui, Nobuo; Taira, Masato

2016-01-01

A moving cast shadow is a powerful monocular depth cue for motion perception in depth. For example, when a cast shadow moves away from or toward an object in a two-dimensional plane, the object appears to move toward or away from the observer in depth, respectively, whereas the size and position of the object are constant. Although the cortical mechanisms underlying motion perception in depth by cast shadow are unknown, the human MT complex (hMT+) is likely involved in the process, as it is sensitive to motion in depth represented by binocular depth cues. In the present study, we examined this possibility by using a functional magnetic resonance imaging (fMRI) technique. First, we identified the cortical regions sensitive to the motion of a square in depth represented via binocular disparity. Consistent with previous studies, we observed significant activation in the bilateral hMT+, and defined functional regions of interest (ROIs) there. We then investigated the activity of the ROIs during observation of the following stimuli: 1) a central square that appeared to move back and forth via a moving cast shadow (mCS); 2) a segmented and scrambled cast shadow presented beside the square (sCS); and 3) no cast shadow (nCS). Participants perceived motion of the square in depth in the mCS condition only. The activity of the hMT+ was significantly higher in the mCS compared with the sCS and nCS conditions. Moreover, the hMT+ was activated equally in both hemispheres in the mCS condition, despite presentation of the cast shadow in the bottom-right quadrant of the stimulus. Perception of the square moving in depth across visual hemifields may be reflected in the bilateral activation of the hMT+. We concluded that the hMT+ is involved in motion perception in depth induced by moving cast shadow and by binocular disparity. PMID:27597999

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.

The moving-least-squares-particle hydrodynamics method (MLSPH)

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

Dilts, G.

1997-12-31

An enhancement of the smooth-particle hydrodynamics (SPH) method has been developed using the moving-least-squares (MLS) interpolants of Lancaster and Salkauskas which simultaneously relieves the method of several well-known undesirable behaviors, including spurious boundary effects, inaccurate strain and rotation rates, pressure spikes at impact boundaries, and the infamous tension instability. The classical SPH method is derived in a novel manner by means of a Galerkin approximation applied to the Lagrangian equations of motion for continua using as basis functions the SPH kernel function multiplied by the particle volume. This derivation is then modified by simply substituting the MLS interpolants for themore » SPH Galerkin basis, taking care to redefine the particle volume and mass appropriately. The familiar SPH kernel approximation is now equivalent to a colocation-Galerkin method. Both classical conservative and recent non-conservative formulations of SPH can be derived and emulated. The non-conservative forms can be made conservative by adding terms that are zero within the approximation at the expense of boundary-value considerations. The familiar Monaghan viscosity is used. Test calculations of uniformly expanding fluids, the Swegle example, spinning solid disks, impacting bars, and spherically symmetric flow illustrate the superiority of the technique over SPH. In all cases it is seen that the marvelous ability of the MLS interpolants to add up correctly everywhere civilizes the noisy, unpredictable nature of SPH. Being a relatively minor perturbation of the SPH method, it is easily retrofitted into existing SPH codes. On the down side, computational expense at this point is significant, the Monaghan viscosity undoes the contribution of the MLS interpolants, and one-point quadrature (colocation) is not accurate enough. Solutions to these difficulties are being pursued vigorously.« less

Bayesian regression models outperform partial least squares methods for predicting milk components and technological properties using infrared spectral data

PubMed Central

Ferragina, A.; de los Campos, G.; Vazquez, A. I.; Cecchinato, A.; Bittante, G.

2017-01-01

The aim of this study was to assess the performance of Bayesian models commonly used for genomic selection to predict “difficult-to-predict” dairy traits, such as milk fatty acid (FA) expressed as percentage of total fatty acids, and technological properties, such as fresh cheese yield and protein recovery, using Fourier-transform infrared (FTIR) spectral data. Our main hypothesis was that Bayesian models that can estimate shrinkage and perform variable selection may improve our ability to predict FA traits and technological traits above and beyond what can be achieved using the current calibration models (e.g., partial least squares, PLS). To this end, we assessed a series of Bayesian methods and compared their prediction performance with that of PLS. The comparison between models was done using the same sets of data (i.e., same samples, same variability, same spectral treatment) for each trait. Data consisted of 1,264 individual milk samples collected from Brown Swiss cows for which gas chromatographic FA composition, milk coagulation properties, and cheese-yield traits were available. For each sample, 2 spectra in the infrared region from 5,011 to 925 cm−1 were available and averaged before data analysis. Three Bayesian models: Bayesian ridge regression (Bayes RR), Bayes A, and Bayes B, and 2 reference models: PLS and modified PLS (MPLS) procedures, were used to calibrate equations for each of the traits. The Bayesian models used were implemented in the R package BGLR (http://cran.r-project.org/web/packages/BGLR/index.html), whereas the PLS and MPLS were those implemented in the WinISI II software (Infrasoft International LLC, State College, PA). Prediction accuracy was estimated for each trait and model using 25 replicates of a training-testing validation procedure. Compared with PLS, which is currently the most widely used calibration method, MPLS and the 3 Bayesian methods showed significantly greater prediction accuracy. Accuracy increased in moving from calibration to external validation methods, and in moving from PLS and MPLS to Bayesian methods, particularly Bayes A and Bayes B. The maximum R2 value of validation was obtained with Bayes B and Bayes A. For the FA, C10:0 (% of each FA on total FA basis) had the highest R2 (0.75, achieved with Bayes A and Bayes B), and among the technological traits, fresh cheese yield R2 of 0.82 (achieved with Bayes B). These 2 methods have proven to be useful instruments in shrinking and selecting very informative wavelengths and inferring the structure and functions of the analyzed traits. We conclude that Bayesian models are powerful tools for deriving calibration equations, and, importantly, these equations can be easily developed using existing open-source software. As part of our study, we provide scripts based on the open source R software BGLR, which can be used to train customized prediction equations for other traits or populations. PMID:26387015

Baseline Correction of Diffuse Reflection Near-Infrared Spectra Using Searching Region Standard Normal Variate (SRSNV).

PubMed

Genkawa, Takuma; Shinzawa, Hideyuki; Kato, Hideaki; Ishikawa, Daitaro; Murayama, Kodai; Komiyama, Makoto; Ozaki, Yukihiro

2015-12-01

An alternative baseline correction method for diffuse reflection near-infrared (NIR) spectra, searching region standard normal variate (SRSNV), was proposed. Standard normal variate (SNV) is an effective pretreatment method for baseline correction of diffuse reflection NIR spectra of powder and granular samples; however, its baseline correction performance depends on the NIR region used for SNV calculation. To search for an optimal NIR region for baseline correction using SNV, SRSNV employs moving window partial least squares regression (MWPLSR), and an optimal NIR region is identified based on the root mean square error (RMSE) of cross-validation of the partial least squares regression (PLSR) models with the first latent variable (LV). The performance of SRSNV was evaluated using diffuse reflection NIR spectra of mixture samples consisting of wheat flour and granular glucose (0-100% glucose at 5% intervals). From the obtained NIR spectra of the mixture in the 10 000-4000 cm(-1) region at 4 cm intervals (1501 spectral channels), a series of spectral windows consisting of 80 spectral channels was constructed, and then SNV spectra were calculated for each spectral window. Using these SNV spectra, a series of PLSR models with the first LV for glucose concentration was built. A plot of RMSE versus the spectral window position obtained using the PLSR models revealed that the 8680–8364 cm(-1) region was optimal for baseline correction using SNV. In the SNV spectra calculated using the 8680–8364 cm(-1) region (SRSNV spectra), a remarkable relative intensity change between a band due to wheat flour at 8500 cm(-1) and that due to glucose at 8364 cm(-1) was observed owing to successful baseline correction using SNV. A PLSR model with the first LV based on the SRSNV spectra yielded a determination coefficient (R2) of 0.999 and an RMSE of 0.70%, while a PLSR model with three LVs based on SNV spectra calculated in the full spectral region gave an R2 of 0.995 and an RMSE of 2.29%. Additional evaluation of SRSNV was carried out using diffuse reflection NIR spectra of marzipan and corn samples, and PLSR models based on SRSNV spectra showed good prediction results. These evaluation results indicate that SRSNV is effective in baseline correction of diffuse reflection NIR spectra and provides regression models with good prediction accuracy.

Anisotropic diffusion in mesh-free numerical magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Hopkins, Philip F.

2017-04-01

We extend recently developed mesh-free Lagrangian methods for numerical magnetohydrodynamics (MHD) to arbitrary anisotropic diffusion equations, including: passive scalar diffusion, Spitzer-Braginskii conduction and viscosity, cosmic ray diffusion/streaming, anisotropic radiation transport, non-ideal MHD (Ohmic resistivity, ambipolar diffusion, the Hall effect) and turbulent 'eddy diffusion'. We study these as implemented in the code GIZMO for both new meshless finite-volume Godunov schemes (MFM/MFV). We show that the MFM/MFV methods are accurate and stable even with noisy fields and irregular particle arrangements, and recover the correct behaviour even in arbitrarily anisotropic cases. They are competitive with state-of-the-art AMR/moving-mesh methods, and can correctly treat anisotropic diffusion-driven instabilities (e.g. the MTI and HBI, Hall MRI). We also develop a new scheme for stabilizing anisotropic tensor-valued fluxes with high-order gradient estimators and non-linear flux limiters, which is trivially generalized to AMR/moving-mesh codes. We also present applications of some of these improvements for SPH, in the form of a new integral-Godunov SPH formulation that adopts a moving-least squares gradient estimator and introduces a flux-limited Riemann problem between particles.

Inverse optimal design of the radiant heating in materials processing and manufacturing

NASA Astrophysics Data System (ADS)

Fedorov, A. G.; Lee, K. H.; Viskanta, R.

1998-12-01

Combined convective, conductive, and radiative heat transfer is analyzed during heating of a continuously moving load in the industrial radiant oven. A transient, quasi-three-dimensional model of heat transfer between a continuous load of parts moving inside an oven on a conveyor belt at a constant speed and an array of radiant heaters/burners placed inside the furnace enclosure is developed. The model accounts for radiative exchange between the heaters and the load, heat conduction in the load, and convective heat transfer between the moving load and oven environment. The thermal model developed has been used to construct a general framework for an inverse optimal design of an industrial oven as an example. In particular, the procedure based on the Levenberg-Marquardt nonlinear least squares optimization algorithm has been developed to obtain the optimal temperatures of the heaters/burners that need to be specified to achieve a prescribed temperature distribution of the surface of a load. The results of calculations for several sample cases are reported to illustrate the capabilities of the procedure developed for the optimal inverse design of an industrial radiant oven.

Solvency supervision based on a total balance sheet approach

NASA Astrophysics Data System (ADS)

Pitselis, Georgios

2009-11-01

In this paper we investigate the adequacy of the own funds a company requires in order to remain healthy and avoid insolvency. Two methods are applied here; the quantile regression method and the method of mixed effects models. Quantile regression is capable of providing a more complete statistical analysis of the stochastic relationship among random variables than least squares estimation. The estimated mixed effects line can be considered as an internal industry equation (norm), which explains a systematic relation between a dependent variable (such as own funds) with independent variables (e.g. financial characteristics, such as assets, provisions, etc.). The above two methods are implemented with two data sets.

Collinearity in Least-Squares Analysis

ERIC Educational Resources Information Center

de Levie, Robert

2012-01-01

How useful are the standard deviations per se, and how reliable are results derived from several least-squares coefficients and their associated standard deviations? When the output parameters obtained from a least-squares analysis are mutually independent, as is often assumed, they are reliable estimators of imprecision and so are the functions…

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...

Adaptive Modal Identification for Flutter Suppression Control

NASA Technical Reports Server (NTRS)

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

2016-01-01

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

Improvement of depth resolution in depth-resolved wavenumber-scanning interferometry using wavenumber-domain least-squares algorithm: comparison and experiment.

PubMed

Bai, Yulei; Jia, Quanjie; Zhang, Yun; Huang, Qiquan; Yang, Qiyu; Ye, Shuangli; He, Zhaoshui; Zhou, Yanzhou; Xie, Shengli

2016-05-01

It is important to improve the depth resolution in depth-resolved wavenumber-scanning interferometry (DRWSI) owing to the limited range of wavenumber scanning. In this work, a new nonlinear iterative least-squares algorithm called the wavenumber-domain least-squares algorithm (WLSA) is proposed for evaluating the phase of DRWSI. The simulated and experimental results of the Fourier transform (FT), complex-number least-squares algorithm (CNLSA), eigenvalue-decomposition and least-squares algorithm (EDLSA), and WLSA were compared and analyzed. According to the results, the WLSA is less dependent on the initial values, and the depth resolution δz is approximately changed from δz to δz/6. Thus, the WLSA exhibits a better performance than the FT, CNLSA, and EDLSA.

Measurement of process variables in solid-state fermentation of wheat straw using FT-NIR spectroscopy and synergy interval PLS algorithm

NASA Astrophysics Data System (ADS)

Jiang, Hui; Liu, Guohai; Mei, Congli; Yu, Shuang; Xiao, Xiahong; Ding, Yuhan

2012-11-01

The feasibility of rapid determination of the process variables (i.e. pH and moisture content) in solid-state fermentation (SSF) of wheat straw using Fourier transform near infrared (FT-NIR) spectroscopy was studied. Synergy interval partial least squares (siPLS) algorithm was implemented to calibrate regression model. The number of PLS factors and the number of subintervals were optimized simultaneously by cross-validation. The performance of the prediction model was evaluated according to the root mean square error of cross-validation (RMSECV), the root mean square error of prediction (RMSEP) and the correlation coefficient (R). The measurement results of the optimal model were obtained as follows: RMSECV = 0.0776, Rc = 0.9777, RMSEP = 0.0963, and Rp = 0.9686 for pH model; RMSECV = 1.3544% w/w, Rc = 0.8871, RMSEP = 1.4946% w/w, and Rp = 0.8684 for moisture content model. Finally, compared with classic PLS and iPLS models, the siPLS model revealed its superior performance. The overall results demonstrate that FT-NIR spectroscopy combined with siPLS algorithm can be used to measure process variables in solid-state fermentation of wheat straw, and NIR spectroscopy technique has a potential to be utilized in SSF industry.

Phase discrepancy induced from least squares wavefront reconstruction of wrapped phase measurements with high noise or large localized wavefront gradients

NASA Astrophysics Data System (ADS)

Steinbock, Michael J.; Hyde, Milo W.

2012-10-01

Adaptive optics is used in applications such as laser communication, remote sensing, and laser weapon systems to estimate and correct for atmospheric distortions of propagated light in real-time. Within an adaptive optics system, a reconstruction process interprets the raw wavefront sensor measurements and calculates an estimate for the unwrapped phase function to be sent through a control law and applied to a wavefront correction device. This research is focused on adaptive optics using a self-referencing interferometer wavefront sensor, which directly measures the wrapped wavefront phase. Therefore, its measurements must be reconstructed for use on a continuous facesheet deformable mirror. In testing and evaluating a novel class of branch-point- tolerant wavefront reconstructors based on the post-processing congruence operation technique, an increase in Strehl ratio compared to a traditional least squares reconstructor was noted even in non-scintillated fields. To investigate this further, this paper uses wave-optics simulations to eliminate many of the variables from a hardware adaptive optics system, so as to focus on the reconstruction techniques alone. The simulation results along with a discussion of the physical reasoning for this phenomenon are provided. For any applications using a self-referencing interferometer wavefront sensor with low signal levels or high localized wavefront gradients, understanding this phenomena is critical when applying a traditional least squares wavefront reconstructor.

Comparison of partial least squares and random forests for evaluating relationship between phenolics and bioactivities of Neptunia oleracea.

PubMed

Lee, Soo Yee; Mediani, Ahmed; Maulidiani, Maulidiani; Khatib, Alfi; Ismail, Intan Safinar; Zawawi, Norhasnida; Abas, Faridah

2018-01-01

Neptunia oleracea is a plant consumed as a vegetable and which has been used as a folk remedy for several diseases. Herein, two regression models (partial least squares, PLS; and random forest, RF) in a metabolomics approach were compared and applied to the evaluation of the relationship between phenolics and bioactivities of N. oleracea. In addition, the effects of different extraction conditions on the phenolic constituents were assessed by pattern recognition analysis. Comparison of the PLS and RF showed that RF exhibited poorer generalization and hence poorer predictive performance. Both the regression coefficient of PLS and the variable importance of RF revealed that quercetin and kaempferol derivatives, caffeic acid and vitexin-2-O-rhamnoside were significant towards the tested bioactivities. Furthermore, principal component analysis (PCA) and partial least squares-discriminant analysis (PLS-DA) results showed that sonication and absolute ethanol are the preferable extraction method and ethanol ratio, respectively, to produce N. oleracea extracts with high phenolic levels and therefore high DPPH scavenging and α-glucosidase inhibitory activities. Both PLS and RF are useful regression models in metabolomics studies. This work provides insight into the performance of different multivariate data analysis tools and the effects of different extraction conditions on the extraction of desired phenolics from plants. © 2017 Society of Chemical Industry. © 2017 Society of Chemical Industry.

An Inequality Constrained Least-Squares Approach as an Alternative Estimation Procedure for Atmospheric Parameters from VLBI Observations

NASA Astrophysics Data System (ADS)

Halsig, Sebastian; Artz, Thomas; Iddink, Andreas; Nothnagel, Axel

2016-12-01

On its way through the atmosphere, radio signals are delayed and affected by bending and attenuation effects relative to a theoretical path in vacuum. In particular, the neutral part of the atmosphere contributes considerably to the error budget of space-geodetic observations. At the same time, space-geodetic techniques become more and more important in the understanding of the Earth's atmosphere, because atmospheric parameters can be linked to the water vapor content in the atmosphere. The tropospheric delay is usually taken into account by applying an adequate model for the hydrostatic component and by additionally estimating zenith wet delays for the highly variable wet component. Sometimes, the Ordinary Least Squares (OLS) approach leads to negative estimates, which would be equivalent to negative water vapor in the atmosphere and does, of course, not reflect meteorological and physical conditions in a plausible way. To cope with this phenomenon, we introduce an Inequality Constrained Least Squares (ICLS) method from the field of convex optimization and use inequality constraints to force the tropospheric parameters to be non-negative allowing for a more realistic tropospheric parameter estimation in a meteorological sense. Because deficiencies in the a priori hydrostatic modeling are almost fully compensated by the tropospheric estimates, the ICLS approach urgently requires suitable a priori hydrostatic delays. In this paper, we briefly describe the ICLS method and validate its impact with regard to station positions.

VLSI implementation of a new LMS-based algorithm for noise removal in ECG signal

NASA Astrophysics Data System (ADS)

Satheeskumaran, S.; Sabrigiriraj, M.

2016-06-01

Least mean square (LMS)-based adaptive filters are widely deployed for removing artefacts in electrocardiogram (ECG) due to less number of computations. But they posses high mean square error (MSE) under noisy environment. The transform domain variable step-size LMS algorithm reduces the MSE at the cost of computational complexity. In this paper, a variable step-size delayed LMS adaptive filter is used to remove the artefacts from the ECG signal for improved feature extraction. The dedicated digital Signal processors provide fast processing, but they are not flexible. By using field programmable gate arrays, the pipelined architectures can be used to enhance the system performance. The pipelined architecture can enhance the operation efficiency of the adaptive filter and save the power consumption. This technique provides high signal-to-noise ratio and low MSE with reduced computational complexity; hence, it is a useful method for monitoring patients with heart-related problem.

Assessing Fit and Dimensionality in Least Squares Metric Multidimensional Scaling Using Akaike's Information Criterion

ERIC Educational Resources Information Center

Ding, Cody S.; Davison, Mark L.

2010-01-01

Akaike's information criterion is suggested as a tool for evaluating fit and dimensionality in metric multidimensional scaling that uses least squares methods of estimation. This criterion combines the least squares loss function with the number of estimated parameters. Numerical examples are presented. The results from analyses of both simulation…

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

ERIC Educational Resources Information Center

Helmreich, James E.; Krog, K. Peter

2018-01-01

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

Enriched reproducing kernel particle method for fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Ying, Yuping; Lian, Yanping; Tang, Shaoqiang; Liu, Wing Kam

2018-06-01

The reproducing kernel particle method (RKPM) has been efficiently applied to problems with large deformations, high gradients and high modal density. In this paper, it is extended to solve a nonlocal problem modeled by a fractional advection-diffusion equation (FADE), which exhibits a boundary layer with low regularity. We formulate this method on a moving least-square approach. Via the enrichment of fractional-order power functions to the traditional integer-order basis for RKPM, leading terms of the solution to the FADE can be exactly reproduced, which guarantees a good approximation to the boundary layer. Numerical tests are performed to verify the proposed approach.

Blind identification of the kinetic parameters in three-compartment models

NASA Astrophysics Data System (ADS)

Riabkov, Dmitri Y.; Di Bella, Edward V. R.

2004-03-01

Quantified knowledge of tissue kinetic parameters in the regions of the brain and other organs can offer information useful in clinical and research applications. Dynamic medical imaging with injection of radioactive or paramagnetic tracer can be used for this measurement. The kinetics of some widely used tracers such as [18F]2-fluoro-2-deoxy-D-glucose can be described by a three-compartment physiological model. The kinetic parameters of the tissue can be estimated from dynamically acquired images. Feasibility of estimation by blind identification, which does not require knowledge of the blood input, is considered analytically and numerically in this work for the three-compartment type of tissue response. The non-uniqueness of the two-region case for blind identification of kinetic parameters in three-compartment model is shown; at least three regions are needed for the blind identification to be unique. Numerical results for the accuracy of these blind identification methods in different conditions were considered. Both a separable variables least-squares (SLS) approach and an eigenvector-based algorithm for multichannel blind deconvolution approach were used. The latter showed poor accuracy. Modifications for non-uniform time sampling were also developed. Also, another method which uses a model for the blood input was compared. Results for the macroparameter K, which reflects the metabolic rate of glucose usage, using three regions with noise showed comparable accuracy for the separable variables least squares method and for the input model-based method, and slightly worse accuracy for SLS with the non-uniform sampling modification.

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

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

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

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

Direct quantification of test bacteria in synthetic water-polluted samples by square wave voltammetry and chemometric methods.

PubMed

Carpani, Irene; Conti, Paolo; Lanteri, Silvia; Legnani, Pier Paolo; Leoni, Erica; Tonelli, Domenica

2008-02-28

A home-made microelectrode array, based on reticulated vitreous carbon, was used as working electrode in square wave voltammetry experiments to quantify the bacterial load of Escherichia coli ATCC 13706 and Pseudomonas aeruginosa ATCC 27853, chosen as test microorganisms, in synthetic samples similar to drinking water (phosphate buffer). Raw electrochemical signals were analysed with partial least squares regression coupled to variable selection in order to correlate these values with the bacterial load estimated by aerobic plate counting. The results demonstrated the ability of the method to detect even low loads of microorganisms in synthetic water samples. In particular, the model detects the bacterial load in the range 3-2,020 CFU ml(-1) for E. coli and in the range 76-155,556 CFU ml(-1) for P. aeruginosa.

A class of least-squares filtering and identification algorithms with systolic array architectures

NASA Technical Reports Server (NTRS)

Kalson, Seth Z.; Yao, Kung

1991-01-01

A unified approach is presented for deriving a large class of new and previously known time- and order-recursive least-squares algorithms with systolic array architectures, suitable for high-throughput-rate and VLSI implementations of space-time filtering and system identification problems. The geometrical derivation given is unique in that no assumption is made concerning the rank of the sample data correlation matrix. This method utilizes and extends the concept of oblique projections, as used previously in the derivations of the least-squares lattice algorithms. Exponentially weighted least-squares criteria are considered for both sliding and growing memory.

Multi-element array signal reconstruction with adaptive least-squares algorithms

NASA Technical Reports Server (NTRS)

Kumar, R.

1992-01-01

Two versions of the adaptive least-squares algorithm are presented for combining signals from multiple feeds placed in the focal plane of a mechanical antenna whose reflector surface is distorted due to various deformations. Coherent signal combining techniques based on the adaptive least-squares algorithm are examined for nearly optimally and adaptively combining the outputs of the feeds. The performance of the two versions is evaluated by simulations. It is demonstrated for the example considered that both of the adaptive least-squares algorithms are capable of offsetting most of the loss in the antenna gain incurred due to reflector surface deformations.

Do knowledge and cultural perceptions of modern female contraceptives predict male involvement in Ayete, Nigeria?

PubMed

Sanusi, A; Akinyemi, Oluwaseun O; Onoviran, Oghemetega O

2014-12-01

Male involvement is crucial to female contraceptive use. This study examined how male knowledge and cultural perceptions of modern female contraceptives influence involvement in contraceptive use. A cross-sectional survey of 389 men from Ayete, Nigeria was used to regress a continuous male involvement score on demographic variables, knowledge of at least one method of modern female contraception and a scored male perception variable using Ordinary Least Squares regression. Controlling for perception, the knowledge of at least one method of modern female contraception was not significantly associated with a change in male involvement (p=0.264). Increasing positive perception was associated with higher male involvement scores (p=0.001). Higher educated males, those with a current desire to have children and males whose partners were currently using a method had greater male involvement scores (p<0.05). Policy and intervention efforts should be focused on changing cultural perceptions, in addition to providing in-depth knowledge of contraceptive methods.

46 CFR 108.463 - Foam rate: Protein.

Code of Federal Regulations, 2012 CFR

2012-10-01

... least 6.52 liters per minute for each square meter (.16 gallons per minute for each square foot) of area... rate at each outlet must be at least 4.07 liters per minute for each square meter (.1 gallon per minute for each square foot) of liquid surface in the tank. ...

46 CFR 108.463 - Foam rate: Protein.

Code of Federal Regulations, 2010 CFR

2010-10-01

... least 6.52 liters per minute for each square meter (.16 gallons per minute for each square foot) of area... rate at each outlet must be at least 4.07 liters per minute for each square meter (.1 gallon per minute for each square foot) of liquid surface in the tank. ...

46 CFR 108.463 - Foam rate: Protein.

Code of Federal Regulations, 2011 CFR

2011-10-01

... least 6.52 liters per minute for each square meter (.16 gallons per minute for each square foot) of area... rate at each outlet must be at least 4.07 liters per minute for each square meter (.1 gallon per minute for each square foot) of liquid surface in the tank. ...

46 CFR 108.463 - Foam rate: Protein.

Code of Federal Regulations, 2013 CFR

2013-10-01

... least 6.52 liters per minute for each square meter (.16 gallons per minute for each square foot) of area... rate at each outlet must be at least 4.07 liters per minute for each square meter (.1 gallon per minute for each square foot) of liquid surface in the tank. ...

46 CFR 108.463 - Foam rate: Protein.

Code of Federal Regulations, 2014 CFR

2014-10-01

... least 6.52 liters per minute for each square meter (.16 gallons per minute for each square foot) of area... rate at each outlet must be at least 4.07 liters per minute for each square meter (.1 gallon per minute for each square foot) of liquid surface in the tank. ...

Solution of a Complex Least Squares Problem with Constrained Phase.

PubMed

Bydder, Mark

2010-12-30

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

An Extension of RSS-based Model Comparison Tests for Weighted Least Squares

DTIC Science & Technology

2012-08-22

use the model comparison test statistic to analyze the null hypothesis. Under the null hypothesis, the weighted least squares cost functional is JWLS ...q̂WLSH ) = 10.3040×106. Under the alternative hypothesis, the weighted least squares cost functional is JWLS (q̂WLS) = 8.8394 × 106. Thus the model

Robust check loss-based variable selection of high-dimensional single-index varying-coefficient model

NASA Astrophysics Data System (ADS)

Song, Yunquan; Lin, Lu; Jian, Ling

2016-07-01

Single-index varying-coefficient model is an important mathematical modeling method to model nonlinear phenomena in science and engineering. In this paper, we develop a variable selection method for high-dimensional single-index varying-coefficient models using a shrinkage idea. The proposed procedure can simultaneously select significant nonparametric components and parametric components. Under defined regularity conditions, with appropriate selection of tuning parameters, the consistency of the variable selection procedure and the oracle property of the estimators are established. Moreover, due to the robustness of the check loss function to outliers in the finite samples, our proposed variable selection method is more robust than the ones based on the least squares criterion. Finally, the method is illustrated with numerical simulations.

The determinant of household tourism expenditure in Central Java Province, Indonesia

NASA Astrophysics Data System (ADS)

Subanti, S.; Respatiwulan; Hakim, A. R.; Handajani, S. S.; Hakim, I. M.

2018-03-01

The purpose of our paper want to determine the factors of household tourism expenditure in Central Java Province, Indonesia. This paper used ordinary least squares regression. The findings from this paper, (1) the significant factors that affecting household tourism expenditure are marital status, sex, household income per capita, education for head of household, education for member of household, number of household, urbanrural, and industrial origin for head of household; (2) For variables which have positive relationship with household tourism expenditure, the variable of marital status has a biggest value from others; and (3) For variables which have negative relationship with household tourism expenditure, the variable of industrial origin for head household has a biggest value from others.

Two-dimensional strain gradient damage modeling: a variational approach

NASA Astrophysics Data System (ADS)

Placidi, Luca; Misra, Anil; Barchiesi, Emilio

2018-06-01

In this paper, we formulate a linear elastic second gradient isotropic two-dimensional continuum model accounting for irreversible damage. The failure is defined as the condition in which the damage parameter reaches 1, at least in one point of the domain. The quasi-static approximation is done, i.e., the kinetic energy is assumed to be negligible. In order to deal with dissipation, a damage dissipation term is considered in the deformation energy functional. The key goal of this paper is to apply a non-standard variational procedure to exploit the damage irreversibility argument. As a result, we derive not only the equilibrium equations but, notably, also the Karush-Kuhn-Tucker conditions. Finally, numerical simulations for exemplary problems are discussed as some constitutive parameters are varying, with the inclusion of a mesh-independence evidence. Element-free Galerkin method and moving least square shape functions have been employed.

Advanced statistics: linear regression, part I: simple linear regression.

PubMed

Marill, Keith A

2004-01-01

Simple linear regression is a mathematical technique used to model the relationship between a single independent predictor variable and a single dependent outcome variable. In this, the first of a two-part series exploring concepts in linear regression analysis, the four fundamental assumptions and the mechanics of simple linear regression are reviewed. The most common technique used to derive the regression line, the method of least squares, is described. The reader will be acquainted with other important concepts in simple linear regression, including: variable transformations, dummy variables, relationship to inference testing, and leverage. Simplified clinical examples with small datasets and graphic models are used to illustrate the points. This will provide a foundation for the second article in this series: a discussion of multiple linear regression, in which there are multiple predictor variables.

Passive acoustic localization of the Atlantic bottlenose dolphin using whistles and echolocation clicks.

PubMed

Freitag, L E; Tyack, P L

1993-04-01

A method for localization and tracking of calling marine mammals was tested under realistic field conditions that include noise, multipath, and arbitrarily located sensors. Experiments were performed in two locations using four and six hydrophones with captive Atlantic bottlenose dolphins (Tursiops truncatus). Acoustic signals from the animals were collected in the field using a digital acoustic data acquisition system. The data were then processed off-line to determine relative hydrophone positions and the animal locations. Accurate hydrophone position estimates are achieved by pinging sequentially from each hydrophone to all the others. A two-step least-squares algorithm is then used to determine sensor locations from the calibration data. Animal locations are determined by estimating the time differences of arrival of the dolphin signals at the different sensors. The peak of a matched filter output or the first cycle of the observed waveform is used to determine arrival time of an echolocation click. Cross correlation between hydrophones is used to determine inter-sensor time delays of whistles. Calculation of source location using the time difference of arrival measurements is done using a least-squares solution to minimize error. These preliminary experimental results based on a small set of data show that realistic trajectories for moving animals may be generated from consecutive location estimates.

Image grating metrology using phase-stepping interferometry in scanning beam interference lithography

NASA Astrophysics Data System (ADS)

Li, Minkang; Zhou, Changhe; Wei, Chunlong; Jia, Wei; Lu, Yancong; Xiang, Changcheng; Xiang, XianSong

2016-10-01

Large-sized gratings are essential optical elements in laser fusion and space astronomy facilities. Scanning beam interference lithography is an effective method to fabricate large-sized gratings. To minimize the nonlinear phase written into the photo-resist, the image grating must be measured to adjust the left and right beams to interfere at their waists. In this paper, we propose a new method to conduct wavefront metrology based on phase-stepping interferometry. Firstly, a transmission grating is used to combine the two beams to form an interferogram which is recorded by a charge coupled device(CCD). Phase steps are introduced by moving the grating with a linear stage monitored by a laser interferometer. A series of interferograms are recorded as the displacement is measured by the laser interferometer. Secondly, to eliminate the tilt and piston error during the phase stepping, the iterative least square phase shift method is implemented to obtain the wrapped phase. Thirdly, we use the discrete cosine transform least square method to unwrap the phase map. Experiment results indicate that the measured wavefront has a nonlinear phase around 0.05 λ@404.7nm. Finally, as the image grating is acquired, we simulate the print-error written into the photo-resist.

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

PubMed

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

2016-04-10

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

Two-dimensional wavefront reconstruction based on double-shearing and least squares fitting

NASA Astrophysics Data System (ADS)

Liang, Peiying; Ding, Jianping; Zhu, Yangqing; Dong, Qian; Huang, Yuhua; Zhu, Zhen

2017-06-01

The two-dimensional wavefront reconstruction method based on double-shearing and least squares fitting is proposed in this paper. Four one-dimensional phase estimates of the measured wavefront, which correspond to the two shears and the two orthogonal directions, could be calculated from the differential phase, which solves the problem of the missing spectrum, and then by using the least squares method the two-dimensional wavefront reconstruction could be done. The numerical simulations of the proposed algorithm are carried out to verify the feasibility of this method. The influence of noise generated from different shear amount and different intensity on the accuracy of the reconstruction is studied and compared with the results from the algorithm based on single-shearing and least squares fitting. Finally, a two-grating lateral shearing interference experiment is carried out to verify the wavefront reconstruction algorithm based on doubleshearing and least squares fitting.

Normality of Residuals Is a Continuous Variable, and Does Seem to Influence the Trustworthiness of Confidence Intervals: A Response to, and Appreciation of, Williams, Grajales, and Kurkiewicz (2013)

ERIC Educational Resources Information Center

Osborne, Jason W.

2013-01-01

Osborne and Waters (2002) focused on checking some of the assumptions of multiple linear regression. In a critique of that paper, Williams, Grajales, and Kurkiewicz correctly clarify that regression models estimated using ordinary least squares require the assumption of normally distributed errors, but not the assumption of normally distributed…

Learning Latent Variable and Predictive Models of Dynamical Systems

DTIC Science & Technology

2009-10-01

stable over the full 1000 frame image sequence without significant damping. C. Sam- ples drawn from a least squares synthesized sequences (top), and...LDS stabilizing algorithms, LB-1 and LB-2. Bars at every 20 timesteps denote variance in the results. CG provides the best stable short term predictions...observations. This thesis contributes (1) novel learning algorithms for existing dynamical system models that overcome significant limitations of previous

Robust regression on noisy data for fusion scaling laws

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

Verdoolaege, Geert, E-mail: geert.verdoolaege@ugent.be; Laboratoire de Physique des Plasmas de l'ERM - Laboratorium voor Plasmafysica van de KMS

2014-11-15

We introduce the method of geodesic least squares (GLS) regression for estimating fusion scaling laws. Based on straightforward principles, the method is easily implemented, yet it clearly outperforms established regression techniques, particularly in cases of significant uncertainty on both the response and predictor variables. We apply GLS for estimating the scaling of the L-H power threshold, resulting in estimates for ITER that are somewhat higher than predicted earlier.

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

Deep Restricted Kernel Machines Using Conjugate Feature Duality.

PubMed

Suykens, Johan A K

2017-08-01

The aim of this letter is to propose a theory of deep restricted kernel machines offering new foundations for deep learning with kernel machines. From the viewpoint of deep learning, it is partially related to restricted Boltzmann machines, which are characterized by visible and hidden units in a bipartite graph without hidden-to-hidden connections and deep learning extensions as deep belief networks and deep Boltzmann machines. From the viewpoint of kernel machines, it includes least squares support vector machines for classification and regression, kernel principal component analysis (PCA), matrix singular value decomposition, and Parzen-type models. A key element is to first characterize these kernel machines in terms of so-called conjugate feature duality, yielding a representation with visible and hidden units. It is shown how this is related to the energy form in restricted Boltzmann machines, with continuous variables in a nonprobabilistic setting. In this new framework of so-called restricted kernel machine (RKM) representations, the dual variables correspond to hidden features. Deep RKM are obtained by coupling the RKMs. The method is illustrated for deep RKM, consisting of three levels with a least squares support vector machine regression level and two kernel PCA levels. In its primal form also deep feedforward neural networks can be trained within this framework.

Statistical modeling methods to analyze the impacts of multiunit process variability on critical quality attributes of Chinese herbal medicine tablets

PubMed Central

Sun, Fei; Xu, Bing; Zhang, Yi; Dai, Shengyun; Yang, Chan; Cui, Xianglong; Shi, Xinyuan; Qiao, Yanjiang

2016-01-01

The quality of Chinese herbal medicine tablets suffers from batch-to-batch variability due to a lack of manufacturing process understanding. In this paper, the Panax notoginseng saponins (PNS) immediate release tablet was taken as the research subject. By defining the dissolution of five active pharmaceutical ingredients and the tablet tensile strength as critical quality attributes (CQAs), influences of both the manipulated process parameters introduced by an orthogonal experiment design and the intermediate granules’ properties on the CQAs were fully investigated by different chemometric methods, such as the partial least squares, the orthogonal projection to latent structures, and the multiblock partial least squares (MBPLS). By analyzing the loadings plots and variable importance in the projection indexes, the granule particle sizes and the minimal punch tip separation distance in tableting were identified as critical process parameters. Additionally, the MBPLS model suggested that the lubrication time in the final blending was also important in predicting tablet quality attributes. From the calculated block importance in the projection indexes, the tableting unit was confirmed to be the critical process unit of the manufacturing line. The results demonstrated that the combinatorial use of different multivariate modeling methods could help in understanding the complex process relationships as a whole. The output of this study can then be used to define a control strategy to improve the quality of the PNS immediate release tablet. PMID:27932865

Impact of multicollinearity on small sample hydrologic regression models

NASA Astrophysics Data System (ADS)

Kroll, Charles N.; Song, Peter

2013-06-01

Often hydrologic regression models are developed with ordinary least squares (OLS) procedures. The use of OLS with highly correlated explanatory variables produces multicollinearity, which creates highly sensitive parameter estimators with inflated variances and improper model selection. It is not clear how to best address multicollinearity in hydrologic regression models. Here a Monte Carlo simulation is developed to compare four techniques to address multicollinearity: OLS, OLS with variance inflation factor screening (VIF), principal component regression (PCR), and partial least squares regression (PLS). The performance of these four techniques was observed for varying sample sizes, correlation coefficients between the explanatory variables, and model error variances consistent with hydrologic regional regression models. The negative effects of multicollinearity are magnified at smaller sample sizes, higher correlations between the variables, and larger model error variances (smaller R2). The Monte Carlo simulation indicates that if the true model is known, multicollinearity is present, and the estimation and statistical testing of regression parameters are of interest, then PCR or PLS should be employed. If the model is unknown, or if the interest is solely on model predictions, is it recommended that OLS be employed since using more complicated techniques did not produce any improvement in model performance. A leave-one-out cross-validation case study was also performed using low-streamflow data sets from the eastern United States. Results indicate that OLS with stepwise selection generally produces models across study regions with varying levels of multicollinearity that are as good as biased regression techniques such as PCR and PLS.

The program LOPT for least-squares optimization of energy levels

NASA Astrophysics Data System (ADS)

Kramida, A. E.

2011-02-01

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

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.

Free variable selection QSPR study to predict 19F chemical shifts of some fluorinated organic compounds using Random Forest and RBF-PLS methods

NASA Astrophysics Data System (ADS)

Goudarzi, Nasser

2016-04-01

In this work, two new and powerful chemometrics methods are applied for the modeling and prediction of the 19F chemical shift values of some fluorinated organic compounds. The radial basis function-partial least square (RBF-PLS) and random forest (RF) are employed to construct the models to predict the 19F chemical shifts. In this study, we didn't used from any variable selection method and RF method can be used as variable selection and modeling technique. Effects of the important parameters affecting the ability of the RF prediction power such as the number of trees (nt) and the number of randomly selected variables to split each node (m) were investigated. The root-mean-square errors of prediction (RMSEP) for the training set and the prediction set for the RBF-PLS and RF models were 44.70, 23.86, 29.77, and 23.69, respectively. Also, the correlation coefficients of the prediction set for the RBF-PLS and RF models were 0.8684 and 0.9313, respectively. The results obtained reveal that the RF model can be used as a powerful chemometrics tool for the quantitative structure-property relationship (QSPR) studies.

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

NASA Technical Reports Server (NTRS)

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

1985-01-01

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

A Weighted Least Squares Approach To Robustify Least Squares Estimates.

ERIC Educational Resources Information Center

Lin, Chowhong; Davenport, Ernest C., Jr.

This study developed a robust linear regression technique based on the idea of weighted least squares. In this technique, a subsample of the full data of interest is drawn, based on a measure of distance, and an initial set of regression coefficients is calculated. The rest of the data points are then taken into the subsample, one after another,…

Domain Decomposition Algorithms for First-Order System Least Squares Methods

NASA Technical Reports Server (NTRS)

Pavarino, Luca F.

1996-01-01

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

Least-squares sequential parameter and state estimation for large space structures

NASA Technical Reports Server (NTRS)

Thau, F. E.; Eliazov, T.; Montgomery, R. C.

1982-01-01

This paper presents the formulation of simultaneous state and parameter estimation problems for flexible structures in terms of least-squares minimization problems. The approach combines an on-line order determination algorithm, with least-squares algorithms for finding estimates of modal approximation functions, modal amplitudes, and modal parameters. The approach combines previous results on separable nonlinear least squares estimation with a regression analysis formulation of the state estimation problem. The technique makes use of sequential Householder transformations. This allows for sequential accumulation of matrices required during the identification process. The technique is used to identify the modal prameters of a flexible beam.

Spacecraft inertia estimation via constrained least squares

NASA Technical Reports Server (NTRS)

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

2006-01-01

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

The Effect of Crop Insurance on Technical Efficiency of Wheat Farmers in Kermanshah Province: A Corrected Ordinary Least Square Approach

NASA Astrophysics Data System (ADS)

Agahi, Hossein; Zarafshani, Kiumars; Behjat, Amir-Mohsen

The purpose of this study was to describe the effect of crop insurance on agricultural production among dry wheat farmers in Kermanshah province. The population of this study consisted of dry wheat farmers. Data used in this study was collected using stratified multi-stage cluster sampling method and face to face interview with 251 farmers in three different climate regions: tropical, temperate and cold during 2003-2004 crop years. The procedures used for determining farmers' technical efficiency was Corrected Ordinary Least Square (COLS). Findings revealed that crop insurance has positive effect on temperate and tropical regions. However, the production difference between insured and uninsured farmers in cold region was non-significant. It is therefore concluded that technical efficiency of agricultural production in Kermanshah province is a function of crop insurance as well as other variables such as crop management practices, personal characteristics and fair distribution of agricultural inputs.

Missing RRI interpolation for HRV analysis using locally-weighted partial least squares regression.

PubMed

Kamata, Keisuke; Fujiwara, Koichi; Yamakawa, Toshiki; Kano, Manabu

2016-08-01

The R-R interval (RRI) fluctuation in electrocardiogram (ECG) is called heart rate variability (HRV). Since HRV reflects autonomic nervous function, HRV-based health monitoring services, such as stress estimation, drowsy driving detection, and epileptic seizure prediction, have been proposed. In these HRV-based health monitoring services, precise R wave detection from ECG is required; however, R waves cannot always be detected due to ECG artifacts. Missing RRI data should be interpolated appropriately for HRV analysis. The present work proposes a missing RRI interpolation method by utilizing using just-in-time (JIT) modeling. The proposed method adopts locally weighted partial least squares (LW-PLS) for RRI interpolation, which is a well-known JIT modeling method used in the filed of process control. The usefulness of the proposed method was demonstrated through a case study of real RRI data collected from healthy persons. The proposed JIT-based interpolation method could improve the interpolation accuracy in comparison with a static interpolation method.

Flu and Finances: Influenza Outbreaks and Loan Defaults in US Cities, 2004-2012.

PubMed

Houle, Jason N; Collins, J Michael; Schmeiser, Maximilian D

2015-09-01

We examined the association between influenza outbreaks in 83 metropolitan areas and credit card and mortgage defaults, as measured in quarterly zip code-level credit data over the period of 2004 to 2012. We used ordinary least squares, fixed effects, and 2-stage least squares instrumental variables regression strategies to examine the relationship between influenza-related Google searches and 30-, 60-, and 90-day credit card and mortgage delinquency rates. We found that a proxy for influenza outbreaks is associated with a small but statistically significant increase in credit card and mortgage default rates, net of other factors. These effects are largest for 90-day defaults, suggesting that influenza outbreaks have a disproportionate impact on vulnerable borrowers who are already behind on their payments. Overall, it appears there is a relationship between exogenous health shocks (such as influenza) and credit default. The results suggest that consumer finances could benefit from policies that aim to reduce the financial shocks of illness, particularly for vulnerable borrowers.

Different approaches in Partial Least Squares and Artificial Neural Network models applied for the analysis of a ternary mixture of Amlodipine, Valsartan and Hydrochlorothiazide

NASA Astrophysics Data System (ADS)

Darwish, Hany W.; Hassan, Said A.; Salem, Maissa Y.; El-Zeany, Badr A.

2014-03-01

Different chemometric models were applied for the quantitative analysis of Amlodipine (AML), Valsartan (VAL) and Hydrochlorothiazide (HCT) in ternary mixture, namely, Partial Least Squares (PLS) as traditional chemometric model and Artificial Neural Networks (ANN) as advanced model. PLS and ANN were applied with and without variable selection procedure (Genetic Algorithm GA) and data compression procedure (Principal Component Analysis PCA). The chemometric methods applied are PLS-1, GA-PLS, ANN, GA-ANN and PCA-ANN. The methods were used for the quantitative analysis of the drugs in raw materials and pharmaceutical dosage form via handling the UV spectral data. A 3-factor 5-level experimental design was established resulting in 25 mixtures containing different ratios of the drugs. Fifteen mixtures were used as a calibration set and the other ten mixtures were used as validation set to validate the prediction ability of the suggested methods. The validity of the proposed methods was assessed using the standard addition technique.

Uncertainties in extracted parameters of a Gaussian emission line profile with continuum background.

PubMed

Minin, Serge; Kamalabadi, Farzad

2009-12-20

We derive analytical equations for uncertainties in parameters extracted by nonlinear least-squares fitting of a Gaussian emission function with an unknown continuum background component in the presence of additive white Gaussian noise. The derivation is based on the inversion of the full curvature matrix (equivalent to Fisher information matrix) of the least-squares error, chi(2), in a four-variable fitting parameter space. The derived uncertainty formulas (equivalent to Cramer-Rao error bounds) are found to be in good agreement with the numerically computed uncertainties from a large ensemble of simulated measurements. The derived formulas can be used for estimating minimum achievable errors for a given signal-to-noise ratio and for investigating some aspects of measurement setup trade-offs and optimization. While the intended application is Fabry-Perot spectroscopy for wind and temperature measurements in the upper atmosphere, the derivation is generic and applicable to other spectroscopy problems with a Gaussian line shape.

Three-Dimensional Simulations of Marangoni-Benard Convection in Small Containers by the Least-Squares Finite Element Method

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao; Jiang, Bo-Nan; Wu, Jie; Duh, J. C.

1996-01-01

This paper reports a numerical study of the Marangoni-Benard (MB) convection in a planar fluid layer. The least-squares finite element method (LSFEM) is employed to solve the three-dimensional Stokes equations and the energy equation. First, the governing equations are reduced to be first-order by introducing variables such as vorticity and heat fluxes. The resultant first-order system is then cast into a div-curl-grad formulation, and its ellipticity and permissible boundary conditions are readily proved. This numerical approach provides an equal-order discretization for velocity, pressure, vorticity, temperature, and heat conduction fluxes, and therefore can provide high fidelity solutions for the complex flow physics of the MB convection. Numerical results reported include the critical Marangoni numbers (M(sub ac)) for the onset of the convection in containers with various aspect ratios, and the planforms of supercritical MB flows. The numerical solutions compared favorably with the experimental results reported by Koschmieder et al..

New distributed fusion filtering algorithm based on covariances over sensor networks with random packet dropouts

NASA Astrophysics Data System (ADS)

Caballero-Águila, R.; Hermoso-Carazo, A.; Linares-Pérez, J.

2017-07-01

This paper studies the distributed fusion estimation problem from multisensor measured outputs perturbed by correlated noises and uncertainties modelled by random parameter matrices. Each sensor transmits its outputs to a local processor over a packet-erasure channel and, consequently, random losses may occur during transmission. Different white sequences of Bernoulli variables are introduced to model the transmission losses. For the estimation, each lost output is replaced by its estimator based on the information received previously, and only the covariances of the processes involved are used, without requiring the signal evolution model. First, a recursive algorithm for the local least-squares filters is derived by using an innovation approach. Then, the cross-correlation matrices between any two local filters is obtained. Finally, the distributed fusion filter weighted by matrices is obtained from the local filters by applying the least-squares criterion. The performance of the estimators and the influence of both sensor uncertainties and transmission losses on the estimation accuracy are analysed in a numerical example.

Development of predictive models for total phenolics and free p-coumaric acid contents in barley grain by near-infrared spectroscopy.

PubMed

Han, Zhigang; Cai, Shengguan; Zhang, Xuelei; Qian, Qiufeng; Huang, Yuqing; Dai, Fei; Zhang, Guoping

2017-07-15

Barley grains are rich in phenolic compounds, which are associated with reduced risk of chronic diseases. Development of barley cultivars with high phenolic acid content has become one of the main objectives in breeding programs. A rapid and accurate method for measuring phenolic compounds would be helpful for crop breeding. We developed predictive models for both total phenolics (TPC) and p-coumaric acid (PA), based on near-infrared spectroscopy (NIRS) analysis. Regressions of partial least squares (PLS) and least squares support vector machine (LS-SVM) were compared for improving the models, and Monte Carlo-Uninformative Variable Elimination (MC-UVE) was applied to select informative wavelengths. The optimal calibration models generated high coefficients of correlation (r pre ) and ratio performance deviation (RPD) for TPC and PA. These results indicated the models are suitable for rapid determination of phenolic compounds in barley grains. Copyright © 2017 Elsevier Ltd. All rights reserved.

Consistent Partial Least Squares Path Modeling via Regularization

PubMed Central

Jung, Sunho; Park, JaeHong

2018-01-01

Partial least squares (PLS) path modeling is a component-based structural equation modeling that has been adopted in social and psychological research due to its data-analytic capability and flexibility. A recent methodological advance is consistent PLS (PLSc), designed to produce consistent estimates of path coefficients in structural models involving common factors. In practice, however, PLSc may frequently encounter multicollinearity in part because it takes a strategy of estimating path coefficients based on consistent correlations among independent latent variables. PLSc has yet no remedy for this multicollinearity problem, which can cause loss of statistical power and accuracy in parameter estimation. Thus, a ridge type of regularization is incorporated into PLSc, creating a new technique called regularized PLSc. A comprehensive simulation study is conducted to evaluate the performance of regularized PLSc as compared to its non-regularized counterpart in terms of power and accuracy. The results show that our regularized PLSc is recommended for use when serious multicollinearity is present. PMID:29515491

Partial least squares based identification of Duchenne muscular dystrophy specific genes.

PubMed

An, Hui-bo; Zheng, Hua-cheng; Zhang, Li; Ma, Lin; Liu, Zheng-yan

2013-11-01

Large-scale parallel gene expression analysis has provided a greater ease for investigating the underlying mechanisms of Duchenne muscular dystrophy (DMD). Previous studies typically implemented variance/regression analysis, which would be fundamentally flawed when unaccounted sources of variability in the arrays existed. Here we aim to identify genes that contribute to the pathology of DMD using partial least squares (PLS) based analysis. We carried out PLS-based analysis with two datasets downloaded from the Gene Expression Omnibus (GEO) database to identify genes contributing to the pathology of DMD. Except for the genes related to inflammation, muscle regeneration and extracellular matrix (ECM) modeling, we found some genes with high fold change, which have not been identified by previous studies, such as SRPX, GPNMB, SAT1, and LYZ. In addition, downregulation of the fatty acid metabolism pathway was found, which may be related to the progressive muscle wasting process. Our results provide a better understanding for the downstream mechanisms of DMD.

Direct determination of danofloxacin and flumequine in milk by use of fluorescence spectrometry in combination with partial least-squares calibration.

PubMed

Murillo Pulgarín, J A; Alañón Molina, A; Boras, N

2013-03-20

A new method for the simultaneous determination of danofloxacin and flumequine in milk samples was developed by using the nonlinear variable-angle synchronous fluorescence technique to acquire data and a partial least-squares chemometric algorithm to process them. A calibration set of standard samples was designed by combination of a factorial design with two levels per factor and a central star design. Whey was used as the third component of the calibration matrix. In order to assess the goodness of the proposed method, a prediction set of 11 synthetic samples was analyzed, obtaining recovery percentages between 96.1% and 104.0%. Limits of detection, calculated by means of a new criterion, were 0.90 and 12.4 ng mL(-1) for danofloxacin and flumequine, respectively. Finally, the simultaneous determination of both fluoroquinoles in milk samples containing the analytes was successfully carried out, obtaining an average recovery percentage of 99.3 ± 4.4 for danofloxacin and 100.7 ± 4.4.

Optimal Frequency-Domain System Realization with Weighting

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan; Maghami, Peiman G.

1999-01-01

Several approaches are presented to identify an experimental system model directly from frequency response data. The formulation uses a matrix-fraction description as the model structure. Frequency weighting such as exponential weighting is introduced to solve a weighted least-squares problem to obtain the coefficient matrices for the matrix-fraction description. A multi-variable state-space model can then be formed using the coefficient matrices of the matrix-fraction description. Three different approaches are introduced to fine-tune the model using nonlinear programming methods to minimize the desired cost function. The first method uses an eigenvalue assignment technique to reassign a subset of system poles to improve the identified model. The second method deals with the model in the real Schur or modal form, reassigns a subset of system poles, and adjusts the columns (rows) of the input (output) influence matrix using a nonlinear optimizer. The third method also optimizes a subset of poles, but the input and output influence matrices are refined at every optimization step through least-squares procedures.

Self organising maps for visualising and modelling

PubMed Central

2012-01-01

The paper describes the motivation of SOMs (Self Organising Maps) and how they are generally more accessible due to the wider available modern, more powerful, cost-effective computers. Their advantages compared to Principal Components Analysis and Partial Least Squares are discussed. These allow application to non-linear data, are not so dependent on least squares solutions, normality of errors and less influenced by outliers. In addition there are a wide variety of intuitive methods for visualisation that allow full use of the map space. Modern problems in analytical chemistry include applications to cultural heritage studies, environmental, metabolomic and biological problems result in complex datasets. Methods for visualising maps are described including best matching units, hit histograms, unified distance matrices and component planes. Supervised SOMs for classification including multifactor data and variable selection are discussed as is their use in Quality Control. The paper is illustrated using four case studies, namely the Near Infrared of food, the thermal analysis of polymers, metabolomic analysis of saliva using NMR, and on-line HPLC for pharmaceutical process monitoring. PMID:22594434

Size distribution of Portuguese firms between 2006 and 2012

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

The impacts of the quantum-dot confining potential on the spin-orbit effect.

PubMed

Li, Rui; Liu, Zhi-Hai; Wu, Yidong; Liu, C S

2018-05-09

For a nanowire quantum dot with the confining potential modeled by both the infinite and the finite square wells, we obtain exactly the energy spectrum and the wave functions in the strong spin-orbit coupling regime. We find that regardless of how small the well height is, there are at least two bound states in the finite square well: one has the σ x [Formula: see text] = -1 symmetry and the other has the σ x [Formula: see text] = 1 symmetry. When the well height is slowly tuned from large to small, the position of the maximal probability density of the first excited state moves from the center to x ≠ 0, while the position of the maximal probability density of the ground state is always at the center. A strong enhancement of the spin-orbit effect is demonstrated by tuning the well height. In particular, there exists a critical height [Formula: see text], at which the spin-orbit effect is enhanced to maximal.

Measurement of non-sugar solids content in Chinese rice wine using near infrared spectroscopy combined with an efficient characteristic variables selection algorithm.

PubMed

Ouyang, Qin; Zhao, Jiewen; Chen, Quansheng

2015-01-01

The non-sugar solids (NSS) content is one of the most important nutrition indicators of Chinese rice wine. This study proposed a rapid method for the measurement of NSS content in Chinese rice wine using near infrared (NIR) spectroscopy. We also systemically studied the efficient spectral variables selection algorithms that have to go through modeling. A new algorithm of synergy interval partial least square with competitive adaptive reweighted sampling (Si-CARS-PLS) was proposed for modeling. The performance of the final model was back-evaluated using root mean square error of calibration (RMSEC) and correlation coefficient (Rc) in calibration set and similarly tested by mean square error of prediction (RMSEP) and correlation coefficient (Rp) in prediction set. The optimum model by Si-CARS-PLS algorithm was achieved when 7 PLS factors and 18 variables were included, and the results were as follows: Rc=0.95 and RMSEC=1.12 in the calibration set, Rp=0.95 and RMSEP=1.22 in the prediction set. In addition, Si-CARS-PLS algorithm showed its superiority when compared with the commonly used algorithms in multivariate calibration. This work demonstrated that NIR spectroscopy technique combined with a suitable multivariate calibration algorithm has a high potential in rapid measurement of NSS content in Chinese rice wine. Copyright © 2015 Elsevier B.V. All rights reserved.

Measurement of process variables in solid-state fermentation of wheat straw using FT-NIR spectroscopy and synergy interval PLS algorithm.

PubMed

Jiang, Hui; Liu, Guohai; Mei, Congli; Yu, Shuang; Xiao, Xiahong; Ding, Yuhan

2012-11-01

The feasibility of rapid determination of the process variables (i.e. pH and moisture content) in solid-state fermentation (SSF) of wheat straw using Fourier transform near infrared (FT-NIR) spectroscopy was studied. Synergy interval partial least squares (siPLS) algorithm was implemented to calibrate regression model. The number of PLS factors and the number of subintervals were optimized simultaneously by cross-validation. The performance of the prediction model was evaluated according to the root mean square error of cross-validation (RMSECV), the root mean square error of prediction (RMSEP) and the correlation coefficient (R). The measurement results of the optimal model were obtained as follows: RMSECV=0.0776, R(c)=0.9777, RMSEP=0.0963, and R(p)=0.9686 for pH model; RMSECV=1.3544% w/w, R(c)=0.8871, RMSEP=1.4946% w/w, and R(p)=0.8684 for moisture content model. Finally, compared with classic PLS and iPLS models, the siPLS model revealed its superior performance. The overall results demonstrate that FT-NIR spectroscopy combined with siPLS algorithm can be used to measure process variables in solid-state fermentation of wheat straw, and NIR spectroscopy technique has a potential to be utilized in SSF industry. Copyright © 2012 Elsevier B.V. All rights reserved.

Quantitative determination of additive Chlorantraniliprole in Abamectin preparation: Investigation of bootstrapping soft shrinkage approach by mid-infrared spectroscopy

NASA Astrophysics Data System (ADS)

Yan, Hong; Song, Xiangzhong; Tian, Kuangda; Chen, Yilin; Xiong, Yanmei; Min, Shungeng

2018-02-01

A novel method, mid-infrared (MIR) spectroscopy, which enables the determination of Chlorantraniliprole in Abamectin within minutes, is proposed. We further evaluate the prediction ability of four wavelength selection methods, including bootstrapping soft shrinkage approach (BOSS), Monte Carlo uninformative variable elimination (MCUVE), genetic algorithm partial least squares (GA-PLS) and competitive adaptive reweighted sampling (CARS) respectively. The results showed that BOSS method obtained the lowest root mean squared error of cross validation (RMSECV) (0.0245) and root mean squared error of prediction (RMSEP) (0.0271), as well as the highest coefficient of determination of cross-validation (Qcv2) (0.9998) and the coefficient of determination of test set (Q2test) (0.9989), which demonstrated that the mid infrared spectroscopy can be used to detect Chlorantraniliprole in Abamectin conveniently. Meanwhile, a suitable wavelength selection method (BOSS) is essential to conducting a component spectral analysis.

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

NASA Astrophysics Data System (ADS)

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

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

Effects of DoD Engagements in Collaborative Humanitarian Assistance

DTIC Science & Technology

2013-09-01

Breusch - Pagan (BP) test , which tests for heteroscedasticity in panel data using Lagrange Multipliers. The null hypothesis for the BP test is that...Two Stage Least Squares AOR Area of Responsibility BP Breusch - Pagan COCOM Combatant Command COMPACT Compact of Free Association DoD...homoscedasticity is present ( Breusch & Pagan , 1979, p. 1288). Each fixed effect, “CountryName,” “FiscalYear,”and the combined effect of both variables, was

Long-term optical flux and colour variability in quasars

NASA Astrophysics Data System (ADS)

Sukanya, N.; Stalin, C. S.; Jeyakumar, S.; Praveen, D.; Dhani, Arnab; Damle, R.

2016-02-01

We have used optical V and R band observations from the Massive Compact Halo Object (MACHO) project on a sample of 59 quasars behind the Magellanic clouds to study their long term optical flux and colour variations. These quasars, lying in the redshift range of 0.2 < z < 2.8 and having apparent V band magnitudes between 16.6 and 20.1 mag, have observations ranging from 49 to 1353 epochs spanning over 7.5 yr with frequency of sampling between 2 to 10 days. All the quasars show variability during the observing period. The normalised excess variance (Fvar) in V and R bands are in the range 0.2% < FVvar < 1.6% and 0.1% < FRvar < 1.5% respectively. In a large fraction of the sources, Fvar is larger in the V band compared to the R band. From the z-transformed discrete cross-correlation function analysis, we find that there is no lag between the V and R band variations. Adopting the Markov Chain Monte Carlo (MCMC) approach, and properly taking into account the correlation between the errors in colours and magnitudes, it is found that the majority of sources show a bluer when brighter trend, while a minor fraction of quasars show the opposite behaviour. This is similar to the results obtained from another two independent algorithms, namely the weighted linear least squares fit (FITEXY) and the bivariate correlated errors and intrinsic scatter regression (BCES). However, the ordinary least squares (OLS) fit, normally used in the colour variability studies of quasars, indicates that all the quasars studied here show a bluer when brighter trend. It is therefore very clear that the OLS algorithm cannot be used for the study of colour variability in quasars.

Neither fixed nor random: weighted least squares meta-analysis.

PubMed

Stanley, T D; Doucouliagos, Hristos

2015-06-15

This study challenges two core conventional meta-analysis methods: fixed effect and random effects. We show how and explain why an unrestricted weighted least squares estimator is superior to conventional random-effects meta-analysis when there is publication (or small-sample) bias and better than a fixed-effect weighted average if there is heterogeneity. Statistical theory and simulations of effect sizes, log odds ratios and regression coefficients demonstrate that this unrestricted weighted least squares estimator provides satisfactory estimates and confidence intervals that are comparable to random effects when there is no publication (or small-sample) bias and identical to fixed-effect meta-analysis when there is no heterogeneity. When there is publication selection bias, the unrestricted weighted least squares approach dominates random effects; when there is excess heterogeneity, it is clearly superior to fixed-effect meta-analysis. In practical applications, an unrestricted weighted least squares weighted average will often provide superior estimates to both conventional fixed and random effects. Copyright © 2015 John Wiley & Sons, Ltd.

Combinatorics of least-squares trees.

PubMed

Mihaescu, Radu; Pachter, Lior

2008-09-09

A recurring theme in the least-squares approach to phylogenetics has been the discovery of elegant combinatorial formulas for the least-squares estimates of edge lengths. These formulas have proved useful for the development of efficient algorithms, and have also been important for understanding connections among popular phylogeny algorithms. For example, the selection criterion of the neighbor-joining algorithm is now understood in terms of the combinatorial formulas of Pauplin for estimating tree length. We highlight a phylogenetically desirable property that weighted least-squares methods should satisfy, and provide a complete characterization of methods that satisfy the property. The necessary and sufficient condition is a multiplicative four-point condition that the variance matrix needs to satisfy. The proof is based on the observation that the Lagrange multipliers in the proof of the Gauss-Markov theorem are tree-additive. Our results generalize and complete previous work on ordinary least squares, balanced minimum evolution, and the taxon-weighted variance model. They also provide a time-optimal algorithm for computation.

Revisiting the Least-squares Procedure for Gradient Reconstruction on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.; Thomas, James L. (Technical Monitor)

2003-01-01

The accuracy of the least-squares technique for gradient reconstruction on unstructured meshes is examined. While least-squares techniques produce accurate results on arbitrary isotropic unstructured meshes, serious difficulties exist for highly stretched meshes in the presence of surface curvature. In these situations, gradients are typically under-estimated by up to an order of magnitude. For vertex-based discretizations on triangular and quadrilateral meshes, and cell-centered discretizations on quadrilateral meshes, accuracy can be recovered using an inverse distance weighting in the least-squares construction. For cell-centered discretizations on triangles, both the unweighted and weighted least-squares constructions fail to provide suitable gradient estimates for highly stretched curved meshes. Good overall flow solution accuracy can be retained in spite of poor gradient estimates, due to the presence of flow alignment in exactly the same regions where the poor gradient accuracy is observed. However, the use of entropy fixes has the potential for generating large but subtle discretization errors.

[On-site evaluation of raw milk qualities by portable Vis/NIR transmittance technique].

PubMed

Wang, Jia-Hua; Zhang, Xiao-Wei; Wang, Jun; Han, Dong-Hai

2014-10-01

To ensure the material safety of dairy products, visible (Vis)/near infrared (NIR) spectroscopy combined with che- mometrics methods was used to develop models for fat, protein, dry matter (DM) and lactose on-site evaluation. A total of 88 raw milk samples were collected from individual livestocks in different years. The spectral of raw milk were measured by a porta- ble Vis/NIR spectrometer with diffused transmittance accessory. To remove the scatter effect and baseline drift, the diffused transmittance spectra were preprocessed by 2nd order derivative with Savitsky-Golay (polynomial order 2, data point 25). Changeable size moving window partial least squares (CSMWPLS) and genetic algorithms partial least squares (GAPLS) meth- ods were suggested to select informative regions for PLS calibration. The PLS and multiple linear regression (MLR) methods were used to develop models for predicting quality index of raw milk. The prediction performance of CSMWPLS models were similar to GAPLS models for fat, protein, DM and lactose evaluation, the root mean standard errors of prediction (RMSEP) were 0.115 6/0.103 3, 0.096 2/0.113 7, 0.201 3/0.123 7 and 0.077 4/0.066 8, and the relative standard deviations of prediction (RPD) were 8.99/10.06, 3.53/2.99, 5.76/9.38 and 1.81/2.10, respectively. Meanwhile, the MLR models were also cal- ibrated with 8, 10, 9 and 7 variables for fat, protein, DM and lactose, respectively. The prediction performance of MLR models was better than or close to PLS models. The MLR models to predict fat, protein, DM and lactose yielded the RMSEP of 0.107 0, 0.093 0, 0.136 0 and 0.065 8, and the RPD of 9.72, 3.66, 8.53 and 2.13, respectively. The results demonstrated the usefulness of Vis/NIR spectra combined with multivariate calibration methods as an objective and rapid method for the quality evaluation of complicated raw milks. And the results obtained also highlight the potential of portable Vis/NIR instruments for on-site assessing quality indexes of raw milk.

A gentle introduction to quantile regression for ecologists

USGS Publications Warehouse

Cade, B.S.; Noon, B.R.

2003-01-01

Quantile regression is a way to estimate the conditional quantiles of a response variable distribution in the linear model that provides a more complete view of possible causal relationships between variables in ecological processes. Typically, all the factors that affect ecological processes are not measured and included in the statistical models used to investigate relationships between variables associated with those processes. As a consequence, there may be a weak or no predictive relationship between the mean of the response variable (y) distribution and the measured predictive factors (X). Yet there may be stronger, useful predictive relationships with other parts of the response variable distribution. This primer relates quantile regression estimates to prediction intervals in parametric error distribution regression models (eg least squares), and discusses the ordering characteristics, interval nature, sampling variation, weighting, and interpretation of the estimates for homogeneous and heterogeneous regression models.

Space moving target detection and tracking method in complex background

NASA Astrophysics Data System (ADS)

Lv, Ping-Yue; Sun, Sheng-Li; Lin, Chang-Qing; Liu, Gao-Rui

2018-06-01

The background of the space-borne detectors in real space-based environment is extremely complex and the signal-to-clutter ratio is very low (SCR ≈ 1), which increases the difficulty for detecting space moving targets. In order to solve this problem, an algorithm combining background suppression processing based on two-dimensional least mean square filter (TDLMS) and target enhancement based on neighborhood gray-scale difference (GSD) is proposed in this paper. The latter can filter out most of the residual background clutter processed by the former such as cloud edge. Through this procedure, both global and local SCR have obtained substantial improvement, indicating that the target has been greatly enhanced. After removing the detector's inherent clutter region through connected domain processing, the image only contains the target point and the isolated noise, in which the isolated noise could be filtered out effectively through multi-frame association. The proposed algorithm in this paper has been compared with some state-of-the-art algorithms for moving target detection and tracking tasks. The experimental results show that the performance of this algorithm is the best in terms of SCR gain, background suppression factor (BSF) and detection results.

A sharp interface Cartesian grid method for viscous simulation of shocked particle-laden flows

NASA Astrophysics Data System (ADS)

Das, Pratik; Sen, Oishik; Jacobs, Gustaaf; Udaykumar, H. S.

2017-09-01

A Cartesian grid-based sharp interface method is presented for viscous simulations of shocked particle-laden flows. The moving solid-fluid interfaces are represented using level sets. A moving least-squares reconstruction is developed to apply the no-slip boundary condition at solid-fluid interfaces and to supply viscous stresses to the fluid. The algorithms developed in this paper are benchmarked against similarity solutions for the boundary layer over a fixed flat plate and against numerical solutions for moving interface problems such as shock-induced lift-off of a cylinder in a channel. The framework is extended to 3D and applied to calculate low Reynolds number steady supersonic flow over a sphere. Viscous simulation of the interaction of a particle cloud with an incident planar shock is demonstrated; the average drag on the particles and the vorticity field in the cloud are compared to the inviscid case to elucidate the effects of viscosity on momentum transfer between the particle and fluid phases. The methods developed will be useful for obtaining accurate momentum and heat transfer closure models for macro-scale shocked particulate flow applications such as blast waves and dust explosions.

Level set immersed boundary method for gas-liquid-solid interactions with phase-change

NASA Astrophysics Data System (ADS)

Dhruv, Akash; Balaras, Elias; Riaz, Amir; Kim, Jungho

2017-11-01

We will discuss an approach to simulate the interaction between two-phase flows with phase changes and stationary/moving structures. In our formulation, the Navier-Stokes and heat advection-diffusion equations are solved on a block-structured grid using adaptive mesh refinement (AMR) along with sharp jump in pressure, velocity and temperature across the interface separating the different phases. The jumps are implemented using a modified Ghost Fluid Method (Lee et al., J. Comput. Physics, 344:381-418, 2017), and the interface is tracked with a level set approach. Phase transition is achieved by calculating mass flux near the interface and extrapolating it to the rest of the domain using a Hamilton-Jacobi equation. Stationary/moving structures are simulated with an immersed boundary formulation based on moving least squares (Vanella & Balaras, J. Comput. Physics, 228:6617-6628, 2009). A variety of canonical problems involving vaporization, film boiling and nucleate boiling is presented to validate the method and demonstrate the its formal accuracy. The robustness of the solver in complex problems, which are crucial in efficient design of heat transfer mechanisms for various applications, will also be demonstrated. Work supported by NASA, Grant NNX16AQ77G.

A Least-Squares Transport Equation Compatible with Voids

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

Hansen, Jon; Peterson, Jacob; Morel, Jim

Standard second-order self-adjoint forms of the transport equation, such as the even-parity, odd-parity, and self-adjoint angular flux equation, cannot be used in voids. Perhaps more important, they experience numerical convergence difficulties in near-voids. Here we present a new form of a second-order self-adjoint transport equation that has an advantage relative to standard forms in that it can be used in voids or near-voids. Our equation is closely related to the standard least-squares form of the transport equation with both equations being applicable in a void and having a nonconservative analytic form. However, unlike the standard least-squares form of the transportmore » equation, our least-squares equation is compatible with source iteration. It has been found that the standard least-squares form of the transport equation with a linear-continuous finite-element spatial discretization has difficulty in the thick diffusion limit. Here we extensively test the 1D slab-geometry version of our scheme with respect to void solutions, spatial convergence rate, and the intermediate and thick diffusion limits. We also define an effective diffusion synthetic acceleration scheme for our discretization. Our conclusion is that our least-squares S n formulation represents an excellent alternative to existing second-order S n transport formulations« less

Multi-model approach to characterize human handwriting motion.

PubMed

Chihi, I; Abdelkrim, A; Benrejeb, M

2016-02-01

This paper deals with characterization and modelling of human handwriting motion from two forearm muscle activity signals, called electromyography signals (EMG). In this work, an experimental approach was used to record the coordinates of a pen tip moving on the (x, y) plane and EMG signals during the handwriting act. The main purpose is to design a new mathematical model which characterizes this biological process. Based on a multi-model approach, this system was originally developed to generate letters and geometric forms written by different writers. A Recursive Least Squares algorithm is used to estimate the parameters of each sub-model of the multi-model basis. Simulations show good agreement between predicted results and the recorded data.

A Highly Durable RNAi Therapeutic Inhibitor of PCSK9

PubMed Central

Fitzgerald, Kevin; White, Suellen; Borodovsky, Anna; Bettencourt, Brian R.; Strahs, Andrew; Clausen, Valerie; Wijngaard, Peter; Horton, Jay D.; Taubel, Jorg; Brooks, Ashley; Fernando, Chamikara; Kauffman, Robert S.; Kallend, David; Vaishnaw, Akshay; Simon, Amy

2018-01-01

BACKGROUND Inclisiran (ALN-PCSsc) is a long-acting RNA interference (RNAi) therapeutic agent that inhibits the synthesis of proprotein convertase subtilisin–kexin type 9 (PCSK9), a target for the lowering of low-density lipoprotein (LDL) cholesterol. METHODS In this phase 1 trial, we randomly assigned healthy volunteers with an LDL cholesterol level of at least 100 mg per deciliter in a 3:1 ratio to receive a subcutaneous injection of inclisiran or placebo in either a single-ascending-dose phase (at a dose of 25, 100, 300, 500, or 800 mg) or a multiple-dose phase (125 mg weekly for four doses, 250 mg every other week for two doses, or 300 or 500 mg monthly for two doses, with or without concurrent statin therapy); each dose cohort included four to eight participants. Safety, the side-effect profile, and pharmacodynamic measures (PCSK9 level, LDL cholesterol level, and exploratory lipid variables) were evaluated. RESULTS The most common adverse events were cough, musculoskeletal pain, nasopharyngitis, headache, back pain, and diarrhea. All the adverse events were mild or moderate in severity. There were no serious adverse events or discontinuations due to adverse events. There was one grade 3 elevation in the γ-glutamyltransferase level, which was considered by the investigator to be related to statin therapy. In the single-dose phase, inclisiran doses of 300 mg or more reduced the PCSK9 level (up to a least-squares mean reduction of 74.5% from baseline to day 84), and doses of 100 mg or more reduced the LDL cholesterol level (up to a least-squares mean reduction of 50.6% from baseline). Reductions in the levels of PCSK9 and LDL cholesterol were maintained at day 180 for doses of 300 mg or more. All multiple-dose regimens reduced the levels of PCSK9 (up to a least-squares mean reduction of 83.8% from baseline to day 84) and LDL cholesterol (up to a least-squares mean reduction of 59.7% from baseline to day 84). CONCLUSIONS In this phase 1 trial, no serious adverse events were observed with inclisiran. Doses of 300 mg or more (in single or multiple doses) significantly reduced levels of PCSK9 and LDL cholesterol for at least 6 months. (Funded by Alnylam Pharmaceuticals and the Medicines Company; ClinicalTrials.gov number, NCT02314442.) PMID:27959715

Road traffic accidents prediction modelling: An analysis of Anambra State, Nigeria.

PubMed

Ihueze, Chukwutoo C; Onwurah, Uchendu O

2018-03-01

One of the major problems in the world today is the rate of road traffic crashes and deaths on our roads. Majority of these deaths occur in low-and-middle income countries including Nigeria. This study analyzed road traffic crashes in Anambra State, Nigeria with the intention of developing accurate predictive models for forecasting crash frequency in the State using autoregressive integrated moving average (ARIMA) and autoregressive integrated moving average with explanatory variables (ARIMAX) modelling techniques. The result showed that ARIMAX model outperformed the ARIMA (1,1,1) model generated when their performances were compared using the lower Bayesian information criterion, mean absolute percentage error, root mean square error; and higher coefficient of determination (R-Squared) as accuracy measures. The findings of this study reveal that incorporating human, vehicle and environmental related factors in time series analysis of crash dataset produces a more robust predictive model than solely using aggregated crash count. This study contributes to the body of knowledge on road traffic safety and provides an approach to forecasting using many human, vehicle and environmental factors. The recommendations made in this study if applied will help in reducing the number of road traffic crashes in Nigeria. Copyright © 2017 Elsevier Ltd. All rights reserved.

A new luminous blue variable - R143 in 30 Doradus

NASA Technical Reports Server (NTRS)

Parker, Joel WM.; Clayton, Geoffrey C.; Winge, Claudia; Conti, Peter S.

1993-01-01

We have discovered that R143 in the Large Magellanic Cloud is a luminous blue variable (LBV), the first and perhaps the lone LBV in the central cluster of 30 Doradus, and only the sixth known LMC LBV. Photometric and spectroscopic observations over the past 40 yr indicate that during that time R143 moved redward (changing from an F5 to F8 supergiant), then blueward (possibly becoming as early as O9.5), and is now moving back to the red (currently appearing as a late B supergiant). Similarly, the V magnitude of the star has changed by at least 1.4 mag. Images of R143 show very unusual filaments of nebulosity extending from the star to a shell at a distance of 3.5 pc, perhaps due to a similar ejection mechanism that created the spiral jets and shell associated with AG Car, another LBV.

Least Square Approach for Estimating of Land Surface Temperature from LANDSAT-8 Satellite Data Using Radiative Transfer Equation

NASA Astrophysics Data System (ADS)

Jouybari-Moghaddam, Y.; Saradjian, M. R.; Forati, A. M.

2017-09-01

Land Surface Temperature (LST) is one of the significant variables measured by remotely sensed data, and it is applied in many environmental and Geoscience studies. The main aim of this study is to develop an algorithm to retrieve the LST from Landsat-8 satellite data using Radiative Transfer Equation (RTE). However, LST can be retrieved from RTE, but, since the RTE has two unknown parameters including LST and surface emissivity, estimating LST from RTE is an under the determined problem. In this study, in order to solve this problem, an approach is proposed an equation set includes two RTE based on Landsat-8 thermal bands (i.e.: band 10 and 11) and two additional equations based on the relation between the Normalized Difference Vegetation Index (NDVI) and emissivity of Landsat-8 thermal bands by using simulated data for Landsat-8 bands. The iterative least square approach was used for solving the equation set. The LST derived from proposed algorithm is evaluated by the simulated dataset, built up by MODTRAN. The result shows the Root Mean Squared Error (RMSE) is less than 1.18°K. Therefore; the proposed algorithm can be a suitable and robust method to retrieve the LST from Landsat-8 satellite data.

Total anthocyanin content determination in intact açaí (Euterpe oleracea Mart.) and palmitero-juçara (Euterpe edulis Mart.) fruit using near infrared spectroscopy (NIR) and multivariate calibration.

PubMed

Inácio, Maria Raquel Cavalcanti; de Lima, Kássio Michell Gomes; Lopes, Valquiria Garcia; Pessoa, José Dalton Cruz; de Almeida Teixeira, Gustavo Henrique

2013-02-15

The aim of this study was to evaluate near-infrared reflectance spectroscopy (NIR), and multivariate calibration potential as a rapid method to determinate anthocyanin content in intact fruit (açaí and palmitero-juçara). Several multivariate calibration techniques, including partial least squares (PLS), interval partial least squares, genetic algorithm, successive projections algorithm, and net analyte signal were compared and validated by establishing figures of merit. Suitable results were obtained with the PLS model (four latent variables and 5-point smoothing) with a detection limit of 6.2 g kg(-1), limit of quantification of 20.7 g kg(-1), accuracy estimated as root mean square error of prediction of 4.8 g kg(-1), mean selectivity of 0.79 g kg(-1), sensitivity of 5.04×10(-3) g kg(-1), precision of 27.8 g kg(-1), and signal-to-noise ratio of 1.04×10(-3) g kg(-1). These results suggest NIR spectroscopy and multivariate calibration can be effectively used to determine anthocyanin content in intact açaí and palmitero-juçara fruit. Copyright © 2012 Elsevier Ltd. All rights reserved.

Simultaneous determination of vitamin B12 and its derivatives using some of multivariate calibration 1 (MVC1) techniques

NASA Astrophysics Data System (ADS)

Samadi-Maybodi, Abdolraouf; Darzi, S. K. Hassani Nejad

2008-10-01

Resolution of binary mixtures of vitamin B12, methylcobalamin and B12 coenzyme with minimum sample pre-treatment and without analyte separation has been successfully achieved by methods of partial least squares algorithm with one dependent variable (PLS1), orthogonal signal correction/partial least squares (OSC/PLS), principal component regression (PCR) and hybrid linear analysis (HLA). Data of analysis were obtained from UV-vis spectra. The UV-vis spectra of the vitamin B12, methylcobalamin and B12 coenzyme were recorded in the same spectral conditions. The method of central composite design was used in the ranges of 10-80 mg L -1 for vitamin B12 and methylcobalamin and 20-130 mg L -1 for B12 coenzyme. The models refinement procedure and validation were performed by cross-validation. The minimum root mean square error of prediction (RMSEP) was 2.26 mg L -1 for vitamin B12 with PLS1, 1.33 mg L -1 for methylcobalamin with OSC/PLS and 3.24 mg L -1 for B12 coenzyme with HLA techniques. Figures of merit such as selectivity, sensitivity, analytical sensitivity and LOD were determined for three compounds. The procedure was successfully applied to simultaneous determination of three compounds in synthetic mixtures and in a pharmaceutical formulation.

Variable complexity online sequential extreme learning machine, with applications to streamflow prediction

NASA Astrophysics Data System (ADS)

Lima, Aranildo R.; Hsieh, William W.; Cannon, Alex J.

2017-12-01

In situations where new data arrive continually, online learning algorithms are computationally much less costly than batch learning ones in maintaining the model up-to-date. The extreme learning machine (ELM), a single hidden layer artificial neural network with random weights in the hidden layer, is solved by linear least squares, and has an online learning version, the online sequential ELM (OSELM). As more data become available during online learning, information on the longer time scale becomes available, so ideally the model complexity should be allowed to change, but the number of hidden nodes (HN) remains fixed in OSELM. A variable complexity VC-OSELM algorithm is proposed to dynamically add or remove HN in the OSELM, allowing the model complexity to vary automatically as online learning proceeds. The performance of VC-OSELM was compared with OSELM in daily streamflow predictions at two hydrological stations in British Columbia, Canada, with VC-OSELM significantly outperforming OSELM in mean absolute error, root mean squared error and Nash-Sutcliffe efficiency at both stations.

Speckle noise removal applied to ultrasound image of carotid artery based on total least squares model.

PubMed

Yang, Lei; Lu, Jun; Dai, Ming; Ren, Li-Jie; Liu, Wei-Zong; Li, Zhen-Zhou; Gong, Xue-Hao

2016-10-06

An ultrasonic image speckle noise removal method by using total least squares model is proposed and applied onto images of cardiovascular structures such as the carotid artery. On the basis of the least squares principle, the related principle of minimum square method is applied to cardiac ultrasound image speckle noise removal process to establish the model of total least squares, orthogonal projection transformation processing is utilized for the output of the model, and the denoising processing for the cardiac ultrasound image speckle noise is realized. Experimental results show that the improved algorithm can greatly improve the resolution of the image, and meet the needs of clinical medical diagnosis and treatment of the cardiovascular system for the head and neck. Furthermore, the success in imaging of carotid arteries has strong implications in neurological complications such as stroke.

Bayesian regression models outperform partial least squares methods for predicting milk components and technological properties using infrared spectral data.

PubMed

Ferragina, A; de los Campos, G; Vazquez, A I; Cecchinato, A; Bittante, G

2015-11-01

The aim of this study was to assess the performance of Bayesian models commonly used for genomic selection to predict "difficult-to-predict" dairy traits, such as milk fatty acid (FA) expressed as percentage of total fatty acids, and technological properties, such as fresh cheese yield and protein recovery, using Fourier-transform infrared (FTIR) spectral data. Our main hypothesis was that Bayesian models that can estimate shrinkage and perform variable selection may improve our ability to predict FA traits and technological traits above and beyond what can be achieved using the current calibration models (e.g., partial least squares, PLS). To this end, we assessed a series of Bayesian methods and compared their prediction performance with that of PLS. The comparison between models was done using the same sets of data (i.e., same samples, same variability, same spectral treatment) for each trait. Data consisted of 1,264 individual milk samples collected from Brown Swiss cows for which gas chromatographic FA composition, milk coagulation properties, and cheese-yield traits were available. For each sample, 2 spectra in the infrared region from 5,011 to 925 cm(-1) were available and averaged before data analysis. Three Bayesian models: Bayesian ridge regression (Bayes RR), Bayes A, and Bayes B, and 2 reference models: PLS and modified PLS (MPLS) procedures, were used to calibrate equations for each of the traits. The Bayesian models used were implemented in the R package BGLR (http://cran.r-project.org/web/packages/BGLR/index.html), whereas the PLS and MPLS were those implemented in the WinISI II software (Infrasoft International LLC, State College, PA). Prediction accuracy was estimated for each trait and model using 25 replicates of a training-testing validation procedure. Compared with PLS, which is currently the most widely used calibration method, MPLS and the 3 Bayesian methods showed significantly greater prediction accuracy. Accuracy increased in moving from calibration to external validation methods, and in moving from PLS and MPLS to Bayesian methods, particularly Bayes A and Bayes B. The maximum R(2) value of validation was obtained with Bayes B and Bayes A. For the FA, C10:0 (% of each FA on total FA basis) had the highest R(2) (0.75, achieved with Bayes A and Bayes B), and among the technological traits, fresh cheese yield R(2) of 0.82 (achieved with Bayes B). These 2 methods have proven to be useful instruments in shrinking and selecting very informative wavelengths and inferring the structure and functions of the analyzed traits. We conclude that Bayesian models are powerful tools for deriving calibration equations, and, importantly, these equations can be easily developed using existing open-source software. As part of our study, we provide scripts based on the open source R software BGLR, which can be used to train customized prediction equations for other traits or populations. Copyright © 2015 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

On the accuracy of least squares methods in the presence of corner singularities

NASA Technical Reports Server (NTRS)

Cox, C. L.; Fix, G. J.

1985-01-01

Elliptic problems with corner singularities are discussed. Finite element approximations based on variational principles of the least squares type tend to display poor convergence properties in such contexts. Moreover, mesh refinement or the use of special singular elements do not appreciably improve matters. It is shown that if the least squares formulation is done in appropriately weighted space, then optimal convergence results in unweighted spaces like L(2).

Avoiding Communication in the Lanczos Bidiagonalization Routine and Associated Least Squares QR Solver

DTIC Science & Technology

2015-04-12

Avoiding communication in the Lanczos bidiagonalization routine and associated Least Squares QR solver Erin Carson Electrical Engineering and...Bidiagonalization Routine and Associated Least Squares QR Solver 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d...throughout scienti c codes , are often the bottlenecks in application perfor- mance due to a low computation/communication ratio. In this paper we develop

Speckle evolution with multiple steps of least-squares phase removal

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

Chen Mingzhou; Dainty, Chris; Roux, Filippus S.

2011-08-15

We study numerically the evolution of speckle fields due to the annihilation of optical vortices after the least-squares phase has been removed. A process with multiple steps of least-squares phase removal is carried out to minimize both vortex density and scintillation index. Statistical results show that almost all the optical vortices can be removed from a speckle field, which finally decays into a quasiplane wave after such an iterative process.

Use of inequality constrained least squares estimation in small area estimation

NASA Astrophysics Data System (ADS)

Abeygunawardana, R. A. B.; Wickremasinghe, W. N.

2017-05-01

Traditional surveys provide estimates that are based only on the sample observations collected for the population characteristic of interest. However, these estimates may have unacceptably large variance for certain domains. Small Area Estimation (SAE) deals with determining precise and accurate estimates for population characteristics of interest for such domains. SAE usually uses least squares or maximum likelihood procedures incorporating prior information and current survey data. Many available methods in SAE use constraints in equality form. However there are practical situations where certain inequality restrictions on model parameters are more realistic. It will lead to Inequality Constrained Least Squares (ICLS) estimates if the method used is least squares. In this study ICLS estimation procedure is applied to many proposed small area estimates.

On the nullspace of TLS multi-station adjustment

NASA Astrophysics Data System (ADS)

Sterle, Oskar; Kogoj, Dušan; Stopar, Bojan; Kregar, Klemen

2018-07-01

In the article we present an analytic aspect of TLS multi-station least-squares adjustment with the main focus on the datum problem. The datum problem is, compared to previously published researches, theoretically analyzed and solved, where the solution is based on nullspace derivation of the mathematical model. The importance of datum problem solution is seen in a complete description of TLS multi-station adjustment solutions from a set of all minimally constrained least-squares solutions. On a basis of known nullspace, estimable parameters are described and the geometric interpretation of all minimally constrained least squares solutions is presented. At the end a simulated example is used to analyze the results of TLS multi-station minimally constrained and inner constrained least-squares adjustment solutions.

School and Neighborhood Predictors of Physical Fitness in Elementary School Students.

PubMed

Kahan, David; McKenzie, Thomas L

2017-06-01

We assessed the associations of 5 school and 7 neighborhood variables with fifth-grade students achieving Healthy Fitness Zone (HFZ) or Needs Improvement-Health Risk (NI-HR) on aerobic capacity (AC) and body composition (BC) physical fitness components of the state-mandated FITNESSGRAM ® physical fitness test. Data for outcome (physical fitness) and predictor (school and neighborhood) variables were extracted from various databases (eg, Data Quest, Walk Score ® ) for 160 schools located in San Diego, California. Predictor variables that were at least moderately correlated (|r| ≥ .30) with ≥1 outcome variables in univariate analyses were retained for ordinary least squares regression analyses. The mean percentages of students achieving HFZ AC (65.7%) and BC (63.5%) were similar (t = 1.13, p = .26), while those for NI-HR zones were significantly different (AC = 6.0% vs BC = 18.6%; t = 12.60, p < .001). Correlations were greater in magnitude for school than neighborhood demographics and stronger for BC than AC. The school variables free/reduced-price lunch (negative) and math achievement (positive) predicted fitness scores. Among neighborhood variables, percent Hispanic predicted failure of meeting the HFZ BC criterion. Creating school and neighborhood environments conducive to promoting physical activity and improving fitness is warranted. © 2017, American School Health Association.

Vision System Measures Motions of Robot and External Objects

NASA Technical Reports Server (NTRS)

Talukder, Ashit; Matthies, Larry

2008-01-01

A prototype of an advanced robotic vision system both (1) measures its own motion with respect to a stationary background and (2) detects other moving objects and estimates their motions, all by use of visual cues. Like some prior robotic and other optoelectronic vision systems, this system is based partly on concepts of optical flow and visual odometry. Whereas prior optoelectronic visual-odometry systems have been limited to frame rates of no more than 1 Hz, a visual-odometry subsystem that is part of this system operates at a frame rate of 60 to 200 Hz, given optical-flow estimates. The overall system operates at an effective frame rate of 12 Hz. Moreover, unlike prior machine-vision systems for detecting motions of external objects, this system need not remain stationary: it can detect such motions while it is moving (even vibrating). The system includes a stereoscopic pair of cameras mounted on a moving robot. The outputs of the cameras are digitized, then processed to extract positions and velocities. The initial image-data-processing functions of this system are the same as those of some prior systems: Stereoscopy is used to compute three-dimensional (3D) positions for all pixels in the camera images. For each pixel of each image, optical flow between successive image frames is used to compute the two-dimensional (2D) apparent relative translational motion of the point transverse to the line of sight of the camera. The challenge in designing this system was to provide for utilization of the 3D information from stereoscopy in conjunction with the 2D information from optical flow to distinguish between motion of the camera pair and motions of external objects, compute the motion of the camera pair in all six degrees of translational and rotational freedom, and robustly estimate the motions of external objects, all in real time. To meet this challenge, the system is designed to perform the following image-data-processing functions: The visual-odometry subsystem (the subsystem that estimates the motion of the camera pair relative to the stationary background) utilizes the 3D information from stereoscopy and the 2D information from optical flow. It computes the relationship between the 3D and 2D motions and uses a least-mean-squares technique to estimate motion parameters. The least-mean-squares technique is suitable for real-time implementation when the number of external-moving-object pixels is smaller than the number of stationary-background pixels.

Welfare analysis of a zero-smoking policy - A case study in Japan.

PubMed

Nakamura, Yuuki; Takahashi, Kenzo; Nomura, Marika; Kamei, Miwako

2018-03-19

Smoking cessation efforts in Japan reduce smoking rates. A future zero-smoking policy would completely prohibit smoking (0% rate). We therefore analyzed the social welfare of smokers and non-smokers under a hypothetical zero-smoking policy. The demand curve for smoking from 1990 to 2014 was estimated by defining quantity as the number of cigarettes smoked and price as total tobacco sales/total cigarettes smoked by the two-stage least squares method using the tax on tobacco as the instrumental variable. In the estimation equation (calculated using the ordinary least squares method), the price of tobacco was the dependent variable and tobacco quantity the explanatory variable. The estimated constant was 31.90, the estimated coefficient of quantity was - 0.0061 (both, p < 0.0004), and the determinant coefficient was 0.9187. Thus, the 2015 consumer surplus was 1.08 trillion yen (US$ 9.82 billion) (95% confidence interval (CI), 889 billion yen (US$ 8.08 billion) - 1.27 trillion yen (US$ 11.6 billion)). Because tax revenue from tobacco in 2011 was 2.38 trillion yen (US$ 21.6 billion), the estimated deadweight loss if smoking were prohibited in 2014 was 3.31 trillion yen (US$ 30.2 billion) (95% CI, 3.13 trillion yen (US$ 28.5 billion) - 3.50 trillion yen (US$ 31.8 billion)), representing a deadweight loss about 0.6 trillion yen (US$ 5.45 billion) below the 2014 disease burden (4.10-4.12 trillion yen (US$ 37.3-37.5 billion)). We conclude that a zero-smoking policy would improve social welfare in Japan.

[The research on separating and extracting overlapping spectral feature lines in LIBS using damped least squares method].

PubMed

Wang, Yin; Zhao, Nan-jing; Liu, Wen-qing; Yu, Yang; Fang, Li; Meng, De-shuo; Hu, Li; Zhang, Da-hai; Ma, Min-jun; Xiao, Xue; Wang, Yu; Liu, Jian-guo

2015-02-01

In recent years, the technology of laser induced breakdown spectroscopy has been developed rapidly. As one kind of new material composition detection technology, laser induced breakdown spectroscopy can simultaneously detect multi elements fast and simply without any complex sample preparation and realize field, in-situ material composition detection of the sample to be tested. This kind of technology is very promising in many fields. It is very important to separate, fit and extract spectral feature lines in laser induced breakdown spectroscopy, which is the cornerstone of spectral feature recognition and subsequent elements concentrations inversion research. In order to realize effective separation, fitting and extraction of spectral feature lines in laser induced breakdown spectroscopy, the original parameters for spectral lines fitting before iteration were analyzed and determined. The spectral feature line of' chromium (Cr I : 427.480 nm) in fly ash gathered from a coal-fired power station, which was overlapped with another line(FeI: 427.176 nm), was separated from the other one and extracted by using damped least squares method. Based on Gauss-Newton iteration, damped least squares method adds damping factor to step and adjust step length dynamically according to the feedback information after each iteration, in order to prevent the iteration from diverging and make sure that the iteration could converge fast. Damped least squares method helps to obtain better results of separating, fitting and extracting spectral feature lines and give more accurate intensity values of these spectral feature lines: The spectral feature lines of chromium in samples which contain different concentrations of chromium were separated and extracted. And then, the intensity values of corresponding spectral lines were given by using damped least squares method and least squares method separately. The calibration curves were plotted, which showed the relationship between spectral line intensity values and chromium concentrations in different samples. And then their respective linear correlations were compared. The experimental results showed that the linear correlation of the intensity values of spectral feature lines and the concentrations of chromium in different samples, which was obtained by damped least squares method, was better than that one obtained by least squares method. And therefore, damped least squares method was stable, reliable and suitable for separating, fitting and extracting spectral feature lines in laser induced breakdown spectroscopy.

Wind Tunnel Strain-Gage Balance Calibration Data Analysis Using a Weighted Least Squares Approach

NASA Technical Reports Server (NTRS)

Ulbrich, N.; Volden, T.

2017-01-01

A new approach is presented that uses a weighted least squares fit to analyze wind tunnel strain-gage balance calibration data. The weighted least squares fit is specifically designed to increase the influence of single-component loadings during the regression analysis. The weighted least squares fit also reduces the impact of calibration load schedule asymmetries on the predicted primary sensitivities of the balance gages. A weighting factor between zero and one is assigned to each calibration data point that depends on a simple count of its intentionally loaded load components or gages. The greater the number of a data point's intentionally loaded load components or gages is, the smaller its weighting factor becomes. The proposed approach is applicable to both the Iterative and Non-Iterative Methods that are used for the analysis of strain-gage balance calibration data in the aerospace testing community. The Iterative Method uses a reasonable estimate of the tare corrected load set as input for the determination of the weighting factors. The Non-Iterative Method, on the other hand, uses gage output differences relative to the natural zeros as input for the determination of the weighting factors. Machine calibration data of a six-component force balance is used to illustrate benefits of the proposed weighted least squares fit. In addition, a detailed derivation of the PRESS residuals associated with a weighted least squares fit is given in the appendices of the paper as this information could not be found in the literature. These PRESS residuals may be needed to evaluate the predictive capabilities of the final regression models that result from a weighted least squares fit of the balance calibration data.

How to deal with the high condition number of the noise covariance matrix of gravity field functionals synthesised from a satellite-only global gravity field model?

NASA Astrophysics Data System (ADS)

Klees, R.; Slobbe, D. C.; Farahani, H. H.

2018-03-01

The posed question arises for instance in regional gravity field modelling using weighted least-squares techniques if the gravity field functionals are synthesised from the spherical harmonic coefficients of a satellite-only global gravity model (GGM), and are used as one of the noisy datasets. The associated noise covariance matrix, appeared to be extremely ill-conditioned with a singular value spectrum that decayed gradually to zero without any noticeable gap. We analysed three methods to deal with the ill-conditioned noise covariance matrix: Tihonov regularisation of the noise covariance matrix in combination with the standard formula for the weighted least-squares estimator, a formula of the weighted least-squares estimator, which does not involve the inverse noise covariance matrix, and an estimator based on Rao's unified theory of least-squares. Our analysis was based on a numerical experiment involving a set of height anomalies synthesised from the GGM GOCO05s, which is provided with a full noise covariance matrix. We showed that the three estimators perform similar, provided that the two regularisation parameters each method knows were chosen properly. As standard regularisation parameter choice rules do not apply here, we suggested a new parameter choice rule, and demonstrated its performance. Using this rule, we found that the differences between the three least-squares estimates were within noise. For the standard formulation of the weighted least-squares estimator with regularised noise covariance matrix, this required an exceptionally strong regularisation, much larger than one expected from the condition number of the noise covariance matrix. The preferred method is the inversion-free formulation of the weighted least-squares estimator, because of its simplicity with respect to the choice of the two regularisation parameters.

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

PubMed

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

2013-06-05

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

Tropical Cyclone Wind Threat for the Bay of Bengal.

DTIC Science & Technology

1979-10-01

7 vn PROcIASILIT:T.S OF Ev=’j’S WI4t4 :40S ’.z"mS 24RS 1WS 4444S ’OtjqS or 0ADO’JESS + . STTK WTI ; LEAT N.K T r.l~ *331 .1% .01 .01 .440 00 AT LE ...the - LEAST SQUARES ViAND LINE a.variability in initial position error or more specifically LIN reconnaissance support. The first component of the

Jig-Shape Optimization of a Low-Boom Supersonic Aircraft

NASA Technical Reports Server (NTRS)

Pak, Chan-gi

2018-01-01

A simple approach for optimizing the jig-shape is proposed in this study. This simple approach is based on an unconstrained optimization problem and applied to a low-boom supersonic aircraft. In this study, the jig-shape optimization is performed using the two-step approach. First, starting design variables are computed using the least squares surface fitting technique. Next, the jig-shape is further tuned using a numerical optimization procedure based on in-house object-oriented optimization tool.

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.

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

ERIC Educational Resources Information Center

Coskuntuncel, Orkun

2013-01-01

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

Simplified Least Squares Shadowing sensitivity analysis for chaotic ODEs and PDEs

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

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

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

Weather variability and the incidence of cryptosporidiosis: comparison of time series poisson regression and SARIMA models.

PubMed

Hu, Wenbiao; Tong, Shilu; Mengersen, Kerrie; Connell, Des

2007-09-01

Few studies have examined the relationship between weather variables and cryptosporidiosis in Australia. This paper examines the potential impact of weather variability on the transmission of cryptosporidiosis and explores the possibility of developing an empirical forecast system. Data on weather variables, notified cryptosporidiosis cases, and population size in Brisbane were supplied by the Australian Bureau of Meteorology, Queensland Department of Health, and Australian Bureau of Statistics for the period of January 1, 1996-December 31, 2004, respectively. Time series Poisson regression and seasonal auto-regression integrated moving average (SARIMA) models were performed to examine the potential impact of weather variability on the transmission of cryptosporidiosis. Both the time series Poisson regression and SARIMA models show that seasonal and monthly maximum temperature at a prior moving average of 1 and 3 months were significantly associated with cryptosporidiosis disease. It suggests that there may be 50 more cases a year for an increase of 1 degrees C maximum temperature on average in Brisbane. Model assessments indicated that the SARIMA model had better predictive ability than the Poisson regression model (SARIMA: root mean square error (RMSE): 0.40, Akaike information criterion (AIC): -12.53; Poisson regression: RMSE: 0.54, AIC: -2.84). Furthermore, the analysis of residuals shows that the time series Poisson regression appeared to violate a modeling assumption, in that residual autocorrelation persisted. The results of this study suggest that weather variability (particularly maximum temperature) may have played a significant role in the transmission of cryptosporidiosis. A SARIMA model may be a better predictive model than a Poisson regression model in the assessment of the relationship between weather variability and the incidence of cryptosporidiosis.

Confounding by dietary patterns of the inverse association between alcohol consumption and type 2 diabetes risk.

PubMed

Imamura, Fumiaki; Lichtenstein, Alice H; Dallal, Gerard E; Meigs, James B; Jacques, Paul F

2009-07-01

The ability to interpret epidemiologic observations is limited because of potential residual confounding by correlated dietary components. Dietary pattern analyses by factor analysis or partial least squares may overcome the limitation. To examine confounding by dietary pattern as well as standard risk factors and selected nutrients, the authors modeled the longitudinal association between alcohol consumption and 7-year risk of type 2 diabetes mellitus in 2,879 healthy adults enrolled in the Framingham Offspring Study (1991-2001) by Cox proportional hazard models. After adjustment for standard risk factors, consumers of > or =9.0 drinks/week had a significantly lower risk of type 2 diabetes mellitus compared with abstainers (hazard ratio = 0.47, 95% confidence interval (CI): 0.27, 0.81). Adjustment for selected nutrients had little effect on the hazard ratio, whereas adjustment for dietary pattern variables by factor analysis significantly shifted the hazard ratio away from null (hazard ratio = 0.33, 95% CI: 0.17, 0.64) by 40.0% (95% CI: 16.8, 57.0; P = 0.002). Dietary pattern variables by partial least squares showed similar results. Therefore, the observed inverse association, consistent with past studies, was confounded by dietary patterns, and this confounding was not captured by individual nutrient adjustment. The data suggest that alcohol intake, not dietary patterns associated with alcohol intake, is responsible for the observed inverse association with type 2 diabetes mellitus risk.

Developing renal nurses' buttonhole cannulation skills using e-learning.

PubMed

Blackman, Ian R; Mannix, Trudi; Sinclair, Peter M

2014-03-01

It has previously been shown that nurses can learn clinical nursing skills by e-learning (online), and that many variables will influence how well nurses adopt learned clinical skills using distance education. This study aimed to identify and measure the strength of those factors which would simultaneously influence registered nurses' (RNs') beliefs about their own learning about buttonhole cannulation, using e-learning. An online Likert style survey consisting of a list of statements related to knowledge and skill domains considered crucial in the area of buttonhole cannulation was distributed to 101 RNs before and after completing an e-learning programme. Participants were required to identify their current level of self-confidence in relationship to each of the statements. Measures of RNs' self-rated abilities to assess and implement buttonhole cannulation after completing a related e-learning program were tested using a Partial Least Squares Analysis (PLS-PATH) programme. The study's results strongly identify that the nurses' ability to meet both clinical and educational outcomes of the renal e-learning module can be predicted by six variables, none of which are directly related to the participants' demographic or clinical backgrounds. These findings support the use of e-learning to teach clinical skills to RNs, and demonstrate the value of Partial Least Squares Analysis in determining influential learning factors. © 2014 European Dialysis and Transplant Nurses Association/European Renal Care Association.

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

PubMed

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

2016-07-01

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

Image interpolation via regularized local linear regression.

PubMed

Liu, Xianming; Zhao, Debin; Xiong, Ruiqin; Ma, Siwei; Gao, Wen; Sun, Huifang

2011-12-01

The linear regression model is a very attractive tool to design effective image interpolation schemes. Some regression-based image interpolation algorithms have been proposed in the literature, in which the objective functions are optimized by ordinary least squares (OLS). However, it is shown that interpolation with OLS may have some undesirable properties from a robustness point of view: even small amounts of outliers can dramatically affect the estimates. To address these issues, in this paper we propose a novel image interpolation algorithm based on regularized local linear regression (RLLR). Starting with the linear regression model where we replace the OLS error norm with the moving least squares (MLS) error norm leads to a robust estimator of local image structure. To keep the solution stable and avoid overfitting, we incorporate the l(2)-norm as the estimator complexity penalty. Moreover, motivated by recent progress on manifold-based semi-supervised learning, we explicitly consider the intrinsic manifold structure by making use of both measured and unmeasured data points. Specifically, our framework incorporates the geometric structure of the marginal probability distribution induced by unmeasured samples as an additional local smoothness preserving constraint. The optimal model parameters can be obtained with a closed-form solution by solving a convex optimization problem. Experimental results on benchmark test images demonstrate that the proposed method achieves very competitive performance with the state-of-the-art interpolation algorithms, especially in image edge structure preservation. © 2011 IEEE

Comparison of Five System Identification Algorithms for Rotorcraft Higher Harmonic Control

NASA Technical Reports Server (NTRS)

Jacklin, Stephen A.

1998-01-01

This report presents an analysis and performance comparison of five system identification algorithms. The methods are presented in the context of identifying a frequency-domain transfer matrix for the higher harmonic control (HHC) of helicopter vibration. The five system identification algorithms include three previously proposed methods: (1) the weighted-least- squares-error approach (in moving-block format), (2) the Kalman filter method, and (3) the least-mean-squares (LMS) filter method. In addition there are two new ones: (4) a generalized Kalman filter method and (5) a generalized LMS filter method. The generalized Kalman filter method and the generalized LMS filter method were derived as extensions of the classic methods to permit identification by using more than one measurement per identification cycle. Simulation results are presented for conditions ranging from the ideal case of a stationary transfer matrix and no measurement noise to the more complex cases involving both measurement noise and transfer-matrix variation. Both open-loop identification and closed- loop identification were simulated. Closed-loop mode identification was more challenging than open-loop identification because of the decreasing signal-to-noise ratio as the vibration became reduced. The closed-loop simulation considered both local-model identification, with measured vibration feedback and global-model identification with feedback of the identified uncontrolled vibration. The algorithms were evaluated in terms of their accuracy, stability, convergence properties, computation speeds, and relative ease of implementation.

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

PubMed

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

2016-03-01

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

Uncertainty based pressure reconstruction from velocity measurement with generalized least squares

NASA Astrophysics Data System (ADS)

Zhang, Jiacheng; Scalo, Carlo; Vlachos, Pavlos

2017-11-01

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

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

PubMed

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

2012-07-01

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

Least-squares model-based halftoning

NASA Astrophysics Data System (ADS)

Pappas, Thrasyvoulos N.; Neuhoff, David L.

1992-08-01

A least-squares model-based approach to digital halftoning is proposed. It exploits both a printer model and a model for visual perception. It attempts to produce an 'optimal' halftoned reproduction, by minimizing the squared error between the response of the cascade of the printer and visual models to the binary image and the response of the visual model to the original gray-scale image. Conventional methods, such as clustered ordered dither, use the properties of the eye only implicitly, and resist printer distortions at the expense of spatial and gray-scale resolution. In previous work we showed that our printer model can be used to modify error diffusion to account for printer distortions. The modified error diffusion algorithm has better spatial and gray-scale resolution than conventional techniques, but produces some well known artifacts and asymmetries because it does not make use of an explicit eye model. Least-squares model-based halftoning uses explicit eye models and relies on printer models that predict distortions and exploit them to increase, rather than decrease, both spatial and gray-scale resolution. We have shown that the one-dimensional least-squares problem, in which each row or column of the image is halftoned independently, can be implemented with the Viterbi's algorithm. Unfortunately, no closed form solution can be found in two dimensions. The two-dimensional least squares solution is obtained by iterative techniques. Experiments show that least-squares model-based halftoning produces more gray levels and better spatial resolution than conventional techniques. We also show that the least- squares approach eliminates the problems associated with error diffusion. Model-based halftoning can be especially useful in transmission of high quality documents using high fidelity gray-scale image encoders. As we have shown, in such cases halftoning can be performed at the receiver, just before printing. Apart from coding efficiency, this approach permits the halftoner to be tuned to the individual printer, whose characteristics may vary considerably from those of other printers, for example, write-black vs. write-white laser printers.

Least Squares Metric, Unidimensional Scaling of Multivariate Linear Models.

ERIC Educational Resources Information Center

Poole, Keith T.

1990-01-01

A general approach to least-squares unidimensional scaling is presented. Ordering information contained in the parameters is used to transform the standard squared error loss function into a discrete rather than continuous form. Monte Carlo tests with 38,094 ratings of 261 senators, and 1,258 representatives demonstrate the procedure's…

An Alternating Least Squares Method for the Weighted Approximation of a Symmetric Matrix.

ERIC Educational Resources Information Center

ten Berge, Jos M. F.; Kiers, Henk A. L.

1993-01-01

R. A. Bailey and J. C. Gower explored approximating a symmetric matrix "B" by another, "C," in the least squares sense when the squared discrepancies for diagonal elements receive specific nonunit weights. A solution is proposed where "C" is constrained to be positive semidefinite and of a fixed rank. (SLD)

Chemometrics comparison of gas chromatography with mass spectrometry and comprehensive two-dimensional gas chromatography with time-of-flight mass spectrometry Daphnia magna metabolic profiles exposed to salinity.

PubMed

Parastar, Hadi; Garreta-Lara, Elba; Campos, Bruno; Barata, Carlos; Lacorte, Silvia; Tauler, Roma

2018-06-01

The performances of gas chromatography with mass spectrometry and of comprehensive two-dimensional gas chromatography with time-of-flight mass spectrometry are examined through the comparison of Daphnia magna metabolic profiles. Gas chromatography with mass spectrometry and comprehensive two-dimensional gas chromatography with mass spectrometry were used to compare the concentration changes of metabolites under saline conditions. In this regard, a chemometric strategy based on wavelet compression and multivariate curve resolution-alternating least squares is used to compare the performances of gas chromatography with mass spectrometry and comprehensive two-dimensional gas chromatography with time-of-flight mass spectrometry for the untargeted metabolic profiling of Daphnia magna in control and salinity-exposed samples. Examination of the results confirmed the outperformance of comprehensive two-dimensional gas chromatography with time-of-flight mass spectrometry over gas chromatography with mass spectrometry for the detection of metabolites in D. magna samples. The peak areas of multivariate curve resolution-alternating least squares resolved elution profiles in every sample analyzed by comprehensive two-dimensional gas chromatography with time-of-flight mass spectrometry were arranged in a new data matrix that was then modeled by partial least squares discriminant analysis. The control and salt-exposed daphnids samples were discriminated and the most relevant metabolites were estimated using variable importance in projection and selectivity ratio values. Salinity de-regulated 18 metabolites from metabolic pathways involved in protein translation, transmembrane cell transport, carbon metabolism, secondary metabolism, glycolysis, and osmoregulation. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Gene features selection for three-class disease classification via multiple orthogonal partial least square discriminant analysis and S-plot using microarray data.

PubMed

Yang, Mingxing; Li, Xiumin; Li, Zhibin; Ou, Zhimin; Liu, Ming; Liu, Suhuan; Li, Xuejun; Yang, Shuyu

2013-01-01

DNA microarray analysis is characterized by obtaining a large number of gene variables from a small number of observations. Cluster analysis is widely used to analyze DNA microarray data to make classification and diagnosis of disease. Because there are so many irrelevant and insignificant genes in a dataset, a feature selection approach must be employed in data analysis. The performance of cluster analysis of this high-throughput data depends on whether the feature selection approach chooses the most relevant genes associated with disease classes. Here we proposed a new method using multiple Orthogonal Partial Least Squares-Discriminant Analysis (mOPLS-DA) models and S-plots to select the most relevant genes to conduct three-class disease classification and prediction. We tested our method using Golub's leukemia microarray data. For three classes with subtypes, we proposed hierarchical orthogonal partial least squares-discriminant analysis (OPLS-DA) models and S-plots to select features for two main classes and their subtypes. For three classes in parallel, we employed three OPLS-DA models and S-plots to choose marker genes for each class. The power of feature selection to classify and predict three-class disease was evaluated using cluster analysis. Further, the general performance of our method was tested using four public datasets and compared with those of four other feature selection methods. The results revealed that our method effectively selected the most relevant features for disease classification and prediction, and its performance was better than that of the other methods.

[Rapid determination of COD in aquaculture water based on LS-SVM with ultraviolet/visible spectroscopy].

PubMed

Liu, Xue-Mei; Zhang, Hai-Liang

2014-10-01

Ultraviolet/visible (UV/Vis) spectroscopy was studied for the rapid determination of chemical oxygen demand (COD), which was an indicator to measure the concentration of organic matter in aquaculture water. In order to reduce the influence of the absolute noises of the spectra, the extracted 135 absorbance spectra were preprocessed by Savitzky-Golay smoothing (SG), EMD, and wavelet transform (WT) methods. The preprocessed spectra were then used to select latent variables (LVs) by partial least squares (PLS) methods. Partial least squares (PLS) was used to build models with the full spectra, and back- propagation neural network (BPNN) and least square support vector machine (LS-SVM) were applied to build models with the selected LVs. The overall results showed that BPNN and LS-SVM models performed better than PLS models, and the LS-SVM models with LVs based on WT preprocessed spectra obtained the best results with the determination coefficient (r2) and RMSE being 0. 83 and 14. 78 mg · L(-1) for calibration set, and 0.82 and 14.82 mg · L(-1) for the prediction set respectively. The method showed the best performance in LS-SVM model. The results indicated that it was feasible to use UV/Vis with LVs which were obtained by PLS method, combined with LS-SVM calibration could be applied to the rapid and accurate determination of COD in aquaculture water. Moreover, this study laid the foundation for further implementation of online analysis of aquaculture water and rapid determination of other water quality parameters.

Analysis of Point Based Image Registration Errors With Applications in Single Molecule Microscopy

PubMed Central

Cohen, E. A. K.; Ober, R. J.

2014-01-01

We present an asymptotic treatment of errors involved in point-based image registration where control point (CP) localization is subject to heteroscedastic noise; a suitable model for image registration in fluorescence microscopy. Assuming an affine transform, CPs are used to solve a multivariate regression problem. With measurement errors existing for both sets of CPs this is an errors-in-variable problem and linear least squares is inappropriate; the correct method being generalized least squares. To allow for point dependent errors the equivalence of a generalized maximum likelihood and heteroscedastic generalized least squares model is achieved allowing previously published asymptotic results to be extended to image registration. For a particularly useful model of heteroscedastic noise where covariance matrices are scalar multiples of a known matrix (including the case where covariance matrices are multiples of the identity) we provide closed form solutions to estimators and derive their distribution. We consider the target registration error (TRE) and define a new measure called the localization registration error (LRE) believed to be useful, especially in microscopy registration experiments. Assuming Gaussianity of the CP localization errors, it is shown that the asymptotic distribution for the TRE and LRE are themselves Gaussian and the parameterized distributions are derived. Results are successfully applied to registration in single molecule microscopy to derive the key dependence of the TRE and LRE variance on the number of CPs and their associated photon counts. Simulations show asymptotic results are robust for low CP numbers and non-Gaussianity. The method presented here is shown to outperform GLS on real imaging data. PMID:24634573

Estimation of selected seasonal streamflow statistics representative of 1930-2002 in West Virginia

USGS Publications Warehouse

Wiley, Jeffrey B.; Atkins, John T.

2010-01-01

Regional equations and procedures were developed for estimating seasonal 1-day 10-year, 7-day 10-year, and 30-day 5-year hydrologically based low-flow frequency values for unregulated streams in West Virginia. Regional equations and procedures also were developed for estimating the seasonal U.S. Environmental Protection Agency harmonic-mean flows and the 50-percent flow-duration values. The seasons were defined as winter (January 1-March 31), spring (April 1-June 30), summer (July 1-September 30), and fall (October 1-December 31). Regional equations were developed using ordinary least squares regression using statistics from 117 U.S. Geological Survey continuous streamgage stations as dependent variables and basin characteristics as independent variables. Equations for three regions in West Virginia-North, South-Central, and Eastern Panhandle Regions-were determined. Drainage area, average annual precipitation, and longitude of the basin centroid are significant independent variables in one or more of the equations. The average standard error of estimates for the equations ranged from 12.6 to 299 percent. Procedures developed to estimate the selected seasonal streamflow statistics in this study are applicable only to rural, unregulated streams within the boundaries of West Virginia that have independent variables within the limits of the stations used to develop the regional equations: drainage area from 16.3 to 1,516 square miles in the North Region, from 2.78 to 1,619 square miles in the South-Central Region, and from 8.83 to 3,041 square miles in the Eastern Panhandle Region; average annual precipitation from 42.3 to 61.4 inches in the South-Central Region and from 39.8 to 52.9 inches in the Eastern Panhandle Region; and longitude of the basin centroid from 79.618 to 82.023 decimal degrees in the North Region. All estimates of seasonal streamflow statistics are representative of the period from the 1930 to the 2002 climatic year.

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

NASA Technical Reports Server (NTRS)

Alvarez, L. S.

1991-01-01

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

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

NASA Technical Reports Server (NTRS)

Chang, Ching L.; Jiang, Bo-Nan

1990-01-01

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

Superresolution restoration of an image sequence: adaptive filtering approach.

PubMed

Elad, M; Feuer, A

1999-01-01

This paper presents a new method based on adaptive filtering theory for superresolution restoration of continuous image sequences. The proposed methodology suggests least squares (LS) estimators which adapt in time, based on adaptive filters, least mean squares (LMS) or recursive least squares (RLS). The adaptation enables the treatment of linear space and time-variant blurring and arbitrary motion, both of them assumed known. The proposed new approach is shown to be of relatively low computational requirements. Simulations demonstrating the superresolution restoration algorithms are presented.

46 CFR 108.415 - Fire pump: General.

Code of Federal Regulations, 2013 CFR

2013-10-01

... have at least two independently driven fire pumps that can each deliver water at a continuous pitot tube pressure of at least 3.5 kilograms per square centimeter (approximately 50 pounds per square inch) at least two fire hose nozzles that are connected to the highest two fire hydrants on the unit...

46 CFR 108.415 - Fire pump: General.

Code of Federal Regulations, 2010 CFR

2010-10-01

... have at least two independently driven fire pumps that can each deliver water at a continuous pitot tube pressure of at least 3.5 kilograms per square centimeter (approximately 50 pounds per square inch) at least two fire hose nozzles that are connected to the highest two fire hydrants on the unit...

46 CFR 108.415 - Fire pump: General.

Code of Federal Regulations, 2012 CFR

2012-10-01

... have at least two independently driven fire pumps that can each deliver water at a continuous pitot tube pressure of at least 3.5 kilograms per square centimeter (approximately 50 pounds per square inch) at least two fire hose nozzles that are connected to the highest two fire hydrants on the unit...

46 CFR 108.415 - Fire pump: General.

Code of Federal Regulations, 2011 CFR

2011-10-01

... have at least two independently driven fire pumps that can each deliver water at a continuous pitot tube pressure of at least 3.5 kilograms per square centimeter (approximately 50 pounds per square inch) at least two fire hose nozzles that are connected to the highest two fire hydrants on the unit...

46 CFR 108.415 - Fire pump: General.

Code of Federal Regulations, 2014 CFR

2014-10-01

... have at least two independently driven fire pumps that can each deliver water at a continuous pitot tube pressure of at least 3.5 kilograms per square centimeter (approximately 50 pounds per square inch) at least two fire hose nozzles that are connected to the highest two fire hydrants on the unit...

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.

Flu and Finances: Influenza Outbreaks and Loan Defaults in US Cities, 2004–2012

PubMed Central

Collins, J. Michael; Schmeiser, Maximilian D.

2015-01-01

Objectives. We examined the association between influenza outbreaks in 83 metropolitan areas and credit card and mortgage defaults, as measured in quarterly zip code–level credit data over the period of 2004 to 2012. Methods. We used ordinary least squares, fixed effects, and 2-stage least squares instrumental variables regression strategies to examine the relationship between influenza-related Google searches and 30-, 60-, and 90-day credit card and mortgage delinquency rates. Results. We found that a proxy for influenza outbreaks is associated with a small but statistically significant increase in credit card and mortgage default rates, net of other factors. These effects are largest for 90-day defaults, suggesting that influenza outbreaks have a disproportionate impact on vulnerable borrowers who are already behind on their payments. Conclusions. Overall, it appears there is a relationship between exogenous health shocks (such as influenza) and credit default. The results suggest that consumer finances could benefit from policies that aim to reduce the financial shocks of illness, particularly for vulnerable borrowers. PMID:26180971

A Generic Nonlinear Aerodynamic Model for Aircraft

NASA Technical Reports Server (NTRS)

Grauer, Jared A.; Morelli, Eugene A.

2014-01-01

A generic model of the aerodynamic coefficients was developed using wind tunnel databases for eight different aircraft and multivariate orthogonal functions. For each database and each coefficient, models were determined using polynomials expanded about the state and control variables, and an othgonalization procedure. A predicted squared-error criterion was used to automatically select the model terms. Modeling terms picked in at least half of the analyses, which totalled 45 terms, were retained to form the generic nonlinear aerodynamic (GNA) model. Least squares was then used to estimate the model parameters and associated uncertainty that best fit the GNA model to each database. Nonlinear flight simulations were used to demonstrate that the GNA model produces accurate trim solutions, local behavior (modal frequencies and damping ratios), and global dynamic behavior (91% accurate state histories and 80% accurate aerodynamic coefficient histories) under large-amplitude excitation. This compact aerodynamics model can be used to decrease on-board memory storage requirements, quickly change conceptual aircraft models, provide smooth analytical functions for control and optimization applications, and facilitate real-time parametric system identification.

Multi-parameters monitoring during traditional Chinese medicine concentration process with near infrared spectroscopy and chemometrics

NASA Astrophysics Data System (ADS)

Liu, Ronghua; Sun, Qiaofeng; Hu, Tian; Li, Lian; Nie, Lei; Wang, Jiayue; Zhou, Wanhui; Zang, Hengchang

2018-03-01

As a powerful process analytical technology (PAT) tool, near infrared (NIR) spectroscopy has been widely used in real-time monitoring. In this study, NIR spectroscopy was applied to monitor multi-parameters of traditional Chinese medicine (TCM) Shenzhiling oral liquid during the concentration process to guarantee the quality of products. Five lab scale batches were employed to construct quantitative models to determine five chemical ingredients and physical change (samples density) during concentration process. The paeoniflorin, albiflorin, liquiritin and samples density were modeled by partial least square regression (PLSR), while the content of the glycyrrhizic acid and cinnamic acid were modeled by support vector machine regression (SVMR). Standard normal variate (SNV) and/or Savitzkye-Golay (SG) smoothing with derivative methods were adopted for spectra pretreatment. Variable selection methods including correlation coefficient (CC), competitive adaptive reweighted sampling (CARS) and interval partial least squares regression (iPLS) were performed for optimizing the models. The results indicated that NIR spectroscopy was an effective tool to successfully monitoring the concentration process of Shenzhiling oral liquid.

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

Liao, Haitao, E-mail: liaoht@cae.ac.cn

The direct differentiation and improved least squares shadowing methods are both developed for accurately and efficiently calculating the sensitivity coefficients of time averaged quantities for chaotic dynamical systems. The key idea is to recast the time averaged integration term in the form of differential equation before applying the sensitivity analysis method. An additional constraint-based equation which forms the augmented equations of motion is proposed to calculate the time averaged integration variable and the sensitivity coefficients are obtained as a result of solving the augmented differential equations. The application of the least squares shadowing formulation to the augmented equations results inmore » an explicit expression for the sensitivity coefficient which is dependent on the final state of the Lagrange multipliers. The LU factorization technique to calculate the Lagrange multipliers leads to a better performance for the convergence problem and the computational expense. Numerical experiments on a set of problems selected from the literature are presented to illustrate the developed methods. The numerical results demonstrate the correctness and effectiveness of the present approaches and some short impulsive sensitivity coefficients are observed by using the direct differentiation sensitivity analysis method.« 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.

Domain-Invariant Partial-Least-Squares Regression.

PubMed

Nikzad-Langerodi, Ramin; Zellinger, Werner; Lughofer, Edwin; Saminger-Platz, Susanne

2018-05-11

Multivariate calibration models often fail to extrapolate beyond the calibration samples because of changes associated with the instrumental response, environmental condition, or sample matrix. Most of the current methods used to adapt a source calibration model to a target domain exclusively apply to calibration transfer between similar analytical devices, while generic methods for calibration-model adaptation are largely missing. To fill this gap, we here introduce domain-invariant partial-least-squares (di-PLS) regression, which extends ordinary PLS by a domain regularizer in order to align the source and target distributions in the latent-variable space. We show that a domain-invariant weight vector can be derived in closed form, which allows the integration of (partially) labeled data from the source and target domains as well as entirely unlabeled data from the latter. We test our approach on a simulated data set where the aim is to desensitize a source calibration model to an unknown interfering agent in the target domain (i.e., unsupervised model adaptation). In addition, we demonstrate unsupervised, semisupervised, and supervised model adaptation by di-PLS on two real-world near-infrared (NIR) spectroscopic data sets.

Efficient sensitivity analysis method for chaotic dynamical systems

NASA Astrophysics Data System (ADS)

Liao, Haitao

2016-05-01

The direct differentiation and improved least squares shadowing methods are both developed for accurately and efficiently calculating the sensitivity coefficients of time averaged quantities for chaotic dynamical systems. The key idea is to recast the time averaged integration term in the form of differential equation before applying the sensitivity analysis method. An additional constraint-based equation which forms the augmented equations of motion is proposed to calculate the time averaged integration variable and the sensitivity coefficients are obtained as a result of solving the augmented differential equations. The application of the least squares shadowing formulation to the augmented equations results in an explicit expression for the sensitivity coefficient which is dependent on the final state of the Lagrange multipliers. The LU factorization technique to calculate the Lagrange multipliers leads to a better performance for the convergence problem and the computational expense. Numerical experiments on a set of problems selected from the literature are presented to illustrate the developed methods. The numerical results demonstrate the correctness and effectiveness of the present approaches and some short impulsive sensitivity coefficients are observed by using the direct differentiation sensitivity analysis method.

Acculturation and changes in body mass index, waist circumference, and waist-hip ratio among Filipino Americans with hypertension.

PubMed

Serafica, Reimund; Angosta, Alona D

2016-09-01

The purpose of this research study was to examine whether level of acculturation is a predictor of body mass index, waist circumference, and waist-hip ratio in Filipino Americans with hypertension in the United States. The Filipino Americans (N = 108) were recruited from a primary care clinic in the United States. Two instruments were used to collect and operationalize the variables, specifically: (1) Socioeconomic/Demographic Questionnaire and (2) A Short Acculturation Scale for Filipino Americans. Descriptive statistics and partial least squares were used to calculate the results. The partial least square path model identified acculturation as a predictor of body mass index, wait circumference, and waist-hip ratio among Filipino Americans. The positive path coefficient (β = 0.384) was statistically significant (t = 5.92, P < .001). Health care providers need to stress the importance of the degree of acculturation when developing culturally appropriate lifestyle and health promotion interventions among immigrant patients with hypertension. Copyright © 2016 American Society of Hypertension. Published by Elsevier Inc. All rights reserved.

Prediction of octanol-water partition coefficients of organic compounds by multiple linear regression, partial least squares, and artificial neural network.

PubMed

Golmohammadi, Hassan

2009-11-30

A quantitative structure-property relationship (QSPR) study was performed to develop models those relate the structure of 141 organic compounds to their octanol-water partition coefficients (log P(o/w)). A genetic algorithm was applied as a variable selection tool. Modeling of log P(o/w) of these compounds as a function of theoretically derived descriptors was established by multiple linear regression (MLR), partial least squares (PLS), and artificial neural network (ANN). The best selected descriptors that appear in the models are: atomic charge weighted partial positively charged surface area (PPSA-3), fractional atomic charge weighted partial positive surface area (FPSA-3), minimum atomic partial charge (Qmin), molecular volume (MV), total dipole moment of molecule (mu), maximum antibonding contribution of a molecule orbital in the molecule (MAC), and maximum free valency of a C atom in the molecule (MFV). The result obtained showed the ability of developed artificial neural network to prediction of partition coefficients of organic compounds. Also, the results revealed the superiority of ANN over the MLR and PLS models. Copyright 2009 Wiley Periodicals, Inc.

Methods and computer program documentation for determining anisotropic transmissivity tensor components of two-dimensional ground-water flow

USGS Publications Warehouse

Maslia, M.L.; Randolph, R.B.

1986-01-01

The theory of anisotropic aquifer hydraulic properties and a computer program, written in Fortran 77, developed to compute the components of the anisotropic transmissivity tensor of two-dimensional groundwater flow are described. To determine the tensor components using one pumping well and three observation wells, the type-curve and straight-line approximation methods are developed. These methods are based on the equation of drawdown developed for two-dimensional nonsteady flow in an infinite anisotropic aquifer. To determine tensor components using more than three observation wells, a weighted least squares optimization procedure is described for use with the type-curve and straight-line approximation methods. The computer program described in this report allows the type-curve, straight-line approximation, and weighted least squares optimization methods to be used in conjunction with data from observation and pumping wells. Three example applications using the computer program and field data gathered during geohydrologic investigations at a site near Dawsonville, Georgia , are provided to illustrate the use of the computer program. The example applications demonstrate the use of the type-curve method using three observation wells, the weighted least squares optimization method using eight observation wells and equal weighting, and the weighted least squares optimization method using eight observation wells and unequal weighting. Results obtained using the computer program indicate major transmissivity in the range of 347-296 sq ft/day, minor transmissivity in the range of 139-99 sq ft/day, aquifer anisotropy in the range of 3.54 to 2.14, principal direction of flow in the range of N. 45.9 degrees E. to N. 58.7 degrees E., and storage coefficient in the range of 0.0063 to 0.0037. The numerical results are in good agreement with field data gathered on the weathered crystalline rocks underlying the investigation site. Supplemental material provides definitions of variables, data requirements and corresponding formats, input data and output results for the example applications, and a listing of the Fortran 77 computer code. (Author 's abstract)

Statistical efficiency of adaptive algorithms.

PubMed

Widrow, Bernard; Kamenetsky, Max

2003-01-01

The statistical efficiency of a learning algorithm applied to the adaptation of a given set of variable weights is defined as the ratio of the quality of the converged solution to the amount of data used in training the weights. Statistical efficiency is computed by averaging over an ensemble of learning experiences. A high quality solution is very close to optimal, while a low quality solution corresponds to noisy weights and less than optimal performance. In this work, two gradient descent adaptive algorithms are compared, the LMS algorithm and the LMS/Newton algorithm. LMS is simple and practical, and is used in many applications worldwide. LMS/Newton is based on Newton's method and the LMS algorithm. LMS/Newton is optimal in the least squares sense. It maximizes the quality of its adaptive solution while minimizing the use of training data. Many least squares adaptive algorithms have been devised over the years, but no other least squares algorithm can give better performance, on average, than LMS/Newton. LMS is easily implemented, but LMS/Newton, although of great mathematical interest, cannot be implemented in most practical applications. Because of its optimality, LMS/Newton serves as a benchmark for all least squares adaptive algorithms. The performances of LMS and LMS/Newton are compared, and it is found that under many circumstances, both algorithms provide equal performance. For example, when both algorithms are tested with statistically nonstationary input signals, their average performances are equal. When adapting with stationary input signals and with random initial conditions, their respective learning times are on average equal. However, under worst-case initial conditions, the learning time of LMS can be much greater than that of LMS/Newton, and this is the principal disadvantage of the LMS algorithm. But the strong points of LMS are ease of implementation and optimal performance under important practical conditions. For these reasons, the LMS algorithm has enjoyed very widespread application. It is used in almost every modem for channel equalization and echo cancelling. Furthermore, it is related to the famous backpropagation algorithm used for training neural networks.

On-line algorithms for forecasting hourly loads of an electric utility

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

Vemuri, S.; Huang, W.L.; Nelson, D.J.

A method that lends itself to on-line forecasting of hourly electric loads is presented, and the results of its use are compared to models developed using the Box-Jenkins method. The method consits of processing the historical hourly loads with a sequential least-squares estimator to identify a finite-order autoregressive model which, in turn, is used to obtain a parsimonious autoregressive-moving average model. The method presented has several advantages in comparison with the Box-Jenkins method including much-less human intervention, improved model identification, and better results. The method is also more robust in that greater confidence can be placed in the accuracy ofmore » models based upon the various measures available at the identification stage.« less

Influence of the least-squares phase on optical vortices in strongly scintillated beams

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

Chen Mingzhou; Roux, Filippus S.; National Laser Centre, CSIR, P.O. Box 395, Pretoria 0001

2009-07-15

The optical vortices that exist in strongly scintillated beams make it difficult for conventional adaptive optics systems to remove the phase distortions. When the least-squares reconstructed phase is removed, the vortices still remain. However, we found that the removal of the least-squares phase induces a portion of the vortices to be annihilated during subsequent propagation, causing a reduction in the total number of vortices. This can be understood in terms of the restoration of equilibrium between explicit vortices, which are visible in the phase function, and vortex bound states, which are somehow encoded in the continuous phase fluctuations. Numerical simulationsmore » are provided to show that the total number of optical vortices in a strongly scintillated beam can be reduced significantly after a few steps of least-squares phase corrections.« less

An on-line modified least-mean-square algorithm for training neurofuzzy controllers.

PubMed

Tan, Woei Wan

2007-04-01

The problem hindering the use of data-driven modelling methods for training controllers on-line is the lack of control over the amount by which the plant is excited. As the operating schedule determines the information available on-line, the knowledge of the process may degrade if the setpoint remains constant for an extended period. This paper proposes an identification algorithm that alleviates "learning interference" by incorporating fuzzy theory into the normalized least-mean-square update rule. The ability of the proposed methodology to achieve faster learning is examined by employing the algorithm to train a neurofuzzy feedforward controller for controlling a liquid level process. Since the proposed identification strategy has similarities with the normalized least-mean-square update rule and the recursive least-square estimator, the on-line learning rates of these algorithms are also compared.

Multiway analysis methods applied to the fluorescence excitation-emission dataset for the simultaneous quantification of valsartan and amlodipine in tablets

NASA Astrophysics Data System (ADS)

Dinç, Erdal; Ertekin, Zehra Ceren; Büker, Eda

2017-09-01

In this study, excitation-emission matrix datasets, which have strong overlapping bands, were processed by using four different chemometric calibration algorithms consisting of parallel factor analysis, Tucker3, three-way partial least squares and unfolded partial least squares for the simultaneous quantitative estimation of valsartan and amlodipine besylate in tablets. In analyses, preliminary separation step was not used before the application of parallel factor analysis Tucker3, three-way partial least squares and unfolded partial least squares approaches for the analysis of the related drug substances in samples. Three-way excitation-emission matrix data array was obtained by concatenating excitation-emission matrices of the calibration set, validation set, and commercial tablet samples. The excitation-emission matrix data array was used to get parallel factor analysis, Tucker3, three-way partial least squares and unfolded partial least squares calibrations and to predict the amounts of valsartan and amlodipine besylate in samples. For all the methods, calibration and prediction of valsartan and amlodipine besylate were performed in the working concentration ranges of 0.25-4.50 μg/mL. The validity and the performance of all the proposed methods were checked by using the validation parameters. From the analysis results, it was concluded that the described two-way and three-way algorithmic methods were very useful for the simultaneous quantitative resolution and routine analysis of the related drug substances in marketed samples.

Sparse High Dimensional Models in Economics

PubMed Central

Fan, Jianqing; Lv, Jinchi; Qi, Lei

2010-01-01

This paper reviews the literature on sparse high dimensional models and discusses some applications in economics and finance. Recent developments of theory, methods, and implementations in penalized least squares and penalized likelihood methods are highlighted. These variable selection methods are proved to be effective in high dimensional sparse modeling. The limits of dimensionality that regularization methods can handle, the role of penalty functions, and their statistical properties are detailed. Some recent advances in ultra-high dimensional sparse modeling are also briefly discussed. PMID:22022635

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.

Chance Constrained Programming and Other Approaches to Risk in Strategic Management. Revision

DTIC Science & Technology

1989-02-01

reflected in ,0 ( Aaker and Jacobson, 1987). In the context of strategic management planning, however, there is another point to consider in that risk...least squares in the same spirit as Aaker and Jacobson (1987), and total risk was measured by the total variability of a security’s return. Lubatkin and...theory, Amihud and Lev (1981), and Eger (1983) in the finance literature, as well as the studies by Aaker and Jacobson (1987), and Lubatkin and O’Neill

Hierarchical cluster-based partial least squares regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models.

PubMed

Tøndel, Kristin; Indahl, Ulf G; Gjuvsland, Arne B; Vik, Jon Olav; Hunter, Peter; Omholt, Stig W; Martens, Harald

2011-06-01

Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. HC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems.

Hierarchical Cluster-based Partial Least Squares Regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models

PubMed Central

2011-01-01

Background Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Results Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. Conclusions HC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems. PMID:21627852

Inferential modeling and predictive feedback control in real-time motion compensation using the treatment couch during radiotherapy

NASA Astrophysics Data System (ADS)

Qiu, Peng; D'Souza, Warren D.; McAvoy, Thomas J.; Liu, K. J. Ray

2007-09-01

Tumor motion induced by respiration presents a challenge to the reliable delivery of conformal radiation treatments. Real-time motion compensation represents the technologically most challenging clinical solution but has the potential to overcome the limitations of existing methods. The performance of a real-time couch-based motion compensation system is mainly dependent on two aspects: the ability to infer the internal anatomical position and the performance of the feedback control system. In this paper, we propose two novel methods for the two aspects respectively, and then combine the proposed methods into one system. To accurately estimate the internal tumor position, we present partial-least squares (PLS) regression to predict the position of the diaphragm using skin-based motion surrogates. Four radio-opaque markers were placed on the abdomen of patients who underwent fluoroscopic imaging of the diaphragm. The coordinates of the markers served as input variables and the position of the diaphragm served as the output variable. PLS resulted in lower prediction errors compared with standard multiple linear regression (MLR). The performance of the feedback control system depends on the system dynamics and dead time (delay between the initiation and execution of the control action). While the dynamics of the system can be inverted in a feedback control system, the dead time cannot be inverted. To overcome the dead time of the system, we propose a predictive feedback control system by incorporating forward prediction using least-mean-square (LMS) and recursive least square (RLS) filtering into the couch-based control system. Motion data were obtained using a skin-based marker. The proposed predictive feedback control system was benchmarked against pure feedback control (no forward prediction) and resulted in a significant performance gain. Finally, we combined the PLS inference model and the predictive feedback control to evaluate the overall performance of the feedback control system. Our results show that, with the tumor motion unknown but inferred by skin-based markers through the PLS model, the predictive feedback control system was able to effectively compensate intra-fraction motion.

Monitoring the fetal heart rate variability during labor.

PubMed

Moslem, B; Mohydeen, A; Bazzi, O

2015-08-01

In respect to the main goal of our ongoing work for estimating the heart rate variability (HRV) from fetal electrocardiogram (FECG) signals for monitoring the health of the fetus, we investigate in this paper the possibility of extracting the fetal heart rate variability (HRV) directly from the abdominal composite recordings. Our proposed approach is based on a combination of two techniques: Periodic Component Analysis (PiCA) and recursive least square (RLS) adaptive filtering. The Fetal HRV of the estimated FECG signal is compared to a reference value extracted from an FECG signal recorded by using a spiral electrode attached directly to the fetal scalp. The results obtained show that the fetal HRV can be directly evaluated from the abdominal composite recordings without the need of recording an external reference signal.

Application of fluorescence spectroscopy for on-line bioprocess monitoring and control

NASA Astrophysics Data System (ADS)

Boehl, Daniela; Solle, D.; Toussaint, Hans J.; Menge, M.; Renemann, G.; Lindemann, Carsten; Hitzmann, Bernd; Scheper, Thomas-Helmut

2001-02-01

12 Modern bioprocess control requires fast data acquisition and in-time evaluation of bioprocess variables. On-line fluorescence spectroscopy for data acquisition and the use of chemometric methods accomplish these requirements. The presented investigations were performed with fluorescence spectrometers with wide ranges of excitation and emission wavelength. By detection of several biogenic fluorophors (amino acids, coenzymes and vitamins) a large amount of information about the state of the bioprocess are obtained. For the evaluation of the process variables partial least squares regression is used. This technique was applied to several bioprocesses: the production of ergotamine by Claviceps purpurea, the production of t-PA (tissue plasminogen activator) by animal cells and brewing processes. The main point of monitoring the brewing processes was to determine the process variables cell count and extract concentration.

Determination of total phenolic compounds in compost by infrared spectroscopy.

PubMed

Cascant, M M; Sisouane, M; Tahiri, S; Krati, M El; Cervera, M L; Garrigues, S; de la Guardia, M

2016-06-01

Middle and near infrared (MIR and NIR) were applied to determine the total phenolic compounds (TPC) content in compost samples based on models built by using partial least squares (PLS) regression. The multiplicative scatter correction, standard normal variate and first derivative were employed as spectra pretreatment, and the number of latent variable were optimized by leave-one-out cross-validation. The performance of PLS-ATR-MIR and PLS-DR-NIR models was evaluated according to root mean square error of cross validation and prediction (RMSECV and RMSEP), the coefficient of determination for prediction (Rpred(2)) and residual predictive deviation (RPD) being obtained for this latter values of 5.83 and 8.26 for MIR and NIR, respectively. Copyright © 2016 Elsevier B.V. All rights reserved.

Multiple hearth furnace for reducing iron oxide

DOEpatents

Brandon, Mark M [Charlotte, NC; True, Bradford G [Charlotte, NC

2012-03-13

A multiple moving hearth furnace (10) having a furnace housing (11) with at least two moving hearths (20) positioned laterally within the furnace housing, the hearths moving in opposite directions and each moving hearth (20) capable of being charged with at least one layer of iron oxide and carbon bearing material at one end, and being capable of discharging reduced material at the other end. A heat insulating partition (92) is positioned between adjacent moving hearths of at least portions of the conversion zones (13), and is capable of communicating gases between the atmospheres of the conversion zones of adjacent moving hearths. A drying/preheat zone (12), a conversion zone (13), and optionally a cooling zone (15) are sequentially positioned along each moving hearth (30) in the furnace housing (11).

Development of a non-destructive method for determining protein nitrogen in a yellow fever vaccine by near infrared spectroscopy and multivariate calibration.

PubMed

Dabkiewicz, Vanessa Emídio; de Mello Pereira Abrantes, Shirley; Cassella, Ricardo Jorgensen

2018-08-05

Near infrared spectroscopy (NIR) with diffuse reflectance associated to multivariate calibration has as main advantage the replacement of the physical separation of interferents by the mathematical separation of their signals, rapidly with no need for reagent consumption, chemical waste production or sample manipulation. Seeking to optimize quality control analyses, this spectroscopic analytical method was shown to be a viable alternative to the classical Kjeldahl method for the determination of protein nitrogen in yellow fever vaccine. The most suitable multivariate calibration was achieved by the partial least squares method (PLS) with multiplicative signal correction (MSC) treatment and data mean centering (MC), using a minimum number of latent variables (LV) equal to 1, with the lower value of the square root of the mean squared prediction error (0.00330) associated with the highest percentage value (91%) of samples. Accuracy ranged 95 to 105% recovery in the 4000-5184 cm -1 region. Copyright © 2018 Elsevier B.V. All rights reserved.

[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.

Advantages of soft versus hard constraints in self-modeling curve resolution problems. Penalty alternating least squares (P-ALS) extension to multi-way problems.

PubMed

Richards, Selena; Miller, Robert; Gemperline, Paul

2008-02-01

An extension to the penalty alternating least squares (P-ALS) method, called multi-way penalty alternating least squares (NWAY P-ALS), is presented. Optionally, hard constraints (no deviation from predefined constraints) or soft constraints (small deviations from predefined constraints) were applied through the application of a row-wise penalty least squares function. NWAY P-ALS was applied to the multi-batch near-infrared (NIR) data acquired from the base catalyzed esterification reaction of acetic anhydride in order to resolve the concentration and spectral profiles of l-butanol with the reaction constituents. Application of the NWAY P-ALS approach resulted in the reduction of the number of active constraints at the solution point, while the batch column-wise augmentation allowed hard constraints in the spectral profiles and resolved rank deficiency problems of the measurement matrix. The results were compared with the multi-way multivariate curve resolution (MCR)-ALS results using hard and soft constraints to determine whether any advantages had been gained through using the weighted least squares function of NWAY P-ALS over the MCR-ALS resolution.

Difficulty Factors, Distribution Effects, and the Least Squares Simplex Data Matrix Solution

ERIC Educational Resources Information Center

Ten Berge, Jos M. F.

1972-01-01

In the present article it is argued that the Least Squares Simplex Data Matrix Solution does not deal adequately with difficulty factors inasmuch as the theoretical foundation is insufficient. (Author/CB)

49 CFR 172.327 - Petroleum sour crude oil in bulk packaging.

Code of Federal Regulations, 2014 CFR

2014-10-01

... least 100 mm (3.9 inches). The width of the border forming the square-on-point marking must be at least... hydrogen sulfide vapors may occur. (b) The border of the square-on-point must be black or red on a white or other suitable contrasting background. The symbol must be black and located in the center of the square...

Validation of Core Temperature Estimation Algorithm

DTIC Science & Technology

2016-01-29

plot of observed versus estimated core temperature with the line of identity (dashed) and the least squares regression line (solid) and line equation...estimated PSI with the line of identity (dashed) and the least squares regression line (solid) and line equation in the top left corner. (b) Bland...for comparison. The root mean squared error (RMSE) was also computed, as given by Equation 2.

Eta Squared and Partial Eta Squared as Measures of Effect Size in Educational Research

ERIC Educational Resources Information Center

Richardson, John T. E.

2011-01-01

Eta squared measures the proportion of the total variance in a dependent variable that is associated with the membership of different groups defined by an independent variable. Partial eta squared is a similar measure in which the effects of other independent variables and interactions are partialled out. The development of these measures is…

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

The least-squares mixing models to generate fraction images derived from remote sensing multispectral data

NASA Technical Reports Server (NTRS)

Shimabukuro, Yosio Edemir; Smith, James A.

1991-01-01

Constrained-least-squares and weighted-least-squares mixing models for generating fraction images derived from remote sensing multispectral data are presented. An experiment considering three components within the pixels-eucalyptus, soil (understory), and shade-was performed. The generated fraction images for shade (shade image) derived from these two methods were compared by considering the performance and computer time. The derived shade images are related to the observed variation in forest structure, i.e., the fraction of inferred shade in the pixel is related to different eucalyptus ages.

A Kernel-based Lagrangian method for imperfectly-mixed chemical reactions

NASA Astrophysics Data System (ADS)

Schmidt, Michael J.; Pankavich, Stephen; Benson, David A.

2017-05-01

Current Lagrangian (particle-tracking) algorithms used to simulate diffusion-reaction equations must employ a certain number of particles to properly emulate the system dynamics-particularly for imperfectly-mixed systems. The number of particles is tied to the statistics of the initial concentration fields of the system at hand. Systems with shorter-range correlation and/or smaller concentration variance require more particles, potentially limiting the computational feasibility of the method. For the well-known problem of bimolecular reaction, we show that using kernel-based, rather than Dirac delta, particles can significantly reduce the required number of particles. We derive the fixed width of a Gaussian kernel for a given reduced number of particles that analytically eliminates the error between kernel and Dirac solutions at any specified time. We also show how to solve for the fixed kernel size by minimizing the squared differences between solutions over any given time interval. Numerical results show that the width of the kernel should be kept below about 12% of the domain size, and that the analytic equations used to derive kernel width suffer significantly from the neglect of higher-order moments. The simulations with a kernel width given by least squares minimization perform better than those made to match at one specific time. A heuristic time-variable kernel size, based on the previous results, performs on par with the least squares fixed kernel size.

Detrended fluctuation analysis as a regression framework: Estimating dependence at different scales

NASA Astrophysics Data System (ADS)

Kristoufek, Ladislav

2015-02-01

We propose a framework combining detrended fluctuation analysis with standard regression methodology. The method is built on detrended variances and covariances and it is designed to estimate regression parameters at different scales and under potential nonstationarity and power-law correlations. The former feature allows for distinguishing between effects for a pair of variables from different temporal perspectives. The latter ones make the method a significant improvement over the standard least squares estimation. Theoretical claims are supported by Monte Carlo simulations. The method is then applied on selected examples from physics, finance, environmental science, and epidemiology. For most of the studied cases, the relationship between variables of interest varies strongly across scales.

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.

Geodesic least squares regression on information manifolds

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

Verdoolaege, Geert, E-mail: geert.verdoolaege@ugent.be

We present a novel regression method targeted at situations with significant uncertainty on both the dependent and independent variables or with non-Gaussian distribution models. Unlike the classic regression model, the conditional distribution of the response variable suggested by the data need not be the same as the modeled distribution. Instead they are matched by minimizing the Rao geodesic distance between them. This yields a more flexible regression method that is less constrained by the assumptions imposed through the regression model. As an example, we demonstrate the improved resistance of our method against some flawed model assumptions and we apply thismore » to scaling laws in magnetic confinement fusion.« less

Estimation in Linear Systems Featuring Correlated Uncertain Observations Coming from Multiple Sensors

NASA Astrophysics Data System (ADS)

Caballero-Águila, R.; Hermoso-Carazo, A.; Linares-Pérez, J.

2009-08-01

In this paper, the state least-squares linear estimation problem from correlated uncertain observations coming from multiple sensors is addressed. It is assumed that, at each sensor, the state is measured in the presence of additive white noise and that the uncertainty in the observations is characterized by a set of Bernoulli random variables which are only correlated at consecutive time instants. Assuming that the statistical properties of such variables are not necessarily the same for all the sensors, a recursive filtering algorithm is proposed, and the performance of the estimators is illustrated by a numerical simulation example wherein a signal is estimated from correlated uncertain observations coming from two sensors with different uncertainty characteristics.

Simple and Reliable Determination of Intravoxel Incoherent Motion Parameters for the Differential Diagnosis of Head and Neck Tumors

PubMed Central

Sasaki, Miho; Sumi, Misa; Eida, Sato; Katayama, Ikuo; Hotokezaka, Yuka; Nakamura, Takashi

2014-01-01

Intravoxel incoherent motion (IVIM) imaging can characterize diffusion and perfusion of normal and diseased tissues, and IVIM parameters are authentically determined by using cumbersome least-squares method. We evaluated a simple technique for the determination of IVIM parameters using geometric analysis of the multiexponential signal decay curve as an alternative to the least-squares method for the diagnosis of head and neck tumors. Pure diffusion coefficients (D), microvascular volume fraction (f), perfusion-related incoherent microcirculation (D*), and perfusion parameter that is heavily weighted towards extravascular space (P) were determined geometrically (Geo D, Geo f, and Geo P) or by least-squares method (Fit D, Fit f, and Fit D*) in normal structures and 105 head and neck tumors. The IVIM parameters were compared for their levels and diagnostic abilities between the 2 techniques. The IVIM parameters were not able to determine in 14 tumors with the least-squares method alone and in 4 tumors with the geometric and least-squares methods. The geometric IVIM values were significantly different (p<0.001) from Fit values (+2±4% and −7±24% for D and f values, respectively). Geo D and Fit D differentiated between lymphomas and SCCs with similar efficacy (78% and 80% accuracy, respectively). Stepwise approaches using combinations of Geo D and Geo P, Geo D and Geo f, or Fit D and Fit D* differentiated between pleomorphic adenomas, Warthin tumors, and malignant salivary gland tumors with the same efficacy (91% accuracy = 21/23). However, a stepwise differentiation using Fit D and Fit f was less effective (83% accuracy = 19/23). Considering cumbersome procedures with the least squares method compared with the geometric method, we concluded that the geometric determination of IVIM parameters can be an alternative to least-squares method in the diagnosis of head and neck tumors. PMID:25402436

Applied Algebra: The Modeling Technique of Least Squares

ERIC Educational Resources Information Center

Zelkowski, Jeremy; Mayes, Robert

2008-01-01

The article focuses on engaging students in algebra through modeling real-world problems. The technique of least squares is explored, encouraging students to develop a deeper understanding of the method. (Contains 2 figures and a bibliography.)

Software For Least-Squares And Robust Estimation

NASA Technical Reports Server (NTRS)

Jeffreys, William H.; Fitzpatrick, Michael J.; Mcarthur, Barbara E.; Mccartney, James

1990-01-01

GAUSSFIT computer program includes full-featured programming language facilitating creation of mathematical models solving least-squares and robust-estimation problems. Programming language designed to make it easy to specify complex reduction models. Written in 100 percent C language.

Beyond Principal Component Analysis: A Trilinear Decomposition Model and Least Squares Estimation.

ERIC Educational Resources Information Center

Pham, Tuan Dinh; Mocks, Joachim

1992-01-01

Sufficient conditions are derived for the consistency and asymptotic normality of the least squares estimator of a trilinear decomposition model for multiway data analysis. The limiting covariance matrix is computed. (Author/SLD)

a Unified Matrix Polynomial Approach to Modal Identification

NASA Astrophysics Data System (ADS)

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

1998-04-01

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

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).

From direct-space discrepancy functions to crystallographic least squares.

PubMed

Giacovazzo, Carmelo

2015-01-01

Crystallographic least squares are a fundamental tool for crystal structure analysis. In this paper their properties are derived from functions estimating the degree of similarity between two electron-density maps. The new approach leads also to modifications of the standard least-squares procedures, potentially able to improve their efficiency. The role of the scaling factor between observed and model amplitudes is analysed: the concept of unlocated model is discussed and its scattering contribution is combined with that arising from the located model. Also, the possible use of an ancillary parameter, to be associated with the classical weight related to the variance of the observed amplitudes, is studied. The crystallographic discrepancy factors, basic tools often combined with least-squares procedures in phasing approaches, are analysed. The mathematical approach here described includes, as a special case, the so-called vector refinement, used when accurate estimates of the target phases are available.

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

PubMed

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

2016-03-01

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

Application of Least Mean Square Algorithms to Spacecraft Vibration Compensation

NASA Technical Reports Server (NTRS)

Woodard , Stanley E.; Nagchaudhuri, Abhijit

1998-01-01

This paper describes the application of the Least Mean Square (LMS) algorithm in tandem with the Filtered-X Least Mean Square algorithm for controlling a science instrument's line-of-sight pointing. Pointing error is caused by a periodic disturbance and spacecraft vibration. A least mean square algorithm is used on-orbit to produce the transfer function between the instrument's servo-mechanism and error sensor. The result is a set of adaptive transversal filter weights tuned to the transfer function. The Filtered-X LMS algorithm, which is an extension of the LMS, tunes a set of transversal filter weights to the transfer function between the disturbance source and the servo-mechanism's actuation signal. The servo-mechanism's resulting actuation counters the disturbance response and thus maintains accurate science instrumental pointing. A simulation model of the Upper Atmosphere Research Satellite is used to demonstrate the algorithms.

A prediction model of compressor with variable-geometry diffuser based on elliptic equation and partial least squares

PubMed Central

Yang, Chuanlei; Wang, Yinyan; Wang, Hechun

2018-01-01

To achieve a much more extensive intake air flow range of the diesel engine, a variable-geometry compressor (VGC) is introduced into a turbocharged diesel engine. However, due to the variable diffuser vane angle (DVA), the prediction for the performance of the VGC becomes more difficult than for a normal compressor. In the present study, a prediction model comprising an elliptical equation and a PLS (partial least-squares) model was proposed to predict the performance of the VGC. The speed lines of the pressure ratio map and the efficiency map were fitted with the elliptical equation, and the coefficients of the elliptical equation were introduced into the PLS model to build the polynomial relationship between the coefficients and the relative speed, the DVA. Further, the maximal order of the polynomial was investigated in detail to reduce the number of sub-coefficients and achieve acceptable fit accuracy simultaneously. The prediction model was validated with sample data and in order to present the superiority of compressor performance prediction, the prediction results of this model were compared with those of the look-up table and back-propagation neural networks (BPNNs). The validation and comparison results show that the prediction accuracy of the new developed model is acceptable, and this model is much more suitable than the look-up table and the BPNN methods under the same condition in VGC performance prediction. Moreover, the new developed prediction model provides a novel and effective prediction solution for the VGC and can be used to improve the accuracy of the thermodynamic model for turbocharged diesel engines in the future. PMID:29410849

Sperm quality variables as indicators of bull fertility may be breed dependent.

PubMed

Morrell, Jane M; Nongbua, Thanapol; Valeanu, Sabina; Lima Verde, Isabel; Lundstedt-Enkel, Katrin; Edman, Anders; Johannisson, Anders

2017-10-01

A means of discriminating among bulls of high fertility based on sperm quality is needed by breeding centers. The objective of the study was to examine parameters of sperm quality in bulls of known fertility to identify useful indicators of fertility. Frozen semen was available from bulls of known fertility (Viking Genetics, Skara, Sweden): Swedish Red (n=31), Holstein (n=25) and Others (one each of Charolais, Limousin, Blonde, SKB). After thawing, the sperm samples were analyzed for motility (computer assisted sperm analysis), plasma membrane integrity, chromatin integrity, acrosome status, mitochondrial activity and reactive oxygen species. A fertility index score based on the adjusted 56-day non-return rate for >1000 inseminations was available for each bull. Multivariate data analysis (Partial Least Squares Regression and Orthogonal Partial Least Squares Regression) was performed to identify variables related to fertility; Pearson univariate correlations were made on the parameters of interest. Breed of bull affected the relationship of sperm quality variables and fertility index score, as follows: Swedish Red: %DNA Fragmentation Index, r=-0.56, P<0.01; intact plasma membrane, r=0.40, P<0.05; membrane damaged, not acrosome reacted, r=-0.6, P<0.01; Linearity, r=0.37, P<0.05; there was a trend towards significance for Wobble, r=0.34, P=0.08. Holstein: Linearity was significant r=0.46, P<0.05; there was a trend towards significance for Wobble, r=0.45, P=0.08. In conclusion, breed has a greater effect on sperm quality than previously realized; different parameters of sperm quality are needed to indicate potential fertility in different breeds. Copyright © 2017 Elsevier B.V. All rights reserved.

Remote sensing of phytoplankton chlorophyll-a concentration by use of ridge function fields.

PubMed

Pelletier, Bruno; Frouin, Robert

2006-02-01

A methodology is presented for retrieving phytoplankton chlorophyll-a concentration from space. The data to be inverted, namely, vectors of top-of-atmosphere reflectance in the solar spectrum, are treated as explanatory variables conditioned by angular geometry. This approach leads to a continuum of inverse problems, i.e., a collection of similar inverse problems continuously indexed by the angular variables. The resolution of the continuum of inverse problems is studied from the least-squares viewpoint and yields a solution expressed as a function field over the set of permitted values for the angular variables, i.e., a map defined on that set and valued in a subspace of a function space. The function fields of interest, for reasons of approximation theory, are those valued in nested sequences of subspaces, such as ridge function approximation spaces, the union of which is dense. Ridge function fields constructed on synthetic yet realistic data for case I waters handle well situations of both weakly and strongly absorbing aerosols, and they are robust to noise, showing improvement in accuracy compared with classic inversion techniques. The methodology is applied to actual imagery from the Sea-Viewing Wide Field-of-View Sensor (SeaWiFS); noise in the data are taken into account. The chlorophyll-a concentration obtained with the function field methodology differs from that obtained by use of the standard SeaWiFS algorithm by 15.7% on average. The results empirically validate the underlying hypothesis that the inversion is solved in a least-squares sense. They also show that large levels of noise can be managed if the noise distribution is known or estimated.

A prediction model of compressor with variable-geometry diffuser based on elliptic equation and partial least squares.

PubMed

Li, Xu; Yang, Chuanlei; Wang, Yinyan; Wang, Hechun

2018-01-01

To achieve a much more extensive intake air flow range of the diesel engine, a variable-geometry compressor (VGC) is introduced into a turbocharged diesel engine. However, due to the variable diffuser vane angle (DVA), the prediction for the performance of the VGC becomes more difficult than for a normal compressor. In the present study, a prediction model comprising an elliptical equation and a PLS (partial least-squares) model was proposed to predict the performance of the VGC. The speed lines of the pressure ratio map and the efficiency map were fitted with the elliptical equation, and the coefficients of the elliptical equation were introduced into the PLS model to build the polynomial relationship between the coefficients and the relative speed, the DVA. Further, the maximal order of the polynomial was investigated in detail to reduce the number of sub-coefficients and achieve acceptable fit accuracy simultaneously. The prediction model was validated with sample data and in order to present the superiority of compressor performance prediction, the prediction results of this model were compared with those of the look-up table and back-propagation neural networks (BPNNs). The validation and comparison results show that the prediction accuracy of the new developed model is acceptable, and this model is much more suitable than the look-up table and the BPNN methods under the same condition in VGC performance prediction. Moreover, the new developed prediction model provides a novel and effective prediction solution for the VGC and can be used to improve the accuracy of the thermodynamic model for turbocharged diesel engines in the future.

Computational procedures for probing interactions in OLS and logistic regression: SPSS and SAS implementations.

PubMed

Hayes, Andrew F; Matthes, Jörg

2009-08-01

Researchers often hypothesize moderated effects, in which the effect of an independent variable on an outcome variable depends on the value of a moderator variable. Such an effect reveals itself statistically as an interaction between the independent and moderator variables in a model of the outcome variable. When an interaction is found, it is important to probe the interaction, for theories and hypotheses often predict not just interaction but a specific pattern of effects of the focal independent variable as a function of the moderator. This article describes the familiar pick-a-point approach and the much less familiar Johnson-Neyman technique for probing interactions in linear models and introduces macros for SPSS and SAS to simplify the computations and facilitate the probing of interactions in ordinary least squares and logistic regression. A script version of the SPSS macro is also available for users who prefer a point-and-click user interface rather than command syntax.

Detection of drug active ingredients by chemometric processing of solid-state NMR spectrometry data -- the case of acetaminophen.

PubMed

Paradowska, Katarzyna; Jamróz, Marta Katarzyna; Kobyłka, Mariola; Gowin, Ewelina; Maczka, Paulina; Skibiński, Robert; Komsta, Łukasz

2012-01-01

This paper presents a preliminary study in building discriminant models from solid-state NMR spectrometry data to detect the presence of acetaminophen in over-the-counter pharmaceutical formulations. The dataset, containing 11 spectra of pure substances and 21 spectra of various formulations, was processed by partial least squares discriminant analysis (PLS-DA). The model found coped with the discrimination, and its quality parameters were acceptable. It was found that standard normal variate preprocessing had almost no influence on unsupervised investigation of the dataset. The influence of variable selection with the uninformative variable elimination by PLS method was studied, reducing the dataset from 7601 variables to around 300 informative variables, but not improving the model performance. The results showed the possibility to construct well-working PLS-DA models from such small datasets without a full experimental design.

An analysis of input errors in precipitation-runoff models using regression with errors in the independent variables

USGS Publications Warehouse

Troutman, Brent M.

1982-01-01

Errors in runoff prediction caused by input data errors are analyzed by treating precipitation-runoff models as regression (conditional expectation) models. Independent variables of the regression consist of precipitation and other input measurements; the dependent variable is runoff. In models using erroneous input data, prediction errors are inflated and estimates of expected storm runoff for given observed input variables are biased. This bias in expected runoff estimation results in biased parameter estimates if these parameter estimates are obtained by a least squares fit of predicted to observed runoff values. The problems of error inflation and bias are examined in detail for a simple linear regression of runoff on rainfall and for a nonlinear U.S. Geological Survey precipitation-runoff model. Some implications for flood frequency analysis are considered. A case study using a set of data from Turtle Creek near Dallas, Texas illustrates the problems of model input errors.

Multiview point clouds denoising based on interference elimination

NASA Astrophysics Data System (ADS)

Hu, Yang; Wu, Qian; Wang, Le; Jiang, Huanyu

2018-03-01

Newly emerging low-cost depth sensors offer huge potentials for three-dimensional (3-D) modeling, but existing high noise restricts these sensors from obtaining accurate results. Thus, we proposed a method for denoising registered multiview point clouds with high noise to solve that problem. The proposed method is aimed at fully using redundant information to eliminate the interferences among point clouds of different views based on an iterative procedure. In each iteration, noisy points are either deleted or moved to their weighted average targets in accordance with two cases. Simulated data and practical data captured by a Kinect v2 sensor were tested in experiments qualitatively and quantitatively. Results showed that the proposed method can effectively reduce noise and recover local features from highly noisy multiview point clouds with good robustness, compared to truncated signed distance function and moving least squares (MLS). Moreover, the resulting low-noise point clouds can be further smoothed by the MLS to achieve improved results. This study provides the feasibility of obtaining fine 3-D models with high-noise devices, especially for depth sensors, such as Kinect.

A fast object-oriented Matlab implementation of the Reproducing Kernel Particle Method

NASA Astrophysics Data System (ADS)

Barbieri, Ettore; Meo, Michele

2012-05-01

Novel numerical methods, known as Meshless Methods or Meshfree Methods and, in a wider perspective, Partition of Unity Methods, promise to overcome most of disadvantages of the traditional finite element techniques. The absence of a mesh makes meshfree methods very attractive for those problems involving large deformations, moving boundaries and crack propagation. However, meshfree methods still have significant limitations that prevent their acceptance among researchers and engineers, namely the computational costs. This paper presents an in-depth analysis of computational techniques to speed-up the computation of the shape functions in the Reproducing Kernel Particle Method and Moving Least Squares, with particular focus on their bottlenecks, like the neighbour search, the inversion of the moment matrix and the assembly of the stiffness matrix. The paper presents numerous computational solutions aimed at a considerable reduction of the computational times: the use of kd-trees for the neighbour search, sparse indexing of the nodes-points connectivity and, most importantly, the explicit and vectorized inversion of the moment matrix without using loops and numerical routines.

Trees grow on money: urban tree canopy cover and environmental justice.

PubMed

Schwarz, Kirsten; Fragkias, Michail; Boone, Christopher G; Zhou, Weiqi; McHale, Melissa; Grove, J Morgan; O'Neil-Dunne, Jarlath; McFadden, Joseph P; Buckley, Geoffrey L; Childers, Dan; Ogden, Laura; Pincetl, Stephanie; Pataki, Diane; Whitmer, Ali; Cadenasso, Mary L

2015-01-01

This study examines the distributional equity of urban tree canopy (UTC) cover for Baltimore, MD, Los Angeles, CA, New York, NY, Philadelphia, PA, Raleigh, NC, Sacramento, CA, and Washington, D.C. using high spatial resolution land cover data and census data. Data are analyzed at the Census Block Group levels using Spearman's correlation, ordinary least squares regression (OLS), and a spatial autoregressive model (SAR). Across all cities there is a strong positive correlation between UTC cover and median household income. Negative correlations between race and UTC cover exist in bivariate models for some cities, but they are generally not observed using multivariate regressions that include additional variables on income, education, and housing age. SAR models result in higher r-square values compared to the OLS models across all cities, suggesting that spatial autocorrelation is an important feature of our data. Similarities among cities can be found based on shared characteristics of climate, race/ethnicity, and size. Our findings suggest that a suite of variables, including income, contribute to the distribution of UTC cover. These findings can help target simultaneous strategies for UTC goals and environmental justice concerns.

Multidimensional model of apathy in older adults using partial least squares--path modeling.

PubMed

Raffard, Stéphane; Bortolon, Catherine; Burca, Marianna; Gely-Nargeot, Marie-Christine; Capdevielle, Delphine

2016-06-01

Apathy defined as a mental state characterized by a lack of goal-directed behavior is prevalent and associated with poor functioning in older adults. The main objective of this study was to identify factors contributing to the distinct dimensions of apathy (cognitive, emotional, and behavioral) in older adults without dementia. One hundred and fifty participants (mean age, 80.42) completed self-rated questionnaires assessing apathy, emotional distress, anticipatory pleasure, motivational systems, physical functioning, quality of life, and cognitive functioning. Data were analyzed using partial least squares variance-based structural equation modeling in order to examine factors contributing to the three different dimensions of apathy in our sample. Overall, the different facets of apathy were associated with cognitive functioning, anticipatory pleasure, sensitivity to reward, and physical functioning, but the contribution of these different factors to the three dimensions of apathy differed significantly. More specifically, the impact of anticipatory pleasure and physical functioning was stronger for the cognitive than for emotional apathy. Conversely, the impact of sensibility to reward, although small, was slightly stronger on emotional apathy. Regarding behavioral apathy, again we found similar latent variables except for the cognitive functioning whose impact was not statistically significant. Our results highlight the need to take into account various mechanisms involved in the different facets of apathy in older adults without dementia, including not only cognitive factors but also motivational variables and aspects related to physical disability. Clinical implications are discussed.

A Maximum Likelihood Approach to Determine Sensor Radiometric Response Coefficients for NPP VIIRS Reflective Solar Bands

NASA Technical Reports Server (NTRS)

Lei, Ning; Chiang, Kwo-Fu; Oudrari, Hassan; Xiong, Xiaoxiong

2011-01-01

Optical sensors aboard Earth orbiting satellites such as the next generation Visible/Infrared Imager/Radiometer Suite (VIIRS) assume that the sensors radiometric response in the Reflective Solar Bands (RSB) is described by a quadratic polynomial, in relating the aperture spectral radiance to the sensor Digital Number (DN) readout. For VIIRS Flight Unit 1, the coefficients are to be determined before launch by an attenuation method, although the linear coefficient will be further determined on-orbit through observing the Solar Diffuser. In determining the quadratic polynomial coefficients by the attenuation method, a Maximum Likelihood approach is applied in carrying out the least-squares procedure. Crucial to the Maximum Likelihood least-squares procedure is the computation of the weight. The weight not only has a contribution from the noise of the sensor s digital count, with an important contribution from digitization error, but also is affected heavily by the mathematical expression used to predict the value of the dependent variable, because both the independent and the dependent variables contain random noise. In addition, model errors have a major impact on the uncertainties of the coefficients. The Maximum Likelihood approach demonstrates the inadequacy of the attenuation method model with a quadratic polynomial for the retrieved spectral radiance. We show that using the inadequate model dramatically increases the uncertainties of the coefficients. We compute the coefficient values and their uncertainties, considering both measurement and model errors.

Parametric and Nonparametric Statistical Methods for Genomic Selection of Traits with Additive and Epistatic Genetic Architectures

PubMed Central

Howard, Réka; Carriquiry, Alicia L.; Beavis, William D.

2014-01-01

Parametric and nonparametric methods have been developed for purposes of predicting phenotypes. These methods are based on retrospective analyses of empirical data consisting of genotypic and phenotypic scores. Recent reports have indicated that parametric methods are unable to predict phenotypes of traits with known epistatic genetic architectures. Herein, we review parametric methods including least squares regression, ridge regression, Bayesian ridge regression, least absolute shrinkage and selection operator (LASSO), Bayesian LASSO, best linear unbiased prediction (BLUP), Bayes A, Bayes B, Bayes C, and Bayes Cπ. We also review nonparametric methods including Nadaraya-Watson estimator, reproducing kernel Hilbert space, support vector machine regression, and neural networks. We assess the relative merits of these 14 methods in terms of accuracy and mean squared error (MSE) using simulated genetic architectures consisting of completely additive or two-way epistatic interactions in an F2 population derived from crosses of inbred lines. Each simulated genetic architecture explained either 30% or 70% of the phenotypic variability. The greatest impact on estimates of accuracy and MSE was due to genetic architecture. Parametric methods were unable to predict phenotypic values when the underlying genetic architecture was based entirely on epistasis. Parametric methods were slightly better than nonparametric methods for additive genetic architectures. Distinctions among parametric methods for additive genetic architectures were incremental. Heritability, i.e., proportion of phenotypic variability, had the second greatest impact on estimates of accuracy and MSE. PMID:24727289

A new approach to enforce element-wise mass/species balance using the augmented Lagrangian method

NASA Astrophysics Data System (ADS)

Chang, J.; Nakshatrala, K.

2015-12-01

The least-squares finite element method (LSFEM) is one of many ways in which one can discretize and express a set of first ordered partial differential equations as a mixed formulation. However, the standard LSFEM is not locally conservative by design. The absence of this physical property can have serious implications in the numerical simulation of subsurface flow and transport. Two commonly employed ways to circumvent this issue is through the Lagrange multiplier method, which explicitly satisfies the element-wise divergence by introducing new unknowns, or through appending a penalty factor to the continuity constraint, which reduces the violation in the mass balance. However, these methodologies have some well-known drawbacks. Herein, we propose a new approach to improve the local balance of species/mass balance. The approach augments constraints to a least-square function by a novel mathematical construction of the local species/mass balance, which is different from the conventional ways. The resulting constrained optimization problem is solved using the augmented Lagrangian, which corrects the balance errors in an iterative fashion. The advantages of this methodology are that the problem size is not increased (thus preserving the symmetry and positive definite-ness) and that one need not provide an accurate guess for the initial penalty to reach a prescribed mass balance tolerance. We derive the least-squares weighting needed to ensure accurate solutions. We also demonstrate the robustness of the weighted LSFEM coupled with the augmented Lagrangian by solving large-scale heterogenous and variably saturated flow through porous media problems. The performance of the iterative solvers with respect to various user-defined augmented Lagrangian parameters will be documented.

The use of least squares methods in functional optimization of energy use prediction models

NASA Astrophysics Data System (ADS)

Bourisli, Raed I.; Al-Shammeri, Basma S.; AlAnzi, Adnan A.

2012-06-01

The least squares method (LSM) is used to optimize the coefficients of a closed-form correlation that predicts the annual energy use of buildings based on key envelope design and thermal parameters. Specifically, annual energy use is related to a number parameters like the overall heat transfer coefficients of the wall, roof and glazing, glazing percentage, and building surface area. The building used as a case study is a previously energy-audited mosque in a suburb of Kuwait City, Kuwait. Energy audit results are used to fine-tune the base case mosque model in the VisualDOE{trade mark, serif} software. Subsequently, 1625 different cases of mosques with varying parameters were developed and simulated in order to provide the training data sets for the LSM optimizer. Coefficients of the proposed correlation are then optimized using multivariate least squares analysis. The objective is to minimize the difference between the correlation-predicted results and the VisualDOE-simulation results. It was found that the resulting correlation is able to come up with coefficients for the proposed correlation that reduce the difference between the simulated and predicted results to about 0.81%. In terms of the effects of the various parameters, the newly-defined weighted surface area parameter was found to have the greatest effect on the normalized annual energy use. Insulating the roofs and walls also had a major effect on the building energy use. The proposed correlation and methodology can be used during preliminary design stages to inexpensively assess the impacts of various design variables on the expected energy use. On the other hand, the method can also be used by municipality officials and planners as a tool for recommending energy conservation measures and fine-tuning energy codes.

Technique for estimating the 2- to 500-year flood discharges on unregulated streams in rural Missouri

USGS Publications Warehouse

Alexander, Terry W.; Wilson, Gary L.

1995-01-01

A generalized least-squares regression technique was used to relate the 2- to 500-year flood discharges from 278 selected streamflow-gaging stations to statistically significant basin characteristics. The regression relations (estimating equations) were defined for three hydrologic regions (I, II, and III) in rural Missouri. Ordinary least-squares regression analyses indicate that drainage area (Regions I, II, and III) and main-channel slope (Regions I and II) are the only basin characteristics needed for computing the 2- to 500-year design-flood discharges at gaged or ungaged stream locations. The resulting generalized least-squares regression equations provide a technique for estimating the 2-, 5-, 10-, 25-, 50-, 100-, and 500-year flood discharges on unregulated streams in rural Missouri. The regression equations for Regions I and II were developed from stream-flow-gaging stations with drainage areas ranging from 0.13 to 11,500 square miles and 0.13 to 14,000 square miles, and main-channel slopes ranging from 1.35 to 150 feet per mile and 1.20 to 279 feet per mile. The regression equations for Region III were developed from streamflow-gaging stations with drainage areas ranging from 0.48 to 1,040 square miles. Standard errors of estimate for the generalized least-squares regression equations in Regions I, II, and m ranged from 30 to 49 percent.

Full spectrum optical safeguard

DOEpatents

Ackerman, Mark R.

2008-12-02

An optical safeguard device with two linear variable Fabry-Perot filters aligned relative to a light source with at least one of the filters having a nonlinear dielectric constant material such that, when a light source produces a sufficiently high intensity light, the light alters the characteristics of the nonlinear dielectric constant material to reduce the intensity of light impacting a connected optical sensor. The device can be incorporated into an imaging system on a moving platform, such as an aircraft or satellite.

Bias correction by use of errors-in-variables regression models in studies with K-X-ray fluorescence bone lead measurements.

PubMed

Lamadrid-Figueroa, Héctor; Téllez-Rojo, Martha M; Angeles, Gustavo; Hernández-Ávila, Mauricio; Hu, Howard

2011-01-01

In-vivo measurement of bone lead by means of K-X-ray fluorescence (KXRF) is the preferred biological marker of chronic exposure to lead. Unfortunately, considerable measurement error associated with KXRF estimations can introduce bias in estimates of the effect of bone lead when this variable is included as the exposure in a regression model. Estimates of uncertainty reported by the KXRF instrument reflect the variance of the measurement error and, although they can be used to correct the measurement error bias, they are seldom used in epidemiological statistical analyzes. Errors-in-variables regression (EIV) allows for correction of bias caused by measurement error in predictor variables, based on the knowledge of the reliability of such variables. The authors propose a way to obtain reliability coefficients for bone lead measurements from uncertainty data reported by the KXRF instrument and compare, by the use of Monte Carlo simulations, results obtained using EIV regression models vs. those obtained by the standard procedures. Results of the simulations show that Ordinary Least Square (OLS) regression models provide severely biased estimates of effect, and that EIV provides nearly unbiased estimates. Although EIV effect estimates are more imprecise, their mean squared error is much smaller than that of OLS estimates. In conclusion, EIV is a better alternative than OLS to estimate the effect of bone lead when measured by KXRF. Copyright © 2010 Elsevier Inc. All rights reserved.

Hyperspectral imaging for predicting the allicin and soluble solid content of garlic with variable selection algorithms and chemometric models.

PubMed

Rahman, Anisur; Faqeerzada, Mohammad A; Cho, Byoung-Kwan

2018-03-14

Allicin and soluble solid content (SSC) in garlic is the responsible for its pungent flavor and odor. However, current conventional methods such as the use of high-pressure liquid chromatography and a refractometer have critical drawbacks in that they are time-consuming, labor-intensive and destructive procedures. The present study aimed to predict allicin and SSC in garlic using hyperspectral imaging in combination with variable selection algorithms and calibration models. Hyperspectral images of 100 garlic cloves were acquired that covered two spectral ranges, from which the mean spectra of each clove were extracted. The calibration models included partial least squares (PLS) and least squares-support vector machine (LS-SVM) regression, as well as different spectral pre-processing techniques, from which the highest performing spectral preprocessing technique and spectral range were selected. Then, variable selection methods, such as regression coefficients, variable importance in projection (VIP) and the successive projections algorithm (SPA), were evaluated for the selection of effective wavelengths (EWs). Furthermore, PLS and LS-SVM regression methods were applied to quantitatively predict the quality attributes of garlic using the selected EWs. Of the established models, the SPA-LS-SVM model obtained an Rpred2 of 0.90 and standard error of prediction (SEP) of 1.01% for SSC prediction, whereas the VIP-LS-SVM model produced the best result with an Rpred2 of 0.83 and SEP of 0.19 mg g -1 for allicin prediction in the range 1000-1700 nm. Furthermore, chemical images of garlic were developed using the best predictive model to facilitate visualization of the spatial distributions of allicin and SSC. The present study clearly demonstrates that hyperspectral imaging combined with an appropriate chemometrics method can potentially be employed as a fast, non-invasive method to predict the allicin and SSC in garlic. © 2018 Society of Chemical Industry. © 2018 Society of Chemical Industry.

Phase-space finite elements in a least-squares solution of the transport equation

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

Drumm, C.; Fan, W.; Pautz, S.

2013-07-01

The linear Boltzmann transport equation is solved using a least-squares finite element approximation in the space, angular and energy phase-space variables. The method is applied to both neutral particle transport and also to charged particle transport in the presence of an electric field, where the angular and energy derivative terms are handled with the energy/angular finite elements approximation, in a manner analogous to the way the spatial streaming term is handled. For multi-dimensional problems, a novel approach is used for the angular finite elements: mapping the surface of a unit sphere to a two-dimensional planar region and using a meshingmore » tool to generate a mesh. In this manner, much of the spatial finite-elements machinery can be easily adapted to handle the angular variable. The energy variable and the angular variable for one-dimensional problems make use of edge/beam elements, also building upon the spatial finite elements capabilities. The methods described here can make use of either continuous or discontinuous finite elements in space, angle and/or energy, with the use of continuous finite elements resulting in a smaller problem size and the use of discontinuous finite elements resulting in more accurate solutions for certain types of problems. The work described in this paper makes use of continuous finite elements, so that the resulting linear system is symmetric positive definite and can be solved with a highly efficient parallel preconditioned conjugate gradients algorithm. The phase-space finite elements capability has been built into the Sceptre code and applied to several test problems, including a simple one-dimensional problem with an analytic solution available, a two-dimensional problem with an isolated source term, showing how the method essentially eliminates ray effects encountered with discrete ordinates, and a simple one-dimensional charged-particle transport problem in the presence of an electric field. (authors)« less

46 CFR 168.15-15 - Size.

Code of Federal Regulations, 2013 CFR

2013-10-01

... accommodate, must be marked outside the space. (b) Each room must be of such size that there is at least 1.8 square meters (20 square feet) of deck area and a volume of at least 4.2 cubic meters (150 cubic feet...

46 CFR 168.15-15 - Size.

Code of Federal Regulations, 2014 CFR

2014-10-01

... accommodate, must be marked outside the space. (b) Each room must be of such size that there is at least 1.8 square meters (20 square feet) of deck area and a volume of at least 4.2 cubic meters (150 cubic feet...

Constrained Least Squares Estimators of Oblique Common Factors.

ERIC Educational Resources Information Center

McDonald, Roderick P.

1981-01-01

An expression is given for weighted least squares estimators of oblique common factors of factor analyses, constrained to have the same covariance matrix as the factors they estimate. A proof of the uniqueness of the solution is given. (Author/JKS)