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.

The augmented Lagrangian method for parameter estimation in elliptic systems

NASA Technical Reports Server (NTRS)

Ito, Kazufumi; Kunisch, Karl

1990-01-01

In this paper a new technique for the estimation of parameters in elliptic partial differential equations is developed. It is a hybrid method combining the output-least-squares and the equation error method. The new method is realized by an augmented Lagrangian formulation, and convergence as well as rate of convergence proofs are provided. Technically the critical step is the verification of a coercivity estimate of an appropriately defined Lagrangian functional. To obtain this coercivity estimate a seminorm regularization technique is used.

Calibration of Valiantzas' reference evapotranspiration equations for the Pilbara region, Western Australia

NASA Astrophysics Data System (ADS)

Ahooghalandari, Matin; Khiadani, Mehdi; Jahromi, Mina Esmi

2017-05-01

Reference evapotranspiration (ET0) is a critical component of water resources management and planning. Different methods have been developed to estimate ET0 with various required data. In this study, Hargreaves, Turc, Oudin, Copais, Abtew methods and three forms of Valiantzas' formulas, developed in recent years, were used to estimate ET0 for the Pilbara region of Western Australia. The estimated ET0 values from these methods were compared with those from the FAO-56 Penman-Monteith (PM) method. The results showed that the Copais methods and two of Valiantzas' equations, in their original forms, are suitable for estimating ET0 for the study area. A modification of Honey-Bee Mating Optimization (MHBMO) algorithm was further implemented, and three Valiantzas' equations for a region located in the southern hemisphere were calibrated.

Comparison of estimates of hardwood bole volume using importance sampling, the centroid method, and some taper equations

Treesearch

Harry V., Jr. Wiant; Michael L. Spangler; John E. Baumgras

2002-01-01

Various taper systems and the centroid method were compared to unbiased volume estimates made by importance sampling for 720 hardwood trees selected throughout the state of West Virginia. Only the centroid method consistently gave volumes estimates that did not differ significantly from those made by importance sampling, although some taper equations did well for most...

Determination of stability and control parameters of a light airplane from flight data using two estimation methods. [equation error and maximum likelihood methods

NASA Technical Reports Server (NTRS)

Klein, V.

1979-01-01

Two identification methods, the equation error method and the output error method, are used to estimate stability and control parameter values from flight data for a low-wing, single-engine, general aviation airplane. The estimated parameters from both methods are in very good agreement primarily because of sufficient accuracy of measured data. The estimated static parameters also agree with the results from steady flights. The effect of power different input forms are demonstrated. Examination of all results available gives the best values of estimated parameters and specifies their accuracies.

Bayesian parameter estimation for nonlinear modelling of biological pathways.

PubMed

Ghasemi, Omid; Lindsey, Merry L; Yang, Tianyi; Nguyen, Nguyen; Huang, Yufei; Jin, Yu-Fang

2011-01-01

The availability of temporal measurements on biological experiments has significantly promoted research areas in systems biology. To gain insight into the interaction and regulation of biological systems, mathematical frameworks such as ordinary differential equations have been widely applied to model biological pathways and interpret the temporal data. Hill equations are the preferred formats to represent the reaction rate in differential equation frameworks, due to their simple structures and their capabilities for easy fitting to saturated experimental measurements. However, Hill equations are highly nonlinearly parameterized functions, and parameters in these functions cannot be measured easily. Additionally, because of its high nonlinearity, adaptive parameter estimation algorithms developed for linear parameterized differential equations cannot be applied. Therefore, parameter estimation in nonlinearly parameterized differential equation models for biological pathways is both challenging and rewarding. In this study, we propose a Bayesian parameter estimation algorithm to estimate parameters in nonlinear mathematical models for biological pathways using time series data. We used the Runge-Kutta method to transform differential equations to difference equations assuming a known structure of the differential equations. This transformation allowed us to generate predictions dependent on previous states and to apply a Bayesian approach, namely, the Markov chain Monte Carlo (MCMC) method. We applied this approach to the biological pathways involved in the left ventricle (LV) response to myocardial infarction (MI) and verified our algorithm by estimating two parameters in a Hill equation embedded in the nonlinear model. We further evaluated our estimation performance with different parameter settings and signal to noise ratios. Our results demonstrated the effectiveness of the algorithm for both linearly and nonlinearly parameterized dynamic systems. Our proposed Bayesian algorithm successfully estimated parameters in nonlinear mathematical models for biological pathways. This method can be further extended to high order systems and thus provides a useful tool to analyze biological dynamics and extract information using temporal data.

Evaluation of equations that estimate glomerular filtration rate in renal transplant recipients.

PubMed

De Alencastro, M G; Veronese, F V; Vicari, A R; Gonçalves, L F; Manfro, R C

2014-03-01

The accuracy of equations that estimate the glomerular filtration rate (GFR) in renal transplant patients has not been established; thus their performance was assessed in stable renal transplant patients. Renal transplant patients (N.=213) with stable graft function were enrolled. The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation was used as the reference method and compared with the Cockcroft-Gault (CG), Modification of Diet in Renal Disease (MDRD), Mayo Clinic (MC) and Nankivell equations. Bias, accuracy and concordance rates were determined for all equation relative to CKD-EPI. Mean estimated GFR values of the equations differed significantly from the CKD-EPI values, though the correlations with the reference method were significant. Values of MDRD differed from the CG, MC and Nankivell estimations. The best agreement to classify the chronic kidney disease (CKD) stages was for the MDRD (Kappa=0.649, P<0.001), and for the other equations the agreement was moderate. The MDRD had less bias and narrower agreement limits but underestimated the GFR at levels above 60 mL/min/1.73 m2. Conversely, the CG, MC and Nankivell equations overestimated the GFR, and the Nankivell equation had the worst performance. The MDRD equation P15 and P30 values were higher than those of the other equations (P<0.001). Despite their correlations, equations estimated the GFR and CKD stage differently. The MDRD equation was the most accurate, but the sub-optimal performance of all the equations precludes their accurate use in clinical practice.

Comparison of Parametric and Nonparametric Bootstrap Methods for Estimating Random Error in Equipercentile Equating

ERIC Educational Resources Information Center

Cui, Zhongmin; Kolen, Michael J.

2008-01-01

This article considers two methods of estimating standard errors of equipercentile equating: the parametric bootstrap method and the nonparametric bootstrap method. Using a simulation study, these two methods are compared under three sample sizes (300, 1,000, and 3,000), for two test content areas (the Iowa Tests of Basic Skills Maps and Diagrams…

Comparison of anatomical, functional and regression methods for estimating the rotation axes of the forearm.

PubMed

Fraysse, François; Thewlis, Dominic

2014-11-07

Numerous methods exist to estimate the pose of the axes of rotation of the forearm. These include anatomical definitions, such as the conventions proposed by the ISB, and functional methods based on instantaneous helical axes, which are commonly accepted as the modelling gold standard for non-invasive, in-vivo studies. We investigated the validity of a third method, based on regression equations, to estimate the rotation axes of the forearm. We also assessed the accuracy of both ISB methods. Axes obtained from a functional method were considered as the reference. Results indicate a large inter-subject variability in the axes positions, in accordance with previous studies. Both ISB methods gave the same level of accuracy in axes position estimations. Regression equations seem to improve estimation of the flexion-extension axis but not the pronation-supination axis. Overall, given the large inter-subject variability, the use of regression equations cannot be recommended. Copyright © 2014 Elsevier Ltd. All rights reserved.

A method for estimating mean and low flows of streams in national forests of Montana

USGS Publications Warehouse

Parrett, Charles; Hull, J.A.

1985-01-01

Equations were developed for estimating mean annual discharge, 80-percent exceedance discharge, and 95-percent exceedance discharge for streams on national forest lands in Montana. The equations for mean annual discharge used active-channel width, drainage area and mean annual precipitation as independent variables, with active-channel width being most significant. The equations for 80-percent exceedance discharge and 95-percent exceedance discharge used only active-channel width as an independent variable. The standard error or estimate for the best equation for estimating mean annual discharge was 27 percent. The standard errors of estimate for the equations were 67 percent for estimating 80-percent exceedance discharge and 75 percent for estimating 95-percent exceedance discharge. (USGS)

A Review of System Identification Methods Applied to Aircraft

NASA Technical Reports Server (NTRS)

Klein, V.

1983-01-01

Airplane identification, equation error method, maximum likelihood method, parameter estimation in frequency domain, extended Kalman filter, aircraft equations of motion, aerodynamic model equations, criteria for the selection of a parsimonious model, and online aircraft identification are addressed.

Reliability of Summed Item Scores Using Structural Equation Modeling: An Alternative to Coefficient Alpha

ERIC Educational Resources Information Center

Green, Samuel B.; Yang, Yanyun

2009-01-01

A method is presented for estimating reliability using structural equation modeling (SEM) that allows for nonlinearity between factors and item scores. Assuming the focus is on consistency of summed item scores, this method for estimating reliability is preferred to those based on linear SEM models and to the most commonly reported estimate of…

Solutions to Some Nonlinear Equations from Nonmetric Data.

ERIC Educational Resources Information Center

Rule, Stanley J.

1979-01-01

A method to provide estimates of parameters of specified nonlinear equations from ordinal data generated from a crossed design is presented. The statistical basis for the method, called NOPE (nonmetric parameter estimation), as well as examples using artifical data, are presented. (Author/JKS)

Error estimation in the neural network solution of ordinary differential equations.

PubMed

Filici, Cristian

2010-06-01

In this article a method of error estimation for the neural approximation of the solution of an Ordinary Differential Equation is presented. Some examples of the application of the method support the theory presented. Copyright 2010. Published by Elsevier Ltd.

Reverberation Modelling Using a Parabolic Equation Method

DTIC Science & Technology

2012-10-01

the limits of their applicability. Results: Transmission loss estimates produced by the PECan parabolic equation acoustic model were used in...environments is possible when used in concert with a parabolic equation passive acoustic model . Future plans: The authors of this report recommend further...technique using other types of acoustic models should be undertaken. Furthermore, as the current method when applied as-is results in estimates that reflect

Variational estimate method for solving autonomous ordinary differential equations

NASA Astrophysics Data System (ADS)

Mungkasi, Sudi

2018-04-01

In this paper, we propose a method for solving first-order autonomous ordinary differential equation problems using a variational estimate formulation. The variational estimate is constructed with a Lagrange multiplier which is chosen optimally, so that the formulation leads to an accurate solution to the problem. The variational estimate is an integral form, which can be computed using a computer software. As the variational estimate is an explicit formula, the solution is easy to compute. This is a great advantage of the variational estimate formulation.

Methods for estimating low-flow statistics for Massachusetts streams

USGS Publications Warehouse

Ries, Kernell G.; Friesz, Paul J.

2000-01-01

Methods and computer software are described in this report for determining flow duration, low-flow frequency statistics, and August median flows. These low-flow statistics can be estimated for unregulated streams in Massachusetts using different methods depending on whether the location of interest is at a streamgaging station, a low-flow partial-record station, or an ungaged site where no data are available. Low-flow statistics for streamgaging stations can be estimated using standard U.S. Geological Survey methods described in the report. The MOVE.1 mathematical method and a graphical correlation method can be used to estimate low-flow statistics for low-flow partial-record stations. The MOVE.1 method is recommended when the relation between measured flows at a partial-record station and daily mean flows at a nearby, hydrologically similar streamgaging station is linear, and the graphical method is recommended when the relation is curved. Equations are presented for computing the variance and equivalent years of record for estimates of low-flow statistics for low-flow partial-record stations when either a single or multiple index stations are used to determine the estimates. The drainage-area ratio method or regression equations can be used to estimate low-flow statistics for ungaged sites where no data are available. The drainage-area ratio method is generally as accurate as or more accurate than regression estimates when the drainage-area ratio for an ungaged site is between 0.3 and 1.5 times the drainage area of the index data-collection site. Regression equations were developed to estimate the natural, long-term 99-, 98-, 95-, 90-, 85-, 80-, 75-, 70-, 60-, and 50-percent duration flows; the 7-day, 2-year and the 7-day, 10-year low flows; and the August median flow for ungaged sites in Massachusetts. Streamflow statistics and basin characteristics for 87 to 133 streamgaging stations and low-flow partial-record stations were used to develop the equations. The streamgaging stations had from 2 to 81 years of record, with a mean record length of 37 years. The low-flow partial-record stations had from 8 to 36 streamflow measurements, with a median of 14 measurements. All basin characteristics were determined from digital map data. The basin characteristics that were statistically significant in most of the final regression equations were drainage area, the area of stratified-drift deposits per unit of stream length plus 0.1, mean basin slope, and an indicator variable that was 0 in the eastern region and 1 in the western region of Massachusetts. The equations were developed by use of weighted-least-squares regression analyses, with weights assigned proportional to the years of record and inversely proportional to the variances of the streamflow statistics for the stations. Standard errors of prediction ranged from 70.7 to 17.5 percent for the equations to predict the 7-day, 10-year low flow and 50-percent duration flow, respectively. The equations are not applicable for use in the Southeast Coastal region of the State, or where basin characteristics for the selected ungaged site are outside the ranges of those for the stations used in the regression analyses. A World Wide Web application was developed that provides streamflow statistics for data collection stations from a data base and for ungaged sites by measuring the necessary basin characteristics for the site and solving the regression equations. Output provided by the Web application for ungaged sites includes a map of the drainage-basin boundary determined for the site, the measured basin characteristics, the estimated streamflow statistics, and 90-percent prediction intervals for the estimates. An equation is provided for combining regression and correlation estimates to obtain improved estimates of the streamflow statistics for low-flow partial-record stations. An equation is also provided for combining regression and drainage-area ratio estimates to obtain improved e

Equating Scores from Adaptive to Linear Tests

ERIC Educational Resources Information Center

van der Linden, Wim J.

2006-01-01

Two local methods for observed-score equating are applied to the problem of equating an adaptive test to a linear test. In an empirical study, the methods were evaluated against a method based on the test characteristic function (TCF) of the linear test and traditional equipercentile equating applied to the ability estimates on the adaptive test…

Novel Equations for Estimating Lean Body Mass in Patients With Chronic Kidney Disease.

PubMed

Tian, Xue; Chen, Yuan; Yang, Zhi-Kai; Qu, Zhen; Dong, Jie

2018-05-01

Simplified methods to estimate lean body mass (LBM), an important nutritional measure representing muscle mass and somatic protein, are lacking in nondialyzed patients with chronic kidney disease (CKD). We developed and tested 2 reliable equations for estimation of LBM in daily clinical practice. The development and validation groups both included 150 nondialyzed patients with CKD Stages 3 to 5. Two equations for estimating LBM based on mid-arm muscle circumference (MAMC) or handgrip strength (HGS) were developed and validated in CKD patients with dual-energy x-ray absorptiometry as referenced gold method. We developed and validated 2 equations for estimating LBM based on HGS and MAMC. These equations, which also incorporated sex, height, and weight, were developed and validated in CKD patients. The new equations were found to exhibit only small biases when compared with dual-energy x-ray absorptiometry, with median differences of 0.94 and 0.46 kg observed in the HGS and MAMC equations, respectively. Good precision and accuracy were achieved for both equations, as reflected by small interquartile ranges in the differences and in the percentages of estimates that were 20% of measured LBM. The bias, precision, and accuracy of each equation were found to be similar when it was applied to groups of patients divided by the median measured LBM, the median ratio of extracellular to total body water, and the stages of CKD. LBM estimated from MAMC or HGS were found to provide accurate estimates of LBM in nondialyzed patients with CKD. Copyright © 2017 National Kidney Foundation, Inc. Published by Elsevier Inc. All rights reserved.

Estimating soil water evaporation using radar measurements

NASA Technical Reports Server (NTRS)

Sadeghi, Ali M.; Scott, H. D.; Waite, W. P.; Asrar, G.

1988-01-01

Field studies were conducted to evaluate the application of radar reflectivity as compared with the shortwave reflectivity (albedo) used in the Idso-Jackson equation for the estimation of daily evaporation under overcast sky and subhumid climatic conditions. Soil water content, water potential, shortwave and radar reflectivity, and soil and air temperatures were monitored during three soil drying cycles. The data from each cycle were used to calculate daily evaporation from the Idso-Jackson equation and from two other standard methods, the modified Penman and plane of zero-flux. All three methods resulted in similar estimates of evaporation under clear sky conditions; however, under overcast sky conditions, evaporation fluxes computed from the Idso-Jackson equation were consistently lower than the other two methods. The shortwave albedo values in the Idso-Jackson equation were then replaced with radar reflectivities and a new set of total daily evaporation fluxes were calculated. This resulted in a significant improvement in computed soil evaporation fluxes from the Idso-Jackson equation, and a better agreement between the three methods under overcast sky conditions.

A new method for parameter estimation in nonlinear dynamical equations

NASA Astrophysics Data System (ADS)

Wang, Liu; He, Wen-Ping; Liao, Le-Jian; Wan, Shi-Quan; He, Tao

2015-01-01

Parameter estimation is an important scientific problem in various fields such as chaos control, chaos synchronization and other mathematical models. In this paper, a new method for parameter estimation in nonlinear dynamical equations is proposed based on evolutionary modelling (EM). This will be achieved by utilizing the following characteristics of EM which includes self-organizing, adaptive and self-learning features which are inspired by biological natural selection, and mutation and genetic inheritance. The performance of the new method is demonstrated by using various numerical tests on the classic chaos model—Lorenz equation (Lorenz 1963). The results indicate that the new method can be used for fast and effective parameter estimation irrespective of whether partial parameters or all parameters are unknown in the Lorenz equation. Moreover, the new method has a good convergence rate. Noises are inevitable in observational data. The influence of observational noises on the performance of the presented method has been investigated. The results indicate that the strong noises, such as signal noise ratio (SNR) of 10 dB, have a larger influence on parameter estimation than the relatively weak noises. However, it is found that the precision of the parameter estimation remains acceptable for the relatively weak noises, e.g. SNR is 20 or 30 dB. It indicates that the presented method also has some anti-noise performance.

Standard Error Estimation of 3PL IRT True Score Equating with an MCMC Method

ERIC Educational Resources Information Center

Liu, Yuming; Schulz, E. Matthew; Yu, Lei

2008-01-01

A Markov chain Monte Carlo (MCMC) method and a bootstrap method were compared in the estimation of standard errors of item response theory (IRT) true score equating. Three test form relationships were examined: parallel, tau-equivalent, and congeneric. Data were simulated based on Reading Comprehension and Vocabulary tests of the Iowa Tests of…

Agreement between different methods and predictive equations for resting energy expenditure in overweight and obese Brazilian men.

PubMed

de Oliveira, Fernanda Cristina Esteves; Alves, Raquel Duarte Moreira; Zuconi, Carolina Pereira; Ribeiro, Andréia Queiroz; Bressan, Josefina

2012-09-01

Predictive equations and methods tend to overestimate or underestimate resting energy expenditure (REE) compared with indirect calorimetry (IC). This cross-sectional study aimed to evaluate the agreement between methods and equations for REE estimation of overweight and obese Brazilian men. Data from 48 healthy volunteers, ages 20 to 43 years and with body mass index ranging from 26.4 to 35.2, were collected between October 2008 and October 2009. REE was measured by IC, using Deltatrac (IC1) and KORR-MetaCheck (IC2) devices. It was estimated by bioelectrical impedance analysis (BIA) using tetrapolar (BIA1) and bipolar (BIA2) devices, and by the equations of Mifflin, World Health Organization/Food and Agriculture Organization/United Nations University, Fleisch, Horie-Waitzberg and Gonzalez, and Ireton-Jones. The association and agreement among the methods and equations were assessed by the interclass correlation coefficient, Bland-Altman analysis, and by the percentage of the difference between values obtained from the standard method and alternative methods and equations. Most methods showed high agreement with IC1. The highest agreements were found for Mifflin (-2.14%), Fleisch (-3.05%), Horie-Waitzberg and Gonzalez (4.41%), and BIA2 (5.25%). Similar results were shown by the Bland-Altman analyses. BIA2, followed by BIA1, Ireton-Jones, Mifflin, and Fleisch, showed the highest association with IC1. Thus, the Mifflin, Fleisch, Horie-Waitzberg and Gonzalez equations, and BIA2, were the most accurate methods for REE estimation in this study. However, because those equations have shown considerable variability, they should be used cautiously. In addition, the IC2 was not found to be an accurate method for REE estimation in overweight and obese men included in this study. Copyright © 2012 Academy of Nutrition and Dietetics. Published by Elsevier Inc. All rights reserved.

Effect of picric acid and enzymatic creatinine on the efficiency of the glomerular filtration rate predicator formula.

PubMed

Qiu, Ling; Guo, Xiuzhi; Zhu, Yan; Shou, Weilin; Gong, Mengchun; Zhang, Lin; Han, Huijuan; Quan, Guoqiang; Xu, Tao; Li, Hang; Li, Xuewang

2013-01-01

To investigate the impact of serum creatinine measurement on the applicability of glomerular filtration rate (GFR) evaluation equations. 99mTc-DTPA plasma clearance rate was used as GFR reference (rGFR) in patients with chronic kidney disease (CKD). Serum creatinine was measureded using enzymatic or picric acid creatinine reagent. The GFR of the patients were estimated using the Cockcroft-Gault equation corrected for body surface area, simplified Modification of Diet in Renal Disease (MDRD) equation, simplified MDRD equation corrected to isotopes dilution mass spectrometry, the CKD epidemiology collaborative research equation, and two Chinese simplified MDRD equations. Significant differences in the eGFR results estimated through enzymatic and picric acid methods were observed for the same evaluation equation. The intraclass correlation coefficient (ICC) of eGFR when the creatinine was measured by the picric acid method was significantly lower than that of the enzymatic method. The assessment accuracy of every equation using the enzymatic method to measure creatinine was significantly higher than that measured by the picric acid method when rGFR was > or = 60 mL/min/1.73m2. A significant difference was demonstrated in the same GFR evaluation equation using the picric acid and enzymatic methods. The enzymatic creatinine method was better than the picric acid method.

Using Grain-Size Distribution Methods for Estimation of Air Permeability.

PubMed

Wang, Tiejun; Huang, Yuanyang; Chen, Xunhong; Chen, Xi

2016-01-01

Knowledge of air permeability (ka ) at dry conditions is critical for the use of air flow models in porous media; however, it is usually difficult and time consuming to measure ka at dry conditions. It is thus desirable to estimate ka at dry conditions from other readily obtainable properties. In this study, the feasibility of using information derived from grain-size distributions (GSDs) for estimating ka at dry conditions was examined. Fourteen GSD-based equations originally developed for estimating saturated hydraulic conductivity were tested using ka measured at dry conditions in both undisturbed and disturbed river sediment samples. On average, the estimated ka from all the equations, except for the method of Slichter, differed by less than ± 4 times from the measured ka for both undisturbed and disturbed groups. In particular, for the two sediment groups, the results given by the methods of Terzaghi and Hazen-modified were comparable to the measured ka . In addition, two methods (e.g., Barr and Beyer) for the undisturbed samples and one method (e.g., Hazen-original) for the undisturbed samples were also able to produce comparable ka estimates. Moreover, after adjusting the values of the coefficient C in the GSD-based equations, the estimation of ka was significantly improved with the differences between the measured and estimated ka less than ±4% on average (except for the method of Barr). As demonstrated by this study, GSD-based equations may provide a promising and efficient way to estimate ka at dry conditions. © 2015, National Ground Water Association.

Evaluation of Maryland abutment scour equation through selected threshold velocity methods

USGS Publications Warehouse

Benedict, S.T.

2010-01-01

The U.S. Geological Survey, in cooperation with the Maryland State Highway Administration, used field measurements of scour to evaluate the sensitivity of the Maryland abutment scour equation to the critical (or threshold) velocity variable. Four selected methods for estimating threshold velocity were applied to the Maryland abutment scour equation, and the predicted scour to the field measurements were compared. Results indicated that performance of the Maryland abutment scour equation was sensitive to the threshold velocity with some threshold velocity methods producing better estimates of predicted scour than did others. In addition, results indicated that regional stream characteristics can affect the performance of the Maryland abutment scour equation with moderate-gradient streams performing differently from low-gradient streams. On the basis of the findings of the investigation, guidance for selecting threshold velocity methods for application to the Maryland abutment scour equation are provided, and limitations are noted.

Using an EM Covariance Matrix to Estimate Structural Equation Models with Missing Data: Choosing an Adjusted Sample Size to Improve the Accuracy of Inferences

ERIC Educational Resources Information Center

Enders, Craig K.; Peugh, James L.

2004-01-01

Two methods, direct maximum likelihood (ML) and the expectation maximization (EM) algorithm, can be used to obtain ML parameter estimates for structural equation models with missing data (MD). Although the 2 methods frequently produce identical parameter estimates, it may be easier to satisfy missing at random assumptions using EM. However, no…

Estimating parameters for tree basal area growth with a system of equations and seemingly unrelated regressions

Treesearch

Charles E. Rose; Thomas B. Lynch

2001-01-01

A method was developed for estimating parameters in an individual tree basal area growth model using a system of equations based on dbh rank classes. The estimation method developed is a compromise between an individual tree and a stand level basal area growth model that accounts for the correlation between trees within a plot by using seemingly unrelated regression (...

Generalized Ordinary Differential Equation Models 1

PubMed Central

Miao, Hongyu; Wu, Hulin; Xue, Hongqi

2014-01-01

Existing estimation methods for ordinary differential equation (ODE) models are not applicable to discrete data. The generalized ODE (GODE) model is therefore proposed and investigated for the first time. We develop the likelihood-based parameter estimation and inference methods for GODE models. We propose robust computing algorithms and rigorously investigate the asymptotic properties of the proposed estimator by considering both measurement errors and numerical errors in solving ODEs. The simulation study and application of our methods to an influenza viral dynamics study suggest that the proposed methods have a superior performance in terms of accuracy over the existing ODE model estimation approach and the extended smoothing-based (ESB) method. PMID:25544787

Generalized Ordinary Differential Equation Models.

PubMed

Miao, Hongyu; Wu, Hulin; Xue, Hongqi

2014-10-01

Existing estimation methods for ordinary differential equation (ODE) models are not applicable to discrete data. The generalized ODE (GODE) model is therefore proposed and investigated for the first time. We develop the likelihood-based parameter estimation and inference methods for GODE models. We propose robust computing algorithms and rigorously investigate the asymptotic properties of the proposed estimator by considering both measurement errors and numerical errors in solving ODEs. The simulation study and application of our methods to an influenza viral dynamics study suggest that the proposed methods have a superior performance in terms of accuracy over the existing ODE model estimation approach and the extended smoothing-based (ESB) method.

Techniques for estimating flood-peak discharges of rural, unregulated streams in Ohio

USGS Publications Warehouse

Koltun, G.F.

2003-01-01

Regional equations for estimating 2-, 5-, 10-, 25-, 50-, 100-, and 500-year flood-peak discharges at ungaged sites on rural, unregulated streams in Ohio were developed by means of ordinary and generalized least-squares (GLS) regression techniques. One-variable, simple equations and three-variable, full-model equations were developed on the basis of selected basin characteristics and flood-frequency estimates determined for 305 streamflow-gaging stations in Ohio and adjacent states. The average standard errors of prediction ranged from about 39 to 49 percent for the simple equations, and from about 34 to 41 percent for the full-model equations. Flood-frequency estimates determined by means of log-Pearson Type III analyses are reported along with weighted flood-frequency estimates, computed as a function of the log-Pearson Type III estimates and the regression estimates. Values of explanatory variables used in the regression models were determined from digital spatial data sets by means of a geographic information system (GIS), with the exception of drainage area, which was determined by digitizing the area within basin boundaries manually delineated on topographic maps. Use of GIS-based explanatory variables represents a major departure in methodology from that described in previous reports on estimating flood-frequency characteristics of Ohio streams. Examples are presented illustrating application of the regression equations to ungaged sites on ungaged and gaged streams. A method is provided to adjust regression estimates for ungaged sites by use of weighted and regression estimates for a gaged site on the same stream. A region-of-influence method, which employs a computer program to estimate flood-frequency characteristics for ungaged sites based on data from gaged sites with similar characteristics, was also tested and compared to the GLS full-model equations. For all recurrence intervals, the GLS full-model equations had superior prediction accuracy relative to the simple equations and therefore are recommended for use.

Comparison of estimation accuracy of body density between different hydrostatics weighing methods without head submersion.

PubMed

Demura, Shinichi; Sato, Susumu; Nakada, Masakatsu; Minami, Masaki; Kitabayashi, Tamotsu

2003-07-01

This study compared the accuracy of body density (Db) estimation methods using hydrostatic weighing without complete head submersion (HW(withoutHS)) of Donnelly et al. (1988) and Donnelly and Sintek (1984) as referenced to Goldman and Buskirk's approach (1961). Donnelly et al.'s method estimates Db from a regression equation using HW(withoutHS), moreover, Donnelly and Sintek's method estimates it from HW(withoutHS) and head anthropometric variables. Fifteen Japanese males (173.8+/-4.5 cm, 63.6+/-5.4 kg, 21.2+/-2.8 years) and fifteen females (161.4+/-5.4 cm, 53.8+/-4.8 kg, 21.0+/-1.4 years) participated in this study. All the subjects were measured for head length, width and HWs under the two conditions of with and without head submersion. In order to examine the consistency of estimation values of Db, the correlation coefficients between the estimation values and the reference (Goldman and Buskirk, 1961) were calculated. The standard errors of estimation (SEE) were calculated by regression analysis using a reference value as a dependent variable and estimation values as independent variables. In addition, the systematic errors of two estimation methods were investigated by the Bland-Altman technique (Bland and Altman, 1986). In the estimation, Donnelly and Sintek's equation showed a high relationship with the reference (r=0.960, p<0.01), but had more differences from the reference compared with Donnelly et al.'s equation. Further studies are needed to develop new prediction equations for Japanese considering sex and individual differences in head anthropometry.

Technique for estimating depth of floods in Tennessee

USGS Publications Warehouse

Gamble, C.R.

1983-01-01

Estimates of flood depths are needed for design of roadways across flood plains and for other types of construction along streams. Equations for estimating flood depths in Tennessee were derived using data for 150 gaging stations. The equations are based on drainage basin size and can be used to estimate depths of the 10-year and 100-year floods for four hydrologic areas. A method also was developed for estimating depth of floods having recurrence intervals between 10 and 100 years. Standard errors range from 22 to 30 percent for the 10-year depth equations and from 23 to 30 percent for the 100-year depth equations. (USGS)

Body composition estimation from selected slices: equations computed from a new semi-automatic thresholding method developed on whole-body CT scans

PubMed Central

Villa, Chiara; Brůžek, Jaroslav

2017-01-01

Background Estimating volumes and masses of total body components is important for the study and treatment monitoring of nutrition and nutrition-related disorders, cancer, joint replacement, energy-expenditure and exercise physiology. While several equations have been offered for estimating total body components from MRI slices, no reliable and tested method exists for CT scans. For the first time, body composition data was derived from 41 high-resolution whole-body CT scans. From these data, we defined equations for estimating volumes and masses of total body AT and LT from corresponding tissue areas measured in selected CT scan slices. Methods We present a new semi-automatic approach to defining the density cutoff between adipose tissue (AT) and lean tissue (LT) in such material. An intra-class correlation coefficient (ICC) was used to validate the method. The equations for estimating the whole-body composition volume and mass from areas measured in selected slices were modeled with ordinary least squares (OLS) linear regressions and support vector machine regression (SVMR). Results and Discussion The best predictive equation for total body AT volume was based on the AT area of a single slice located between the 4th and 5th lumbar vertebrae (L4-L5) and produced lower prediction errors (|PE| = 1.86 liters, %PE = 8.77) than previous equations also based on CT scans. The LT area of the mid-thigh provided the lowest prediction errors (|PE| = 2.52 liters, %PE = 7.08) for estimating whole-body LT volume. We also present equations to predict total body AT and LT masses from a slice located at L4-L5 that resulted in reduced error compared with the previously published equations based on CT scans. The multislice SVMR predictor gave the theoretical upper limit for prediction precision of volumes and cross-validated the results. PMID:28533960

Prediction of distribution coefficient from structure. 1. Estimation method.

PubMed

Csizmadia, F; Tsantili-Kakoulidou, A; Panderi, I; Darvas, F

1997-07-01

A method has been developed for the estimation of the distribution coefficient (D), which considers the microspecies of a compound. D is calculated from the microscopic dissociation constants (microconstants), the partition coefficients of the microspecies, and the counterion concentration. A general equation for the calculation of D at a given pH is presented. The microconstants are calculated from the structure using Hammett and Taft equations. The partition coefficients of the ionic microspecies are predicted by empirical equations using the dissociation constants and the partition coefficient of the uncharged species, which are estimated from the structure by a Linear Free Energy Relationship method. The algorithm is implemented in a program module called PrologD.

A New Linearized Crank-Nicolson Mixed Element Scheme for the Extended Fisher-Kolmogorov Equation

PubMed Central

Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei

2013-01-01

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L 2(Ω))2 space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L 2 and H 1-norm for both the scalar unknown u and the diffusion term w = −Δu and a priori error estimates in (L 2)2-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes. PMID:23864831

A new linearized Crank-Nicolson mixed element scheme for the extended Fisher-Kolmogorov equation.

PubMed

Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei; Liu, Yang

2013-01-01

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L²(Ω))² space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L² and H¹-norm for both the scalar unknown u and the diffusion term w = -Δu and a priori error estimates in (L²)²-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes.

Using instrumental variables to estimate a Cox's proportional hazards regression subject to additive confounding

PubMed Central

Tosteson, Tor D.; Morden, Nancy E.; Stukel, Therese A.; O'Malley, A. James

2014-01-01

The estimation of treatment effects is one of the primary goals of statistics in medicine. Estimation based on observational studies is subject to confounding. Statistical methods for controlling bias due to confounding include regression adjustment, propensity scores and inverse probability weighted estimators. These methods require that all confounders are recorded in the data. The method of instrumental variables (IVs) can eliminate bias in observational studies even in the absence of information on confounders. We propose a method for integrating IVs within the framework of Cox's proportional hazards model and demonstrate the conditions under which it recovers the causal effect of treatment. The methodology is based on the approximate orthogonality of an instrument with unobserved confounders among those at risk. We derive an estimator as the solution to an estimating equation that resembles the score equation of the partial likelihood in much the same way as the traditional IV estimator resembles the normal equations. To justify this IV estimator for a Cox model we perform simulations to evaluate its operating characteristics. Finally, we apply the estimator to an observational study of the effect of coronary catheterization on survival. PMID:25506259

Using instrumental variables to estimate a Cox's proportional hazards regression subject to additive confounding.

PubMed

MacKenzie, Todd A; Tosteson, Tor D; Morden, Nancy E; Stukel, Therese A; O'Malley, A James

2014-06-01

The estimation of treatment effects is one of the primary goals of statistics in medicine. Estimation based on observational studies is subject to confounding. Statistical methods for controlling bias due to confounding include regression adjustment, propensity scores and inverse probability weighted estimators. These methods require that all confounders are recorded in the data. The method of instrumental variables (IVs) can eliminate bias in observational studies even in the absence of information on confounders. We propose a method for integrating IVs within the framework of Cox's proportional hazards model and demonstrate the conditions under which it recovers the causal effect of treatment. The methodology is based on the approximate orthogonality of an instrument with unobserved confounders among those at risk. We derive an estimator as the solution to an estimating equation that resembles the score equation of the partial likelihood in much the same way as the traditional IV estimator resembles the normal equations. To justify this IV estimator for a Cox model we perform simulations to evaluate its operating characteristics. Finally, we apply the estimator to an observational study of the effect of coronary catheterization on survival.

Estimating Soil Hydraulic Parameters using Gradient Based Approach

NASA Astrophysics Data System (ADS)

Rai, P. K.; Tripathi, S.

2017-12-01

The conventional way of estimating parameters of a differential equation is to minimize the error between the observations and their estimates. The estimates are produced from forward solution (numerical or analytical) of differential equation assuming a set of parameters. Parameter estimation using the conventional approach requires high computational cost, setting-up of initial and boundary conditions, and formation of difference equations in case the forward solution is obtained numerically. Gaussian process based approaches like Gaussian Process Ordinary Differential Equation (GPODE) and Adaptive Gradient Matching (AGM) have been developed to estimate the parameters of Ordinary Differential Equations without explicitly solving them. Claims have been made that these approaches can straightforwardly be extended to Partial Differential Equations; however, it has been never demonstrated. This study extends AGM approach to PDEs and applies it for estimating parameters of Richards equation. Unlike the conventional approach, the AGM approach does not require setting-up of initial and boundary conditions explicitly, which is often difficult in real world application of Richards equation. The developed methodology was applied to synthetic soil moisture data. It was seen that the proposed methodology can estimate the soil hydraulic parameters correctly and can be a potential alternative to the conventional method.

Estimating the magnitude of peak flows at selected recurrence intervals for streams in Idaho

USGS Publications Warehouse

Berenbrock, Charles

2002-01-01

The region-of-influence method is not recommended for use in determining flood-frequency estimates for ungaged sites in Idaho because the results, overall, are less accurate and the calculations are more complex than those of regional regression equations. The regional regression equations were considered to be the primary method of estimating the magnitude and frequency of peak flows for ungaged sites in Idaho.

Quasi-Maximum Likelihood Estimation of Structural Equation Models with Multiple Interaction and Quadratic Effects

ERIC Educational Resources Information Center

Klein, Andreas G.; Muthen, Bengt O.

2007-01-01

In this article, a nonlinear structural equation model is introduced and a quasi-maximum likelihood method for simultaneous estimation and testing of multiple nonlinear effects is developed. The focus of the new methodology lies on efficiency, robustness, and computational practicability. Monte-Carlo studies indicate that the method is highly…

Network Reconstruction From High-Dimensional Ordinary Differential Equations.

PubMed

Chen, Shizhe; Shojaie, Ali; Witten, Daniela M

2017-01-01

We consider the task of learning a dynamical system from high-dimensional time-course data. For instance, we might wish to estimate a gene regulatory network from gene expression data measured at discrete time points. We model the dynamical system nonparametrically as a system of additive ordinary differential equations. Most existing methods for parameter estimation in ordinary differential equations estimate the derivatives from noisy observations. This is known to be challenging and inefficient. We propose a novel approach that does not involve derivative estimation. We show that the proposed method can consistently recover the true network structure even in high dimensions, and we demonstrate empirical improvement over competing approaches. Supplementary materials for this article are available online.

Estimation of true height: a study in population-specific methods among young South African adults.

PubMed

Lahner, Christen Renée; Kassier, Susanna Maria; Veldman, Frederick Johannes

2017-02-01

To investigate the accuracy of arm-associated height estimation methods in the calculation of true height compared with stretch stature in a sample of young South African adults. A cross-sectional descriptive design was employed. Pietermaritzburg, Westville and Durban, KwaZulu-Natal, South Africa, 2015. Convenience sample (N 900) aged 18-24 years, which included an equal number of participants from both genders (150 per gender) stratified across race (Caucasian, Black African and Indian). Continuous variables that were investigated included: (i) stretch stature; (ii) total armspan; (iii) half-armspan; (iv) half-armspan ×2; (v) demi-span; (vi) demi-span gender-specific equation; (vii) WHO equation; and (viii) WHO-adjusted equations; as well as categorization according to gender and race. Statistical analysis was conducted using IBM SPSS Statistics Version 21.0. Significant correlations were identified between gender and height estimation measurements, with males being anatomically larger than females (P<0·001). Significant differences were documented when study participants were stratified according to race and gender (P<0·001). Anatomical similarities were noted between Indians and Black Africans, whereas Caucasians were anatomically different from the other race groups. Arm-associated height estimation methods were able to estimate true height; however, each method was specific to each gender and race group. Height can be calculated by using arm-associated measurements. Although universal equations for estimating true height exist, for the enhancement of accuracy, the use of equations that are race-, gender- and population-specific should be considered.

Correlation of cystatin C and creatinine based estimates of renal function in children with hydronephrosis.

PubMed

Momtaz, Hossein-Emad; Dehghan, Arash; Karimian, Mohammad

2016-01-01

The use of a simple and accurate glomerular filtration rate (GFR) estimating method aiming minute assessment of renal function can be of great clinical importance. This study aimed to determine the association of a GFR estimating by equation that includes only cystatin C (Gentian equation) to equation that include only creatinine (Schwartz equation) among children. A total of 31 children aged from 1 day to 5 years with the final diagnosis of unilateral or bilateral hydronephrosis referred to Besat hospital in Hamadan, between March 2010 and February 2011 were consecutively enrolled. Schwartz and Gentian equations were employed to determine GFR based on plasma creatinine and cystatin C levels, respectively. The proportion of GFR based on Schwartz equation was 70.19± 24.86 ml/min/1.73 m(2), while the level of this parameter based on Gentian method and using cystatin C was 86.97 ± 21.57 ml/min/1.73 m(2). The Pearson correlation coefficient analysis showed a strong direct association between the two levels of GFR measured by Schwartz equation based on serum creatinine level and Gentian method and using cystatin C (r = 0.594, P < 0.001). The linear association between GFR values measured with the two methods included cystatin C based GFR = 50.8+ 0.515 × Schwartz GFR. The correlation between GFR values measured by using serum creatinine and serum cystatin C measurements remained meaningful even after adjustment for patients' gender and age (r = 0.724, P < 0.001). The equation developed based on cystatin C level is comparable with another equation, based on serum creatinine (Schwartz formula) to estimate GFR in children.

Comparison of methods to assess change in children’s body composition123

PubMed Central

Elberg, Jane; McDuffie, Jennifer R; Sebring, Nancy G; Salaita, Christine; Keil, Margaret; Robotham, Delphine; Reynolds, James C; Yanovski, Jack A

2008-01-01

Background Little is known about how simpler and more available methods to measure change in body fatness compare with criterion methods such as dual-energy X-ray absorptiometry (DXA) in children. Objective Our objective was to determine the ability of air-displacement plethysmography (ADP) and formulas based on triceps skinfold thickness (TSF) and bioelectrical impedance analysis (BIA) to estimate changes in body fat over time in children. Design Eighty-six nonoverweight and overweight boys (n = 34) and girls (n = 52) with an average age of 11.0 ± 2.4 y underwent ADP, TSF measurement, BIA, and DXA to estimate body fatness at baseline and 1 ± 0.3 y later. Recent equations were used to estimate percentage body fat by TSF measurement (Dezenberg equation) and by BIA (Suprasongsin and Lewy equations). Percentage body fat estimates by ADP, TSF measurement, and BIA were compared with those by DXA. Results All methods were highly correlated with DXA (P < 0.001). No mean bias for estimates of percentage body fat change was found for ADP (Siri equation) compared with DXA for all subjects examined together, and agreement between body fat estimation by ADP and DXA did not vary with race or sex. Magnitude bias was present for ADP relative to DXA (P < 0.01). Estimates of change in percentage body fat were systematically overestimated by BIA equations (1.37 ± 6.98%; P < 0.001). TSF accounted for only 13% of the variance in percentage body fat change. Conclusion Compared with DXA, there appears to be no noninvasive and simple method to measure changes in children’s percentage body fat accurately and precisely, but ADP performed better than did TSF or BIA. ADP could prove useful for measuring changes in adiposity in children. PMID:15213029

Estimating equations estimates of trends

USGS Publications Warehouse

Link, W.A.; Sauer, J.R.

1994-01-01

The North American Breeding Bird Survey monitors changes in bird populations through time using annual counts at fixed survey sites. The usual method of estimating trends has been to use the logarithm of the counts in a regression analysis. It is contended that this procedure is reasonably satisfactory for more abundant species, but produces biased estimates for less abundant species. An alternative estimation procedure based on estimating equations is presented.

Weight estimation techniques for composite airplanes in general aviation industry

NASA Technical Reports Server (NTRS)

Paramasivam, T.; Horn, W. J.; Ritter, J.

1986-01-01

Currently available weight estimation methods for general aviation airplanes were investigated. New equations with explicit material properties were developed for the weight estimation of aircraft components such as wing, fuselage and empennage. Regression analysis was applied to the basic equations for a data base of twelve airplanes to determine the coefficients. The resulting equations can be used to predict the component weights of either metallic or composite airplanes.

Error analysis of finite element method for Poisson–Nernst–Planck equations

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

Sun, Yuzhou; Sun, Pengtao; Zheng, Bin

A priori error estimates of finite element method for time-dependent Poisson-Nernst-Planck equations are studied in this work. We obtain the optimal error estimates in L∞(H1) and L2(H1) norms, and suboptimal error estimates in L∞(L2) norm, with linear element, and optimal error estimates in L∞(L2) norm with quadratic or higher-order element, for both semi- and fully discrete finite element approximations. Numerical experiments are also given to validate the theoretical results.

A one-step method for modelling longitudinal data with differential equations.

PubMed

Hu, Yueqin; Treinen, Raymond

2018-04-06

Differential equation models are frequently used to describe non-linear trajectories of longitudinal data. This study proposes a new approach to estimate the parameters in differential equation models. Instead of estimating derivatives from the observed data first and then fitting a differential equation to the derivatives, our new approach directly fits the analytic solution of a differential equation to the observed data, and therefore simplifies the procedure and avoids bias from derivative estimations. A simulation study indicates that the analytic solutions of differential equations (ASDE) approach obtains unbiased estimates of parameters and their standard errors. Compared with other approaches that estimate derivatives first, ASDE has smaller standard error, larger statistical power and accurate Type I error. Although ASDE obtains biased estimation when the system has sudden phase change, the bias is not serious and a solution is also provided to solve the phase problem. The ASDE method is illustrated and applied to a two-week study on consumers' shopping behaviour after a sale promotion, and to a set of public data tracking participants' grammatical facial expression in sign language. R codes for ASDE, recommendations for sample size and starting values are provided. Limitations and several possible expansions of ASDE are also discussed. © 2018 The British Psychological Society.

Alternative Regression Equations for Estimation of Annual Peak-Streamflow Frequency for Undeveloped Watersheds in Texas using PRESS Minimization

USGS Publications Warehouse

Asquith, William H.; Thompson, David B.

2008-01-01

The U.S. Geological Survey, in cooperation with the Texas Department of Transportation and in partnership with Texas Tech University, investigated a refinement of the regional regression method and developed alternative equations for estimation of peak-streamflow frequency for undeveloped watersheds in Texas. A common model for estimation of peak-streamflow frequency is based on the regional regression method. The current (2008) regional regression equations for 11 regions of Texas are based on log10 transformations of all regression variables (drainage area, main-channel slope, and watershed shape). Exclusive use of log10-transformation does not fully linearize the relations between the variables. As a result, some systematic bias remains in the current equations. The bias results in overestimation of peak streamflow for both the smallest and largest watersheds. The bias increases with increasing recurrence interval. The primary source of the bias is the discernible curvilinear relation in log10 space between peak streamflow and drainage area. Bias is demonstrated by selected residual plots with superimposed LOWESS trend lines. To address the bias, a statistical framework based on minimization of the PRESS statistic through power transformation of drainage area is described and implemented, and the resulting regression equations are reported. Compared to log10-exclusive equations, the equations derived from PRESS minimization have PRESS statistics and residual standard errors less than the log10 exclusive equations. Selected residual plots for the PRESS-minimized equations are presented to demonstrate that systematic bias in regional regression equations for peak-streamflow frequency estimation in Texas can be reduced. Because the overall error is similar to the error associated with previous equations and because the bias is reduced, the PRESS-minimized equations reported here provide alternative equations for peak-streamflow frequency estimation.

Male-Female Wage Differentials in the United States.

ERIC Educational Resources Information Center

Kiker, B. F.; Crouch, Henry L.

The primary objective of this paper is to describe a method of estimating female-male wage ratios. The estimating technique presented is two stage least squares (2SLS), in which equations are estimated for both men and women. After specifying and estimating the wage equations, the male-female wage differential is calculated that would remain if…

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.

Estimating total forest biomass in Maine, 1995

Treesearch

Eric H. Wharton; Douglas M. Griffith; Douglas M. Griffith

1998-01-01

Presents methods for synthesizing information from existing biomass literature for estimating biomass over extensive forest areas with specific applications to Maine. Tables of appropriate regression equations and the tree and shrub species to which these equations can be applied are presented as well as biomass estimates at the county and state level.

Methods for estimating the optical constants of atmospheric hazes based on complex optical measurements

NASA Technical Reports Server (NTRS)

Zuev, V. E.; Kostin, B. S.; Naats, I. E.

1986-01-01

The methods of multifrequency laser sounding (MLS) are the most effective remote methods for investigating the atmospheric aerosols, since it is possible to obtain complete information on aerosol microstructure and the effective methods for estimating the aerosol optical constants can be developed. The MLS data interpretation consists in the solution of the set of equations containing those of laser sounding and equations for polydispersed optical characteristics. As a rule, the laser sounding equation is written in the approximation of single scattering and the equations for optical characteristics are written assuming that the atmospheric aerosol is formed by spherical and homogeneous particles. To remove the indeterminacy of equations, the method of optical sounding of atmospheric aerosol, consisting in a joint use of a mutifrequency lidar and a spectral photometer in common geometrical scheme of the optical experiment was suggested. The method is used for investigating aerosols in the cases when absorption by particles is small and indicates the minimum necessary for interpretation of a series of measurements.

Revised techniques for estimating peak discharges from channel width in Montana

USGS Publications Warehouse

Parrett, Charles; Hull, J.A.; Omang, R.J.

1987-01-01

This study was conducted to develop new estimating equations based on channel width and the updated flood frequency curves of previous investigations. Simple regression equations for estimating peak discharges with recurrence intervals of 2, 5, 10 , 25, 50, and 100 years were developed for seven regions in Montana. The standard errors of estimates for the equations that use active channel width as the independent variables ranged from 30% to 87%. The standard errors of estimate for the equations that use bankfull width as the independent variable ranged from 34% to 92%. The smallest standard errors generally occurred in the prediction equations for the 2-yr flood, 5-yr flood, and 10-yr flood, and the largest standard errors occurred in the prediction equations for the 100-yr flood. The equations that use active channel width and the equations that use bankfull width were determined to be about equally reliable in five regions. In the West Region, the equations that use bankfull width were slightly more reliable than those based on active channel width, whereas in the East-Central Region the equations that use active channel width were slightly more reliable than those based on bankfull width. Compared with similar equations previously developed, the standard errors of estimate for the new equations are substantially smaller in three regions and substantially larger in two regions. Limitations on the use of the estimating equations include: (1) The equations are based on stable conditions of channel geometry and prevailing water and sediment discharge; (2) The measurement of channel width requires a site visit, preferably by a person with experience in the method, and involves appreciable measurement errors; (3) Reliability of results from the equations for channel widths beyond the range of definition is unknown. In spite of the limitations, the estimating equations derived in this study are considered to be as reliable as estimating equations based on basin and climatic variables. Because the two types of estimating equations are independent, results from each can be weighted inversely proportional to their variances, and averaged. The weighted average estimate has a variance less than either individual estimate. (Author 's abstract)

Percent body fat estimations in college men using field and laboratory methods: A three-compartment model approach

PubMed Central

Moon, Jordan R; Tobkin, Sarah E; Smith, Abbie E; Roberts, Michael D; Ryan, Eric D; Dalbo, Vincent J; Lockwood, Chris M; Walter, Ashley A; Cramer, Joel T; Beck, Travis W; Stout, Jeffrey R

2008-01-01

Background Methods used to estimate percent body fat can be classified as a laboratory or field technique. However, the validity of these methods compared to multiple-compartment models has not been fully established. The purpose of this study was to determine the validity of field and laboratory methods for estimating percent fat (%fat) in healthy college-age men compared to the Siri three-compartment model (3C). Methods Thirty-one Caucasian men (22.5 ± 2.7 yrs; 175.6 ± 6.3 cm; 76.4 ± 10.3 kg) had their %fat estimated by bioelectrical impedance analysis (BIA) using the BodyGram™ computer program (BIA-AK) and population-specific equation (BIA-Lohman), near-infrared interactance (NIR) (Futrex® 6100/XL), four circumference-based military equations [Marine Corps (MC), Navy and Air Force (NAF), Army (A), and Friedl], air-displacement plethysmography (BP), and hydrostatic weighing (HW). Results All circumference-based military equations (MC = 4.7% fat, NAF = 5.2% fat, A = 4.7% fat, Friedl = 4.7% fat) along with NIR (NIR = 5.1% fat) produced an unacceptable total error (TE). Both laboratory methods produced acceptable TE values (HW = 2.5% fat; BP = 2.7% fat). The BIA-AK, and BIA-Lohman field methods produced acceptable TE values (2.1% fat). A significant difference was observed for the MC and NAF equations compared to both the 3C model and HW (p < 0.006). Conclusion Results indicate that the BP and HW are valid laboratory methods when compared to the 3C model to estimate %fat in college-age Caucasian men. When the use of a laboratory method is not feasible, BIA-AK, and BIA-Lohman are acceptable field methods to estimate %fat in this population. PMID:18426582

Relative Performance of Rescaling and Resampling Approaches to Model Chi Square and Parameter Standard Error Estimation in Structural Equation Modeling.

ERIC Educational Resources Information Center

Nevitt, Johnathan; Hancock, Gregory R.

Though common structural equation modeling (SEM) methods are predicated upon the assumption of multivariate normality, applied researchers often find themselves with data clearly violating this assumption and without sufficient sample size to use distribution-free estimation methods. Fortunately, promising alternatives are being integrated into…

Water-budget methods

USGS Publications Warehouse

Healy, Richard W.; Scanlon, Bridget R.

2010-01-01

A water budget is an accounting of water movement into and out of, and storage change within, some control volume. Universal and adaptable are adjectives that reflect key features of water-budget methods for estimating recharge. The universal concept of mass conservation of water implies that water-budget methods are applicable over any space and time scales (Healy et al., 2007). The water budget of a soil column in a laboratory can be studied at scales of millimeters and seconds. A water-budget equation is also an integral component of atmospheric general circulation models used to predict global climates over periods of decades or more. Water-budget equations can be easily customized by adding or removing terms to accurately portray the peculiarities of any hydrologic system. The equations are generally not bound by assumptions on mechanisms by which water moves into, through, and out of the control volume of interest. So water-budget methods can be used to estimate both diffuse and focused recharge, and recharge estimates are unaffected by phenomena such as preferential flow paths within the unsaturated zone.Water-budget methods represent the largest class of techniques for estimating recharge. Most hydrologic models are derived from a water-budget equation and can therefore be classified as water-budget models. It is not feasible to address all water-budget methods in a single chapter. This chapter is limited to discussion of the “residual” water-budget approach, whereby all variables in a water-budget equation, except for recharge, are independently measured or estimated and recharge is set equal to the residual. This chapter is closely linked with Chapter 3, on modeling methods, because the equations presented here form the basis of many models and because models are often used to estimate individual components in water-budget studies. Water budgets for streams and other surface-water bodies are addressed in Chapter 4. The use of soil-water budgets and lysimeters for determining potential recharge and evapotranspiration from changes in water storage is discussed in Chapter 5. Aquifer water-budget methods based on the measurement of groundwater levels are described in Chapter 6.

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.

Skinfold Prediction Equations Fail to Provide an Accurate Estimate of Body Composition in Elite Rugby Union Athletes of Caucasian and Polynesian Ethnicity.

PubMed

Zemski, Adam J; Broad, Elizabeth M; Slater, Gary J

2018-01-01

Body composition in elite rugby union athletes is routinely assessed using surface anthropometry, which can be utilized to provide estimates of absolute body composition using regression equations. This study aims to assess the ability of available skinfold equations to estimate body composition in elite rugby union athletes who have unique physique traits and divergent ethnicity. The development of sport-specific and ethnicity-sensitive equations was also pursued. Forty-three male international Australian rugby union athletes of Caucasian and Polynesian descent underwent surface anthropometry and dual-energy X-ray absorptiometry (DXA) assessment. Body fat percent (BF%) was estimated using five previously developed equations and compared to DXA measures. Novel sport and ethnicity-sensitive prediction equations were developed using forward selection multiple regression analysis. Existing skinfold equations provided unsatisfactory estimates of BF% in elite rugby union athletes, with all equations demonstrating a 95% prediction interval in excess of 5%. The equations tended to underestimate BF% at low levels of adiposity, whilst overestimating BF% at higher levels of adiposity, regardless of ethnicity. The novel equations created explained a similar amount of variance to those previously developed (Caucasians 75%, Polynesians 90%). The use of skinfold equations, including the created equations, cannot be supported to estimate absolute body composition. Until a population-specific equation is established that can be validated to precisely estimate body composition, it is advocated to use a proven method, such as DXA, when absolute measures of lean and fat mass are desired, and raw anthropometry data routinely to derive an estimate of body composition change.

Using a Linear Regression Method to Detect Outliers in IRT Common Item Equating

ERIC Educational Resources Information Center

He, Yong; Cui, Zhongmin; Fang, Yu; Chen, Hanwei

2013-01-01

Common test items play an important role in equating alternate test forms under the common item nonequivalent groups design. When the item response theory (IRT) method is applied in equating, inconsistent item parameter estimates among common items can lead to large bias in equated scores. It is prudent to evaluate inconsistency in parameter…

Robust Scale Transformation Methods in IRT True Score Equating under Common-Item Nonequivalent Groups Design

ERIC Educational Resources Information Center

He, Yong

2013-01-01

Common test items play an important role in equating multiple test forms under the common-item nonequivalent groups design. Inconsistent item parameter estimates among common items can lead to large bias in equated scores for IRT true score equating. Current methods extensively focus on detection and elimination of outlying common items, which…

Enhancing the Equating of Item Difficulty Metrics: Estimation of Reference Distribution. Research Report. ETS RR-14-07

ERIC Educational Resources Information Center

Ali, Usama S.; Walker, Michael E.

2014-01-01

Two methods are currently in use at Educational Testing Service (ETS) for equating observed item difficulty statistics. The first method involves the linear equating of item statistics in an observed sample to reference statistics on the same items. The second method, or the item response curve (IRC) method, involves the summation of conditional…

Polynomial mixture method of solving ordinary differential equations

NASA Astrophysics Data System (ADS)

Shahrir, Mohammad Shazri; Nallasamy, Kumaresan; Ratnavelu, Kuru; Kamali, M. Z. M.

2017-11-01

In this paper, a numerical solution of fuzzy quadratic Riccati differential equation is estimated using a proposed new approach that provides mixture of polynomials where iteratively the right mixture will be generated. This mixture provide a generalized formalism of traditional Neural Networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). This can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that Polynomial Mixture Method (PMM) shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over Mabood et al, RK-4, Multi-Agent NN and Neuro Method (NM).

An Improved Estimation Using Polya-Gamma Augmentation for Bayesian Structural Equation Models with Dichotomous Variables

ERIC Educational Resources Information Center

Kim, Seohyun; Lu, Zhenqiu; Cohen, Allan S.

2018-01-01

Bayesian algorithms have been used successfully in the social and behavioral sciences to analyze dichotomous data particularly with complex structural equation models. In this study, we investigate the use of the Polya-Gamma data augmentation method with Gibbs sampling to improve estimation of structural equation models with dichotomous variables.…

Comparative evaluation of technetium-99m-diethylenetriaminepentaacetic acid renal dynamic imaging versus the Modification of Diet in Renal Disease equation and the Chronic Kidney Disease Epidemiology Collaboration equation for the estimation of GFR.

PubMed

Huang, Qi; Chen, Yunshuang; Zhang, Min; Wang, Sihe; Zhang, Weiguang; Cai, Guangyan; Chen, Xiangmei; Sun, Xuefeng

2018-04-01

We compared the performance of technetium-99m-diethylenetriaminepentaacetic acid ( 99m Tc-DTPA) renal dynamic imaging (RDI), the MDRD equation, and the CKD EPI equation to estimate glomerular filtration rate (GFR). A total of 551 subjects, including CKD patients and healthy individuals, were enrolled in this study. Dual plasma sample clearance method of 99m Tc-DTPA was used as the true value for GFR (tGFR). RDI and the MDRD and CKD EPI equations for estimating GFR were compared and evaluated. Data indicate that RDI and the MDRD equation underestimated GFR and CKD EPI overestimated GFR. RDI was associated with significantly higher bias than the MDRD and CKD EPI equations. The regression coefficient, diagnostic precision, and consistency of RDI were significantly lower than either equation. RDI and the MDRD equation underestimated GFR to a greater degree in subjects with tGFR ≥ 90 ml/min/1.73 m 2 compared with the results obtained from all subjects. In the tGFR60-89 ml/min/1.73 m 2 group, the precision of RDI was significantly lower than that of both equations. In the tGFR30-59 ml/min/1.73 m 2 group, RDI had the least bias, the most precision, and significantly higher accuracy compared with either equation. In tGFR < 30 ml/min/1.73 m 2 , the three methods had similar performance and were not significantly different. RDI significantly underestimates GFR and performs no better than MDRD and CKD EPI equations for GFR estimation; thus, it should not be recommended as a reference standard against which other GFR measurement methods are assessed. However, RDI better estimates GFR than either equation for individuals in the tGFR30-59 ml/min/1.73 m 2 group and thus may be helpful to distinguish stage 3a and 3b CKD.

Five-equation and robust three-equation methods for solution verification of large eddy simulation

NASA Astrophysics Data System (ADS)

Dutta, Rabijit; Xing, Tao

2018-02-01

This study evaluates the recently developed general framework for solution verification methods for large eddy simulation (LES) using implicitly filtered LES of periodic channel flows at friction Reynolds number of 395 on eight systematically refined grids. The seven-equation method shows that the coupling error based on Hypothesis I is much smaller as compared with the numerical and modeling errors and therefore can be neglected. The authors recommend five-equation method based on Hypothesis II, which shows a monotonic convergence behavior of the predicted numerical benchmark ( S C ), and provides realistic error estimates without the need of fixing the orders of accuracy for either numerical or modeling errors. Based on the results from seven-equation and five-equation methods, less expensive three and four-equation methods for practical LES applications were derived. It was found that the new three-equation method is robust as it can be applied to any convergence types and reasonably predict the error trends. It was also observed that the numerical and modeling errors usually have opposite signs, which suggests error cancellation play an essential role in LES. When Reynolds averaged Navier-Stokes (RANS) based error estimation method is applied, it shows significant error in the prediction of S C on coarse meshes. However, it predicts reasonable S C when the grids resolve at least 80% of the total turbulent kinetic energy.

A theory of fine structure image models with an application to detection and classification of dementia.

PubMed

O'Neill, William; Penn, Richard; Werner, Michael; Thomas, Justin

2015-06-01

Estimation of stochastic process models from data is a common application of time series analysis methods. Such system identification processes are often cast as hypothesis testing exercises whose intent is to estimate model parameters and test them for statistical significance. Ordinary least squares (OLS) regression and the Levenberg-Marquardt algorithm (LMA) have proven invaluable computational tools for models being described by non-homogeneous, linear, stationary, ordinary differential equations. In this paper we extend stochastic model identification to linear, stationary, partial differential equations in two independent variables (2D) and show that OLS and LMA apply equally well to these systems. The method employs an original nonparametric statistic as a test for the significance of estimated parameters. We show gray scale and color images are special cases of 2D systems satisfying a particular autoregressive partial difference equation which estimates an analogous partial differential equation. Several applications to medical image modeling and classification illustrate the method by correctly classifying demented and normal OLS models of axial magnetic resonance brain scans according to subject Mini Mental State Exam (MMSE) scores. Comparison with 13 image classifiers from the literature indicates our classifier is at least 14 times faster than any of them and has a classification accuracy better than all but one. Our modeling method applies to any linear, stationary, partial differential equation and the method is readily extended to 3D whole-organ systems. Further, in addition to being a robust image classifier, estimated image models offer insights into which parameters carry the most diagnostic image information and thereby suggest finer divisions could be made within a class. Image models can be estimated in milliseconds which translate to whole-organ models in seconds; such runtimes could make real-time medicine and surgery modeling possible.

Percent body fat estimations in college men using field and laboratory methods: a three-compartment model approach.

PubMed

Moon, Jordan R; Tobkin, Sarah E; Smith, Abbie E; Roberts, Michael D; Ryan, Eric D; Dalbo, Vincent J; Lockwood, Chris M; Walter, Ashley A; Cramer, Joel T; Beck, Travis W; Stout, Jeffrey R

2008-04-21

Methods used to estimate percent body fat can be classified as a laboratory or field technique. However, the validity of these methods compared to multiple-compartment models has not been fully established. The purpose of this study was to determine the validity of field and laboratory methods for estimating percent fat (%fat) in healthy college-age men compared to the Siri three-compartment model (3C). Thirty-one Caucasian men (22.5 +/- 2.7 yrs; 175.6 +/- 6.3 cm; 76.4 +/- 10.3 kg) had their %fat estimated by bioelectrical impedance analysis (BIA) using the BodyGram computer program (BIA-AK) and population-specific equation (BIA-Lohman), near-infrared interactance (NIR) (Futrex(R) 6100/XL), four circumference-based military equations [Marine Corps (MC), Navy and Air Force (NAF), Army (A), and Friedl], air-displacement plethysmography (BP), and hydrostatic weighing (HW). All circumference-based military equations (MC = 4.7% fat, NAF = 5.2% fat, A = 4.7% fat, Friedl = 4.7% fat) along with NIR (NIR = 5.1% fat) produced an unacceptable total error (TE). Both laboratory methods produced acceptable TE values (HW = 2.5% fat; BP = 2.7% fat). The BIA-AK, and BIA-Lohman field methods produced acceptable TE values (2.1% fat). A significant difference was observed for the MC and NAF equations compared to both the 3C model and HW (p < 0.006). Results indicate that the BP and HW are valid laboratory methods when compared to the 3C model to estimate %fat in college-age Caucasian men. When the use of a laboratory method is not feasible, BIA-AK, and BIA-Lohman are acceptable field methods to estimate %fat in this population.

A Two-Stage Estimation Method for Random Coefficient Differential Equation Models with Application to Longitudinal HIV Dynamic Data.

PubMed

Fang, Yun; Wu, Hulin; Zhu, Li-Xing

2011-07-01

We propose a two-stage estimation method for random coefficient ordinary differential equation (ODE) models. A maximum pseudo-likelihood estimator (MPLE) is derived based on a mixed-effects modeling approach and its asymptotic properties for population parameters are established. The proposed method does not require repeatedly solving ODEs, and is computationally efficient although it does pay a price with the loss of some estimation efficiency. However, the method does offer an alternative approach when the exact likelihood approach fails due to model complexity and high-dimensional parameter space, and it can also serve as a method to obtain the starting estimates for more accurate estimation methods. In addition, the proposed method does not need to specify the initial values of state variables and preserves all the advantages of the mixed-effects modeling approach. The finite sample properties of the proposed estimator are studied via Monte Carlo simulations and the methodology is also illustrated with application to an AIDS clinical data set.

An improved method for nonlinear parameter estimation: a case study of the Rössler model

NASA Astrophysics Data System (ADS)

He, Wen-Ping; Wang, Liu; Jiang, Yun-Di; Wan, Shi-Quan

2016-08-01

Parameter estimation is an important research topic in nonlinear dynamics. Based on the evolutionary algorithm (EA), Wang et al. (2014) present a new scheme for nonlinear parameter estimation and numerical tests indicate that the estimation precision is satisfactory. However, the convergence rate of the EA is relatively slow when multiple unknown parameters in a multidimensional dynamical system are estimated simultaneously. To solve this problem, an improved method for parameter estimation of nonlinear dynamical equations is provided in the present paper. The main idea of the improved scheme is to use all of the known time series for all of the components in some dynamical equations to estimate the parameters in single component one by one, instead of estimating all of the parameters in all of the components simultaneously. Thus, we can estimate all of the parameters stage by stage. The performance of the improved method was tested using a classic chaotic system—Rössler model. The numerical tests show that the amended parameter estimation scheme can greatly improve the searching efficiency and that there is a significant increase in the convergence rate of the EA, particularly for multiparameter estimation in multidimensional dynamical equations. Moreover, the results indicate that the accuracy of parameter estimation and the CPU time consumed by the presented method have no obvious dependence on the sample size.

Estimating total forest biomass in New York, 1993

Treesearch

Eric Wharton; Carol Alerich; David A. Drake; David A. Drake

1997-01-01

Presents methods for synthesizing information from existing biomass literature for estimating biomass over extensive forest areas with specific applications to New York. Tables of appropriate regression equations and the tree and shrub species to which these equations can be applied are presented well as biomass estimates at the county, geographic unit, and state level...

Body composition estimation from selected slices: equations computed from a new semi-automatic thresholding method developed on whole-body CT scans.

PubMed

Lacoste Jeanson, Alizé; Dupej, Ján; Villa, Chiara; Brůžek, Jaroslav

2017-01-01

Estimating volumes and masses of total body components is important for the study and treatment monitoring of nutrition and nutrition-related disorders, cancer, joint replacement, energy-expenditure and exercise physiology. While several equations have been offered for estimating total body components from MRI slices, no reliable and tested method exists for CT scans. For the first time, body composition data was derived from 41 high-resolution whole-body CT scans. From these data, we defined equations for estimating volumes and masses of total body AT and LT from corresponding tissue areas measured in selected CT scan slices. We present a new semi-automatic approach to defining the density cutoff between adipose tissue (AT) and lean tissue (LT) in such material. An intra-class correlation coefficient (ICC) was used to validate the method. The equations for estimating the whole-body composition volume and mass from areas measured in selected slices were modeled with ordinary least squares (OLS) linear regressions and support vector machine regression (SVMR). The best predictive equation for total body AT volume was based on the AT area of a single slice located between the 4th and 5th lumbar vertebrae (L4-L5) and produced lower prediction errors (|PE| = 1.86 liters, %PE = 8.77) than previous equations also based on CT scans. The LT area of the mid-thigh provided the lowest prediction errors (|PE| = 2.52 liters, %PE = 7.08) for estimating whole-body LT volume. We also present equations to predict total body AT and LT masses from a slice located at L4-L5 that resulted in reduced error compared with the previously published equations based on CT scans. The multislice SVMR predictor gave the theoretical upper limit for prediction precision of volumes and cross-validated the results.

A Monte Carlo Evaluation of Estimated Parameters of Five Shrinkage Estimate Formuli.

ERIC Educational Resources Information Center

Newman, Isadore; And Others

A Monte Carlo study was conducted to estimate the efficiency of and the relationship between five equations and the use of cross validation as methods for estimating shrinkage in multiple correlations. Two of the methods were intended to estimate shrinkage to population values and the other methods were intended to estimate shrinkage from sample…

Estimating fire-caused mortality and injury in oak-hickory forests.

Treesearch

Robert M. Loomis

1973-01-01

Presents equations and graphs for predicting fire-caused tree mortality and equations for estimating basal wound dimensions for surviving trees. The methods apply to black oak, white oak, and some other species of the oak-hickory forest type.

Spatiotemporal motion boundary detection and motion boundary velocity estimation for tracking moving objects with a moving camera: a level sets PDEs approach with concurrent camera motion compensation.

PubMed

Feghali, Rosario; Mitiche, Amar

2004-11-01

The purpose of this study is to investigate a method of tracking moving objects with a moving camera. This method estimates simultaneously the motion induced by camera movement. The problem is formulated as a Bayesian motion-based partitioning problem in the spatiotemporal domain of the image quence. An energy functional is derived from the Bayesian formulation. The Euler-Lagrange descent equations determine imultaneously an estimate of the image motion field induced by camera motion and an estimate of the spatiotemporal motion undary surface. The Euler-Lagrange equation corresponding to the surface is expressed as a level-set partial differential equation for topology independence and numerically stable implementation. The method can be initialized simply and can track multiple objects with nonsimultaneous motions. Velocities on motion boundaries can be estimated from geometrical properties of the motion boundary. Several examples of experimental verification are given using synthetic and real-image sequences.

Peak-flow characteristics of Virginia streams

USGS Publications Warehouse

Austin, Samuel H.; Krstolic, Jennifer L.; Wiegand, Ute

2011-01-01

Peak-flow annual exceedance probabilities, also called probability-percent chance flow estimates, and regional regression equations are provided describing the peak-flow characteristics of Virginia streams. Statistical methods are used to evaluate peak-flow data. Analysis of Virginia peak-flow data collected from 1895 through 2007 is summarized. Methods are provided for estimating unregulated peak flow of gaged and ungaged streams. Station peak-flow characteristics identified by fitting the logarithms of annual peak flows to a Log Pearson Type III frequency distribution yield annual exceedance probabilities of 0.5, 0.4292, 0.2, 0.1, 0.04, 0.02, 0.01, 0.005, and 0.002 for 476 streamgaging stations. Stream basin characteristics computed using spatial data and a geographic information system are used as explanatory variables in regional regression model equations for six physiographic regions to estimate regional annual exceedance probabilities at gaged and ungaged sites. Weighted peak-flow values that combine annual exceedance probabilities computed from gaging station data and from regional regression equations provide improved peak-flow estimates. Text, figures, and lists are provided summarizing selected peak-flow sites, delineated physiographic regions, peak-flow estimates, basin characteristics, regional regression model equations, error estimates, definitions, data sources, and candidate regression model equations. This study supersedes previous studies of peak flows in Virginia.

An evaluation of regression methods to estimate nutritional condition of canvasbacks and other water birds

USGS Publications Warehouse

Sparling, D.W.; Barzen, J.A.; Lovvorn, J.R.; Serie, J.R.

1992-01-01

Regression equations that use mensural data to estimate body condition have been developed for several water birds. These equations often have been based on data that represent different sexes, age classes, or seasons, without being adequately tested for intergroup differences. We used proximate carcass analysis of 538 adult and juvenile canvasbacks (Aythya valisineria ) collected during fall migration, winter, and spring migrations in 1975-76 and 1982-85 to test regression methods for estimating body condition.

Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

NASA Astrophysics Data System (ADS)

Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

2017-04-01

This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

A variational approach to parameter estimation in ordinary differential equations.

PubMed

Kaschek, Daniel; Timmer, Jens

2012-08-14

Ordinary differential equations are widely-used in the field of systems biology and chemical engineering to model chemical reaction networks. Numerous techniques have been developed to estimate parameters like rate constants, initial conditions or steady state concentrations from time-resolved data. In contrast to this countable set of parameters, the estimation of entire courses of network components corresponds to an innumerable set of parameters. The approach presented in this work is able to deal with course estimation for extrinsic system inputs or intrinsic reactants, both not being constrained by the reaction network itself. Our method is based on variational calculus which is carried out analytically to derive an augmented system of differential equations including the unconstrained components as ordinary state variables. Finally, conventional parameter estimation is applied to the augmented system resulting in a combined estimation of courses and parameters. The combined estimation approach takes the uncertainty in input courses correctly into account. This leads to precise parameter estimates and correct confidence intervals. In particular this implies that small motifs of large reaction networks can be analysed independently of the rest. By the use of variational methods, elements from control theory and statistics are combined allowing for future transfer of methods between the two fields.

Low-flow characteristics of Virginia streams

USGS Publications Warehouse

Austin, Samuel H.; Krstolic, Jennifer L.; Wiegand, Ute

2011-01-01

Low-flow annual non-exceedance probabilities (ANEP), called probability-percent chance (P-percent chance) flow estimates, regional regression equations, and transfer methods are provided describing the low-flow characteristics of Virginia streams. Statistical methods are used to evaluate streamflow data. Analysis of Virginia streamflow data collected from 1895 through 2007 is summarized. Methods are provided for estimating low-flow characteristics of gaged and ungaged streams. The 1-, 4-, 7-, and 30-day average streamgaging station low-flow characteristics for 290 long-term, continuous-record, streamgaging stations are determined, adjusted for instances of zero flow using a conditional probability adjustment method, and presented for non-exceedance probabilities of 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0.05, 0.02, 0.01, and 0.005. Stream basin characteristics computed using spatial data and a geographic information system are used as explanatory variables in regional regression equations to estimate annual non-exceedance probabilities at gaged and ungaged sites and are summarized for 290 long-term, continuous-record streamgaging stations, 136 short-term, continuous-record streamgaging stations, and 613 partial-record streamgaging stations. Regional regression equations for six physiographic regions use basin characteristics to estimate 1-, 4-, 7-, and 30-day average low-flow annual non-exceedance probabilities at gaged and ungaged sites. Weighted low-flow values that combine computed streamgaging station low-flow characteristics and annual non-exceedance probabilities from regional regression equations provide improved low-flow estimates. Regression equations developed using the Maintenance of Variance with Extension (MOVE.1) method describe the line of organic correlation (LOC) with an appropriate index site for low-flow characteristics at 136 short-term, continuous-record streamgaging stations and 613 partial-record streamgaging stations. Monthly streamflow statistics computed on the individual daily mean streamflows of selected continuous-record streamgaging stations and curves describing flow-duration are presented. Text, figures, and lists are provided summarizing low-flow estimates, selected low-flow sites, delineated physiographic regions, basin characteristics, regression equations, error estimates, definitions, and data sources. This study supersedes previous studies of low flows in Virginia.

A mass-energy preserving Galerkin FEM for the coupled nonlinear fractional Schrödinger equations

NASA Astrophysics Data System (ADS)

Zhang, Guoyu; Huang, Chengming; Li, Meng

2018-04-01

We consider the numerical simulation of the coupled nonlinear space fractional Schrödinger equations. Based on the Galerkin finite element method in space and the Crank-Nicolson (CN) difference method in time, a fully discrete scheme is constructed. Firstly, we focus on a rigorous analysis of conservation laws for the discrete system. The definitions of discrete mass and energy here correspond with the original ones in physics. Then, we prove that the fully discrete system is uniquely solvable. Moreover, we consider the unconditionally convergent properties (that is to say, we complete the error estimates without any mesh ratio restriction). We derive L2-norm error estimates for the nonlinear equations and L^{∞}-norm error estimates for the linear equations. Finally, some numerical experiments are included showing results in agreement with the theoretical predictions.

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.

A superlinear convergence estimate for an iterative method for the biharmonic equation

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

Horn, M.A.

In [CDH] a method for the solution of boundary value problems for the biharmonic equation using conformal mapping was investigated. The method is an implementation of the classical method of Muskhelishvili. In [CDH] it was shown, using the Hankel structure, that the linear system in [Musk] is the discretization of the identify plus a compact operator, and therefore the conjugate gradient method will converge superlinearly. The purpose of this paper is to give an estimate of the superlinear convergence in the case when the boundary curve is in a Hoelder class.

An adaptive finite element method for the inequality-constrained Reynolds equation

NASA Astrophysics Data System (ADS)

Gustafsson, Tom; Rajagopal, Kumbakonam R.; Stenberg, Rolf; Videman, Juha

2018-07-01

We present a stabilized finite element method for the numerical solution of cavitation in lubrication, modeled as an inequality-constrained Reynolds equation. The cavitation model is written as a variable coefficient saddle-point problem and approximated by a residual-based stabilized method. Based on our recent results on the classical obstacle problem, we present optimal a priori estimates and derive novel a posteriori error estimators. The method is implemented as a Nitsche-type finite element technique and shown in numerical computations to be superior to the usually applied penalty methods.

A theory of fine structure image models with an application to detection and classification of dementia

PubMed Central

Penn, Richard; Werner, Michael; Thomas, Justin

2015-01-01

Background Estimation of stochastic process models from data is a common application of time series analysis methods. Such system identification processes are often cast as hypothesis testing exercises whose intent is to estimate model parameters and test them for statistical significance. Ordinary least squares (OLS) regression and the Levenberg-Marquardt algorithm (LMA) have proven invaluable computational tools for models being described by non-homogeneous, linear, stationary, ordinary differential equations. Methods In this paper we extend stochastic model identification to linear, stationary, partial differential equations in two independent variables (2D) and show that OLS and LMA apply equally well to these systems. The method employs an original nonparametric statistic as a test for the significance of estimated parameters. Results We show gray scale and color images are special cases of 2D systems satisfying a particular autoregressive partial difference equation which estimates an analogous partial differential equation. Several applications to medical image modeling and classification illustrate the method by correctly classifying demented and normal OLS models of axial magnetic resonance brain scans according to subject Mini Mental State Exam (MMSE) scores. Comparison with 13 image classifiers from the literature indicates our classifier is at least 14 times faster than any of them and has a classification accuracy better than all but one. Conclusions Our modeling method applies to any linear, stationary, partial differential equation and the method is readily extended to 3D whole-organ systems. Further, in addition to being a robust image classifier, estimated image models offer insights into which parameters carry the most diagnostic image information and thereby suggest finer divisions could be made within a class. Image models can be estimated in milliseconds which translate to whole-organ models in seconds; such runtimes could make real-time medicine and surgery modeling possible. PMID:26029638

Daily reference crop evapotranspiration in the humid environments of Azores islands using reduced data sets: accuracy of FAO-PM temperature and Hargreaves-Samani methods

NASA Astrophysics Data System (ADS)

Paredes, P.; Fontes, J. C.; Azevedo, E. B.; Pereira, L. S.

2017-11-01

Reference crop evapotranspiration (ETo) estimations using the FAO Penman-Monteith equation (PM-ETo) require several weather variables that are often not available. Then, ETo may be computed with procedures proposed in FAO56, either using the PM-ETo equation with temperature estimates of actual vapor pressure (e a) and solar radiation (R s), and default wind speed values (u 2), the PMT method, or using the Hargreaves-Samani equation (HS). The accuracy of estimates of daily e a, R s, and u 2 is provided in a companion paper (Paredes et al. 2017) applied to data of 20 locations distributed through eight islands of Azores, thus focusing on humid environments. Both estimation procedures using the PMT method (ETo PMT) and the HS equation (ETo HS) were assessed by statistically comparing their results with those obtained for the PM-ETo with data of the same 20 locations. Results show that both approaches provide for accurate ETo estimations, with RMSE for PMT ranging 0.48-0.73 mm day-1 and for HS varying 0.47-0.86 mm day-1. It was observed that ETo PMT is linearly related with PM-ETo, while non-linearity was observed for ETo HS in weather stations located at high elevation. Impacts of wind were not important for HS but required proper adjustments in the case of PMT. Results show that the PMT approach is more accurate than HS. Moreover, PMT allows the use of observed variables together with estimators of the missing ones, which improves the accuracy of the PMT approach. The preference for the PMT method, fully based upon the PM-ETo equation, is therefore obvious.

Multiple-reflection model of human skin and estimation of pigment concentrations

NASA Astrophysics Data System (ADS)

Ohtsuki, Rie; Tominaga, Shoji; Tanno, Osamu

2012-07-01

We describe a new method for estimating the concentrations of pigments in the human skin using surface spectral reflectance. We derive an equation that expresses the surface spectral reflectance of the human skin. First, we propose an optical model of the human skin that accounts for the stratum corneum. We also consider the difference between the scattering coefficient of the epidermis and that of the dermis. We then derive an equation by applying the Kubelka-Munk theory to an optical model of the human skin. Unlike a model developed in a recent study, the present equation considers pigments as well as multiple reflections and the thicknesses of the skin layers as factors that affect the color of the human skin. In two experiments, we estimate the pigment concentrations using the measured surface spectral reflectances. Finally, we confirm the feasibility of the concentrations estimated by the proposed method by evaluating the estimated pigment concentrations in the skin.

Verification of the Jenkins and FIA sapling biomass equations for hardwood species in Maine

Treesearch

Andrew S. Nelson; Aaron R. Weiskittel; Robert G. Wagner; Michael R. Saunders

2012-01-01

In 2009, the Forest Inventory and Analysis Program (FIA) updated its biomass estimation protocols by switching to the component ratio method to estimate biomass of medium and large trees. Additionally, FIA switched from using regional equations to the current FIA aboveground sapling biomass equations that predict woody sapling (2.5 to 12.4 cm d.b.h.) biomass using the...

Calibration of d.b.h.-height equations for southern hardwoods

Treesearch

Thomas B. Lynch; A. Gordon Holley; Douglas J. Stevenson

2006-01-01

Data from southern hardwood stands in East Texas were used to estimate parameters for d.b.h.-height equations. Mixed model estimation methods were used, so that the stand from which a tree was sampled was considered a random effect. This makes it possible to calibrate these equations using data collected in a local stand of interest, by using d.b.h. and total height...

Integral-equation based methods for parameter estimation in output pulses of radiation detectors: Application in nuclear medicine and spectroscopy

NASA Astrophysics Data System (ADS)

Mohammadian-Behbahani, Mohammad-Reza; Saramad, Shahyar

2018-04-01

Model based analysis methods are relatively new approaches for processing the output data of radiation detectors in nuclear medicine imaging and spectroscopy. A class of such methods requires fast algorithms for fitting pulse models to experimental data. In order to apply integral-equation based methods for processing the preamplifier output pulses, this article proposes a fast and simple method for estimating the parameters of the well-known bi-exponential pulse model by solving an integral equation. The proposed method needs samples from only three points of the recorded pulse as well as its first and second order integrals. After optimizing the sampling points, the estimation results were calculated and compared with two traditional integration-based methods. Different noise levels (signal-to-noise ratios from 10 to 3000) were simulated for testing the functionality of the proposed method, then it was applied to a set of experimental pulses. Finally, the effect of quantization noise was assessed by studying different sampling rates. Promising results by the proposed method endorse it for future real-time applications.

Estimation of left ventricular mass in conscious dogs

NASA Technical Reports Server (NTRS)

Coleman, Bernell; Cothran, Laval N.; Ison-Franklin, E. L.; Hawthorne, E. W.

1986-01-01

A method for the assessment of the development or the regression of left ventricular hypertrophy (LVH) in a conscious instrumented animal is described. First, the single-slice short-axis area-length method for estimating the left-ventricular mass (LVM) and volume (LVV) was validated in 24 formaldehyde-fixed canine hearts, and a regression equation was developed that could be used in the intact animal to correct the sonomicrometrically estimated LVM. The LVM-assessment method, which uses the combined techniques of echocardiography and sonomicrometry (in conjunction with the regression equation), was shown to provide reliable and reproducible day-to-day estimates of LVM and LVV, and to be sensitive enough to detect serial changes during the development of LVH.

Control for well-posedness about a class of non-Newtonian incompressible porous medium fluid equations

NASA Astrophysics Data System (ADS)

Deng, Shuxian; Ge, Xinxin

2017-10-01

Considering the non-Newtonian fluid equation of incompressible porous media, using the properties of operator semigroup and measure space and the principle of squeezed image, Fourier analysis and a priori estimate in the measurement space are used to discuss the non-compressible porous media, the properness of the solution of the equation, its gradual behavior and its topological properties. Through the diffusion regularization method and the compressed limit compact method, we study the overall decay rate of the solution of the equation in a certain space when the initial value is sufficient. The decay estimation of the solution of the incompressible seepage equation is obtained, and the asymptotic behavior of the solution is obtained by using the double regularization model and the Duhamel principle.

Novel Equations for Estimating Lean Body Mass in Peritoneal Dialysis Patients

PubMed Central

Dong, Jie; Li, Yan-Jun; Xu, Rong; Yang, Zhi-Kai; Zheng, Ying-Dong

2015-01-01

♦ Objectives: To develop and validate equations for estimating lean body mass (LBM) in peritoneal dialysis (PD) patients. ♦ Methods: Two equations for estimating LBM, one based on mid-arm muscle circumference (MAMC) and hand grip strength (HGS), i.e., LBM-M-H, and the other based on HGS, i.e., LBM-H, were developed and validated with LBM obtained by dual-energy X-ray absorptiometry (DEXA). The developed equations were compared to LBM estimated from creatinine kinetics (LBM-CK) and anthropometry (LBM-A) in terms of bias, precision, and accuracy. The prognostic values of LBM estimated from the equations in all-cause mortality risk were assessed. ♦ Results: The developed equations incorporated gender, height, weight, and dialysis duration. Compared to LBM-DEXA, the bias of the developed equations was lower than that of LBM-CK and LBM-A. Additionally, LBM-M-H and LBM-H had better accuracy and precision. The prognostic values of LBM in all-cause mortality risk based on LBM-M-H, LBM-H, LBM-CK, and LBM-A were similar. ♦ Conclusions: Lean body mass estimated by the new equations based on MAMC and HGS was correlated with LBM obtained by DEXA and may serve as practical surrogate markers of LBM in PD patients. PMID:26293839

The Missing Data Assumptions of the NEAT Design and Their Implications for Test Equating

ERIC Educational Resources Information Center

Sinharay, Sandip; Holland, Paul W.

2010-01-01

The Non-Equivalent groups with Anchor Test (NEAT) design involves "missing data" that are "missing by design." Three nonlinear observed score equating methods used with a NEAT design are the "frequency estimation equipercentile equating" (FEEE), the "chain equipercentile equating" (CEE), and the "item-response-theory observed-score-equating" (IRT…

Evolutionary optimization with data collocation for reverse engineering of biological networks.

PubMed

Tsai, Kuan-Yao; Wang, Feng-Sheng

2005-04-01

Modern experimental biology is moving away from analyses of single elements to whole-organism measurements. Such measured time-course data contain a wealth of information about the structure and dynamic of the pathway or network. The dynamic modeling of the whole systems is formulated as a reverse problem that requires a well-suited mathematical model and a very efficient computational method to identify the model structure and parameters. Numerical integration for differential equations and finding global parameter values are still two major challenges in this field of the parameter estimation of nonlinear dynamic biological systems. We compare three techniques of parameter estimation for nonlinear dynamic biological systems. In the proposed scheme, the modified collocation method is applied to convert the differential equations to the system of algebraic equations. The observed time-course data are then substituted into the algebraic system equations to decouple system interactions in order to obtain the approximate model profiles. Hybrid differential evolution (HDE) with population size of five is able to find a global solution. The method is not only suited for parameter estimation but also can be applied for structure identification. The solution obtained by HDE is then used as the starting point for a local search method to yield the refined estimates.

Estimation of coupling between time-delay systems from time series

NASA Astrophysics Data System (ADS)

Prokhorov, M. D.; Ponomarenko, V. I.

2005-07-01

We propose a method for estimation of coupling between the systems governed by scalar time-delay differential equations of the Mackey-Glass type from the observed time series data. The method allows one to detect the presence of certain types of linear coupling between two time-delay systems, to define the type, strength, and direction of coupling, and to recover the model equations of coupled time-delay systems from chaotic time series corrupted by noise. We verify our method using both numerical and experimental data.

Streamflow characteristics related to channel geometry of streams in western United States

USGS Publications Warehouse

Hedman, E.R.; Osterkamp, W.R.

1982-01-01

Assessment of surface-mining and reclamation activities generally requires extensive hydrologic data. Adequate streamflow data from instrumented gaging stations rarely are available, and estimates of surface- water discharge based on rainfall-runoff models, drainage area, and basin characteristics sometimes have proven unreliable. Channel-geometry measurements offer an alternative method of quickly and inexpensively estimating stream-flow characteristics for ungaged streams. The method uses the empirical development of equations to yield a discharge value from channel-geometry and channel-material data. The equations are developed by collecting data at numerous streamflow-gaging sites and statistically relating those data to selected discharge characteristics. Mean annual runoff and flood discharges with selected recurrence intervals can be estimated for perennial, intermittent, and ephemeral streams. The equations were developed from data collected in the western one-half of the conterminous United States. The effect of the channel-material and runoff characteristics are accounted for with the equations.

Percent body fat estimations in college women using field and laboratory methods: a three-compartment model approach

PubMed Central

Moon, Jordan R; Hull, Holly R; Tobkin, Sarah E; Teramoto, Masaru; Karabulut, Murat; Roberts, Michael D; Ryan, Eric D; Kim, So Jung; Dalbo, Vincent J; Walter, Ashley A; Smith, Abbie T; Cramer, Joel T; Stout, Jeffrey R

2007-01-01

Background Methods used to estimate percent body fat can be classified as a laboratory or field technique. However, the validity of these methods compared to multiple-compartment models has not been fully established. This investigation sought to determine the validity of field and laboratory methods for estimating percent fat (%fat) in healthy college-age women compared to the Siri three-compartment model (3C). Methods Thirty Caucasian women (21.1 ± 1.5 yrs; 164.8 ± 4.7 cm; 61.2 ± 6.8 kg) had their %fat estimated by BIA using the BodyGram™ computer program (BIA-AK) and population-specific equation (BIA-Lohman), NIR (Futrex® 6100/XL), a quadratic (SF3JPW) and linear (SF3WB) skinfold equation, air-displacement plethysmography (BP), and hydrostatic weighing (HW). Results All methods produced acceptable total error (TE) values compared to the 3C model. Both laboratory methods produced similar TE values (HW, TE = 2.4%fat; BP, TE = 2.3%fat) when compared to the 3C model, though a significant constant error (CE) was detected for HW (1.5%fat, p ≤ 0.006). The field methods produced acceptable TE values ranging from 1.8 – 3.8 %fat. BIA-AK (TE = 1.8%fat) yielded the lowest TE among the field methods, while BIA-Lohman (TE = 2.1%fat) and NIR (TE = 2.7%fat) produced lower TE values than both skinfold equations (TE > 2.7%fat) compared to the 3C model. Additionally, the SF3JPW %fat estimation equation resulted in a significant CE (2.6%fat, p ≤ 0.007). Conclusion Data suggest that the BP and HW are valid laboratory methods when compared to the 3C model to estimate %fat in college-age Caucasian women. When the use of a laboratory method is not feasible, NIR, BIA-AK, BIA-Lohman, SF3JPW, and SF3WB are acceptable field methods to estimate %fat in this population. PMID:17988393

An accurate computational method for the diffusion regime verification

NASA Astrophysics Data System (ADS)

Zhokh, Alexey A.; Strizhak, Peter E.

2018-04-01

The diffusion regime (sub-diffusive, standard, or super-diffusive) is defined by the order of the derivative in the corresponding transport equation. We develop an accurate computational method for the direct estimation of the diffusion regime. The method is based on the derivative order estimation using the asymptotic analytic solutions of the diffusion equation with the integer order and the time-fractional derivatives. The robustness and the computational cheapness of the proposed method are verified using the experimental methane and methyl alcohol transport kinetics through the catalyst pellet.

Stochastic differential equations as a tool to regularize the parameter estimation problem for continuous time dynamical systems given discrete time measurements.

PubMed

Leander, Jacob; Lundh, Torbjörn; Jirstrand, Mats

2014-05-01

In this paper we consider the problem of estimating parameters in ordinary differential equations given discrete time experimental data. The impact of going from an ordinary to a stochastic differential equation setting is investigated as a tool to overcome the problem of local minima in the objective function. Using two different models, it is demonstrated that by allowing noise in the underlying model itself, the objective functions to be minimized in the parameter estimation procedures are regularized in the sense that the number of local minima is reduced and better convergence is achieved. The advantage of using stochastic differential equations is that the actual states in the model are predicted from data and this will allow the prediction to stay close to data even when the parameters in the model is incorrect. The extended Kalman filter is used as a state estimator and sensitivity equations are provided to give an accurate calculation of the gradient of the objective function. The method is illustrated using in silico data from the FitzHugh-Nagumo model for excitable media and the Lotka-Volterra predator-prey system. The proposed method performs well on the models considered, and is able to regularize the objective function in both models. This leads to parameter estimation problems with fewer local minima which can be solved by efficient gradient-based methods. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

Generalized approach to cooling charge-coupled devices using thermoelectric coolers

NASA Technical Reports Server (NTRS)

Petrick, S. Walter

1987-01-01

This paper is concerned with the use of thermoelectric coolers (TECs) to cool charge-coupled devices (CCDs). Heat inputs to the CCD from the warmer environment are identified, and generalized graphs are used to approximate the major heat inputs. A method of choosing and estimating the power consumption of the TEC is discussed. This method includes the use of TEC performance information supplied by the manufacturer and equations derived from this information. Parameters of the equations are tabulated to enable the reader to use the TEC performance equations for choosing and estimating the power needed for specific TEC applications.

An exterior Poisson solver using fast direct methods and boundary integral equations with applications to nonlinear potential flow

NASA Technical Reports Server (NTRS)

Young, D. P.; Woo, A. C.; Bussoletti, J. E.; Johnson, F. T.

1986-01-01

A general method is developed combining fast direct methods and boundary integral equation methods to solve Poisson's equation on irregular exterior regions. The method requires O(N log N) operations where N is the number of grid points. Error estimates are given that hold for regions with corners and other boundary irregularities. Computational results are given in the context of computational aerodynamics for a two-dimensional lifting airfoil. Solutions of boundary integral equations for lifting and nonlifting aerodynamic configurations using preconditioned conjugate gradient are examined for varying degrees of thinness.

Investigation of IRT-Based Equating Methods in the Presence of Outlier Common Items

ERIC Educational Resources Information Center

Hu, Huiqin; Rogers, W. Todd; Vukmirovic, Zarko

2008-01-01

Common items with inconsistent b-parameter estimates may have a serious impact on item response theory (IRT)--based equating results. To find a better way to deal with the outlier common items with inconsistent b-parameters, the current study investigated the comparability of 10 variations of four IRT-based equating methods (i.e., concurrent…

On-line estimation and compensation of measurement delay in GPS/SINS integration

NASA Astrophysics Data System (ADS)

Yang, Tao; Wang, Wei

2008-10-01

The chief aim of this paper is to propose a simple on-line estimation and compensation method of GPS/SINS measurement delay. The causes of time delay for GPS/SINS integration are analyzed in this paper. New Kalman filter state equations augmented by measurement delay and modified measurement equations are derived. Based on an open-loop Kalman filter, several simulations are run, results of which show that by the proposed method, the estimation and compensation error of measurement delay is below 0.1s.

Analytical Plug-In Method for Kernel Density Estimator Applied to Genetic Neutrality Study

NASA Astrophysics Data System (ADS)

Troudi, Molka; Alimi, Adel M.; Saoudi, Samir

2008-12-01

The plug-in method enables optimization of the bandwidth of the kernel density estimator in order to estimate probability density functions (pdfs). Here, a faster procedure than that of the common plug-in method is proposed. The mean integrated square error (MISE) depends directly upon [InlineEquation not available: see fulltext.] which is linked to the second-order derivative of the pdf. As we intend to introduce an analytical approximation of [InlineEquation not available: see fulltext.], the pdf is estimated only once, at the end of iterations. These two kinds of algorithm are tested on different random variables having distributions known for their difficult estimation. Finally, they are applied to genetic data in order to provide a better characterisation in the mean of neutrality of Tunisian Berber populations.

Enabling real-time ultrasound imaging of soft tissue mechanical properties by simplification of the shear wave motion equation.

PubMed

Engel, Aaron J; Bashford, Gregory R

2015-08-01

Ultrasound based shear wave elastography (SWE) is a technique used for non-invasive characterization and imaging of soft tissue mechanical properties. Robust estimation of shear wave propagation speed is essential for imaging of soft tissue mechanical properties. In this study we propose to estimate shear wave speed by inversion of the first-order wave equation following directional filtering. This approach relies on estimation of first-order derivatives which allows for accurate estimations using smaller smoothing filters than when estimating second-order derivatives. The performance was compared to three current methods used to estimate shear wave propagation speed: direct inversion of the wave equation (DIWE), time-to-peak (TTP) and cross-correlation (CC). The shear wave speed of three homogeneous phantoms of different elastic moduli (gelatin by weight of 5%, 7%, and 9%) were measured with each method. The proposed method was shown to produce shear speed estimates comparable to the conventional methods (standard deviation of measurements being 0.13 m/s, 0.05 m/s, and 0.12 m/s), but with simpler processing and usually less time (by a factor of 1, 13, and 20 for DIWE, CC, and TTP respectively). The proposed method was able to produce a 2-D speed estimate from a single direction of wave propagation in about four seconds using an off-the-shelf PC, showing the feasibility of performing real-time or near real-time elasticity imaging with dedicated hardware.

An Estimating Equations Approach for the LISCOMP Model.

ERIC Educational Resources Information Center

Reboussin, Beth A.; Liang, Kung-Lee

1998-01-01

A quadratic estimating equations approach for the LISCOMP model is proposed that only requires specification of the first two moments. This method is compared with a three-stage generalized least squares approach through a numerical study and application to a study of life events and neurotic illness. (SLD)

Penalized Nonlinear Least Squares Estimation of Time-Varying Parameters in Ordinary Differential Equations

PubMed Central

Cao, Jiguo; Huang, Jianhua Z.; Wu, Hulin

2012-01-01

Ordinary differential equations (ODEs) are widely used in biomedical research and other scientific areas to model complex dynamic systems. It is an important statistical problem to estimate parameters in ODEs from noisy observations. In this article we propose a method for estimating the time-varying coefficients in an ODE. Our method is a variation of the nonlinear least squares where penalized splines are used to model the functional parameters and the ODE solutions are approximated also using splines. We resort to the implicit function theorem to deal with the nonlinear least squares objective function that is only defined implicitly. The proposed penalized nonlinear least squares method is applied to estimate a HIV dynamic model from a real dataset. Monte Carlo simulations show that the new method can provide much more accurate estimates of functional parameters than the existing two-step local polynomial method which relies on estimation of the derivatives of the state function. Supplemental materials for the article are available online. PMID:23155351

Quantifying evapotranspiration from urban green roofs: a comparison of chamber measurements with commonly used predictive methods.

PubMed

Marasco, Daniel E; Hunter, Betsy N; Culligan, Patricia J; Gaffin, Stuart R; McGillis, Wade R

2014-09-02

Quantifying green roof evapotranspiration (ET) in urban climates is important for assessing environmental benefits, including stormwater runoff attenuation and urban heat island mitigation. In this study, a dynamic chamber method was developed to quantify ET on two extensive green roofs located in New York City, NY. Hourly chamber measurements taken from July 2009 to December 2009 and April 2012 to October 2013 illustrate both diurnal and seasonal variations in ET. Observed monthly total ET depth ranged from 0.22 cm in winter to 15.36 cm in summer. Chamber results were compared to two predictive methods for estimating ET; namely the Penman-based ASCE Standardized Reference Evapotranspiration (ASCE RET) equation, and an energy balance model, both parametrized using on-site environmental conditions. Dynamic chamber ET results were similar to ASCE RET estimates; however, the ASCE RET equation overestimated bottommost ET values during the winter months, and underestimated peak ET values during the summer months. The energy balance method was shown to underestimate ET compared the ASCE RET equation. The work highlights the utility of the chamber method for quantifying green roof evapotranspiration and indicates green roof ET might be better estimated by Penman-based evapotranspiration equations than energy balance methods.

Applying Meta-Analysis to Structural Equation Modeling

ERIC Educational Resources Information Center

Hedges, Larry V.

2016-01-01

Structural equation models play an important role in the social sciences. Consequently, there is an increasing use of meta-analytic methods to combine evidence from studies that estimate the parameters of structural equation models. Two approaches are used to combine evidence from structural equation models: A direct approach that combines…

A new approach for electrical properties estimation using a global integral equation and improvements using high permittivity materials.

PubMed

Schmidt, Rita; Webb, Andrew

2016-01-01

Electrical Properties Tomography (EPT) using MRI is a technique that has been developed to provide a new contrast mechanism for in vivo imaging. Currently the most common method relies on the solution of the homogeneous Helmholtz equation, which has limitations in accurate estimation at tissue interfaces. A new method proposed in this work combines a Maxwell's integral equation representation of the problem, and the use of high permittivity materials (HPM) to control the RF field, in order to reconstruct the electrical properties image. The magnetic field is represented by an integral equation considering each point as a contrast source. This equation can be solved in an inverse method. In this study we use a reference simulation or scout scan of a uniform phantom to provide an initial estimate for the inverse solution, which allows the estimation of the complex permittivity within a single iteration. Incorporating two setups with and without the HPM improves the reconstructed result, especially with respect to the very low electric field in the center of the sample. Electromagnetic simulations of the brain were performed at 3T to generate the B1(+) field maps and reconstruct the electric properties images. The standard deviations of the relative permittivity and conductivity were within 14% and 18%, respectively for a volume consisting of white matter, gray matter and cerebellum. Copyright © 2015 Elsevier Inc. All rights reserved.

FIA's volume-to-biomass conversion method (CRM) generally underestimates biomass in comparison to published equations

Treesearch

David. C. Chojnacky

2012-01-01

An update of the Jenkins et al. (2003) biomass estimation equations for North American tree species resulted in 35 generalized equations developed from published equations. These 35 equations, which predict aboveground biomass of individual species grouped according to a taxa classification (based on genus or family and sometimes specific gravity), generally predicted...

Using the Kernel Method of Test Equating for Estimating the Standard Errors of Population Invariance Measures

ERIC Educational Resources Information Center

Moses, Tim

2008-01-01

Equating functions are supposed to be population invariant, meaning that the choice of subpopulation used to compute the equating function should not matter. The extent to which equating functions are population invariant is typically assessed in terms of practical difference criteria that do not account for equating functions' sampling…

Determination of the best method to estimate glomerular filtration rate from serum creatinine in adult patients with sickle cell disease: a prospective observational cohort study.

PubMed

Arlet, Jean-Benoît; Ribeil, Jean-Antoine; Chatellier, Gilles; Eladari, Dominique; De Seigneux, Sophie; Souberbielle, Jean-Claude; Friedlander, Gérard; de Montalembert, Marianne; Pouchot, Jacques; Prié, Dominique; Courbebaisse, Marie

2012-08-06

Sickle cell disease (SCD) leads to tissue hypoxia resulting in chronic organ dysfunction including SCD associated nephropathy. The goal of our study was to determine the best equation to estimate glomerular filtration rate (GFR) in SCD adult patients. We conducted a prospective observational cohort study. Since 2007, all adult SCD patients in steady state, followed in two medical departments, have had their GFR measured using iohexol plasma clearance (gold standard). The Cockcroft-Gault, MDRD-v4, CKP-EPI and finally, MDRD and CKD-EPI equations without adjustment for ethnicity were tested to estimate GFR from serum creatinine. Estimated GFRs were compared to measured GFRs according to the graphical Bland and Altman method. Sixty-four SCD patients (16 men, median age 27.5 years [range 18.0-67.5], 41 with SS-genotype were studied. They were Sub-Saharan Africa and French West Indies natives and predominantly lean (median body mass index: 22 kg/m2 [16-33]). Hyperfiltration (defined as measured GFR >110 mL/min/1.73 m2) was detected in 53.1% of patients. Urinary albumin/creatinine ratio was higher in patients with hyperfiltration than in patients with normal GFR (4.05 mg/mmol [0.14-60] versus 0.4 mg/mmol [0.7-81], p = 0.01). The CKD-EPI equation without adjustment for ethnicity had both the lowest bias and the greatest precision. Differences between estimated GFRs using the CKP-EPI equation and measured GFRs decreased with increasing GFR values, whereas it increased with the Cockcroft-Gault and MDRD-v4 equations. We confirm that SCD patients have a high rate of glomerular hyperfiltration, which is frequently associated with microalbuminuria or macroalbuminuria. In non-Afro-American SCD patients, the best method for estimating GFR from serum creatinine is the CKD-EPI equation without adjustment for ethnicity. This equation is particularly accurate to estimate high GFR values, including glomerular hyperfiltration, and thus should be recommended to screen SCD adult patients at high risk for SCD nephropathy.

Estimating parameter of influenza transmission using regularized least square

NASA Astrophysics Data System (ADS)

Nuraini, N.; Syukriah, Y.; Indratno, S. W.

2014-02-01

Transmission process of influenza can be presented in a mathematical model as a non-linear differential equations system. In this model the transmission of influenza is determined by the parameter of contact rate of the infected host and susceptible host. This parameter will be estimated using a regularized least square method where the Finite Element Method and Euler Method are used for approximating the solution of the SIR differential equation. The new infected data of influenza from CDC is used to see the effectiveness of the method. The estimated parameter represents the contact rate proportion of transmission probability in a day which can influence the number of infected people by the influenza. Relation between the estimated parameter and the number of infected people by the influenza is measured by coefficient of correlation. The numerical results show positive correlation between the estimated parameters and the infected people.

Validation of equations for pleural effusion volume estimation by ultrasonography.

PubMed

Hassan, Maged; Rizk, Rana; Essam, Hatem; Abouelnour, Ahmed

2017-12-01

To validate the accuracy of previously published equations that estimate pleural effusion volume using ultrasonography. Only equations using simple measurements were tested. Three measurements were taken at the posterior axillary line for each case with effusion: lateral height of effusion ( H ), distance between collapsed lung and chest wall ( C ) and distance between lung and diaphragm ( D ). Cases whose effusion was aspirated to dryness were included and drained volume was recorded. Intra-class correlation coefficient (ICC) was used to determine the predictive accuracy of five equations against the actual volume of aspirated effusion. 46 cases with effusion were included. The most accurate equation in predicting effusion volume was ( H  +  D ) × 70 (ICC 0.83). The simplest and yet accurate equation was H  × 100 (ICC 0.79). Pleural effusion height measured by ultrasonography gives a reasonable estimate of effusion volume. Incorporating distance between lung base and diaphragm into estimation improves accuracy from 79% with the first method to 83% with the latter.

Estimating varying coefficients for partial differential equation models.

PubMed

Zhang, Xinyu; Cao, Jiguo; Carroll, Raymond J

2017-09-01

Partial differential equations (PDEs) are used to model complex dynamical systems in multiple dimensions, and their parameters often have important scientific interpretations. In some applications, PDE parameters are not constant but can change depending on the values of covariates, a feature that we call varying coefficients. We propose a parameter cascading method to estimate varying coefficients in PDE models from noisy data. Our estimates of the varying coefficients are shown to be consistent and asymptotically normally distributed. The performance of our method is evaluated by a simulation study and by an empirical study estimating three varying coefficients in a PDE model arising from LIDAR data. © 2017, The International Biometric Society.

On finite element methods for the Helmholtz equation

NASA Technical Reports Server (NTRS)

Aziz, A. K.; Werschulz, A. G.

1979-01-01

The numerical solution of the Helmholtz equation is considered via finite element methods. A two-stage method which gives the same accuracy in the computed gradient as in the computed solution is discussed. Error estimates for the method using a newly developed proof are given, and the computational considerations which show this method to be computationally superior to previous methods are presented.

Comparison of anthropometric-based equations for estimation of body fat percentage in a normal-weight and overweight female cohort: validation via air-displacement plethysmography.

PubMed

Temple, Derry; Denis, Romain; Walsh, Marianne C; Dicker, Patrick; Byrne, Annette T

2015-02-01

To evaluate the accuracy of the most commonly used anthropometric-based equations in the estimation of percentage body fat (%BF) in both normal-weight and overweight women using air-displacement plethysmography (ADP) as the criterion measure. A comparative study in which the equations of Durnin and Womersley (1974; DW) and Jackson, Pollock and Ward (1980) at three, four and seven sites (JPW₃, JPW₄ and JPW₇) were validated against ADP in three groups. Group 1 included all participants, group 2 included participants with a BMI <25·0 kg/m² and group 3 included participants with a BMI ≥25·0 kg/m². Human Performance Laboratory, Institute for Sport and Health, University College Dublin, Republic of Ireland. Forty-three female participants aged between 18 and 55 years. In all three groups, the %BF values estimated from the DW equation were closer to the criterion measure (i.e. ADP) than those estimated from the other equations. Of the three JPW equations, JPW₃ provided the most accurate estimation of %BF when compared with ADP in all three groups. In comparison to ADP, these findings suggest that the DW equation is the most accurate anthropometric method for the estimation of %BF in both normal-weight and overweight females.

Dynamical behavior for the three-dimensional generalized Hasegawa-Mima equations

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

Zhang Ruifeng; Guo Boling; Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088

2007-01-15

The long time behavior of solution of the three-dimensional generalized Hasegawa-Mima [Phys. Fluids 21, 87 (1978)] equations with dissipation term is considered. The global attractor problem of the three-dimensional generalized Hasegawa-Mima equations with periodic boundary condition was studied. Applying the method of uniform a priori estimates, the existence of global attractor of this problem was proven, and also the dimensions of the global attractor are estimated.

Stature estimation equations for South Asian skeletons based on DXA scans of contemporary adults.

PubMed

Pomeroy, Emma; Mushrif-Tripathy, Veena; Wells, Jonathan C K; Kulkarni, Bharati; Kinra, Sanjay; Stock, Jay T

2018-05-03

Stature estimation from the skeleton is a classic anthropological problem, and recent years have seen the proliferation of population-specific regression equations. Many rely on the anatomical reconstruction of stature from archaeological skeletons to derive regression equations based on long bone lengths, but this requires a collection with very good preservation. In some regions, for example, South Asia, typical environmental conditions preclude the sufficient preservation of skeletal remains. Large-scale epidemiological studies that include medical imaging of the skeleton by techniques such as dual-energy X-ray absorptiometry (DXA) offer new potential datasets for developing such equations. We derived estimation equations based on known height and bone lengths measured from DXA scans from the Andhra Pradesh Children and Parents Study (Hyderabad, India). Given debates on the most appropriate regression model to use, multiple methods were compared, and the performance of the equations was tested on a published skeletal dataset of individuals with known stature. The equations have standard errors of estimates and prediction errors similar to those derived using anatomical reconstruction or from cadaveric datasets. As measured by the number of significant differences between true and estimated stature, and the prediction errors, the new equations perform as well as, and generally better than, published equations commonly used on South Asian skeletons or based on Indian cadaveric datasets. This study demonstrates the utility of DXA scans as a data source for developing stature estimation equations and offer a new set of equations for use with South Asian datasets. © 2018 Wiley Periodicals, Inc.

Recalibration of the Klales et al. (2012) method of sexing the human innominate for Mexican populations.

PubMed

Gómez-Valdés, Jorge A; Menéndez Garmendia, Antinea; García-Barzola, Lizbeth; Sánchez-Mejorada, Gabriela; Karam, Carlos; Baraybar, José Pablo; Klales, Alexandra

2017-03-01

The aim of this study was to test the accuracy of the Klales et al. (2012) equation for sex estimation in contemporary Mexican population. Our investigation was carried out on a sample of 203 left innominates of identified adult skeletons from the UNAM-Collection and the Santa María Xigui Cemetery, in Central Mexico. The Klales' original equation produces a sex bias in sex estimation against males (86-92% accuracy versus 100% accuracy in females). Based on these results, the Klales et al. (2012) method was recalibrated for a new cutt-of-point for sex estimation in contemporary Mexican populations. The results show cross-validated classification accuracy rates as high as 100% after recalibrating the original logistic regression equation. Recalibration improved classification accuracy and eliminated sex bias. This new formula will improve sex estimation for Mexican contemporary populations. © 2017 Wiley Periodicals, Inc.

Finite-sample corrected generalized estimating equation of population average treatment effects in stepped wedge cluster randomized trials.

PubMed

Scott, JoAnna M; deCamp, Allan; Juraska, Michal; Fay, Michael P; Gilbert, Peter B

2017-04-01

Stepped wedge designs are increasingly commonplace and advantageous for cluster randomized trials when it is both unethical to assign placebo, and it is logistically difficult to allocate an intervention simultaneously to many clusters. We study marginal mean models fit with generalized estimating equations for assessing treatment effectiveness in stepped wedge cluster randomized trials. This approach has advantages over the more commonly used mixed models that (1) the population-average parameters have an important interpretation for public health applications and (2) they avoid untestable assumptions on latent variable distributions and avoid parametric assumptions about error distributions, therefore, providing more robust evidence on treatment effects. However, cluster randomized trials typically have a small number of clusters, rendering the standard generalized estimating equation sandwich variance estimator biased and highly variable and hence yielding incorrect inferences. We study the usual asymptotic generalized estimating equation inferences (i.e., using sandwich variance estimators and asymptotic normality) and four small-sample corrections to generalized estimating equation for stepped wedge cluster randomized trials and for parallel cluster randomized trials as a comparison. We show by simulation that the small-sample corrections provide improvement, with one correction appearing to provide at least nominal coverage even with only 10 clusters per group. These results demonstrate the viability of the marginal mean approach for both stepped wedge and parallel cluster randomized trials. We also study the comparative performance of the corrected methods for stepped wedge and parallel designs, and describe how the methods can accommodate interval censoring of individual failure times and incorporate semiparametric efficient estimators.

Stochastic differential equation (SDE) model of opening gold share price of bursa saham malaysia

NASA Astrophysics Data System (ADS)

Hussin, F. N.; Rahman, H. A.; Bahar, A.

2017-09-01

Black and Scholes option pricing model is one of the most recognized stochastic differential equation model in mathematical finance. Two parameter estimation methods have been utilized for the Geometric Brownian model (GBM); historical and discrete method. The historical method is a statistical method which uses the property of independence and normality logarithmic return, giving out the simplest parameter estimation. Meanwhile, discrete method considers the function of density of transition from the process of diffusion normal log which has been derived from maximum likelihood method. These two methods are used to find the parameter estimates samples of Malaysians Gold Share Price data such as: Financial Times and Stock Exchange (FTSE) Bursa Malaysia Emas, and Financial Times and Stock Exchange (FTSE) Bursa Malaysia Emas Shariah. Modelling of gold share price is essential since fluctuation of gold affects worldwide economy nowadays, including Malaysia. It is found that discrete method gives the best parameter estimates than historical method due to the smallest Root Mean Square Error (RMSE) value.

A deterministic method for estimating free energy genetic network landscapes with applications to cell commitment and reprogramming paths.

PubMed

Olariu, Victor; Manesso, Erica; Peterson, Carsten

2017-06-01

Depicting developmental processes as movements in free energy genetic landscapes is an illustrative tool. However, exploring such landscapes to obtain quantitative or even qualitative predictions is hampered by the lack of free energy functions corresponding to the biochemical Michaelis-Menten or Hill rate equations for the dynamics. Being armed with energy landscapes defined by a network and its interactions would open up the possibility of swiftly identifying cell states and computing optimal paths, including those of cell reprogramming, thereby avoiding exhaustive trial-and-error simulations with rate equations for different parameter sets. It turns out that sigmoidal rate equations do have approximate free energy associations. With this replacement of rate equations, we develop a deterministic method for estimating the free energy surfaces of systems of interacting genes at different noise levels or temperatures. Once such free energy landscape estimates have been established, we adapt a shortest path algorithm to determine optimal routes in the landscapes. We explore the method on three circuits for haematopoiesis and embryonic stem cell development for commitment and reprogramming scenarios and illustrate how the method can be used to determine sequential steps for onsets of external factors, essential for efficient reprogramming.

A deterministic method for estimating free energy genetic network landscapes with applications to cell commitment and reprogramming paths

PubMed Central

Olariu, Victor; Manesso, Erica

2017-01-01

Depicting developmental processes as movements in free energy genetic landscapes is an illustrative tool. However, exploring such landscapes to obtain quantitative or even qualitative predictions is hampered by the lack of free energy functions corresponding to the biochemical Michaelis–Menten or Hill rate equations for the dynamics. Being armed with energy landscapes defined by a network and its interactions would open up the possibility of swiftly identifying cell states and computing optimal paths, including those of cell reprogramming, thereby avoiding exhaustive trial-and-error simulations with rate equations for different parameter sets. It turns out that sigmoidal rate equations do have approximate free energy associations. With this replacement of rate equations, we develop a deterministic method for estimating the free energy surfaces of systems of interacting genes at different noise levels or temperatures. Once such free energy landscape estimates have been established, we adapt a shortest path algorithm to determine optimal routes in the landscapes. We explore the method on three circuits for haematopoiesis and embryonic stem cell development for commitment and reprogramming scenarios and illustrate how the method can be used to determine sequential steps for onsets of external factors, essential for efficient reprogramming. PMID:28680655

Fitting ordinary differential equations to short time course data.

PubMed

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

2008-02-28

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

Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation.

PubMed

Erban, Radek; Kevrekidis, Ioannis G; Adalsteinsson, David; Elston, Timothy C

2006-02-28

We present computer-assisted methods for analyzing stochastic models of gene regulatory networks. The main idea that underlies this equation-free analysis is the design and execution of appropriately initialized short bursts of stochastic simulations; the results of these are processed to estimate coarse-grained quantities of interest, such as mesoscopic transport coefficients. In particular, using a simple model of a genetic toggle switch, we illustrate the computation of an effective free energy Phi and of a state-dependent effective diffusion coefficient D that characterize an unavailable effective Fokker-Planck equation. Additionally we illustrate the linking of equation-free techniques with continuation methods for performing a form of stochastic "bifurcation analysis"; estimation of mean switching times in the case of a bistable switch is also implemented in this equation-free context. The accuracy of our methods is tested by direct comparison with long-time stochastic simulations. This type of equation-free analysis appears to be a promising approach to computing features of the long-time, coarse-grained behavior of certain classes of complex stochastic models of gene regulatory networks, circumventing the need for long Monte Carlo simulations.

Cross-validation of resting metabolic rate prediction equations

USDA-ARS?s Scientific Manuscript database

Background: Knowledge of the resting metabolic rate (RMR) is necessary for determining individual total energy requirements. Measurement of RMR is time consuming and requires specialized equipment. Prediction equations provide an easy method to estimate RMR; however, the accuracy of these equations...

Methods for estimating aboveground biomass and its components for five Pacific Northwest tree species

Treesearch

Krishna P. Poudel; Temesgen. Hailemariam

2015-01-01

Performance of three groups of methods to estimate total and/or component aboveground biomass was evaluated using the data collected from destructively sampled trees in different parts of Oregon. First group of methods used analytical approach to estimate total and component biomass using existing equations, and produced biased estimates for our dataset. The second...

Methods for estimating selected low-flow frequency statistics for unregulated streams in Kentucky

USGS Publications Warehouse

Martin, Gary R.; Arihood, Leslie D.

2010-01-01

This report provides estimates of, and presents methods for estimating, selected low-flow frequency statistics for unregulated streams in Kentucky including the 30-day mean low flows for recurrence intervals of 2 and 5 years (30Q2 and 30Q5) and the 7-day mean low flows for recurrence intervals of 5, 10, and 20 years (7Q2, 7Q10, and 7Q20). Estimates of these statistics are provided for 121 U.S. Geological Survey streamflow-gaging stations with data through the 2006 climate year, which is the 12-month period ending March 31 of each year. Data were screened to identify the periods of homogeneous, unregulated flows for use in the analyses. Logistic-regression equations are presented for estimating the annual probability of the selected low-flow frequency statistics being equal to zero. Weighted-least-squares regression equations were developed for estimating the magnitude of the nonzero 30Q2, 30Q5, 7Q2, 7Q10, and 7Q20 low flows. Three low-flow regions were defined for estimating the 7-day low-flow frequency statistics. The explicit explanatory variables in the regression equations include total drainage area and the mapped streamflow-variability index measured from a revised statewide coverage of this characteristic. The percentage of the station low-flow statistics correctly classified as zero or nonzero by use of the logistic-regression equations ranged from 87.5 to 93.8 percent. The average standard errors of prediction of the weighted-least-squares regression equations ranged from 108 to 226 percent. The 30Q2 regression equations have the smallest standard errors of prediction, and the 7Q20 regression equations have the largest standard errors of prediction. The regression equations are applicable only to stream sites with low flows unaffected by regulation from reservoirs and local diversions of flow and to drainage basins in specified ranges of basin characteristics. Caution is advised when applying the equations for basins with characteristics near the applicable limits and for basins with karst drainage features.

Maximum Likelihood Estimation in Meta-Analytic Structural Equation Modeling

ERIC Educational Resources Information Center

Oort, Frans J.; Jak, Suzanne

2016-01-01

Meta-analytic structural equation modeling (MASEM) involves fitting models to a common population correlation matrix that is estimated on the basis of correlation coefficients that are reported by a number of independent studies. MASEM typically consist of two stages. The method that has been found to perform best in terms of statistical…

Intraocular lens power estimation by accurate ray tracing for eyes underwent previous refractive surgeries

NASA Astrophysics Data System (ADS)

Yang, Que; Wang, Shanshan; Wang, Kai; Zhang, Chunyu; Zhang, Lu; Meng, Qingyu; Zhu, Qiudong

2015-08-01

For normal eyes without history of any ocular surgery, traditional equations for calculating intraocular lens (IOL) power, such as SRK-T, Holladay, Higis, SRK-II, et al., all were relativley accurate. However, for eyes underwent refractive surgeries, such as LASIK, or eyes diagnosed as keratoconus, these equations may cause significant postoperative refractive error, which may cause poor satisfaction after cataract surgery. Although some methods have been carried out to solve this problem, such as Hagis-L equation[1], or using preoperative data (data before LASIK) to estimate K value[2], no precise equations were available for these eyes. Here, we introduced a novel intraocular lens power estimation method by accurate ray tracing with optical design software ZEMAX. Instead of using traditional regression formula, we adopted the exact measured corneal elevation distribution, central corneal thickness, anterior chamber depth, axial length, and estimated effective lens plane as the input parameters. The calculation of intraocular lens power for a patient with keratoconus and another LASIK postoperative patient met very well with their visual capacity after cataract surgery.

June and August median streamflows estimated for ungaged streams in southern Maine

USGS Publications Warehouse

Lombard, Pamela J.

2010-01-01

Methods for estimating June and August median streamflows were developed for ungaged, unregulated streams in southern Maine. The methods apply to streams with drainage areas ranging in size from 0.4 to 74 square miles, with percentage of basin underlain by a sand and gravel aquifer ranging from 0 to 84 percent, and with distance from the centroid of the basin to a Gulf of Maine line paralleling the coast ranging from 14 to 94 miles. Equations were developed with data from 4 long-term continuous-record streamgage stations and 27 partial-record streamgage stations. Estimates of median streamflows at the continuous-record and partial-record stations are presented. A mathematical technique for estimating standard low-flow statistics, such as June and August median streamflows, at partial-record streamgage stations was applied by relating base-flow measurements at these stations to concurrent daily streamflows at nearby long-term (at least 10 years of record) continuous-record streamgage stations (index stations). Weighted least-squares regression analysis (WLS) was used to relate estimates of June and August median streamflows at streamgage stations to basin characteristics at these same stations to develop equations that can be used to estimate June and August median streamflows on ungaged streams. WLS accounts for different periods of record at the gaging stations. Three basin characteristics-drainage area, percentage of basin underlain by a sand and gravel aquifer, and distance from the centroid of the basin to a Gulf of Maine line paralleling the coast-are used in the final regression equation to estimate June and August median streamflows for ungaged streams. The three-variable equation to estimate June median streamflow has an average standard error of prediction from -35 to 54 percent. The three-variable equation to estimate August median streamflow has an average standard error of prediction from -45 to 83 percent. Simpler one-variable equations that use only drainage area to estimate June and August median streamflows were developed for use when less accuracy is acceptable. These equations have average standard errors of prediction from -46 to 87 percent and from -57 to 133 percent, respectively.

State Estimation Using Dependent Evidence Fusion: Application to Acoustic Resonance-Based Liquid Level Measurement.

PubMed

Xu, Xiaobin; Li, Zhenghui; Li, Guo; Zhou, Zhe

2017-04-21

Estimating the state of a dynamic system via noisy sensor measurement is a common problem in sensor methods and applications. Most state estimation methods assume that measurement noise and state perturbations can be modeled as random variables with known statistical properties. However in some practical applications, engineers can only get the range of noises, instead of the precise statistical distributions. Hence, in the framework of Dempster-Shafer (DS) evidence theory, a novel state estimatation method by fusing dependent evidence generated from state equation, observation equation and the actual observations of the system states considering bounded noises is presented. It can be iteratively implemented to provide state estimation values calculated from fusion results at every time step. Finally, the proposed method is applied to a low-frequency acoustic resonance level gauge to obtain high-accuracy measurement results.

Assessing the accuracy of body mass estimation equations from pelvic and femoral variables among modern British women of known mass.

PubMed

Young, Mariel; Johannesdottir, Fjola; Poole, Ken; Shaw, Colin; Stock, J T

2018-02-01

Femoral head diameter is commonly used to estimate body mass from the skeleton. The three most frequently employed methods, designed by Ruff, Grine, and McHenry, were developed using different populations to address different research questions. They were not specifically designed for application to female remains, and their accuracy for this purpose has rarely been assessed or compared in living populations. This study analyzes the accuracy of these methods using a sample of modern British women through the use of pelvic CT scans (n = 97) and corresponding information about the individuals' known height and weight. Results showed that all methods provided reasonably accurate body mass estimates (average percent prediction errors under 20%) for the normal weight and overweight subsamples, but were inaccurate for the obese and underweight subsamples (average percent prediction errors over 20%). When women of all body mass categories were combined, the methods provided reasonable estimates (average percent prediction errors between 16 and 18%). The results demonstrate that different methods provide more accurate results within specific body mass index (BMI) ranges. The McHenry Equation provided the most accurate estimation for women of small body size, while the original Ruff Equation is most likely to be accurate if the individual was obese or severely obese. The refined Ruff Equation was the most accurate predictor of body mass on average for the entire sample, indicating that it should be utilized when there is no knowledge of the individual's body size or if the individual is assumed to be of a normal body size. The study also revealed a correlation between pubis length and body mass, and an equation for body mass estimation using pubis length was accurate in a dummy sample, suggesting that pubis length can also be used to acquire reliable body mass estimates. This has implications for how we interpret body mass in fossil hominins and has particular relevance to the interpretation of the long pubic ramus that is characteristic of Neandertals. Copyright © 2017 Elsevier Ltd. All rights reserved.

Growth and mortality of larval sunfish in backwaters of the upper Mississippi River

USGS Publications Warehouse

Zigler, S.J.; Jennings, C.A.

1993-01-01

The authors estimated the growth and mortality of larval sunfish Lepomis spp. in backwater habitats of the upper Mississippi River with an otolith-based method and a length-based method. Fish were sampled with plankton nets at one station in Navigation Pools 8 and 14 in 1989 and at two stations in Pool 8 in 1990. For both methods, growth was modeled with an exponential equation, and instantaneous mortality was estimated by regressing the natural logarithm of fish catch for each 1-mm size-group against the estimated age of the group, which was derived from the growth equations. At two of the stations, the otolith-based method provided more precise estimates of sunfish growth than the length-based method. We were able to compare length-based and otolith-based estimates of sunfish mortality only at the two stations where we caught the largest numbers of sunfish. Estimates of mortality were similar for both methods in Pool 14, where catches were higher, but the length-based method gave significantly higher estimates in Pool 8, where the catches were lower. The otolith- based method required more laboratory analysis, but provided better estimates of the growth and mortality than the length-based method when catches were low. However, the length-based method was more cost- effective for estimating growth and mortality when catches were large.

A New Expanded Mixed Element Method for Convection-Dominated Sobolev Equation

PubMed Central

Wang, Jinfeng; Li, Hong; Fang, Zhichao

2014-01-01

We propose and analyze a new expanded mixed element method, whose gradient belongs to the simple square integrable space instead of the classical H(div; Ω) space of Chen's expanded mixed element method. We study the new expanded mixed element method for convection-dominated Sobolev equation, prove the existence and uniqueness for finite element solution, and introduce a new expanded mixed projection. We derive the optimal a priori error estimates in L 2-norm for the scalar unknown u and a priori error estimates in (L 2)2-norm for its gradient λ and its flux σ. Moreover, we obtain the optimal a priori error estimates in H 1-norm for the scalar unknown u. Finally, we obtained some numerical results to illustrate efficiency of the new method. PMID:24701153

Body Composition of Bangladeshi Children: Comparison and Development of Leg-to-Leg Bioelectrical Impedance Equation

PubMed Central

Khan, I.; Hawlader, Sophie Mohammad Delwer Hossain; Arifeen, Shams El; Moore, Sophie; Hills, Andrew P.; Wells, Jonathan C.; Persson, Lars-Åke; Kabir, Iqbal

2012-01-01

The aim of this study was to investigate the validity of the Tanita TBF 300A leg-to-leg bioimpedance analyzer for estimating fat-free mass (FFM) in Bangladeshi children aged 4-10 years and to develop novel prediction equations for use in this population, using deuterium dilution as the reference method. Two hundred Bangladeshi children were enrolled. The isotope dilution technique with deuterium oxide was used for estimation of total body water (TBW). FFM estimated by Tanita was compared with results of deuterium oxide dilution technique. Novel prediction equations were created for estimating FFM, using linear regression models, fitting child's height and impedance as predictors. There was a significant difference in FFM and percentage of body fat (BF%) between methods (p<0.01), Tanita underestimating TBW in boys (p=0.001) and underestimating BF% in girls (p<0.001). A basic linear regression model with height and impedance explained 83% of the variance in FFM estimated by deuterium oxide dilution technique. The best-fit equation to predict FFM from linear regression modelling was achieved by adding weight, sex, and age to the basic model, bringing the adjusted R2 to 89% (standard error=0.90, p<0.001). These data suggest Tanita analyzer may be a valid field-assessment technique in Bangladeshi children when using population-specific prediction equations, such as the ones developed here. PMID:23082630

Quantitative Estimation of Seismic Velocity Changes Using Time-Lapse Seismic Data and Elastic-Wave Sensitivity Approach

NASA Astrophysics Data System (ADS)

Denli, H.; Huang, L.

2008-12-01

Quantitative monitoring of reservoir property changes is essential for safe geologic carbon sequestration. Time-lapse seismic surveys have the potential to effectively monitor fluid migration in the reservoir that causes geophysical property changes such as density, and P- and S-wave velocities. We introduce a novel method for quantitative estimation of seismic velocity changes using time-lapse seismic data. The method employs elastic sensitivity wavefields, which are the derivatives of elastic wavefield with respect to density, P- and S-wave velocities of a target region. We derive the elastic sensitivity equations from analytical differentiations of the elastic-wave equations with respect to seismic-wave velocities. The sensitivity equations are coupled with the wave equations in a way that elastic waves arriving in a target reservoir behave as a secondary source to sensitivity fields. We use a staggered-grid finite-difference scheme with perfectly-matched layers absorbing boundary conditions to simultaneously solve the elastic-wave equations and the elastic sensitivity equations. By elastic-wave sensitivities, a linear relationship between relative seismic velocity changes in the reservoir and time-lapse seismic data at receiver locations can be derived, which leads to an over-determined system of equations. We solve this system of equations using a least- square method for each receiver to obtain P- and S-wave velocity changes. We validate the method using both surface and VSP synthetic time-lapse seismic data for a multi-layered model and the elastic Marmousi model. Then we apply it to the time-lapse field VSP data acquired at the Aneth oil field in Utah. A total of 10.5K tons of CO2 was injected into the oil reservoir between the two VSP surveys for enhanced oil recovery. The synthetic and field data studies show that our new method can quantitatively estimate changes in seismic velocities within a reservoir due to CO2 injection/migration.

Do group-specific equations provide the best estimates of stature?

PubMed

Albanese, John; Osley, Stephanie E; Tuck, Andrew

2016-04-01

An estimate of stature can be used by a forensic anthropologist with the preliminary identification of an unknown individual when human skeletal remains are recovered. Fordisc is a computer application that can be used to estimate stature; like many other methods it requires the user to assign an unknown individual to a specific group defined by sex, race/ancestry, and century of birth before an equation is applied. The assumption is that a group-specific equation controls for group differences and should provide the best results most often. In this paper we assess the utility and benefits of using group-specific equations to estimate stature using Fordisc. Using the maximum length of the humerus and the maximum length of the femur from individuals with documented stature, we address the question: Do sex-, race/ancestry- and century-specific stature equations provide the best results when estimating stature? The data for our sample of 19th Century White males (n=28) were entered into Fordisc and stature was estimated using 22 different equation options for a total of 616 trials: 19th and 20th Century Black males, 19th and 20th Century Black females, 19th and 20th Century White females, 19th and 20th Century White males, 19th and 20th Century any, and 20th Century Hispanic males. The equations were assessed for utility in any one case (how many times the estimated range bracketed the documented stature) and in aggregate using 1-way ANOVA and other approaches. This group-specific equation that should have provided the best results was outperformed by several other equations for both the femur and humerus. These results suggest that group-specific equations do not provide better results for estimating stature while at the same time are more difficult to apply because an unknown must be allocated to a given group before stature can be estimated. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Methods for estimating tributary streamflow in the Chattahoochee River basin between Buford Dam and Franklin, Georgia

USGS Publications Warehouse

Stamey, Timothy C.

1998-01-01

Simple and reliable methods for estimating hourly streamflow are needed for the calibration and verification of a Chattahoochee River basin model between Buford Dam and Franklin, Ga. The river basin model is being developed by Georgia Department of Natural Resources, Environmental Protection Division, as part of their Chattahoochee River Modeling Project. Concurrent streamflow data collected at 19 continuous-record, and 31 partial-record streamflow stations, were used in ordinary least-squares linear regression analyses to define estimating equations, and in verifying drainage-area prorations. The resulting regression or drainage-area ratio estimating equations were used to compute hourly streamflow at the partial-record stations. The coefficients of determination (r-squared values) for the regression estimating equations ranged from 0.90 to 0.99. Observed and estimated hourly and daily streamflow data were computed for May 1, 1995, through October 31, 1995. Comparisons of observed and estimated daily streamflow data for 12 continuous-record tributary stations, that had available streamflow data for all or part of the period from May 1, 1995, to October 31, 1995, indicate that the mean error of estimate for the daily streamflow was about 25 percent.

Reaeration equations derived from U.S. geological survey database

USGS Publications Warehouse

Melching, C.S.; Flores, H.E.

1999-01-01

Accurate estimation of the reaeration-rate coefficient (K2) is extremely important for waste-load allocation. Currently, available K2 estimation equations generally yield poor estimates when applied to stream conditions different from those for which the equations were derived because they were derived from small databases composed of potentially highly inaccurate measurements. A large data set of K2 measurements made with tracer-gas methods was compiled from U.S. Geological Survey studies. This compilation included 493 reaches on 166 streams in 23 states. Careful screening to detect and eliminate erroneous measurements reduced the date set to 371 measurements. These measurements were divided into four subgroups on the basis of flow regime (channel control or pool and riffle) and stream scale (discharge greater than or less than 0.556 m3/s). Multiple linear regression in logarithms was applied to relate K2 to 12 stream hydraulic and water-quality characteristics. The resulting best-estimation equations had the form of semiempirical equations that included the rate of energy dissipation and discharge or depth and width as variables. For equation verification, a data set of K2 measurements made with tracer-gas procedures by other agencies was compiled from the literature. This compilation included 127 reaches on at least 24 streams in at least seven states. The standard error of estimate obtained when applying the developed equations to the U.S. Geological Survey data set ranged from 44 to 61%, whereas the standard error of estimate was 78% when applied to the verification data set.Accurate estimation of the reaeration-rate coefficient (K2) is extremely important for waste-load allocation. Currently, available K2 estimation equations generally yield poor estimates when applied to stream conditions different from those for which the equations were derived because they were derived from small databases composed of potentially highly inaccurate measurements. A large data set of K2 measurements made with tracer-gas methods was compiled from U.S. Geological Survey studies. This compilation included 493 reaches on 166 streams in 23 states. Careful screening to detect and eliminate erroneous measurements reduced the data set to 371 measurements. These measurements were divided into four subgroups on the basis of flow regime (channel control or pool and riffle) and stream scale (discharge greater than or less than 0.556 m3/s). Multiple linear regression in logarithms was applied to relate K2 to 12 stream hydraulic and water-quality characteristics. The resulting best-estimation equations had the form of semiempirical equations that included the rate of energy dissipation and discharge or depth and width as variables. For equation verification, a data set of K2 measurements made with tracer-gas procedures by other agencies was compiled from the literature. This compilation included 127 reaches on at least 24 streams in at least seven states. The standard error of estimate obtained when applying the developed equations to the U.S. Geological Survey data set ranged from 44 to 61%, whereas the standard error of estimate was 78% when applied to the verification data set.

Methods for estimating the magnitude and frequency of peak streamflows for unregulated streams in Oklahoma

USGS Publications Warehouse

Lewis, Jason M.

2010-01-01

Peak-streamflow regression equations were determined for estimating flows with exceedance probabilities from 50 to 0.2 percent for the state of Oklahoma. These regression equations incorporate basin characteristics to estimate peak-streamflow magnitude and frequency throughout the state by use of a generalized least squares regression analysis. The most statistically significant independent variables required to estimate peak-streamflow magnitude and frequency for unregulated streams in Oklahoma are contributing drainage area, mean-annual precipitation, and main-channel slope. The regression equations are applicable for watershed basins with drainage areas less than 2,510 square miles that are not affected by regulation. The resulting regression equations had a standard model error ranging from 31 to 46 percent. Annual-maximum peak flows observed at 231 streamflow-gaging stations through water year 2008 were used for the regression analysis. Gage peak-streamflow estimates were used from previous work unless 2008 gaging-station data were available, in which new peak-streamflow estimates were calculated. The U.S. Geological Survey StreamStats web application was used to obtain the independent variables required for the peak-streamflow regression equations. Limitations on the use of the regression equations and the reliability of regression estimates for natural unregulated streams are described. Log-Pearson Type III analysis information, basin and climate characteristics, and the peak-streamflow frequency estimates for the 231 gaging stations in and near Oklahoma are listed. Methodologies are presented to estimate peak streamflows at ungaged sites by using estimates from gaging stations on unregulated streams. For ungaged sites on urban streams and streams regulated by small floodwater retarding structures, an adjustment of the statewide regression equations for natural unregulated streams can be used to estimate peak-streamflow magnitude and frequency.

Predictive equations for the estimation of body size in seals and sea lions (Carnivora: Pinnipedia)

PubMed Central

Churchill, Morgan; Clementz, Mark T; Kohno, Naoki

2014-01-01

Body size plays an important role in pinniped ecology and life history. However, body size data is often absent for historical, archaeological, and fossil specimens. To estimate the body size of pinnipeds (seals, sea lions, and walruses) for today and the past, we used 14 commonly preserved cranial measurements to develop sets of single variable and multivariate predictive equations for pinniped body mass and total length. Principal components analysis (PCA) was used to test whether separate family specific regressions were more appropriate than single predictive equations for Pinnipedia. The influence of phylogeny was tested with phylogenetic independent contrasts (PIC). The accuracy of these regressions was then assessed using a combination of coefficient of determination, percent prediction error, and standard error of estimation. Three different methods of multivariate analysis were examined: bidirectional stepwise model selection using Akaike information criteria; all-subsets model selection using Bayesian information criteria (BIC); and partial least squares regression. The PCA showed clear discrimination between Otariidae (fur seals and sea lions) and Phocidae (earless seals) for the 14 measurements, indicating the need for family-specific regression equations. The PIC analysis found that phylogeny had a minor influence on relationship between morphological variables and body size. The regressions for total length were more accurate than those for body mass, and equations specific to Otariidae were more accurate than those for Phocidae. Of the three multivariate methods, the all-subsets approach required the fewest number of variables to estimate body size accurately. We then used the single variable predictive equations and the all-subsets approach to estimate the body size of two recently extinct pinniped taxa, the Caribbean monk seal (Monachus tropicalis) and the Japanese sea lion (Zalophus japonicus). Body size estimates using single variable regressions generally under or over-estimated body size; however, the all-subset regression produced body size estimates that were close to historically recorded body length for these two species. This indicates that the all-subset regression equations developed in this study can estimate body size accurately. PMID:24916814

Prediction of fat-free body mass from bioelectrical impedance and anthropometry among 3-year-old children using DXA

PubMed Central

Ejlerskov, Katrine T.; Jensen, Signe M.; Christensen, Line B.; Ritz, Christian; Michaelsen, Kim F.; Mølgaard, Christian

2014-01-01

For 3-year-old children suitable methods to estimate body composition are sparse. We aimed to develop predictive equations for estimating fat-free mass (FFM) from bioelectrical impedance (BIA) and anthropometry using dual-energy X-ray absorptiometry (DXA) as reference method using data from 99 healthy 3-year-old Danish children. Predictive equations were derived from two multiple linear regression models, a comprehensive model (height2/resistance (RI), six anthropometric measurements) and a simple model (RI, height, weight). Their uncertainty was quantified by means of 10-fold cross-validation approach. Prediction error of FFM was 3.0% for both equations (root mean square error: 360 and 356 g, respectively). The derived equations produced BIA-based prediction of FFM and FM near DXA scan results. We suggest that the predictive equations can be applied in similar population samples aged 2–4 years. The derived equations may prove useful for studies linking body composition to early risk factors and early onset of obesity. PMID:24463487

Prediction of fat-free body mass from bioelectrical impedance and anthropometry among 3-year-old children using DXA.

PubMed

Ejlerskov, Katrine T; Jensen, Signe M; Christensen, Line B; Ritz, Christian; Michaelsen, Kim F; Mølgaard, Christian

2014-01-27

For 3-year-old children suitable methods to estimate body composition are sparse. We aimed to develop predictive equations for estimating fat-free mass (FFM) from bioelectrical impedance (BIA) and anthropometry using dual-energy X-ray absorptiometry (DXA) as reference method using data from 99 healthy 3-year-old Danish children. Predictive equations were derived from two multiple linear regression models, a comprehensive model (height(2)/resistance (RI), six anthropometric measurements) and a simple model (RI, height, weight). Their uncertainty was quantified by means of 10-fold cross-validation approach. Prediction error of FFM was 3.0% for both equations (root mean square error: 360 and 356 g, respectively). The derived equations produced BIA-based prediction of FFM and FM near DXA scan results. We suggest that the predictive equations can be applied in similar population samples aged 2-4 years. The derived equations may prove useful for studies linking body composition to early risk factors and early onset of obesity.

A methodology for airplane parameter estimation and confidence interval determination in nonlinear estimation problems. Ph.D. Thesis - George Washington Univ., Apr. 1985

NASA Technical Reports Server (NTRS)

Murphy, P. C.

1986-01-01

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. With the fitted surface, sensitivity information can be updated at each iteration with less computational effort than that required by either a finite-difference method or integration of the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, and thus provides flexibility to use model equations in any convenient format. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. The degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels and to predict the degree of agreement between CR bounds and search estimates.

Orbital stability and energy estimate of ground states of saturable nonlinear Schrödinger equations with intensity functions in R2

NASA Astrophysics Data System (ADS)

Lin, Tai-Chia; Wang, Xiaoming; Wang, Zhi-Qiang

2017-10-01

Conventionally, the existence and orbital stability of ground states of nonlinear Schrödinger (NLS) equations with power-law nonlinearity (subcritical case) can be proved by an argument using strict subadditivity of the ground state energy and the concentration compactness method of Cazenave and Lions [4]. However, for saturable nonlinearity, such an argument is not applicable because strict subadditivity of the ground state energy fails in this case. Here we use a convexity argument to prove the existence and orbital stability of ground states of NLS equations with saturable nonlinearity and intensity functions in R2. Besides, we derive the energy estimate of ground states of saturable NLS equations with intensity functions using the eigenvalue estimate of saturable NLS equations without intensity function.

Structural Equation Models in a Redundancy Analysis Framework With Covariates.

PubMed

Lovaglio, Pietro Giorgio; Vittadini, Giorgio

2014-01-01

A recent method to specify and fit structural equation modeling in the Redundancy Analysis framework based on so-called Extended Redundancy Analysis (ERA) has been proposed in the literature. In this approach, the relationships between the observed exogenous variables and the observed endogenous variables are moderated by the presence of unobservable composites, estimated as linear combinations of exogenous variables. However, in the presence of direct effects linking exogenous and endogenous variables, or concomitant indicators, the composite scores are estimated by ignoring the presence of the specified direct effects. To fit structural equation models, we propose a new specification and estimation method, called Generalized Redundancy Analysis (GRA), allowing us to specify and fit a variety of relationships among composites, endogenous variables, and external covariates. The proposed methodology extends the ERA method, using a more suitable specification and estimation algorithm, by allowing for covariates that affect endogenous indicators indirectly through the composites and/or directly. To illustrate the advantages of GRA over ERA we propose a simulation study of small samples. Moreover, we propose an application aimed at estimating the impact of formal human capital on the initial earnings of graduates of an Italian university, utilizing a structural model consistent with well-established economic theory.

Parameter estimation of kinetic models from metabolic profiles: two-phase dynamic decoupling method.

PubMed

Jia, Gengjie; Stephanopoulos, Gregory N; Gunawan, Rudiyanto

2011-07-15

Time-series measurements of metabolite concentration have become increasingly more common, providing data for building kinetic models of metabolic networks using ordinary differential equations (ODEs). In practice, however, such time-course data are usually incomplete and noisy, and the estimation of kinetic parameters from these data is challenging. Practical limitations due to data and computational aspects, such as solving stiff ODEs and finding global optimal solution to the estimation problem, give motivations to develop a new estimation procedure that can circumvent some of these constraints. In this work, an incremental and iterative parameter estimation method is proposed that combines and iterates between two estimation phases. One phase involves a decoupling method, in which a subset of model parameters that are associated with measured metabolites, are estimated using the minimization of slope errors. Another phase follows, in which the ODE model is solved one equation at a time and the remaining model parameters are obtained by minimizing concentration errors. The performance of this two-phase method was tested on a generic branched metabolic pathway and the glycolytic pathway of Lactococcus lactis. The results showed that the method is efficient in getting accurate parameter estimates, even when some information is missing.

Derivation and validation of simple anthropometric equations to predict adipose tissue mass and total fat mass with MRI as the reference method

PubMed Central

Al-Gindan, Yasmin Y.; Hankey, Catherine R.; Govan, Lindsay; Gallagher, Dympna; Heymsfield, Steven B.; Lean, Michael E. J.

2017-01-01

The reference organ-level body composition measurement method is MRI. Practical estimations of total adipose tissue mass (TATM), total adipose tissue fat mass (TATFM) and total body fat are valuable for epidemiology, but validated prediction equations based on MRI are not currently available. We aimed to derive and validate new anthropometric equations to estimate MRI-measured TATM/TATFM/total body fat and compare them with existing prediction equations using older methods. The derivation sample included 416 participants (222 women), aged between 18 and 88 years with BMI between 15·9 and 40·8 (kg/m2). The validation sample included 204 participants (110 women), aged between 18 and 86 years with BMI between 15·7 and 36·4 (kg/m2). Both samples included mixed ethnic/racial groups. All the participants underwent whole-body MRI to quantify TATM (dependent variable) and anthropometry (independent variables). Prediction equations developed using stepwise multiple regression were further investigated for agreement and bias before validation in separate data sets. Simplest equations with optimal R2 and Bland–Altman plots demonstrated good agreement without bias in the validation analyses: men: TATM (kg) = 0·198 weight (kg) + 0·478 waist (cm) − 0·147 height (cm) − 12·8 (validation: R2 0·79, CV = 20 %, standard error of the estimate (SEE)=3·8 kg) and women: TATM (kg)=0·789 weight (kg) + 0·0786 age (years) − 0·342 height (cm) + 24·5 (validation: R2 0·84, CV = 13 %, SEE = 3·0 kg). Published anthropometric prediction equations, based on MRI and computed tomographic scans, correlated strongly with MRI-measured TATM: (R2 0·70 – 0·82). Estimated TATFM correlated well with published prediction equations for total body fat based on underwater weighing (R2 0·70–0·80), with mean bias of 2·5–4·9 kg, correctable with log-transformation in most equations. In conclusion, new equations, using simple anthropometric measurements, estimated MRI-measured TATM with correlations and agreements suitable for use in groups and populations across a wide range of fatness. PMID:26435103

Energy requirement assessed by doubly-labeled water method in patients with advanced amyotrophic lateral sclerosis managed by tracheotomy positive pressure ventilation.

PubMed

Ichihara, Noriko; Namba, Kazuyoshi; Ishikawa-Takata, Kazuko; Sekine, Kazunori; Takase, Mitsunori; Kamada, Yuko; Fujii, Seigo

2012-10-01

This study aimed to clarify the energy requirement in patients with amyotrophic lateral sclerosis (ALS) undergoing tracheostomy positive pressure ventilation with tracheostomy. Total energy expenditure (TEE) was measured in 10 hospitalized bedridden ALS patients using the doubly-labeled water (DLW) method. The mean TEE/day and TEE/fat- free mass estimated by DLW method were 934 ± 201 kcal/day and 34.8 ± 5.5 kcal/kg/day, respectively. The mean TEE/resting metabolic rate (RMR) was 0.85 when RMR was estimated by the Harris-Benedict equation, 0.91 by Dietary Reference Intake (DRI), and 0.97 by Ganpule's equation using fat-free mass (FFM). The ratios of TEE to measured RMR were 1.05, 1.15 and 1.23 in three patients. In conclusion, multiplying measured RMR by 1.1 to 1.2 is considered to be appropriate to estimate energy need. However, because it is difficult to measure RMR directly in a clinical setting, an appropriate equation for estimating RMR for ALS patient should be developed.

Estimating the time evolution of NMR systems via a quantum-speed-limit-like expression

NASA Astrophysics Data System (ADS)

Villamizar, D. V.; Duzzioni, E. I.; Leal, A. C. S.; Auccaise, R.

2018-05-01

Finding the solutions of the equations that describe the dynamics of a given physical system is crucial in order to obtain important information about its evolution. However, by using estimation theory, it is possible to obtain, under certain limitations, some information on its dynamics. The quantum-speed-limit (QSL) theory was originally used to estimate the shortest time in which a Hamiltonian drives an initial state to a final one for a given fidelity. Using the QSL theory in a slightly different way, we are able to estimate the running time of a given quantum process. For that purpose, we impose the saturation of the Anandan-Aharonov bound in a rotating frame of reference where the state of the system travels slower than in the original frame (laboratory frame). Through this procedure it is possible to estimate the actual evolution time in the laboratory frame of reference with good accuracy when compared to previous methods. Our method is tested successfully to predict the time spent in the evolution of nuclear spins 1/2 and 3/2 in NMR systems. We find that the estimated time according to our method is better than previous approaches by up to four orders of magnitude. One disadvantage of our method is that we need to solve a number of transcendental equations, which increases with the system dimension and parameter discretization used to solve such equations numerically.

Estimating, Testing, and Comparing Specific Effects in Structural Equation Models: The Phantom Model Approach

ERIC Educational Resources Information Center

Macho, Siegfried; Ledermann, Thomas

2011-01-01

The phantom model approach for estimating, testing, and comparing specific effects within structural equation models (SEMs) is presented. The rationale underlying this novel method consists in representing the specific effect to be assessed as a total effect within a separate latent variable model, the phantom model that is added to the main…

Estimation of body density based on hydrostatic weighing without head submersion in young Japanese adults.

PubMed

Demura, S; Sato, S; Kitabayashi, T

2006-06-01

This study examined a method of predicting body density based on hydrostatic weighing without head submersion (HWwithoutHS). Donnelly and Sintek (1984) developed a method to predict body density based on hydrostatic weight without head submersion. This method predicts the difference (D) between HWwithoutHS and hydrostatic weight with head submersion (HWwithHS) from anthropometric variables (head length and head width), and then calculates body density using D as a correction factor. We developed several prediction equations to estimate D based on head anthropometry and differences between the sexes, and compared their prediction accuracy with Donnelly and Sintek's equation. Thirty-two males and 32 females aged 17-26 years participated in the study. Multiple linear regression analysis was performed to obtain the prediction equations, and the systematic errors of their predictions were assessed by Bland-Altman plots. The best prediction equations obtained were: Males: D(g) = -164.12X1 - 125.81X2 - 111.03X3 + 100.66X4 + 6488.63, where X1 = head length (cm), X2 = head circumference (cm), X3 = head breadth (cm), X4 = head thickness (cm) (R = 0.858, R2 = 0.737, adjusted R2 = 0.687, standard error of the estimate = 224.1); Females: D(g) = -156.03X1 - 14.03X2 - 38.45X3 - 8.87X4 + 7852.45, where X1 = head circumference (cm), X2 = body mass (g), X3 = head length (cm), X4 = height (cm) (R = 0.913, R2 = 0.833, adjusted R2 = 0.808, standard error of the estimate = 137.7). The effective predictors in these prediction equations differed from those of Donnelly and Sintek's equation, and head circumference and head length were included in both equations. The prediction accuracy was improved by statistically selecting effective predictors. Since we did not assess cross-validity, the equations cannot be used to generalize to other populations, and further investigation is required.

Comparison of total body water estimates from O-18 and bioelectrical response prediction equations

NASA Technical Reports Server (NTRS)

Barrows, Linda H.; Inners, L. Daniel; Stricklin, Marcella D.; Klein, Peter D.; Wong, William W.; Siconolfi, Steven F.

1993-01-01

Identification of an indirect, rapid means to measure total body water (TBW) during space flight may aid in quantifying hydration status and assist in countermeasure development. Bioelectrical response testing and hydrostatic weighing were performed on 27 subjects who ingested O-18, a naturally occurring isotope of oxygen, to measure true TBW. TBW estimates from three bioelectrical response prediction equations and fat-free mass (FFM) were compared to TBW measured from O-18. A repeated measures MANOVA with post-hoc Dunnett's Test indicated a significant (p less than 0.05) difference between TBW estimates from two of the three bioelectrical response prediction equations and O-18. TBW estimates from FFM and the Kushner & Schoeller (1986) equation yielded results that were similar to those given by O-18. Strong correlations existed between each prediction method and O-18; however, standard errors, identified through regression analyses, were higher for the bioelectrical response prediction equations compared to those derived from FFM. These findings suggest (1) the Kushner & Schoeller (1986) equation may provide a valid measure of TBW, (2) other TBW prediction equations need to be identified that have variability similar to that of FFM, and (3) bioelectrical estimates of TBW may prove valuable in quantifying hydration status during space flight.

Measurement-based perturbation theory and differential equation parameter estimation with applications to satellite gravimetry

NASA Astrophysics Data System (ADS)

Xu, Peiliang

2018-06-01

The numerical integration method has been routinely used by major institutions worldwide, for example, NASA Goddard Space Flight Center and German Research Center for Geosciences (GFZ), to produce global gravitational models from satellite tracking measurements of CHAMP and/or GRACE types. Such Earth's gravitational products have found widest possible multidisciplinary applications in Earth Sciences. The method is essentially implemented by solving the differential equations of the partial derivatives of the orbit of a satellite with respect to the unknown harmonic coefficients under the conditions of zero initial values. From the mathematical and statistical point of view, satellite gravimetry from satellite tracking is essentially the problem of estimating unknown parameters in the Newton's nonlinear differential equations from satellite tracking measurements. We prove that zero initial values for the partial derivatives are incorrect mathematically and not permitted physically. The numerical integration method, as currently implemented and used in mathematics and statistics, chemistry and physics, and satellite gravimetry, is groundless, mathematically and physically. Given the Newton's nonlinear governing differential equations of satellite motion with unknown equation parameters and unknown initial conditions, we develop three methods to derive new local solutions around a nominal reference orbit, which are linked to measurements to estimate the unknown corrections to approximate values of the unknown parameters and the unknown initial conditions. Bearing in mind that satellite orbits can now be tracked almost continuously at unprecedented accuracy, we propose the measurement-based perturbation theory and derive global uniformly convergent solutions to the Newton's nonlinear governing differential equations of satellite motion for the next generation of global gravitational models. Since the solutions are global uniformly convergent, theoretically speaking, they are able to extract smallest possible gravitational signals from modern and future satellite tracking measurements, leading to the production of global high-precision, high-resolution gravitational models. By directly turning the nonlinear differential equations of satellite motion into the nonlinear integral equations, and recognizing the fact that satellite orbits are measured with random errors, we further reformulate the links between satellite tracking measurements and the global uniformly convergent solutions to the Newton's governing differential equations as a condition adjustment model with unknown parameters, or equivalently, the weighted least squares estimation of unknown differential equation parameters with equality constraints, for the reconstruction of global high-precision, high-resolution gravitational models from modern (and future) satellite tracking measurements.

Using the Kernel Method of Test Equating for Estimating the Standard Errors of Population Invariance Measures. Research Report. ETS RR-06-20

ERIC Educational Resources Information Center

Moses, Tim

2006-01-01

Population invariance is an important requirement of test equating. An equating function is said to be population invariant when the choice of (sub)population used to compute the equating function does not matter. In recent studies, the extent to which equating functions are population invariant is typically addressed in terms of practical…

Methods for estimating peak-flow frequencies at ungaged sites in Montana based on data through water year 2011: Chapter F in Montana StreamStats

USGS Publications Warehouse

Sando, Roy; Sando, Steven K.; McCarthy, Peter M.; Dutton, DeAnn M.

2016-04-05

The U.S. Geological Survey (USGS), in cooperation with the Montana Department of Natural Resources and Conservation, completed a study to update methods for estimating peak-flow frequencies at ungaged sites in Montana based on peak-flow data at streamflow-gaging stations through water year 2011. The methods allow estimation of peak-flow frequencies (that is, peak-flow magnitudes, in cubic feet per second, associated with annual exceedance probabilities of 66.7, 50, 42.9, 20, 10, 4, 2, 1, 0.5, and 0.2 percent) at ungaged sites. The annual exceedance probabilities correspond to 1.5-, 2-, 2.33-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-year recurrence intervals, respectively.Regional regression analysis is a primary focus of Chapter F of this Scientific Investigations Report, and regression equations for estimating peak-flow frequencies at ungaged sites in eight hydrologic regions in Montana are presented. The regression equations are based on analysis of peak-flow frequencies and basin characteristics at 537 streamflow-gaging stations in or near Montana and were developed using generalized least squares regression or weighted least squares regression.All of the data used in calculating basin characteristics that were included as explanatory variables in the regression equations were developed for and are available through the USGS StreamStats application (http://water.usgs.gov/osw/streamstats/) for Montana. StreamStats is a Web-based geographic information system application that was created by the USGS to provide users with access to an assortment of analytical tools that are useful for water-resource planning and management. The primary purpose of the Montana StreamStats application is to provide estimates of basin characteristics and streamflow characteristics for user-selected ungaged sites on Montana streams. The regional regression equations presented in this report chapter can be conveniently solved using the Montana StreamStats application.Selected results from this study were compared with results of previous studies. For most hydrologic regions, the regression equations reported for this study had lower mean standard errors of prediction (in percent) than the previously reported regression equations for Montana. The equations presented for this study are considered to be an improvement on the previously reported equations primarily because this study (1) included 13 more years of peak-flow data; (2) included 35 more streamflow-gaging stations than previous studies; (3) used a detailed geographic information system (GIS)-based definition of the regulation status of streamflow-gaging stations, which allowed better determination of the unregulated peak-flow records that are appropriate for use in the regional regression analysis; (4) included advancements in GIS and remote-sensing technologies, which allowed more convenient calculation of basin characteristics and investigation of many more candidate basin characteristics; and (5) included advancements in computational and analytical methods, which allowed more thorough and consistent data analysis.This report chapter also presents other methods for estimating peak-flow frequencies at ungaged sites. Two methods for estimating peak-flow frequencies at ungaged sites located on the same streams as streamflow-gaging stations are described. Additionally, envelope curves relating maximum recorded annual peak flows to contributing drainage area for each of the eight hydrologic regions in Montana are presented and compared to a national envelope curve. In addition to providing general information on characteristics of large peak flows, the regional envelope curves can be used to assess the reasonableness of peak-flow frequency estimates determined using the regression equations.

Statistical Assessment of Estimated Transformations in Observed-Score Equating

ERIC Educational Resources Information Center

Wiberg, Marie; González, Jorge

2016-01-01

Equating methods make use of an appropriate transformation function to map the scores of one test form into the scale of another so that scores are comparable and can be used interchangeably. The equating literature shows that the ways of judging the success of an equating (i.e., the score transformation) might differ depending on the adopted…

Assessing glomerular filtration rate (GFR) in critically ill patients with acute kidney injury - true GFR versus urinary creatinine clearance and estimating equations

PubMed Central

2013-01-01

Introduction Estimation of kidney function in critically ill patients with acute kidney injury (AKI), is important for appropriate dosing of drugs and adjustment of therapeutic strategies, but challenging due to fluctuations in kidney function, creatinine metabolism and fluid balance. Data on the agreement between estimating and gold standard methods to assess glomerular filtration rate (GFR) in early AKI are lacking. We evaluated the agreement of urinary creatinine clearance (CrCl) and three commonly used estimating equations, the Cockcroft Gault (CG), the Modification of Diet in Renal Disease (MDRD) and the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equations, in comparison to GFR measured by the infusion clearance of chromium-ethylenediaminetetraacetic acid (51Cr-EDTA), in critically ill patients with early AKI after complicated cardiac surgery. Methods Thirty patients with early AKI were studied in the intensive care unit, 2 to 12 days after complicated cardiac surgery. The infusion clearance for 51Cr-EDTA obtained as a measure of GFR (GFR51Cr-EDTA) was calculated from the formula: GFR (mL/min/1.73m2) = (51Cr-EDTA infusion rate × 1.73)/(arterial 51Cr-EDTA × body surface area) and compared with the urinary CrCl and the estimated GFR (eGFR) from the three estimating equations. Urine was collected in two 30-minute periods to measure urine flow and urine creatinine. Urinary CrCl was calculated from the formula: CrCl (mL/min/1.73m2) = (urine volume × urine creatinine × 1.73)/(serum creatinine × 30 min × body surface area). Results The within-group error was lower for GFR51Cr-EDTA than the urinary CrCl method, 7.2% versus 55.0%. The between-method bias was 2.6, 11.6, 11.1 and 7.39 ml/min for eGFRCrCl, eGFRMDRD, eGFRCKD-EPI and eGFRCG, respectively, when compared to GFR51Cr-EDTA. The error was 103%, 68.7%, 67.7% and 68.0% for eGFRCrCl, eGFRMDRD, eGFRCKD-EPI and eGFRCG, respectively, when compared to GFR51Cr-EDTA. Conclusions The study demonstrated poor precision of the commonly utilized urinary CrCl method for assessment of GFR in critically ill patients with early AKI, suggesting that this should not be used as a reference method when validating new methods for assessing kidney function in this patient population. The commonly used estimating equations perform poorly when estimating GFR, with high biases and unacceptably high errors. PMID:23767877

Accuracy of Bioelectrical Impedance Analysis in Estimated Longitudinal Fat-Free Mass Changes in Male Army Cadets.

PubMed

Langer, Raquel D; Matias, Catarina N; Borges, Juliano H; Cirolini, Vagner X; Páscoa, Mauro A; Guerra-Júnior, Gil; Gonçalves, Ezequiel M

2018-03-26

Bioelectrical impedance analysis (BIA) is a practical and rapid method for making a longitudinal analysis of changes in body composition. However, most BIA validation studies have been performed in a clinical population and only at one moment, or point in time (cross-sectional study). The aim of this study is to investigate the accuracy of predictive equations based on BIA with regard to the changes in fat-free mass (FFM) in Brazilian male army cadets after 7 mo of military training. The values used were determined using dual-energy X-ray absorptiometry (DXA) as a reference method. The study included 310 male Brazilian Army cadets (aged 17-24 yr). FFM was measured using eight general predictive BIA equations, with one equation specifically applied to this population sample, and the values were compared with results obtained using DXA. The student's t-test, adjusted coefficient of determination (R2), standard error of estimation (SEE), Lin's approach, and the Bland-Altman test were used to determine the accuracy of the predictive BIA equations used to estimate FFM in this population and between the two moments (pre- and post-moment). The FFM measured using the nine predictive BIA equations, and determined using DXA at the post-moment, showed a significant increase when compared with the pre-moment (p < 0.05). All nine predictive BIA equations were able to detect FFM changes in the army cadets between the two moments in a very similar way to the reference method (DXA). However, only the one BIA equation specific to this population showed no significant differences in the FFM estimation between DXA at pre- and post-moment of military routine. All predictive BIA equations showed large limits of agreement using the Bland-Altman approach. The eight general predictive BIA equations used in this study were not found to be valid for analyzing the FFM changes in the Brazilian male army cadets, after a period of approximately 7 mo of military training. Although the BIA equation specific to this population is dependent on the amount of FFM, it appears to be a good alternative to DXA for assessing FFM in Brazilian male army cadets.

Tree Biomass Estimation of Chinese fir (Cunninghamia lanceolata) Based on Bayesian Method

PubMed Central

Zhang, Jianguo

2013-01-01

Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) is the most important conifer species for timber production with huge distribution area in southern China. Accurate estimation of biomass is required for accounting and monitoring Chinese forest carbon stocking. In the study, allometric equation was used to analyze tree biomass of Chinese fir. The common methods for estimating allometric model have taken the classical approach based on the frequency interpretation of probability. However, many different biotic and abiotic factors introduce variability in Chinese fir biomass model, suggesting that parameters of biomass model are better represented by probability distributions rather than fixed values as classical method. To deal with the problem, Bayesian method was used for estimating Chinese fir biomass model. In the Bayesian framework, two priors were introduced: non-informative priors and informative priors. For informative priors, 32 biomass equations of Chinese fir were collected from published literature in the paper. The parameter distributions from published literature were regarded as prior distributions in Bayesian model for estimating Chinese fir biomass. Therefore, the Bayesian method with informative priors was better than non-informative priors and classical method, which provides a reasonable method for estimating Chinese fir biomass. PMID:24278198

Tree biomass estimation of Chinese fir (Cunninghamia lanceolata) based on Bayesian method.

PubMed

Zhang, Xiongqing; Duan, Aiguo; Zhang, Jianguo

2013-01-01

Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) is the most important conifer species for timber production with huge distribution area in southern China. Accurate estimation of biomass is required for accounting and monitoring Chinese forest carbon stocking. In the study, allometric equation W = a(D2H)b was used to analyze tree biomass of Chinese fir. The common methods for estimating allometric model have taken the classical approach based on the frequency interpretation of probability. However, many different biotic and abiotic factors introduce variability in Chinese fir biomass model, suggesting that parameters of biomass model are better represented by probability distributions rather than fixed values as classical method. To deal with the problem, Bayesian method was used for estimating Chinese fir biomass model. In the Bayesian framework, two priors were introduced: non-informative priors and informative priors. For informative priors, 32 biomass equations of Chinese fir were collected from published literature in the paper. The parameter distributions from published literature were regarded as prior distributions in Bayesian model for estimating Chinese fir biomass. Therefore, the Bayesian method with informative priors was better than non-informative priors and classical method, which provides a reasonable method for estimating Chinese fir biomass.

Error Estimation for the Linearized Auto-Localization Algorithm

PubMed Central

Guevara, Jorge; Jiménez, Antonio R.; Prieto, Jose Carlos; Seco, Fernando

2012-01-01

The Linearized Auto-Localization (LAL) algorithm estimates the position of beacon nodes in Local Positioning Systems (LPSs), using only the distance measurements to a mobile node whose position is also unknown. The LAL algorithm calculates the inter-beacon distances, used for the estimation of the beacons’ positions, from the linearized trilateration equations. In this paper we propose a method to estimate the propagation of the errors of the inter-beacon distances obtained with the LAL algorithm, based on a first order Taylor approximation of the equations. Since the method depends on such approximation, a confidence parameter τ is defined to measure the reliability of the estimated error. Field evaluations showed that by applying this information to an improved weighted-based auto-localization algorithm (WLAL), the standard deviation of the inter-beacon distances can be improved by more than 30% on average with respect to the original LAL method. PMID:22736965

Estimating equations for glomerular filtration rate in the era of creatinine standardization: a systematic review.

PubMed

Earley, Amy; Miskulin, Dana; Lamb, Edmund J; Levey, Andrew S; Uhlig, Katrin

2012-06-05

Clinical laboratories are increasingly reporting estimated glomerular filtration rate (GFR) by using serum creatinine assays traceable to a standard reference material. To review the performance of GFR estimating equations to inform the selection of a single equation by laboratories and the interpretation of estimated GFR by clinicians. A systematic search of MEDLINE, without language restriction, between 1999 and 21 October 2011. Cross-sectional studies in adults that compared the performance of 2 or more creatinine-based GFR estimating equations with a reference GFR measurement. Eligible equations were derived or reexpressed and validated by using creatinine measurements traceable to the standard reference material. Reviewers extracted data on study population characteristics, measured GFR, creatinine assay, and equation performance. Eligible studies compared the MDRD (Modification of Diet in Renal Disease) Study and CKD-EPI (Chronic Kidney Disease Epidemiology Collaboration) equations or modifications thereof. In 12 studies in North America, Europe, and Australia, the CKD-EPI equation performed better at higher GFRs (approximately >60 mL/min per 1.73 m(2)) and the MDRD Study equation performed better at lower GFRs. In 5 of 8 studies in Asia and Africa, the equations were modified to improve their performance by adding a coefficient derived in the local population or removing a coefficient. Methods of GFR measurement and study populations were heterogeneous. Neither the CKD-EPI nor the MDRD Study equation is optimal for all populations and GFR ranges. Using a single equation for reporting requires a tradeoff to optimize performance at either higher or lower GFR ranges. A general practice and public health perspective favors the CKD-EPI equation. Kidney Disease: Improving Global Outcomes.

Simple method for quick estimation of aquifer hydrogeological parameters

NASA Astrophysics Data System (ADS)

Ma, C.; Li, Y. Y.

2017-08-01

Development of simple and accurate methods to determine the aquifer hydrogeological parameters was of importance for groundwater resources assessment and management. Aiming at the present issue of estimating aquifer parameters based on some data of the unsteady pumping test, a fitting function of Theis well function was proposed using fitting optimization method and then a unitary linear regression equation was established. The aquifer parameters could be obtained by solving coefficients of the regression equation. The application of the proposed method was illustrated, using two published data sets. By the error statistics and analysis on the pumping drawdown, it showed that the method proposed in this paper yielded quick and accurate estimates of the aquifer parameters. The proposed method could reliably identify the aquifer parameters from long distance observed drawdowns and early drawdowns. It was hoped that the proposed method in this paper would be helpful for practicing hydrogeologists and hydrologists.

A Comparison of Normal and Elliptical Estimation Methods in Structural Equation Models.

ERIC Educational Resources Information Center

Schumacker, Randall E.; Cheevatanarak, Suchittra

Monte Carlo simulation compared chi-square statistics, parameter estimates, and root mean square error of approximation values using normal and elliptical estimation methods. Three research conditions were imposed on the simulated data: sample size, population contamination percent, and kurtosis. A Bentler-Weeks structural model established the…

Method for estimating low-flow characteristics of ungaged streams in Indiana

USGS Publications Warehouse

Arihood, Leslie D.; Glatfelter, Dale R.

1991-01-01

Equations for estimating the 7-day, 2-year and 7oday, 10-year low flows at sites on ungaged streams are presented. Regression analysis was used to develop equations relating basin characteristics and low-flow characteristics at 82 gaging stations. Significant basin characteristics in the equations are contributing drainage area and flow-duration ratio, which is the 20-percent flow duration divided by the 90-percent flow duration. Flow-duration ratio has been regionalized for Indiana on a plate. Ratios for use in the equations are obtained from the plate. Drainage areas are determined from maps or are obtained from reports. The predictive capability of the method was determined by tests of the equations and of the flow-duration ratios on the plate. The accuracy of the equations alone was tested by estimating the low-flow characteristics at 82 gaging stations where flow-duration ratio is already known. In this case, the standard errors of estimate for 7-day, 2-year and 7-day, 10-year low flows are 19 and 28 percent. When flow-duration ratios for the 82 gaging stations are obtained from the map, the standard errors are 46 and 61 percent. However, when stations having drainage areas of less than 10 square miles are excluded from the test, the standard errors decrease to 38 and 49 percent. Standard errors increase when stations with small basins are included, probably because some of the flow-duration ratios obtained for these small basins are incorrect. Local geology and its effect on the ratio are not adequately reflected on the plate, which shows the regional variation in flow-duration ratio. In all the tests, no bias is apparent areally, with increasing drainage area or with increasing ratio. Guidelines and limitations should be considered when using the method. The method can be applied only at sites in the northern and central physiographic zones of the State. Low-flow characteristics cannot be estimated for regulated streams unless the amount of regulation is known so that the estimated low-flow characteristic can be adjusted. The method is most accurate for sites having drainage areas ranging from 10 to 1,000 square miles and for predictions of 7-day, 10-year low flows ranging from 0.5 to 340 cubic feet per second.

Method for estimating low-flow characteristics of ungaged streams in Indiana

USGS Publications Warehouse

Arihood, L.D.; Glatfelter, D.R.

1986-01-01

Equations for estimating the 7-day, 2-yr and 7-day, 10-yr low flows at sites on ungaged streams are presented. Regression analysis was used to develop equations relating basin characteristics and low flow characteristics at 82 gaging stations. Significant basin characteristics in the equations are contributing drainage area and flow duration ratio, which is the 20% flow duration divided by the 90% flow duration. Flow duration ratio has been regionalized for Indiana on a plate. Ratios for use in the equations are obtained from this plate. Drainage areas are determined from maps or are obtained from reports. The predictive capability of the method was determined by tests of the equations and of the flow duration ratios on the plate. The accuracy of the equations alone was tested by estimating the low flow characteristics at 82 gaging stations where flow duration ratio is already known. In this case, the standard errors of estimate for 7-day, 2-yr and 7-day, 10-yr low flows are 19% and 28%. When flow duration ratios for the 82 gaging stations are obtained from the map, the standard errors are 46% and 61%. However, when stations with drainage areas < 10 sq mi are excluded from the test, the standard errors reduce to 38% and 49%. Standard errors increase when stations with small basins are included, probably because some of the flow duration ratios obtained for these small basins are incorrect. Local geology and its effect on the ratio are not adequately reflected on the plate, which shows the regional variation in flow duration ratio. In all the tests, no bias is apparent areally, with increasing drainage area or with increasing ratio. Guidelines and limitations should be considered when using the method. The method can be applied only at sites in the northern and the central physiographic zones of the state. Low flow characteristics cannot be estimated for regulated streams unless the amount of regulation is known so that the estimated low flow characteristic can be adjusted. The method is most accurate for sites with drainage areas ranging from 10 to 1,000 sq mi and for predictions of 7-day, 10-yr low flows ranging from 0.5 to 340 cu ft/sec. (Author 's abstract)

The Inverse Problem for Confined Aquifer Flow: Identification and Estimation With Extensions

NASA Astrophysics Data System (ADS)

Loaiciga, Hugo A.; MariñO, Miguel A.

1987-01-01

The contributions of this work are twofold. First, a methodology for estimating the elements of parameter matrices in the governing equation of flow in a confined aquifer is developed. The estimation techniques for the distributed-parameter inverse problem pertain to linear least squares and generalized least squares methods. The linear relationship among the known heads and unknown parameters of the flow equation provides the background for developing criteria for determining the identifiability status of unknown parameters. Under conditions of exact or overidentification it is possible to develop statistically consistent parameter estimators and their asymptotic distributions. The estimation techniques, namely, two-stage least squares and three stage least squares, are applied to a specific groundwater inverse problem and compared between themselves and with an ordinary least squares estimator. The three-stage estimator provides the closer approximation to the actual parameter values, but it also shows relatively large standard errors as compared to the ordinary and two-stage estimators. The estimation techniques provide the parameter matrices required to simulate the unsteady groundwater flow equation. Second, a nonlinear maximum likelihood estimation approach to the inverse problem is presented. The statistical properties of maximum likelihood estimators are derived, and a procedure to construct confidence intervals and do hypothesis testing is given. The relative merits of the linear and maximum likelihood estimators are analyzed. Other topics relevant to the identification and estimation methodologies, i.e., a continuous-time solution to the flow equation, coping with noise-corrupted head measurements, and extension of the developed theory to nonlinear cases are also discussed. A simulation study is used to evaluate the methods developed in this study.

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

ERIC Educational Resources Information Center

Furlow, Carolyn F.; Beretvas, S. Natasha

2005-01-01

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

Procedure for estimating stability and control parameters from flight test data by using maximum likelihood methods employing a real-time digital system

NASA Technical Reports Server (NTRS)

Grove, R. D.; Bowles, R. L.; Mayhew, S. C.

1972-01-01

A maximum likelihood parameter estimation procedure and program were developed for the extraction of the stability and control derivatives of aircraft from flight test data. Nonlinear six-degree-of-freedom equations describing aircraft dynamics were used to derive sensitivity equations for quasilinearization. The maximum likelihood function with quasilinearization was used to derive the parameter change equations, the covariance matrices for the parameters and measurement noise, and the performance index function. The maximum likelihood estimator was mechanized into an iterative estimation procedure utilizing a real time digital computer and graphic display system. This program was developed for 8 measured state variables and 40 parameters. Test cases were conducted with simulated data for validation of the estimation procedure and program. The program was applied to a V/STOL tilt wing aircraft, a military fighter airplane, and a light single engine airplane. The particular nonlinear equations of motion, derivation of the sensitivity equations, addition of accelerations into the algorithm, operational features of the real time digital system, and test cases are described.

Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models

PubMed Central

Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

2016-01-01

Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization. PMID:27243005

Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models.

PubMed

Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

2016-01-01

Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.

Accuracy of Anthropometric Equations for Estimating Body Fat in Professional Male Soccer Players Compared with DXA

PubMed Central

López-Taylor, Juan R.; Jiménez-Alvarado, Juan Antonio; Villegas-Balcázar, Marisol; Jáuregui-Ulloa, Edtna E.; Torres-Naranjo, Francisco

2018-01-01

Background There are several published anthropometric equations to estimate body fat percentage (BF%), and this may prompt uncertainty about their application. Purpose To analyze the accuracy of several anthropometric equations (developed in athletic [AT] and nonathletic [NAT] populations) that estimate BF% comparing them with DXA. Methods We evaluated 131 professional male soccer players (body mass: 73.2 ± 8.0 kg; height: 177.5 ± 5.8 cm; DXA BF% [median, 25th–75th percentile]: 14.0, 11.9–16.4%) aged 18 to 37 years. All subjects were evaluated with anthropometric measurements and a whole body DXA scan. BF% was estimated through 14 AT and 17 NAT anthropometric equations and compared with the measured DXA BF%. Mean differences and 95% limits of agreement were calculated for those anthropometric equations without significant differences with DXA. Results Five AT and seven NAT anthropometric equations did not differ significantly with DXA. From these, Oliver's and Civar's (AT) and Ball's and Wilmore's (NAT) equations showed the highest agreement with DXA. Their 95% limits of agreement ranged from −3.9 to 2.3%, −4.8 to 1.8%, −3.4 to 3.1%, and −3.9 to 3.0%, respectively. Conclusion Oliver's, Ball's, Civar's, and Wilmore's equations were the best to estimate BF% accurately compared with DXA in professional male soccer players. PMID:29736402

Rainfall Threshold for Flash Flood Early Warning Based on Rational Equation: A Case Study of Zuojiao Watershed in Yunnan Province

NASA Astrophysics Data System (ADS)

Li, Q.; Wang, Y. L.; Li, H. C.; Zhang, M.; Li, C. Z.; Chen, X.

2017-12-01

Rainfall threshold plays an important role in flash flood warning. A simple and easy method, using Rational Equation to calculate rainfall threshold, was proposed in this study. The critical rainfall equation was deduced from the Rational Equation. On the basis of the Manning equation and the results of Chinese Flash Flood Survey and Evaluation (CFFSE) Project, the critical flow was obtained, and the net rainfall was calculated. Three aspects of the rainfall losses, i.e. depression storage, vegetation interception, and soil infiltration were considered. The critical rainfall was the sum of the net rainfall and the rainfall losses. Rainfall threshold was estimated after considering the watershed soil moisture using the critical rainfall. In order to demonstrate this method, Zuojiao watershed in Yunnan Province was chosen as study area. The results showed the rainfall thresholds calculated by the Rational Equation method were approximated to the rainfall thresholds obtained from CFFSE, and were in accordance with the observed rainfall during flash flood events. Thus the calculated results are reasonable and the method is effective. This study provided a quick and convenient way to calculated rainfall threshold of flash flood warning for the grass root staffs and offered technical support for estimating rainfall threshold.

Assessment and correction of skinfold thickness equations in estimating body fat in children with cerebral palsy

PubMed Central

GURKA, MATTHEW J; KUPERMINC, MICHELLE N; BUSBY, MARJORIE G; BENNIS, JACEY A; GROSSBERG, RICHARD I; HOULIHAN, CHRISTINE M; STEVENSON, RICHARD D; HENDERSON, RICHARD C

2010-01-01

AIM To assess the accuracy of skinfold equations in estimating percentage body fat in children with cerebral palsy (CP), compared with assessment of body fat from dual energy X-ray absorptiometry (DXA). METHOD Data were collected from 71 participants (30 females, 41 males) with CP (Gross Motor Function Classification System [GMFCS] levels I–V) between the ages of 8 and 18 years. Estimated percentage body fat was computed using established (Slaughter) equations based on the triceps and subscapular skinfolds. A linear model was fitted to assess the use of a simple correction to these equations for children with CP. RESULTS Slaughter’s equations consistently underestimated percentage body fat (mean difference compared with DXA percentage body fat −9.6/100 [SD 6.2]; 95% confidence interval [CI] −11.0 to −8.1). New equations were developed in which a correction factor was added to the existing equations based on sex, race, GMFCS level, size, and pubertal status. These corrected equations for children with CP agree better with DXA (mean difference 0.2/100 [SD=4.8]; 95% CI −1.0 to 1.3) than existing equations. INTERPRETATION A simple correction factor to commonly used equations substantially improves the ability to estimate percentage body fat from two skinfold measures in children with CP. PMID:19811518

Online Updating of Statistical Inference in the Big Data Setting.

PubMed

Schifano, Elizabeth D; Wu, Jing; Wang, Chun; Yan, Jun; Chen, Ming-Hui

2016-01-01

We present statistical methods for big data arising from online analytical processing, where large amounts of data arrive in streams and require fast analysis without storage/access to the historical data. In particular, we develop iterative estimating algorithms and statistical inferences for linear models and estimating equations that update as new data arrive. These algorithms are computationally efficient, minimally storage-intensive, and allow for possible rank deficiencies in the subset design matrices due to rare-event covariates. Within the linear model setting, the proposed online-updating framework leads to predictive residual tests that can be used to assess the goodness-of-fit of the hypothesized model. We also propose a new online-updating estimator under the estimating equation setting. Theoretical properties of the goodness-of-fit tests and proposed estimators are examined in detail. In simulation studies and real data applications, our estimator compares favorably with competing approaches under the estimating equation setting.

Methods for estimating selected low-flow frequency statistics and harmonic mean flows for streams in Iowa

USGS Publications Warehouse

Eash, David A.; Barnes, Kimberlee K.

2017-01-01

A statewide study was conducted to develop regression equations for estimating six selected low-flow frequency statistics and harmonic mean flows for ungaged stream sites in Iowa. The estimation equations developed for the six low-flow frequency statistics include: the annual 1-, 7-, and 30-day mean low flows for a recurrence interval of 10 years, the annual 30-day mean low flow for a recurrence interval of 5 years, and the seasonal (October 1 through December 31) 1- and 7-day mean low flows for a recurrence interval of 10 years. Estimation equations also were developed for the harmonic-mean-flow statistic. Estimates of these seven selected statistics are provided for 208 U.S. Geological Survey continuous-record streamgages using data through September 30, 2006. The study area comprises streamgages located within Iowa and 50 miles beyond the State's borders. Because trend analyses indicated statistically significant positive trends when considering the entire period of record for the majority of the streamgages, the longest, most recent period of record without a significant trend was determined for each streamgage for use in the study. The median number of years of record used to compute each of these seven selected statistics was 35. Geographic information system software was used to measure 54 selected basin characteristics for each streamgage. Following the removal of two streamgages from the initial data set, data collected for 206 streamgages were compiled to investigate three approaches for regionalization of the seven selected statistics. Regionalization, a process using statistical regression analysis, provides a relation for efficiently transferring information from a group of streamgages in a region to ungaged sites in the region. The three regionalization approaches tested included statewide, regional, and region-of-influence regressions. For the regional regression, the study area was divided into three low-flow regions on the basis of hydrologic characteristics, landform regions, and soil regions. A comparison of root mean square errors and average standard errors of prediction for the statewide, regional, and region-of-influence regressions determined that the regional regression provided the best estimates of the seven selected statistics at ungaged sites in Iowa. Because a significant number of streams in Iowa reach zero flow as their minimum flow during low-flow years, four different types of regression analyses were used: left-censored, logistic, generalized-least-squares, and weighted-least-squares regression. A total of 192 streamgages were included in the development of 27 regression equations for the three low-flow regions. For the northeast and northwest regions, a censoring threshold was used to develop 12 left-censored regression equations to estimate the 6 low-flow frequency statistics for each region. For the southern region a total of 12 regression equations were developed; 6 logistic regression equations were developed to estimate the probability of zero flow for the 6 low-flow frequency statistics and 6 generalized least-squares regression equations were developed to estimate the 6 low-flow frequency statistics, if nonzero flow is estimated first by use of the logistic equations. A weighted-least-squares regression equation was developed for each region to estimate the harmonic-mean-flow statistic. Average standard errors of estimate for the left-censored equations for the northeast region range from 64.7 to 88.1 percent and for the northwest region range from 85.8 to 111.8 percent. Misclassification percentages for the logistic equations for the southern region range from 5.6 to 14.0 percent. Average standard errors of prediction for generalized least-squares equations for the southern region range from 71.7 to 98.9 percent and pseudo coefficients of determination for the generalized-least-squares equations range from 87.7 to 91.8 percent. Average standard errors of prediction for weighted-least-squares equations developed for estimating the harmonic-mean-flow statistic for each of the three regions range from 66.4 to 80.4 percent. The regression equations are applicable only to stream sites in Iowa with low flows not significantly affected by regulation, diversion, or urbanization and with basin characteristics within the range of those used to develop the equations. If the equations are used at ungaged sites on regulated streams, or on streams affected by water-supply and agricultural withdrawals, then the estimates will need to be adjusted by the amount of regulation or withdrawal to estimate the actual flow conditions if that is of interest. Caution is advised when applying the equations for basins with characteristics near the applicable limits of the equations and for basins located in karst topography. A test of two drainage-area ratio methods using 31 pairs of streamgages, for the annual 7-day mean low-flow statistic for a recurrence interval of 10 years, indicates a weighted drainage-area ratio method provides better estimates than regional regression equations for an ungaged site on a gaged stream in Iowa when the drainage-area ratio is between 0.5 and 1.4. These regression equations will be implemented within the U.S. Geological Survey StreamStats web-based geographic-information-system tool. StreamStats allows users to click on any ungaged site on a river and compute estimates of the seven selected statistics; in addition, 90-percent prediction intervals and the measured basin characteristics for the ungaged sites also are provided. StreamStats also allows users to click on any streamgage in Iowa and estimates computed for these seven selected statistics are provided for the streamgage.

Adaptive Elastic Net for Generalized Methods of Moments.

PubMed

Caner, Mehmet; Zhang, Hao Helen

2014-01-30

Model selection and estimation are crucial parts of econometrics. This paper introduces a new technique that can simultaneously estimate and select the model in generalized method of moments (GMM) context. The GMM is particularly powerful for analyzing complex data sets such as longitudinal and panel data, and it has wide applications in econometrics. This paper extends the least squares based adaptive elastic net estimator of Zou and Zhang (2009) to nonlinear equation systems with endogenous variables. The extension is not trivial and involves a new proof technique due to estimators lack of closed form solutions. Compared to Bridge-GMM of Caner (2009), we allow for the number of parameters to diverge to infinity as well as collinearity among a large number of variables, also the redundant parameters set to zero via a data dependent technique. This method has the oracle property, meaning that we can estimate nonzero parameters with their standard limit and the redundant parameters are dropped from the equations simultaneously. Numerical examples are used to illustrate the performance of the new method.

Robust estimation of partially linear models for longitudinal data with dropouts and measurement error.

PubMed

Qin, Guoyou; Zhang, Jiajia; Zhu, Zhongyi; Fung, Wing

2016-12-20

Outliers, measurement error, and missing data are commonly seen in longitudinal data because of its data collection process. However, no method can address all three of these issues simultaneously. This paper focuses on the robust estimation of partially linear models for longitudinal data with dropouts and measurement error. A new robust estimating equation, simultaneously tackling outliers, measurement error, and missingness, is proposed. The asymptotic properties of the proposed estimator are established under some regularity conditions. The proposed method is easy to implement in practice by utilizing the existing standard generalized estimating equations algorithms. The comprehensive simulation studies show the strength of the proposed method in dealing with longitudinal data with all three features. Finally, the proposed method is applied to data from the Lifestyle Education for Activity and Nutrition study and confirms the effectiveness of the intervention in producing weight loss at month 9. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

An Adaptive Kalman Filter using a Simple Residual Tuning Method

NASA Technical Reports Server (NTRS)

Harman, Richard R.

1999-01-01

One difficulty in using Kalman filters in real world situations is the selection of the correct process noise, measurement noise, and initial state estimate and covariance. These parameters are commonly referred to as tuning parameters. Multiple methods have been developed to estimate these parameters. Most of those methods such as maximum likelihood, subspace, and observer Kalman Identification require extensive offline processing and are not suitable for real time processing. One technique, which is suitable for real time processing, is the residual tuning method. Any mismodeling of the filter tuning parameters will result in a non-white sequence for the filter measurement residuals. The residual tuning technique uses this information to estimate corrections to those tuning parameters. The actual implementation results in a set of sequential equations that run in parallel with the Kalman filter. Equations for the estimation of the measurement noise have also been developed. These algorithms are used to estimate the process noise and measurement noise for the Wide Field Infrared Explorer star tracker and gyro.

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

PubMed

Kumar, K Vasanth; Sivanesan, S

2005-08-31

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

Comparison of predictive equations for resting metabolic rate in healthy nonobese and obese adults: a systematic review.

PubMed

Frankenfield, David; Roth-Yousey, Lori; Compher, Charlene

2005-05-01

An assessment of energy needs is a necessary component in the development and evaluation of a nutrition care plan. The metabolic rate can be measured or estimated by equations, but estimation is by far the more common method. However, predictive equations might generate errors large enough to impact outcome. Therefore, a systematic review of the literature was undertaken to document the accuracy of predictive equations preliminary to deciding on the imperative to measure metabolic rate. As part of a larger project to determine the role of indirect calorimetry in clinical practice, an evidence team identified published articles that examined the validity of various predictive equations for resting metabolic rate (RMR) in nonobese and obese people and also in individuals of various ethnic and age groups. Articles were accepted based on defined criteria and abstracted using evidence analysis tools developed by the American Dietetic Association. Because these equations are applied by dietetics practitioners to individuals, a key inclusion criterion was research reports of individual data. The evidence was systematically evaluated, and a conclusion statement and grade were developed. Four prediction equations were identified as the most commonly used in clinical practice (Harris-Benedict, Mifflin-St Jeor, Owen, and World Health Organization/Food and Agriculture Organization/United Nations University [WHO/FAO/UNU]). Of these equations, the Mifflin-St Jeor equation was the most reliable, predicting RMR within 10% of measured in more nonobese and obese individuals than any other equation, and it also had the narrowest error range. No validation work concentrating on individual errors was found for the WHO/FAO/UNU equation. Older adults and US-residing ethnic minorities were underrepresented both in the development of predictive equations and in validation studies. The Mifflin-St Jeor equation is more likely than the other equations tested to estimate RMR to within 10% of that measured, but noteworthy errors and limitations exist when it is applied to individuals and possibly when it is generalized to certain age and ethnic groups. RMR estimation errors would be eliminated by valid measurement of RMR with indirect calorimetry, using an evidence-based protocol to minimize measurement error. The Expert Panel advises clinical judgment regarding when to accept estimated RMR using predictive equations in any given individual. Indirect calorimetry may be an important tool when, in the judgment of the clinician, the predictive methods fail an individual in a clinically relevant way. For members of groups that are greatly underrepresented by existing validation studies of predictive equations, a high level of suspicion regarding the accuracy of the equations is warranted.

Estimation of potential bridge scour at bridges on state routes in South Dakota, 2003-07

USGS Publications Warehouse

Thompson, Ryan F.; Fosness, Ryan L.

2008-01-01

Flowing water can erode (scour) soils and cause structural failure of a bridge by exposing or undermining bridge foundations (abutments and piers). A rapid scour-estimation technique, known as the level-1.5 method and developed by the U.S. Geological Survey, was used to evaluate potential scour at bridges in South Dakota in a study conducted in cooperation with the South Dakota Department of Transportation. This method was used during 2003-07 to estimate scour for the 100-year and 500-year floods at 734 selected bridges managed by the South Dakota Department of Transportation on State routes in South Dakota. Scour depths and other parameters estimated from the level-1.5 analyses are presented in tabular form. Estimates of potential contraction scour at the 734 bridges ranged from 0 to 33.9 feet for the 100-year flood and from 0 to 35.8 feet for the 500-year flood. Abutment scour ranged from 0 to 36.9 feet for the 100-year flood and from 0 to 45.9 feet for the 500-year flood. Pier scour ranged from 0 to 30.8 feet for the 100-year flood and from 0 to 30.7 feet for the 500-year flood. The scour depths estimated by using the level-1.5 method can be used by the South Dakota Department of Transportation and others to identify bridges that may be susceptible to scour. Scour at 19 selected bridges also was estimated by using the level-2 method. Estimates of contraction, abutment, and pier scour calculated by using the level-1.5 and level-2 methods are presented in tabular and graphical formats. Compared to level-2 scour estimates, the level-1.5 method generally overestimated scour as designed, or in a few cases slightly underestimated scour. Results of the level-2 analyses were used to develop regression equations for change in head and average velocity through the bridge opening. These regression equations derived from South Dakota data are compared to similar regression equations derived from Montana and Colorado data. Future level-1.5 scour investigations in South Dakota may benefit from the use of these South Dakota-specific regression equations for estimating change in stream head and average velocity at the bridge.

Genetic network inference as a series of discrimination tasks.

PubMed

Kimura, Shuhei; Nakayama, Satoshi; Hatakeyama, Mariko

2009-04-01

Genetic network inference methods based on sets of differential equations generally require a great deal of time, as the equations must be solved many times. To reduce the computational cost, researchers have proposed other methods for inferring genetic networks by solving sets of differential equations only a few times, or even without solving them at all. When we try to obtain reasonable network models using these methods, however, we must estimate the time derivatives of the gene expression levels with great precision. In this study, we propose a new method to overcome the drawbacks of inference methods based on sets of differential equations. Our method infers genetic networks by obtaining classifiers capable of predicting the signs of the derivatives of the gene expression levels. For this purpose, we defined a genetic network inference problem as a series of discrimination tasks, then solved the defined series of discrimination tasks with a linear programming machine. Our experimental results demonstrated that the proposed method is capable of correctly inferring genetic networks, and doing so more than 500 times faster than the other inference methods based on sets of differential equations. Next, we applied our method to actual expression data of the bacterial SOS DNA repair system. And finally, we demonstrated that our approach relates to the inference method based on the S-system model. Though our method provides no estimation of the kinetic parameters, it should be useful for researchers interested only in the network structure of a target system. Supplementary data are available at Bioinformatics online.

A scientific and statistical analysis of accelerated aging for pharmaceuticals. Part 1: accuracy of fitting methods.

PubMed

Waterman, Kenneth C; Swanson, Jon T; Lippold, Blake L

2014-10-01

Three competing mathematical fitting models (a point-by-point estimation method, a linear fit method, and an isoconversion method) of chemical stability (related substance growth) when using high temperature data to predict room temperature shelf-life were employed in a detailed comparison. In each case, complex degradant formation behavior was analyzed by both exponential and linear forms of the Arrhenius equation. A hypothetical reaction was used where a drug (A) degrades to a primary degradant (B), which in turn degrades to a secondary degradation product (C). Calculated data with the fitting models were compared with the projected room-temperature shelf-lives of B and C, using one to four time points (in addition to the origin) for each of three accelerated temperatures. Isoconversion methods were found to provide more accurate estimates of shelf-life at ambient conditions. Of the methods for estimating isoconversion, bracketing the specification limit at each condition produced the best estimates and was considerably more accurate than when extrapolation was required. Good estimates of isoconversion produced similar shelf-life estimates fitting either linear or nonlinear forms of the Arrhenius equation, whereas poor isoconversion estimates favored one method or the other depending on which condition was most in error. © 2014 Wiley Periodicals, Inc. and the American Pharmacists Association.

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.

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.

Method to monitor HC-SCR catalyst NOx reduction performance for lean exhaust applications

DOEpatents

Viola, Michael B [Macomb Township, MI; Schmieg, Steven J [Troy, MI; Sloane, Thompson M [Oxford, MI; Hilden, David L [Shelby Township, MI; Mulawa, Patricia A [Clinton Township, MI; Lee, Jong H [Rochester Hills, MI; Cheng, Shi-Wai S [Troy, MI

2012-05-29

A method for initiating a regeneration mode in selective catalytic reduction device utilizing hydrocarbons as a reductant includes monitoring a temperature within the aftertreatment system, monitoring a fuel dosing rate to the selective catalytic reduction device, monitoring an initial conversion efficiency, selecting a determined equation to estimate changes in a conversion efficiency of the selective catalytic reduction device based upon the monitored temperature and the monitored fuel dosing rate, estimating changes in the conversion efficiency based upon the determined equation and the initial conversion efficiency, and initiating a regeneration mode for the selective catalytic reduction device based upon the estimated changes in conversion efficiency.

A review of models and micrometeorological methods used to estimate wetland evapotranspiration

USGS Publications Warehouse

Drexler, J.Z.; Snyder, R.L.; Spano, D.; Paw, U.K.T.

2004-01-01

Within the past decade or so, the accuracy of evapotranspiration (ET) estimates has improved due to new and increasingly sophisticated methods. Yet despite a plethora of choices concerning methods, estimation of wetland ET remains insufficiently characterized due to the complexity of surface characteristics and the diversity of wetland types. In this review, we present models and micrometeorological methods that have been used to estimate wetland ET and discuss their suitability for particular wetland types. Hydrological, soil monitoring and lysimetric methods to determine ET are not discussed. Our review shows that, due to the variability and complexity of wetlands, there is no single approach that is the best for estimating wetland ET. Furthermore, there is no single foolproof method to obtain an accurate, independent measure of wetland ET. Because all of the methods reviewed, with the exception of eddy covariance and LIDAR, require measurements of net radiation (Rn) and soil heat flux (G), highly accurate measurements of these energy components are key to improving measurements of wetland ET. Many of the major methods used to determine ET can be applied successfully to wetlands of uniform vegetation and adequate fetch, however, certain caveats apply. For example, with accurate Rn and G data and small Bowen ratio (??) values, the Bowen ratio energy balance method can give accurate estimates of wetland ET. However, large errors in latent heat flux density can occur near sunrise and sunset when the Bowen ratio ?? ??? - 1??0. The eddy covariance method provides a direct measurement of latent heat flux density (??E) and sensible heat flux density (II), yet this method requires considerable expertise and expensive instrumentation to implement. A clear advantage of using the eddy covariance method is that ??E can be compared with Rn-G H, thereby allowing for an independent test of accuracy. The surface renewal method is inexpensive to replicate and, therefore, shows particular promise for characterizing variability in ET as a result of spatial heterogeneity. LIDAR is another method that has special utility in a heterogeneous wetland environment, because it provides an integrated value for ET from a surface. The main drawback of LIDAR is the high cost of equipment and the need for an independent ET measure to assess accuracy. If Rn and G are measured accurately, the Priestley-Taylor equation can be used successfully with site-specific calibration factors to estimate wetland ET. The 'crop' cover coefficient (Kc) method can provide accurate wetland ET estimates if calibrated for the environmental and climatic characteristics of a particular area. More complicated equations such as the Penman and Penman-Monteith equations also can be used to estimate wetland ET, but surface variability and lack of information on aerodynamic and surface resistances make use of such equations somewhat questionable. ?? 2004 John Wiley and Sons, Ltd.

Estimating population salt intake in India using spot urine samples.

PubMed

Petersen, Kristina S; Johnson, Claire; Mohan, Sailesh; Rogers, Kris; Shivashankar, Roopa; Thout, Sudhir Raj; Gupta, Priti; He, Feng J; MacGregor, Graham A; Webster, Jacqui; Santos, Joseph Alvin; Krishnan, Anand; Maulik, Pallab K; Reddy, K Srinath; Gupta, Ruby; Prabhakaran, Dorairaj; Neal, Bruce

2017-11-01

To compare estimates of mean population salt intake in North and South India derived from spot urine samples versus 24-h urine collections. In a cross-sectional survey, participants were sampled from slum, urban and rural communities in North and in South India. Participants provided 24-h urine collections, and random morning spot urine samples. Salt intake was estimated from the spot urine samples using a series of established estimating equations. Salt intake data from the 24-h urine collections and spot urine equations were weighted to provide estimates of salt intake for Delhi and Haryana, and Andhra Pradesh. A total of 957 individuals provided a complete 24-h urine collection and a spot urine sample. Weighted mean salt intake based on the 24-h urine collection, was 8.59 (95% confidence interval 7.73-9.45) and 9.46 g/day (8.95-9.96) in Delhi and Haryana, and Andhra Pradesh, respectively. Corresponding estimates based on the Tanaka equation [9.04 (8.63-9.45) and 9.79 g/day (9.62-9.96) for Delhi and Haryana, and Andhra Pradesh, respectively], the Mage equation [8.80 (7.67-9.94) and 10.19 g/day (95% CI 9.59-10.79)], the INTERSALT equation [7.99 (7.61-8.37) and 8.64 g/day (8.04-9.23)] and the INTERSALT equation with potassium [8.13 (7.74-8.52) and 8.81 g/day (8.16-9.46)] were all within 1 g/day of the estimate based upon 24-h collections. For the Toft equation, estimates were 1-2 g/day higher [9.94 (9.24-10.64) and 10.69 g/day (9.44-11.93)] and for the Kawasaki equation they were 3-4 g/day higher [12.14 (11.30-12.97) and 13.64 g/day (13.15-14.12)]. In urban and rural areas in North and South India, most spot urine-based equations provided reasonable estimates of mean population salt intake. Equations that did not provide good estimates may have failed because specimen collection was not aligned with the original method.

Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

NASA Technical Reports Server (NTRS)

Yan, Jue; Shu, Chi-Wang; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

In this paper we review the existing and develop new continuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L(exp 2) stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh.

A Longitudinal Study on Human Outdoor Decomposition in Central Texas.

PubMed

Suckling, Joanna K; Spradley, M Katherine; Godde, Kanya

2016-01-01

The development of a methodology that estimates the postmortem interval (PMI) from stages of decomposition is a goal for which forensic practitioners strive. A proposed equation (Megyesi et al. 2005) that utilizes total body score (TBS) and accumulated degree days (ADD) was tested using longitudinal data collected from human remains donated to the Forensic Anthropology Research Facility (FARF) at Texas State University-San Marcos. Exact binomial tests examined the rate of the equation to successfully predict ADD. Statistically significant differences were found between ADD estimated by the equation and the observed value for decomposition stage. Differences remained significant after carnivore scavenged donations were removed from analysis. Low success rates for the equation to predict ADD from TBS and the wide standard errors demonstrate the need to re-evaluate the use of this equation and methodology for PMI estimation in different environments; rather, multivariate methods and equations should be derived that are environmentally specific. © 2015 American Academy of Forensic Sciences.

Estimating sugar maple bark thickness and volume.

Treesearch

Charles L. Stayton; Michael Hoffman

1970-01-01

Sugar maple bark thickness and volume were estimated using first a published method, then equations developed by the authors. Both methods gave estimates that compared closely with measured values. Information is also presented on variation in bark thickness and on weight and volume of bark as a percentage of total merchantable stem weight and volume.

A new fictitious domain approach for Stokes equation

NASA Astrophysics Data System (ADS)

Yang, Min

2017-10-01

The purpose of this paper is to present a new fictitious domain approach based on the Nietzsche’s method combining with a penalty method for the Stokes equation. This method allows for an easy and flexible handling of the geometrical aspects. Stability and a priori error estimate are proved. Finally, a numerical experiment is provided to verify the theoretical findings.

An Adaptive Kalman Filter Using a Simple Residual Tuning Method

NASA Technical Reports Server (NTRS)

Harman, Richard R.

1999-01-01

One difficulty in using Kalman filters in real world situations is the selection of the correct process noise, measurement noise, and initial state estimate and covariance. These parameters are commonly referred to as tuning parameters. Multiple methods have been developed to estimate these parameters. Most of those methods such as maximum likelihood, subspace, and observer Kalman Identification require extensive offline processing and are not suitable for real time processing. One technique, which is suitable for real time processing, is the residual tuning method. Any mismodeling of the filter tuning parameters will result in a non-white sequence for the filter measurement residuals. The residual tuning technique uses this information to estimate corrections to those tuning parameters. The actual implementation results in a set of sequential equations that run in parallel with the Kalman filter. A. H. Jazwinski developed a specialized version of this technique for estimation of process noise. Equations for the estimation of the measurement noise have also been developed. These algorithms are used to estimate the process noise and measurement noise for the Wide Field Infrared Explorer star tracker and gyro.

The Accuracy of Anthropometric Equations to Assess Body Fat in Adults with Down Syndrome

ERIC Educational Resources Information Center

Rossato, Mateus; Dellagrana, Rodolfo André; da Costa, Rafael Martins; de Souza Bezerra, Ewertton; dos Santos, João Otacílio Libardoni; Rech, Cassiano Ricardo

2018-01-01

Background: The aim of this study was to verify the accuracy of anthropometric equations to estimate the body density (BD) of adults with Down syndrome (DS), and propose new regression equations. Materials and methods: Twenty-one males (30.5 ± 9.4 years) and 17 females (27.3 ± 7.7 years) with DS participated in this study. The reference method for…

Model error estimation for distributed systems described by elliptic equations

NASA Technical Reports Server (NTRS)

Rodriguez, G.

1983-01-01

A function space approach is used to develop a theory for estimation of the errors inherent in an elliptic partial differential equation model for a distributed parameter system. By establishing knowledge of the inevitable deficiencies in the model, the error estimates provide a foundation for updating the model. The function space solution leads to a specification of a method for computation of the model error estimates and development of model error analysis techniques for comparison between actual and estimated errors. The paper summarizes the model error estimation approach as well as an application arising in the area of modeling for static shape determination of large flexible systems.

Development of weight and cost estimates for lifting surfaces with active controls

NASA Technical Reports Server (NTRS)

Anderson, R. D.; Flora, C. C.; Nelson, R. M.; Raymond, E. T.; Vincent, J. H.

1976-01-01

Equations and methodology were developed for estimating the weight and cost incrementals due to active controls added to the wing and horizontal tail of a subsonic transport airplane. The methods are sufficiently generalized to be suitable for preliminary design. Supporting methodology and input specifications for the weight and cost equations are provided. The weight and cost equations are structured to be flexible in terms of the active control technology (ACT) flight control system specification. In order to present a self-contained package, methodology is also presented for generating ACT flight control system characteristics for the weight and cost equations. Use of the methodology is illustrated.

A neuro approach to solve fuzzy Riccati differential equations

NASA Astrophysics Data System (ADS)

Shahrir, Mohammad Shazri; Kumaresan, N.; Kamali, M. Z. M.; Ratnavelu, Kurunathan

2015-10-01

There are many applications of optimal control theory especially in the area of control systems in engineering. In this paper, fuzzy quadratic Riccati differential equation is estimated using neural networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). The solution can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that NN approach shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over RK4.

A neuro approach to solve fuzzy Riccati differential equations

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

Shahrir, Mohammad Shazri, E-mail: mshazri@gmail.com; Telekom Malaysia, R&D TM Innovation Centre, LingkaranTeknokrat Timur, 63000 Cyberjaya, Selangor; Kumaresan, N., E-mail: drnk2008@gmail.com

There are many applications of optimal control theory especially in the area of control systems in engineering. In this paper, fuzzy quadratic Riccati differential equation is estimated using neural networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). The solution can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that NN approach shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over RK4.

Performance of Creatinine and Cystatin C GFR Estimating Equations in an HIV-positive population on Antiretrovirals

PubMed Central

INKER, Lesley A; WYATT, Christina; CREAMER, Rebecca; HELLINGER, James; HOTTA, Matthew; LEPPO, Maia; LEVEY, Andrew S; OKPARAVERO, Aghogho; GRAHAM, Hiba; SAVAGE, Karen; SCHMID, Christopher H; TIGHIOUART, Hocine; WALLACH, Fran; KRISHNASAMI, Zipporah

2013-01-01

Objective To evaluate the performance of CKD-EPI creatinine, cystatin C and creatinine-cystatin C estimating equations in HIV-positive patients. Methods We evaluated the performance of the MDRD Study and CKD-EPI creatinine 2009, CKD-EPI cystatin C 2012 and CKD-EPI creatinine-cystatin C 2012 glomerular filtration rate (GFR) estimating equations compared to GFR measured using plasma clearance of iohexol in 200 HIV-positive patients on stable antiretroviral therapy. Creatinine and cystatin C assays were standardized to certified reference materials. Results Of the 200 participants, median (IQR) CD4 count was 536 (421) and 61% had an undetectable HIV-viral load. Mean (SD) measured GFR (mGFR) was 87 (26) ml/min/1.73m2. All CKD-EPI equations performed better than the MDRD Study equation. All three CKD-EPI equations had similar bias and precision. The cystatin C equation was not more accurate than the creatinine equation. The creatinine-cystatin C equation was significantly more accurate than the cystatin C equation and there was a trend toward greater accuracy than the creatinine equation. Accuracy was equal or better in most subgroups with the combined equation compared to either alone. Conclusions The CKD-EPI cystatin C equation does not appear to be more accurate than the CKD-EPI creatinine equation in patients who are HIV-positive, supporting the use of the CKD-EPI creatinine equation for routine clinical care for use in North American populations with HIV. The use of both filtration markers together as a confirmatory test for decreased estimated GFR based on creatinine in individuals who are HIV-positive requires further study. PMID:22842844

Bias and Efficiency in Structural Equation Modeling: Maximum Likelihood versus Robust Methods

ERIC Educational Resources Information Center

Zhong, Xiaoling; Yuan, Ke-Hai

2011-01-01

In the structural equation modeling literature, the normal-distribution-based maximum likelihood (ML) method is most widely used, partly because the resulting estimator is claimed to be asymptotically unbiased and most efficient. However, this may not hold when data deviate from normal distribution. Outlying cases or nonnormally distributed data,…

Applying transfer matrix method to the estimation of the modal characteristics of the NASA Mini-Mass Truss

NASA Technical Reports Server (NTRS)

Shen, Ji-Yao; Taylor, Lawrence W., Jr.

1994-01-01

It is beneficial to use a distributed parameter model for large space structures because the approach minimizes the number of model parameters. Holzer's transfer matrix method provides a useful means to simplify and standardize the procedure for solving the system of partial differential equations. Any large space structures can be broken down into sub-structures with simple elastic and dynamical properties. For each single element, such as beam, tether, or rigid body, we can derive the corresponding transfer matrix. Combining these elements' matrices enables the solution of the global system equations. The characteristics equation can then be formed by satisfying the appropriate boundary conditions. Then natural frequencies and mode shapes can be determined by searching the roots of the characteristic equation at frequencies within the range of interest. This paper applies this methodology, and the maximum likelihood estimation method, to refine the modal characteristics of the NASA Mini-Mast Truss by successively matching the theoretical response to the test data of the truss. The method is being applied to more complex configurations.

Temperature and redox path of biotite-bearing intrusives: A method of estimation applied to S- and I-type granites from Australia

NASA Astrophysics Data System (ADS)

Burkhard, Dorothee J. M.

1991-05-01

Estimations of the oxidation state and development of ƒO 2 during magmatic evolution are usually not possible because ƒO 2 is a function of temperature (and pressure). If two independent equations for ƒO 2 = ƒO 2(T) can be obtained, ƒO 2 and the corresponding temperature can be estimated. For biotite-bearing rocks an estimation of ƒO 2 (bio) can be combined with an estimation of ƒO 2 (rock). This latter estimation requires an extrapolation of high-temperature data because low-temperature data are not available. The combination of the two equations provides a quadratic equation in T with the common (negative) solution: Tint= 1/4 c 2{- k1-2 c 1-√(k 1+2 c 1) 2+8 c 2k 2} which permits back calculation of ƒO 2. The usefulness of the method is demonstrated for typical S-type, ilmenite, and I-type, magnetite granites from Australia. Two distinct oxidation states are obtained. It is suggested that the availability of H 2O during granite emplacement largely determines ƒO 2 conditions.

Spacecraft mass estimation, relationships and engine data: Task 1.1 of the lunar base systems study

NASA Technical Reports Server (NTRS)

1988-01-01

A collection of scaling equations, weight statements, scaling factors, etc., useful for doing conceptual designs of spacecraft are given. Rules of thumb and methods of calculating quantities of interest are provided. Basic relationships for conventional, and several non-conventional, propulsion systems (nuclear, solar electric and solar thermal) are included. The equations and other data were taken from a number of sources and are not at all consistent with each other in level of detail or method, but provide useful references for early estimation purposes.

ADAPTIVE METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS VIA NATURAL EMBEDDINGS AND REJECTION SAMPLING WITH MEMORY.

PubMed

Rackauckas, Christopher; Nie, Qing

2017-01-01

Adaptive time-stepping with high-order embedded Runge-Kutta pairs and rejection sampling provides efficient approaches for solving differential equations. While many such methods exist for solving deterministic systems, little progress has been made for stochastic variants. One challenge in developing adaptive methods for stochastic differential equations (SDEs) is the construction of embedded schemes with direct error estimates. We present a new class of embedded stochastic Runge-Kutta (SRK) methods with strong order 1.5 which have a natural embedding of strong order 1.0 methods. This allows for the derivation of an error estimate which requires no additional function evaluations. Next we derive a general method to reject the time steps without losing information about the future Brownian path termed Rejection Sampling with Memory (RSwM). This method utilizes a stack data structure to do rejection sampling, costing only a few floating point calculations. We show numerically that the methods generate statistically-correct and tolerance-controlled solutions. Lastly, we show that this form of adaptivity can be applied to systems of equations, and demonstrate that it solves a stiff biological model 12.28x faster than common fixed timestep algorithms. Our approach only requires the solution to a bridging problem and thus lends itself to natural generalizations beyond SDEs.

ADAPTIVE METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS VIA NATURAL EMBEDDINGS AND REJECTION SAMPLING WITH MEMORY

PubMed Central

Rackauckas, Christopher

2017-01-01

Adaptive time-stepping with high-order embedded Runge-Kutta pairs and rejection sampling provides efficient approaches for solving differential equations. While many such methods exist for solving deterministic systems, little progress has been made for stochastic variants. One challenge in developing adaptive methods for stochastic differential equations (SDEs) is the construction of embedded schemes with direct error estimates. We present a new class of embedded stochastic Runge-Kutta (SRK) methods with strong order 1.5 which have a natural embedding of strong order 1.0 methods. This allows for the derivation of an error estimate which requires no additional function evaluations. Next we derive a general method to reject the time steps without losing information about the future Brownian path termed Rejection Sampling with Memory (RSwM). This method utilizes a stack data structure to do rejection sampling, costing only a few floating point calculations. We show numerically that the methods generate statistically-correct and tolerance-controlled solutions. Lastly, we show that this form of adaptivity can be applied to systems of equations, and demonstrate that it solves a stiff biological model 12.28x faster than common fixed timestep algorithms. Our approach only requires the solution to a bridging problem and thus lends itself to natural generalizations beyond SDEs. PMID:29527134

Methods for estimating streamflow at mountain fronts in southern New Mexico

USGS Publications Warehouse

Waltemeyer, S.D.

1994-01-01

The infiltration of streamflow is potential recharge to alluvial-basin aquifers at or near mountain fronts in southern New Mexico. Data for 13 streamflow-gaging stations were used to determine a relation between mean annual stream- flow and basin and climatic conditions. Regression analysis was used to develop an equation that can be used to estimate mean annual streamflow on the basis of drainage areas and mean annual precipi- tation. The average standard error of estimate for this equation is 46 percent. Regression analysis also was used to develop an equation to estimate mean annual streamflow on the basis of active- channel width. Measurements of the width of active channels were determined for 6 of the 13 gaging stations. The average standard error of estimate for this relation is 29 percent. Stream- flow estimates made using a regression equation based on channel geometry are considered more reliable than estimates made from an equation based on regional relations of basin and climatic conditions. The sample size used to develop these relations was small, however, and the reported standard error of estimate may not represent that of the entire population. Active-channel-width measurements were made at 23 ungaged sites along the Rio Grande upstream from Elephant Butte Reservoir. Data for additional sites would be needed for a more comprehensive assessment of mean annual streamflow in southern New Mexico.

Methods for estimating the magnitude and frequency of peak discharges of rural, unregulated streams in Virginia

USGS Publications Warehouse

Bisese, James A.

1995-01-01

Methods are presented for estimating the peak discharges of rural, unregulated streams in Virginia. A Pearson Type III distribution is fitted to the logarithms of the unregulated annual peak-discharge records from 363 stream-gaging stations in Virginia to estimate the peak discharge at these stations for recurrence intervals of 2 to 500 years. Peak-discharge characteristics for 284 unregulated stations are divided into eight regions based on physiographic province, and regressed on basin characteristics, including drainage area, main channel length, main channel slope, mean basin elevation, percentage of forest cover, mean annual precipitation, and maximum rainfall intensity. Regression equations for each region are computed by use of the generalized least-squares method, which accounts for spatial and temporal correlation between nearby gaging stations. This regression technique weights the significance of each station to the regional equation based on the length of records collected at each cation, the correlation between annual peak discharges among the stations, and the standard deviation of the annual peak discharge for each station.Drainage area proved to be the only significant explanatory variable in four regions, while other regions have as many as three significant variables. Standard errors of the regression equations range from 30 to 80 percent. Alternate equations using drainage area only are provided for the five regions with more than one significant explanatory variable.Methods and sample computations are provided to estimate peak discharges at gaged and engaged sites in Virginia for recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years, and to adjust the regression estimates for sites on gaged streams where nearby gaging-station records are available.

Establish Effective Lower Bounds of Watershed Slope for Traditional Hydrologic Methods

DOT National Transportation Integrated Search

2012-06-01

Equations to estimate timing parameters for a watershed contain watershed slope as a principal parameter and : estimates are usually inversely proportional to topographic slope. Hence as slope vanishes, the estimates approach : infinity. The research...

Estimating live fuels for shrubs and herbs with BIOPAK.

Treesearch

Joseph E. Means; Olga N Krankina; Hao Jiang; Hongyan Li

1996-01-01

This paper describes use of BIOPAK to calculate size classes of live fuels for shrubs and herbs. A library of equations to estimate such fuels in the Pacific Northwest and northern Rocky Mountains is presented and used in an example. These methods can be used in other regions if the user first enters fuel size-class equations for a given region into a new library by...

Fitting ARMA Time Series by Structural Equation Models.

ERIC Educational Resources Information Center

van Buuren, Stef

1997-01-01

This paper outlines how the stationary ARMA (p,q) model (G. Box and G. Jenkins, 1976) can be specified as a structural equation model. Maximum likelihood estimates for the parameters in the ARMA model can be obtained by software for fitting structural equation models. The method is applied to three problem types. (SLD)

Updated generalized biomass equations for North American tree species

Treesearch

David C. Chojnacky; Linda S. Heath; Jennifer C. Jenkins

2014-01-01

Historically, tree biomass at large scales has been estimated by applying dimensional analysis techniques and field measurements such as diameter at breast height (dbh) in allometric regression equations. Equations often have been developed using differing methods and applied only to certain species or isolated areas. We previously had compiled and combined (in meta-...

Fourth order difference methods for hyperbolic IBVP's

NASA Technical Reports Server (NTRS)

Gustafsson, Bertil; Olsson, Pelle

1994-01-01

Fourth order difference approximations of initial-boundary value problems for hyperbolic partial differential equations are considered. We use the method of lines approach with both explicit and compact implicit difference operators in space. The explicit operator satisfies an energy estimate leading to strict stability. For the implicit operator we develop boundary conditions and give a complete proof of strong stability using the Laplace transform technique. We also present numerical experiments for the linear advection equation and Burgers' equation with discontinuities in the solution or in its derivative. The first equation is used for modeling contact discontinuities in fluid dynamics, the second one for modeling shocks and rarefaction waves. The time discretization is done with a third order Runge-Kutta TVD method. For solutions with discontinuities in the solution itself we add a filter based on second order viscosity. In case of the non-linear Burger's equation we use a flux splitting technique that results in an energy estimate for certain different approximations, in which case also an entropy condition is fulfilled. In particular we shall demonstrate that the unsplit conservative form produces a non-physical shock instead of the physically correct rarefaction wave. In the numerical experiments we compare our fourth order methods with a standard second order one and with a third order TVD-method. The results show that the fourth order methods are the only ones that give good results for all the considered test problems.

Accuracy of an equation for estimating age from mandibular third molar development in a Thai population

PubMed Central

Verochana, Karune; Prapayasatok, Sangsom; Mahasantipiya, Phattaranant May; Korwanich, Narumanas

2016-01-01

Purpose This study assessed the accuracy of age estimates produced by a regression equation derived from lower third molar development in a Thai population. Materials and Methods The first part of this study relied on measurements taken from panoramic radiographs of 614 Thai patients aged from 9 to 20. The stage of lower left and right third molar development was observed in each radiograph and a modified Gat score was assigned. Linear regression on this data produced the following equation: Y=9.309+1.673 mG+0.303S (Y=age; mG=modified Gat score; S=sex). In the second part of this study, the predictive accuracy of this equation was evaluated using data from a second set of panoramic radiographs (539 Thai subjects, 9 to 24 years old). Each subject's age was estimated using the above equation and compared against age calculated from a provided date of birth. Estimated and known age data were analyzed using the Pearson correlation coefficient and descriptive statistics. Results Ages estimated from lower left and lower right third molar development stage were significantly correlated with the known ages (r=0.818, 0.808, respectively, P≤0.01). 50% of age estimates in the second part of the study fell within a range of error of ±1 year, while 75% fell within a range of error of ±2 years. The study found that the equation tends to estimate age accurately when individuals are 9 to 20 years of age. Conclusion The equation can be used for age estimation for Thai populations when the individuals are 9 to 20 years of age. PMID:27051633

Goal-based angular adaptivity applied to a wavelet-based discretisation of the neutral particle transport equation

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

Goffin, Mark A., E-mail: mark.a.goffin@gmail.com; Buchan, Andrew G.; Dargaville, Steven

2015-01-15

A method for applying goal-based adaptive methods to the angular resolution of the neutral particle transport equation is presented. The methods are applied to an octahedral wavelet discretisation of the spherical angular domain which allows for anisotropic resolution. The angular resolution is adapted across both the spatial and energy dimensions. The spatial domain is discretised using an inner-element sub-grid scale finite element method. The goal-based adaptive methods optimise the angular discretisation to minimise the error in a specific functional of the solution. The goal-based error estimators require the solution of an adjoint system to determine the importance to the specifiedmore » functional. The error estimators and the novel methods to calculate them are described. Several examples are presented to demonstrate the effectiveness of the methods. It is shown that the methods can significantly reduce the number of unknowns and computational time required to obtain a given error. The novelty of the work is the use of goal-based adaptive methods to obtain anisotropic resolution in the angular domain for solving the transport equation. -- Highlights: •Wavelet angular discretisation used to solve transport equation. •Adaptive method developed for the wavelet discretisation. •Anisotropic angular resolution demonstrated through the adaptive method. •Adaptive method provides improvements in computational efficiency.« less

Estimating Glomerular Filtration Rate in Kidney Transplant Recipients: Comparing a Novel Equation With Commonly Used Equations in this Population

PubMed Central

Salvador, Cathrin L.; Hartmann, Anders; Åsberg, Anders; Bergan, Stein; Rowe, Alexander D.; Mørkrid, Lars

2017-01-01

Background Assessment of glomerular filtration rate (GFR) is important in kidney transplantation. The aim was to develop a kidney transplant specific equation for estimating GFR and evaluate against published equations commonly used for GFR estimation in these patients. Methods Adult kidney recipients (n = 594) were included, and blood samples were collected 10 weeks posttransplant. GFR was measured by 51Cr-ethylenediaminetetraacetic acid clearance. Patients were randomized into a reference group (n = 297) to generate a new equation and a test group (n = 297) for comparing it with 7 alternative equations. Results Two thirds of the test group were males. The median (2.5-97.5 percentile) age was 52 (23-75) years, cystatin C, 1.63 (1.00-3.04) mg/L; creatinine, 117 (63-220) μmol/L; and measured GFR, 51 (29-78) mL/min per 1.73 m2. We also performed external evaluation in 133 recipients without the use of trimethoprim, using iohexol clearance for measured GFR. The Modification of Diet in Renal Disease equation was the most accurate of the creatinine-equations. The new equation, estimated GFR (eGFR) = 991.15 × (1.120sex/([age0.097] × [cystatin C0.306] × [creatinine0.527]); where sex is denoted: 0, female; 1, male, demonstrating a better accuracy with a low bias as well as good precision compared with reference equations. Trimethoprim did not influence the performance of the new equation. Conclusions The new equation demonstrated superior accuracy, precision, and low bias. The Modification of Diet in Renal Disease equation was the most accurate of the creatinine-based equations. PMID:29536033

Adaptive mesh strategies for the spectral element method

NASA Technical Reports Server (NTRS)

Mavriplis, Catherine

1992-01-01

An adaptive spectral method was developed for the efficient solution of time dependent partial differential equations. Adaptive mesh strategies that include resolution refinement and coarsening by three different methods are illustrated on solutions to the 1-D viscous Burger equation and the 2-D Navier-Stokes equations for driven flow in a cavity. Sharp gradients, singularities, and regions of poor resolution are resolved optimally as they develop in time using error estimators which indicate the choice of refinement to be used. The adaptive formulation presents significant increases in efficiency, flexibility, and general capabilities for high order spectral methods.

Retrieving air humidity, global solar radiation, and reference evapotranspiration from daily temperatures: development and validation of new methods for Mexico. Part III: reference evapotranspiration

NASA Astrophysics Data System (ADS)

Lobit, P.; Gómez Tagle, A.; Bautista, F.; Lhomme, J. P.

2017-07-01

We evaluated two methods to estimate evapotranspiration (ETo) from minimal weather records (daily maximum and minimum temperatures) in Mexico: a modified reduced set FAO-Penman-Monteith method (Allen et al. 1998, Rome, Italy) and the Hargreaves and Samani (Appl Eng Agric 1(2): 96-99, 1985) method. In the reduced set method, the FAO-Penman-Monteith equation was applied with vapor pressure and radiation estimated from temperature data using two new models (see first and second articles in this series): mean temperature as the average of maximum and minimum temperature corrected for a constant bias and constant wind speed. The Hargreaves-Samani method combines two empirical relationships: one between diurnal temperature range ΔT and shortwave radiation Rs, and another one between average temperature and the ratio ETo/Rs: both relationships were evaluated and calibrated for Mexico. After performing a sensitivity analysis to evaluate the impact of different approximations on the estimation of Rs and ETo, several model combinations were tested to predict ETo from daily maximum and minimum temperature alone. The quality of fit of these models was evaluated on 786 weather stations covering most of the territory of Mexico. The best method was found to be a combination of the FAO-Penman-Monteith reduced set equation with the new radiation estimation and vapor pressure model. As an alternative, a recalibration of the Hargreaves-Samani equation is proposed.

Methods for estimating magnitude and frequency of peak flows for natural streams in Utah

USGS Publications Warehouse

Kenney, Terry A.; Wilkowske, Chris D.; Wright, Shane J.

2007-01-01

Estimates of the magnitude and frequency of peak streamflows is critical for the safe and cost-effective design of hydraulic structures and stream crossings, and accurate delineation of flood plains. Engineers, planners, resource managers, and scientists need accurate estimates of peak-flow return frequencies for locations on streams with and without streamflow-gaging stations. The 2-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-year recurrence-interval flows were estimated for 344 unregulated U.S. Geological Survey streamflow-gaging stations in Utah and nearby in bordering states. These data along with 23 basin and climatic characteristics computed for each station were used to develop regional peak-flow frequency and magnitude regression equations for 7 geohydrologic regions of Utah. These regression equations can be used to estimate the magnitude and frequency of peak flows for natural streams in Utah within the presented range of predictor variables. Uncertainty, presented as the average standard error of prediction, was computed for each developed equation. Equations developed using data from more than 35 gaging stations had standard errors of prediction that ranged from 35 to 108 percent, and errors for equations developed using data from less than 35 gaging stations ranged from 50 to 357 percent.

Robust estimation for ordinary differential equation models.

PubMed

Cao, J; Wang, L; Xu, J

2011-12-01

Applied scientists often like to use ordinary differential equations (ODEs) to model complex dynamic processes that arise in biology, engineering, medicine, and many other areas. It is interesting but challenging to estimate ODE parameters from noisy data, especially when the data have some outliers. We propose a robust method to address this problem. The dynamic process is represented with a nonparametric function, which is a linear combination of basis functions. The nonparametric function is estimated by a robust penalized smoothing method. The penalty term is defined with the parametric ODE model, which controls the roughness of the nonparametric function and maintains the fidelity of the nonparametric function to the ODE model. The basis coefficients and ODE parameters are estimated in two nested levels of optimization. The coefficient estimates are treated as an implicit function of ODE parameters, which enables one to derive the analytic gradients for optimization using the implicit function theorem. Simulation studies show that the robust method gives satisfactory estimates for the ODE parameters from noisy data with outliers. The robust method is demonstrated by estimating a predator-prey ODE model from real ecological data. © 2011, The International Biometric Society.

Techniques for estimating flood hydrographs for ungaged urban watersheds

USGS Publications Warehouse

Stricker, V.A.; Sauer, V.B.

1984-01-01

The Clark Method, modified slightly was used to develop a synthetic, dimensionless hydrograph which can be used to estimate flood hydrographs for ungaged urban watersheds. Application of the technique results in a typical (average) flood hydrograph for a given peak discharge. Input necessary to apply the technique is an estimate of basin lagtime and the recurrence interval peak discharge. Equations for this purpose were obtained from a recent nationwide study on flood frequency in urban watersheds. A regression equation was developed which relates flood volumes to drainage area size, basin lagtime, and peak discharge. This equation is useful where storage of floodwater may be a part of design of flood prevention. (USGS)

Equations for estimating synthetic unit-hydrograph parameter values for small watersheds in Lake County, Illinois

USGS Publications Warehouse

Melching, C.S.; Marquardt, J.S.

1997-01-01

Design hydrographs computed from design storms, simple models of abstractions (interception, depression storage, and infiltration), and synthetic unit hydrographs provide vital information for stormwater, flood-plain, and water-resources management throughout the United States. Rainfall and runoff data for small watersheds in Lake County collected between 1990 and 1995 were studied to develop equations for estimation of synthetic unit-hydrograph parameters on the basis of watershed and storm characteristics. The synthetic unit-hydrograph parameters of interest were the time of concentration (TC) and watershed-storage coefficient (R) for the Clark unit-hydrograph method, the unit-graph lag (UL) for the Soil Conservation Service (now known as the Natural Resources Conservation Service) dimensionless unit hydrograph, and the hydrograph-time lag (TL) for the linear-reservoir method for unit-hydrograph estimation. Data from 66 storms with effective-precipitation depths greater than 0.4 inches on 9 small watersheds (areas between 0.06 and 37 square miles (mi2)) were utilized to develop the estimation equations, and data from 11 storms on 8 of these watersheds were utilized to verify (test) the estimation equations. The synthetic unit-hydrograph parameters were determined by calibration using the U.S. Army Corps of Engineers Flood Hydrograph Package HEC-1 (TC, R, and UL) or by manual analysis of the rainfall and run-off data (TL). The relation between synthetic unit-hydrograph parameters, and watershed and storm characteristics was determined by multiple linear regression of the logarithms of the parameters and characteristics. Separate sets of equations were developed with watershed area and main channel length as the starting parameters. Percentage of impervious cover, main channel slope, and depth of effective precipitation also were identified as important characteristics for estimation of synthetic unit-hydrograph parameters. The estimation equations utilizing area had multiple correlation coefficients of 0.873, 0.961, 0.968, and 0.963 for TC, R, UL, and TL, respectively, and the estimation equations utilizing main channel length had multiple correlation coefficients of 0.845, 0.957, 0.961, and 0.963 for TC, R, UL, and TL, respectively. Simulation of the measured hydrographs for the verification storms utilizing TC and R obtained from the estimation equations yielded good results without calibration. The peak discharge for 8 of the 11 storms was estimated within 25 percent and the time-to-peak discharge for 10 of the 11 storms was estimated within 20 percent. Thus, application of the estimation equations to determine synthetic unit-hydrograph parameters for design-storm simulation may result in reliable design hydrographs; as long as the physical characteristics of the watersheds under consideration are within the range of those for the watersheds in this study (area: 0.06-37 mi2, main channel length: 0.33-16.6 miles, main channel slope: 3.13-55.3 feet per mile, and percentage of impervious cover: 7.32-40.6 percent). The estimation equations are most reliable when applied to watersheds with areas less than 25 mi2.

Parameter Estimation of Partial Differential Equation Models.

PubMed

Xun, Xiaolei; Cao, Jiguo; Mallick, Bani; Carroll, Raymond J; Maity, Arnab

2013-01-01

Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown, and need to be estimated from the measurements of the dynamic system in the present of measurement errors. Most PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus the computational load is high. In this article, we propose two methods to estimate parameters in PDE models: a parameter cascading method and a Bayesian approach. In both methods, the underlying dynamic process modeled with the PDE model is represented via basis function expansion. For the parameter cascading method, we develop two nested levels of optimization to estimate the PDE parameters. For the Bayesian method, we develop a joint model for data and the PDE, and develop a novel hierarchical model allowing us to employ Markov chain Monte Carlo (MCMC) techniques to make posterior inference. Simulation studies show that the Bayesian method and parameter cascading method are comparable, and both outperform other available methods in terms of estimation accuracy. The two methods are demonstrated by estimating parameters in a PDE model from LIDAR data.

Comparison of artificial intelligence methods and empirical equations to estimate daily solar radiation

NASA Astrophysics Data System (ADS)

Mehdizadeh, Saeid; Behmanesh, Javad; Khalili, Keivan

2016-08-01

In the present research, three artificial intelligence methods including Gene Expression Programming (GEP), Artificial Neural Networks (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) as well as, 48 empirical equations (10, 12 and 26 equations were temperature-based, sunshine-based and meteorological parameters-based, respectively) were used to estimate daily solar radiation in Kerman, Iran in the period of 1992-2009. To develop the GEP, ANN and ANFIS models, depending on the used empirical equations, various combinations of minimum air temperature, maximum air temperature, mean air temperature, extraterrestrial radiation, actual sunshine duration, maximum possible sunshine duration, sunshine duration ratio, relative humidity and precipitation were considered as inputs in the mentioned intelligent methods. To compare the accuracy of empirical equations and intelligent models, root mean square error (RMSE), mean absolute error (MAE), mean absolute relative error (MARE) and determination coefficient (R2) indices were used. The results showed that in general, sunshine-based and meteorological parameters-based scenarios in ANN and ANFIS models presented high accuracy than mentioned empirical equations. Moreover, the most accurate method in the studied region was ANN11 scenario with five inputs. The values of RMSE, MAE, MARE and R2 indices for the mentioned model were 1.850 MJ m-2 day-1, 1.184 MJ m-2 day-1, 9.58% and 0.935, respectively.

Temporal upscaling of instantaneous evapotranspiration on clear-sky days using the constant reference evaporative fraction method with fixed or variable surface resistances at two cropland sites

NASA Astrophysics Data System (ADS)

Tang, Ronglin; Li, Zhao-Liang; Sun, Xiaomin; Bi, Yuyun

2017-01-01

Surface evapotranspiration (ET) is an important component of water and energy in land and atmospheric systems. This paper investigated whether using variable surface resistances in the reference ET estimates from the full-form Penman-Monteith (PM) equation could improve the upscaled daily ET estimates in the constant reference evaporative fraction (EFr, the ratio of actual to reference grass/alfalfa ET) method on clear-sky days using ground-based measurements. Half-hourly near-surface meteorological variables and eddy covariance (EC) system-measured latent heat flux data on clear-sky days were collected at two sites with different climatic conditions, namely, the subhumid Yucheng station in northern China and the arid Yingke site in northwestern China and were used as the model input and ground-truth, respectively. The results showed that using the Food and Agriculture Organization (FAO)-PM equation, the American Society of Civil Engineers-PM equation, and the full-form PM equation to estimate the reference ET in the constant EFr method produced progressively smaller upscaled daily ET at a given time from midmorning to midafternoon. Using all three PM equations produced the best results at noon at both sites regardless of whether the energy imbalance of the EC measurements was closed. When the EC measurements were not corrected for energy imbalance, using variable surface resistance in the full-form PM equation could improve the ET upscaling in the midafternoon, but worse results may occur in the midmorning to noon. Site-to-site and time-to-time variations were found in the performances of a given PM equation (with fixed or variable surface resistances) before and after the energy imbalance was closed.

Methods for determining magnitude and frequency of floods in California, based on data through water year 2006

USGS Publications Warehouse

Gotvald, Anthony J.; Barth, Nancy A.; Veilleux, Andrea G.; Parrett, Charles

2012-01-01

Methods for estimating the magnitude and frequency of floods in California that are not substantially affected by regulation or diversions have been updated. Annual peak-flow data through water year 2006 were analyzed for 771 streamflow-gaging stations (streamgages) in California having 10 or more years of data. Flood-frequency estimates were computed for the streamgages by using the expected moments algorithm to fit a Pearson Type III distribution to logarithms of annual peak flows for each streamgage. Low-outlier and historic information were incorporated into the flood-frequency analysis, and a generalized Grubbs-Beck test was used to detect multiple potentially influential low outliers. Special methods for fitting the distribution were developed for streamgages in the desert region in southeastern California. Additionally, basin characteristics for the streamgages were computed by using a geographical information system. Regional regression analysis, using generalized least squares regression, was used to develop a set of equations for estimating flows with 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities for ungaged basins in California that are outside of the southeastern desert region. Flood-frequency estimates and basin characteristics for 630 streamgages were combined to form the final database used in the regional regression analysis. Five hydrologic regions were developed for the area of California outside of the desert region. The final regional regression equations are functions of drainage area and mean annual precipitation for four of the five regions. In one region, the Sierra Nevada region, the final equations are functions of drainage area, mean basin elevation, and mean annual precipitation. Average standard errors of prediction for the regression equations in all five regions range from 42.7 to 161.9 percent. For the desert region of California, an analysis of 33 streamgages was used to develop regional estimates of all three parameters (mean, standard deviation, and skew) of the log-Pearson Type III distribution. The regional estimates were then used to develop a set of equations for estimating flows with 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities for ungaged basins. The final regional regression equations are functions of drainage area. Average standard errors of prediction for these regression equations range from 214.2 to 856.2 percent. Annual peak-flow data through water year 2006 were analyzed for eight streamgages in California having 10 or more years of data considered to be affected by urbanization. Flood-frequency estimates were computed for the urban streamgages by fitting a Pearson Type III distribution to logarithms of annual peak flows for each streamgage. Regression analysis could not be used to develop flood-frequency estimation equations for urban streams because of the limited number of sites. Flood-frequency estimates for the eight urban sites were graphically compared to flood-frequency estimates for 630 non-urban sites. The regression equations developed from this study will be incorporated into the U.S. Geological Survey (USGS) StreamStats program. The StreamStats program is a Web-based application that provides streamflow statistics and basin characteristics for USGS streamgages and ungaged sites of interest. StreamStats can also compute basin characteristics and provide estimates of streamflow statistics for ungaged sites when users select the location of a site along any stream in California.

Superlinear convergence estimates for a conjugate gradient method for the biharmonic equation

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

Chan, R.H.; Delillo, T.K.; Horn, M.A.

1998-01-01

The method of Muskhelishvili for solving the biharmonic equation using conformal mapping is investigated. In [R.H. Chan, T.K. DeLillo, and M.A. Horn, SIAM J. Sci. Comput., 18 (1997), pp. 1571--1582] it was shown, using the Hankel structure, that the linear system in [N.I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen, the Netherlands] is the discretization of the identity plus a compact operator, and therefore the conjugate gradient method will converge superlinearly. Estimates are given here of the superlinear convergence in the cases when the boundary curve is analytic or in a Hoelder class.

Harmonizing multiple methods for reconstructing historical potential and reference evapotranspiration

USGS Publications Warehouse

Belaineh, Getachew; Sumner, David; Carter, Edward; Clapp, David

2013-01-01

Potential evapotranspiration (PET) and reference evapotranspiration (RET) data are usually critical components of hydrologic analysis. Many different equations are available to estimate PET and RET. Most of these equations, such as the Priestley-Taylor and Penman- Monteith methods, rely on detailed meteorological data collected at ground-based weather stations. Few weather stations collect enough data to estimate PET or RET using one of the more complex evapotranspiration equations. Currently, satellite data integrated with ground meteorological data are used with one of these evapotranspiration equations to accurately estimate PET and RET. However, earlier than the last few decades, historical reconstructions of PET and RET needed for many hydrologic analyses are limited by the paucity of satellite data and of some types of ground data. Air temperature stands out as the most generally available meteorological ground data type over the last century. Temperature-based approaches used with readily available historical temperature data offer the potential for long period-of-record PET and RET historical reconstructions. A challenge is the inconsistency between the more accurate, but more data intensive, methods appropriate for more recent periods and the less accurate, but less data intensive, methods appropriate to the more distant past. In this study, multiple methods are harmonized in a seamless reconstruction of historical PET and RET by quantifying and eliminating the biases of the simple Hargreaves-Samani method relative to the more complex and accurate Priestley-Taylor and Penman-Monteith methods. This harmonization process is used to generate long-term, internally consistent, spatiotemporal databases of PET and RET.

A Comparison of Methods for Estimating Quadratic Effects in Nonlinear Structural Equation Models

ERIC Educational Resources Information Center

Harring, Jeffrey R.; Weiss, Brandi A.; Hsu, Jui-Chen

2012-01-01

Two Monte Carlo simulations were performed to compare methods for estimating and testing hypotheses of quadratic effects in latent variable regression models. The methods considered in the current study were (a) a 2-stage moderated regression approach using latent variable scores, (b) an unconstrained product indicator approach, (c) a latent…

Fourth order exponential time differencing method with local discontinuous Galerkin approximation for coupled nonlinear Schrodinger equations

DOE PAGES

Liang, Xiao; Khaliq, Abdul Q. M.; Xing, Yulong

2015-01-23

In this paper, we study a local discontinuous Galerkin method combined with fourth order exponential time differencing Runge-Kutta time discretization and a fourth order conservative method for solving the nonlinear Schrödinger equations. Based on different choices of numerical fluxes, we propose both energy-conserving and energy-dissipative local discontinuous Galerkin methods, and have proven the error estimates for the semi-discrete methods applied to linear Schrödinger equation. The numerical methods are proven to be highly efficient and stable for long-range soliton computations. Finally, extensive numerical examples are provided to illustrate the accuracy, efficiency and reliability of the proposed methods.

Recursive least squares method of regression coefficients estimation as a special case of Kalman filter

NASA Astrophysics Data System (ADS)

Borodachev, S. M.

2016-06-01

The simple derivation of recursive least squares (RLS) method equations is given as special case of Kalman filter estimation of a constant system state under changing observation conditions. A numerical example illustrates application of RLS to multicollinearity problem.

Predicting Costs of Eastern National Forest Wildernesses.

ERIC Educational Resources Information Center

Guldin, Richard W.

1981-01-01

A method for estimating the total direct social costs for proposed wilderness areas is presented. A cost framework is constructed and equations are developed for cost components. To illustrate the study's method, social costs are estimated for a proposed wilderness area in New England. (Author/JN)

A new parametric method to smooth time-series data of metabolites in metabolic networks.

PubMed

Miyawaki, Atsuko; Sriyudthsak, Kansuporn; Hirai, Masami Yokota; Shiraishi, Fumihide

2016-12-01

Mathematical modeling of large-scale metabolic networks usually requires smoothing of metabolite time-series data to account for measurement or biological errors. Accordingly, the accuracy of smoothing curves strongly affects the subsequent estimation of model parameters. Here, an efficient parametric method is proposed for smoothing metabolite time-series data, and its performance is evaluated. To simplify parameter estimation, the method uses S-system-type equations with simple power law-type efflux terms. Iterative calculation using this method was found to readily converge, because parameters are estimated stepwise. Importantly, smoothing curves are determined so that metabolite concentrations satisfy mass balances. Furthermore, the slopes of smoothing curves are useful in estimating parameters, because they are probably close to their true behaviors regardless of errors that may be present in the actual data. Finally, calculations for each differential equation were found to converge in much less than one second if initial parameters are set at appropriate (guessed) values. Copyright © 2016 Elsevier Inc. All rights reserved.

Body composition in Nepalese children using isotope dilution: the production of ethnic-specific calibration equations and an exploration of methodological issues.

PubMed

Devakumar, Delan; Grijalva-Eternod, Carlos S; Roberts, Sebastian; Chaube, Shiva Shankar; Saville, Naomi M; Manandhar, Dharma S; Costello, Anthony; Osrin, David; Wells, Jonathan C K

2015-01-01

Background. Body composition is important as a marker of both current and future health. Bioelectrical impedance (BIA) is a simple and accurate method for estimating body composition, but requires population-specific calibration equations. Objectives. (1) To generate population specific calibration equations to predict lean mass (LM) from BIA in Nepalese children aged 7-9 years. (2) To explore methodological changes that may extend the range and improve accuracy. Methods. BIA measurements were obtained from 102 Nepalese children (52 girls) using the Tanita BC-418. Isotope dilution with deuterium oxide was used to measure total body water and to estimate LM. Prediction equations for estimating LM from BIA data were developed using linear regression, and estimates were compared with those obtained from the Tanita system. We assessed the effects of flexing the arms of children to extend the range of coverage towards lower weights. We also estimated potential error if the number of children included in the study was reduced. Findings. Prediction equations were generated, incorporating height, impedance index, weight and sex as predictors (R (2) 93%). The Tanita system tended to under-estimate LM, with a mean error of 2.2%, but extending up to 25.8%. Flexing the arms to 90° increased the lower weight range, but produced a small error that was not significant when applied to children <16 kg (p 0.42). Reducing the number of children increased the error at the tails of the weight distribution. Conclusions. Population-specific isotope calibration of BIA for Nepalese children has high accuracy. Arm position is important and can be used to extend the range of low weight covered. Smaller samples reduce resource requirements, but leads to large errors at the tails of the weight distribution.

Development and validation of anthropometric equations to estimate appendicular muscle mass in elderly women

PubMed Central

2013-01-01

Objective This study aimed to examine the cross validity of two anthropometric equations commonly used and propose simple anthropometric equations to estimate appendicular muscle mass (AMM) in elderly women. Methods Among 234 physically active and functionally independent elderly women, 101 (60 to 89 years) were selected through simple drawing to compose the study sample. The paired t test and the Pearson correlation coefficient were used to perform cross-validation and concordance was verified by intraclass correction coefficient (ICC) and by the Bland and Altman technique. To propose predictive models, multiple linear regression analysis, anthropometric measures of body mass (BM), height, girth, skinfolds, body mass index (BMI) were used, and muscle perimeters were included in the analysis as independent variables. Dual-Energy X-ray Absorptiometry (AMMDXA) was used as criterion measurement. The sample power calculations were carried out by Post Hoc Compute Achieved Power. Sample power values from 0.88 to 0.91 were observed. Results When compared, the two equations tested differed significantly from the AMMDXA (p <0.001 and p = 0.001). Ten population / specific anthropometric equations were developed to estimate AMM, among them, three equations achieved all validation criteria used: AMM (E2) = 4.150 +0.251 [bodymass (BM)] - 0.411 [bodymass index (BMI)] + 0.011 [Right forearm perimeter (PANTd) 2]; AMM (E3) = 4.087 + 0.255 (BM) - 0.371 (BMI) + 0.011 (PANTd) 2 - 0.035 [thigh skinfold (DCCO)]; MMA (E6) = 2.855 + 0.298 (BM) + 0.019 (Age) - 0,082 [hip circumference (PQUAD)] + 0.400 (PANTd) - 0.332 (BMI). The equations estimated the criterion method (p = 0.056 p = 0.158), and explained from 0.69% to 0.74% of variations observed in AMMDXA with low standard errors of the estimate (1.36 to 1.55 kg) and high concordance (ICC between 0,90 and 0.91 and concordance limits from -2,93 to 2,33 kg). Conclusion The equations tested were not valid for use in physically active and functionally independent elderly women. The simple anthropometric equations developed in this study showed good practical applicability and high validity to estimate AMM in elderly women. PMID:23815948

The integration of the motion equations of low-orbiting earth satellites using Taylor's method

NASA Astrophysics Data System (ADS)

Krivov, A. V.; Chernysheva, N. A.

1990-04-01

A method for the numerical integration of the equations of motion for a satellite is proposed, taking the earth's oblateness and atmospheric drag into account. The method is based on Taylor's representation of the solution to the corresponding polynomial system. The algorithm for choosing the integration step and error estimation is constructed. The method is realized as a subrouting package. The method is applied to a low-orbiting earth satellite and the results are compared with those obtained using Everhart's method.

August median streamflow on ungaged streams in Eastern Coastal Maine

USGS Publications Warehouse

Lombard, Pamela J.

2004-01-01

Methods for estimating August median streamflow were developed for ungaged, unregulated streams in eastern coastal Maine. The methods apply to streams with drainage areas ranging in size from 0.04 to 73.2 square miles and fraction of basin underlain by a sand and gravel aquifer ranging from 0 to 71 percent. The equations were developed with data from three long-term (greater than or equal to 10 years of record) continuous-record streamflow-gaging stations, 23 partial-record streamflow- gaging stations, and 5 short-term (less than 10 years of record) continuous-record streamflow-gaging stations. A mathematical technique for estimating a standard low-flow statistic, August median streamflow, at partial-record streamflow-gaging stations and short-term continuous-record streamflow-gaging stations was applied by relating base-flow measurements at these stations to concurrent daily streamflows at nearby long-term continuous-record streamflow-gaging stations (index stations). Generalized least-squares regression analysis (GLS) was used to relate estimates of August median streamflow at streamflow-gaging stations to basin characteristics at these same stations to develop equations that can be applied to estimate August median streamflow on ungaged streams. GLS accounts for different periods of record at the gaging stations and the cross correlation of concurrent streamflows among gaging stations. Thirty-one stations were used for the final regression equations. Two basin characteristics?drainage area and fraction of basin underlain by a sand and gravel aquifer?are used in the calculated regression equation to estimate August median streamflow for ungaged streams. The equation has an average standard error of prediction from -27 to 38 percent. A one-variable equation uses only drainage area to estimate August median streamflow when less accuracy is acceptable. This equation has an average standard error of prediction from -30 to 43 percent. Model error is larger than sampling error for both equations, indicating that additional or improved estimates of basin characteristics could be important to improved estimates of low-flow statistics. Weighted estimates of August median streamflow at partial- record or continuous-record gaging stations range from 0.003 to 31.0 cubic feet per second or from 0.1 to 0.6 cubic feet per second per square mile. Estimates of August median streamflow on ungaged streams in eastern coastal Maine, within the range of acceptable explanatory variables, range from 0.003 to 45 cubic feet per second or 0.1 to 0.6 cubic feet per second per square mile. Estimates of August median streamflow per square mile of drainage area generally increase as drainage area and fraction of basin underlain by a sand and gravel aquifer increase.

A Bayesian Framework for Coupled Estimation of Key Unknown Parameters of Land Water and Energy Balance Equations

NASA Astrophysics Data System (ADS)

Farhadi, L.; Abdolghafoorian, A.

2015-12-01

The land surface is a key component of climate system. It controls the partitioning of available energy at the surface between sensible and latent heat, and partitioning of available water between evaporation and runoff. Water and energy cycle are intrinsically coupled through evaporation, which represents a heat exchange as latent heat flux. Accurate estimation of fluxes of heat and moisture are of significant importance in many fields such as hydrology, climatology and meteorology. In this study we develop and apply a Bayesian framework for estimating the key unknown parameters of terrestrial water and energy balance equations (i.e. moisture and heat diffusion) and their uncertainty in land surface models. These equations are coupled through flux of evaporation. The estimation system is based on the adjoint method for solving a least-squares optimization problem. The cost function consists of aggregated errors on state (i.e. moisture and temperature) with respect to observation and parameters estimation with respect to prior values over the entire assimilation period. This cost function is minimized with respect to parameters to identify models of sensible heat, latent heat/evaporation and drainage and runoff. Inverse of Hessian of the cost function is an approximation of the posterior uncertainty of parameter estimates. Uncertainty of estimated fluxes is estimated by propagating the uncertainty for linear and nonlinear function of key parameters through the method of First Order Second Moment (FOSM). Uncertainty analysis is used in this method to guide the formulation of a well-posed estimation problem. Accuracy of the method is assessed at point scale using surface energy and water fluxes generated by the Simultaneous Heat and Water (SHAW) model at the selected AmeriFlux stations. This method can be applied to diverse climates and land surface conditions with different spatial scales, using remotely sensed measurements of surface moisture and temperature states

Forest volume-to-biomass models and estimates of mass for live and standing dead trees of U.S. forests.

Treesearch

James E. Smith; Linda S. Heath; Jennifer C. Jenkins

2003-01-01

Includes methods and equations for nationally consistent estimates of tree-mass density at the stand level (Mg/ha) as predicted by growing-stock volumes reported by the USDA Forest Service for forests of the conterminous United States. Developed for use in FORCARB, a carbon budget model for U.S. forests, the equations also are useful for converting plot-, stand- and...

Backward semi-linear parabolic equations with time-dependent coefficients and local Lipschitz source

NASA Astrophysics Data System (ADS)

Nho Hào, Dinh; Van Duc, Nguyen; Van Thang, Nguyen

2018-05-01

Let H be a Hilbert space with the inner product and the norm , a positive self-adjoint unbounded time-dependent operator on H and . We establish stability estimates of Hölder type and propose a regularization method with error estimates of Hölder type for the ill-posed backward semi-linear parabolic equation with the source function f satisfying a local Lipschitz condition.

Pose and Wind Estimation for Autonomous Parafoils

DTIC Science & Technology

2014-09-01

Communications GT Georgia Institute of Technology IDVD Inverse Dynamics in the Virtual Domain IMU inertial measurement unit INRIA Institut National de Recherche en...sensor. The method used is a nonlinear estimator that combines the visual sensor measurements with those of an inertial measurement unit ( IMU ) on... isolated on the left side of the equation. On the other hand, when the measurement equation of (3.27) is implemented, the probabil- 58 ity

ESTIMATION OF CONSTANT AND TIME-VARYING DYNAMIC PARAMETERS OF HIV INFECTION IN A NONLINEAR DIFFERENTIAL EQUATION MODEL.

PubMed

Liang, Hua; Miao, Hongyu; Wu, Hulin

2010-03-01

Modeling viral dynamics in HIV/AIDS studies has resulted in deep understanding of pathogenesis of HIV infection from which novel antiviral treatment guidance and strategies have been derived. Viral dynamics models based on nonlinear differential equations have been proposed and well developed over the past few decades. However, it is quite challenging to use experimental or clinical data to estimate the unknown parameters (both constant and time-varying parameters) in complex nonlinear differential equation models. Therefore, investigators usually fix some parameter values, from the literature or by experience, to obtain only parameter estimates of interest from clinical or experimental data. However, when such prior information is not available, it is desirable to determine all the parameter estimates from data. In this paper, we intend to combine the newly developed approaches, a multi-stage smoothing-based (MSSB) method and the spline-enhanced nonlinear least squares (SNLS) approach, to estimate all HIV viral dynamic parameters in a nonlinear differential equation model. In particular, to the best of our knowledge, this is the first attempt to propose a comparatively thorough procedure, accounting for both efficiency and accuracy, to rigorously estimate all key kinetic parameters in a nonlinear differential equation model of HIV dynamics from clinical data. These parameters include the proliferation rate and death rate of uninfected HIV-targeted cells, the average number of virions produced by an infected cell, and the infection rate which is related to the antiviral treatment effect and is time-varying. To validate the estimation methods, we verified the identifiability of the HIV viral dynamic model and performed simulation studies. We applied the proposed techniques to estimate the key HIV viral dynamic parameters for two individual AIDS patients treated with antiretroviral therapies. We demonstrate that HIV viral dynamics can be well characterized and quantified for individual patients. As a result, personalized treatment decision based on viral dynamic models is possible.

Theoretical stability in coefficient inverse problems for general hyperbolic equations with numerical reconstruction

NASA Astrophysics Data System (ADS)

Yu, Jie; Liu, Yikan; Yamamoto, Masahiro

2018-04-01

In this article, we investigate the determination of the spatial component in the time-dependent second order coefficient of a hyperbolic equation from both theoretical and numerical aspects. By the Carleman estimates for general hyperbolic operators and an auxiliary Carleman estimate, we establish local Hölder stability with either partial boundary or interior measurements under certain geometrical conditions. For numerical reconstruction, we minimize a Tikhonov functional which penalizes the gradient of the unknown function. Based on the resulting variational equation, we design an iteration method which is updated by solving a Poisson equation at each step. One-dimensional prototype examples illustrate the numerical performance of the proposed iteration.

Generalized Path Analysis and Generalized Simultaneous Equations Model for Recursive Systems with Responses of Mixed Types

ERIC Educational Resources Information Center

Tsai, Tien-Lung; Shau, Wen-Yi; Hu, Fu-Chang

2006-01-01

This article generalizes linear path analysis (PA) and simultaneous equations models (SiEM) to deal with mixed responses of different types in a recursive or triangular system. An efficient instrumental variable (IV) method for estimating the structural coefficients of a 2-equation partially recursive generalized path analysis (GPA) model and…

Hierarchical Boltzmann simulations and model error estimation

NASA Astrophysics Data System (ADS)

Torrilhon, Manuel; Sarna, Neeraj

2017-08-01

A hierarchical simulation approach for Boltzmann's equation should provide a single numerical framework in which a coarse representation can be used to compute gas flows as accurately and efficiently as in computational fluid dynamics, but a subsequent refinement allows to successively improve the result to the complete Boltzmann result. We use Hermite discretization, or moment equations, for the steady linearized Boltzmann equation for a proof-of-concept of such a framework. All representations of the hierarchy are rotationally invariant and the numerical method is formulated on fully unstructured triangular and quadrilateral meshes using a implicit discontinuous Galerkin formulation. We demonstrate the performance of the numerical method on model problems which in particular highlights the relevance of stability of boundary conditions on curved domains. The hierarchical nature of the method allows also to provide model error estimates by comparing subsequent representations. We present various model errors for a flow through a curved channel with obstacles.

POSTPROCESSING MIXED FINITE ELEMENT METHODS FOR SOLVING CAHN-HILLIARD EQUATION: METHODS AND ERROR ANALYSIS

PubMed Central

Wang, Wansheng; Chen, Long; Zhou, Jie

2015-01-01

A postprocessing technique for mixed finite element methods for the Cahn-Hilliard equation is developed and analyzed. Once the mixed finite element approximations have been computed at a fixed time on the coarser mesh, the approximations are postprocessed by solving two decoupled Poisson equations in an enriched finite element space (either on a finer grid or a higher-order space) for which many fast Poisson solvers can be applied. The nonlinear iteration is only applied to a much smaller size problem and the computational cost using Newton and direct solvers is negligible compared with the cost of the linear problem. The analysis presented here shows that this technique remains the optimal rate of convergence for both the concentration and the chemical potential approximations. The corresponding error estimate obtained in our paper, especially the negative norm error estimates, are non-trivial and different with the existing results in the literatures. PMID:27110063

Nonparametric estimation of stochastic differential equations with sparse Gaussian processes.

PubMed

García, Constantino A; Otero, Abraham; Félix, Paulo; Presedo, Jesús; Márquez, David G

2017-08-01

The application of stochastic differential equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we introduce a nonparametric method for estimating the drift and diffusion terms of SDEs from a densely observed discrete time series. The use of Gaussian processes as priors permits working directly in a function-space view and thus the inference takes place directly in this space. To cope with the computational complexity that requires the use of Gaussian processes, a sparse Gaussian process approximation is provided. This approximation permits the efficient computation of predictions for the drift and diffusion terms by using a distribution over a small subset of pseudosamples. The proposed method has been validated using both simulated data and real data from economy and paleoclimatology. The application of the method to real data demonstrates its ability to capture the behavior of complex systems.

A Rapid Empirical Method for Estimating the Gross Takeoff Weight of a High Speed Civil Transport

NASA Technical Reports Server (NTRS)

Mack, Robert J.

1999-01-01

During the cruise segment of the flight mission, aircraft flying at supersonic speeds generate sonic booms that are usually maximum at the beginning of cruise. The pressure signature with the shocks causing these perceived booms can be predicted if the aircraft's geometry, Mach number, altitude, angle of attack, and cruise weight are known. Most methods for estimating aircraft weight, especially beginning-cruise weight, are empirical and based on least- square-fit equations that best represent a body of component weight data. The empirical method discussed in this report used simplified weight equations based on a study of performance and weight data from conceptual and real transport aircraft. Like other weight-estimation methods, weights were determined at several points in the mission. While these additional weights were found to be useful, it is the determination of beginning-cruise weight that is most important for the prediction of the aircraft's sonic-boom characteristics.

Detection the nonlinear ultrasonic signals based on modified Duffing equations

NASA Astrophysics Data System (ADS)

Zhang, Yuhua; Mao, Hanling; Mao, Hanying; Huang, Zhenfeng

The nonlinear ultrasonic signals, like second harmonic generation (SHG) signals, could reflect the nonlinearity of material induced by fatigue damage in nonlinear ultrasonic technique which are weak nonlinear signals and usually submerged by strong background noise. In this paper the modified Duffing equations are applied to detect the SHG signals relating to the fatigue damage of material. Due to the Duffing equation could only detect the signal with specific frequency and initial phase, firstly the frequency transformation is carried on the Duffing equation which could detect the signal with any frequency. Then the influence of initial phases of to-be-detected signal and reference signal on the detection result is studied in detail, four modified Duffing equations are proposed to detect actual engineering signals with any initial phase. The relationship between the response amplitude and the total driving force is applied to estimate the amplitude of weak periodic signal. The detection results show the modified Duffing equations could effectively detect the second harmonic in SHG signals. When the SHG signals include strong background noise, the noise doesn't change the motion state of Duffing equation and the second harmonic signal could be detected until the SNR of noisy SHG signals are -26.3, yet the frequency spectrum method could only identify when the SNR is greater than 0.5. When estimation the amplitude of second harmonic signal, the estimation error of Duffing equation is obviously less than the frequency spectrum analysis method under the same noise level, which illustrates the Duffing equation has the noise immune capacity. The presence of the second harmonic signal in nonlinear ultrasonic experiments could provide an insight about the early fatigue damage of engineering components.

Validation of equations and proposed reference values to estimate fat mass in Chilean university students.

PubMed

Gómez Campos, Rossana; Pacheco Carrillo, Jaime; Almonacid Fierro, Alejandro; Urra Albornoz, Camilo; Cossío-Bolaños, Marco

2018-03-01

(i) To propose regression equations based on anthropometric measures to estimate fat mass (FM) using dual energy X-ray absorptiometry (DXA) as reference method, and (ii)to establish population reference standards for equation-derived FM. A cross-sectional study on 6,713 university students (3,354 males and 3,359 females) from Chile aged 17.0 to 27.0years. Anthropometric measures (weight, height, waist circumference) were taken in all participants. Whole body DXA was performed in 683 subjects. A total of 478 subjects were selected to develop regression equations, and 205 for their cross-validation. Data from 6,030 participants were used to develop reference standards for FM. Equations were generated using stepwise multiple regression analysis. Percentiles were developed using the LMS method. Equations for men were: (i) FM=-35,997.486 +232.285 *Weight +432.216 *CC (R 2 =0.73, SEE=4.1); (ii)FM=-37,671.303 +309.539 *Weight +66,028.109 *ICE (R2=0.76, SEE=3.8), while equations for women were: (iii)FM=-13,216.917 +461,302 *Weight+91.898 *CC (R 2 =0.70, SEE=4.6), and (iv) FM=-14,144.220 +464.061 *Weight +16,189.297 *ICE (R 2 =0.70, SEE=4.6). Percentiles proposed included p10, p50, p85, and p95. The developed equations provide valid and accurate estimation of FM in both sexes. The values obtained using the equations may be analyzed from percentiles that allow for categorizing body fat levels by age and sex. Copyright © 2017 SEEN y SED. Publicado por Elsevier España, S.L.U. All rights reserved.

Methods for estimating drought streamflow probabilities for Virginia streams

USGS Publications Warehouse

Austin, Samuel H.

2014-01-01

Maximum likelihood logistic regression model equations used to estimate drought flow probabilities for Virginia streams are presented for 259 hydrologic basins in Virginia. Winter streamflows were used to estimate the likelihood of streamflows during the subsequent drought-prone summer months. The maximum likelihood logistic regression models identify probable streamflows from 5 to 8 months in advance. More than 5 million streamflow daily values collected over the period of record (January 1, 1900 through May 16, 2012) were compiled and analyzed over a minimum 10-year (maximum 112-year) period of record. The analysis yielded the 46,704 equations with statistically significant fit statistics and parameter ranges published in two tables in this report. These model equations produce summer month (July, August, and September) drought flow threshold probabilities as a function of streamflows during the previous winter months (November, December, January, and February). Example calculations are provided, demonstrating how to use the equations to estimate probable streamflows as much as 8 months in advance.

Numerical solution to generalized Burgers'-Fisher equation using Exp-function method hybridized with heuristic computation.

PubMed

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.

Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation

PubMed Central

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems. PMID:25811858

An estimating equation approach to dimension reduction for longitudinal data

PubMed Central

Xu, Kelin; Guo, Wensheng; Xiong, Momiao; Zhu, Liping; Jin, Li

2016-01-01

Sufficient dimension reduction has been extensively explored in the context of independent and identically distributed data. In this article we generalize sufficient dimension reduction to longitudinal data and propose an estimating equation approach to estimating the central mean subspace. The proposed method accounts for the covariance structure within each subject and improves estimation efficiency when the covariance structure is correctly specified. Even if the covariance structure is misspecified, our estimator remains consistent. In addition, our method relaxes distributional assumptions on the covariates and is doubly robust. To determine the structural dimension of the central mean subspace, we propose a Bayesian-type information criterion. We show that the estimated structural dimension is consistent and that the estimated basis directions are root-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{upgreek} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} }{}$n$\\end{document} consistent, asymptotically normal and locally efficient. Simulations and an analysis of the Framingham Heart Study data confirm the effectiveness of our approach. PMID:27017956

The Effect of Error in Item Parameter Estimates on the Test Response Function Method of Linking.

ERIC Educational Resources Information Center

Kaskowitz, Gary S.; De Ayala, R. J.

2001-01-01

Studied the effect of item parameter estimation for computation of linking coefficients for the test response function (TRF) linking/equating method. Simulation results showed that linking was more accurate when there was less error in the parameter estimates, and that 15 or 25 common items provided better results than 5 common items under both…

A comparison of above-ground dry-biomass estimators for trees in the Northeastern United States

Treesearch

James A. Westfall

2012-01-01

In the northeastern United States, both component and total aboveground tree dry-biomass estimates are available from several sources. In this study, comparisons were made among four methods to promote understanding of the similarities and differences in live-tree biomass estimators. The methods use various equations developed from biomass data collected in the United...

Cost estimators for construction of forest roads in the central Appalachians

Treesearch

Deborah, A. Layton; Chris O. LeDoux; Curt C. Hassler; Curt C. Hassler

1992-01-01

Regression equations were developed for estimating the total cost of road construction in the central Appalachian region. Estimators include methods for predicting total costs for roads constructed using hourly rental methods and roads built on a total-job bid basis. Results show that total-job bid roads cost up to five times as much as roads built than when equipment...

Greenhouse gases inventory and carbon balance of two dairy systems obtained from two methane-estimation methods.

PubMed

Cunha, C S; Lopes, N L; Veloso, C M; Jacovine, L A G; Tomich, T R; Pereira, L G R; Marcondes, M I

2016-11-15

The adoption of carbon inventories for dairy farms in tropical countries based on models developed from animals and diets of temperate climates is questionable. Thus, the objectives of this study were to estimate enteric methane (CH4) emissions through the SF6 tracer gas technique and through equations proposed by the Intergovernmental Panel on Climate Change (IPCC) Tier 2 and to calculate the inventory of greenhouse gas (GHG) emissions from two dairy systems. In addition, the carbon balance of these properties was estimated using enteric CH4 emissions obtained using both methodologies. In trial 1, the CH4 emissions were estimated from seven Holstein dairy cattle categories based on the SF6 tracer gas technique and on IPCC equations. The categories used in the study were prepubertal heifers (n=6); pubertal heifers (n=4); pregnant heifers (n=5); high-producing (n=6); medium-producing (n=5); low-producing (n=4) and dry cows (n=5). Enteric methane emission was higher for the category comprising prepubertal heifers when estimated by the equations proposed by the IPCC Tier 2. However, higher CH4 emissions were estimated by the SF6 technique in the categories including medium- and high-producing cows and dry cows. Pubertal heifers, pregnant heifers, and low-producing cows had equal CH4 emissions as estimated by both methods. In trial 2, two dairy farms were monitored for one year to identify all activities that contributed in any way to GHG emissions. The total emission from Farm 1 was 3.21t CO2e/animal/yr, of which 1.63t corresponded to enteric CH4. Farm 2 emitted 3.18t CO2e/animal/yr, with 1.70t of enteric CH4. IPCC estimations can underestimate CH4 emissions from some categories while overestimate others. However, considering the whole property, these discrepancies are offset and we would submit that the equations suggested by the IPCC properly estimate the total CH4 emission and carbon balance of the properties. Thus, the IPCC equations should be utilized with caution, and the herd composition should be analysed at the property level. When the carbon stock in pasture and other crops was considered, the carbon balance suggested that both farms are sustainable for GHG, by both methods. On the other hand, carbon balance without carbon stock, by both methods, suggests that farms emit more carbon than the system is capable of stock. Copyright © 2016 Elsevier B.V. All rights reserved.

Connection equation and shaly-sand correction for electrical resistivity

USGS Publications Warehouse

Lee, Myung W.

2011-01-01

Estimating the amount of conductive and nonconductive constituents in the pore space of sediments by using electrical resistivity logs generally loses accuracy where clays are present in the reservoir. Many different methods and clay models have been proposed to account for the conductivity of clay (termed the shaly-sand correction). In this study, the connectivity equation (CE), which is a new approach to model non-Archie rocks, is used to correct for the clay effect and is compared with results using the Waxman and Smits method. The CE presented here requires no parameters other than an adjustable constant, which can be derived from the resistivity of water-saturated sediments. The new approach was applied to estimate water saturation of laboratory data and to estimate gas hydrate saturations at the Mount Elbert well on the Alaska North Slope. Although not as accurate as the Waxman and Smits method to estimate water saturations for the laboratory measurements, gas hydrate saturations estimated at the Mount Elbert well using the proposed CE are comparable to estimates from the Waxman and Smits method. Considering its simplicity, it has high potential to be used to account for the clay effect on electrical resistivity measurement in other systems.

Estimates of the seasonal mean vertical velocity fields of the extratropical Northern Hemisphere

NASA Technical Reports Server (NTRS)

White, G. H.

1983-01-01

Indirect methods are employed to estimate the wintertime and summertime mean vertical velocity fields of the extratropical Northern Hemisphere and intercomparisons are made, together with comparisons with mean seasonal patterns of cloudiness and precipitation. Twice-daily NMC operational analyses produced general circulation statistics for 11 winters and 12 summers, permitting calculation of the seasonal NMC averages for 6 hr forecasts, solution of the omega equation, integration of continuity equation downward from 100 mb, and solution of the thermodynamic energy equation in the absence of diabatic heating. The methods all yielded similar vertical velocity patterns; however, the magnitude of the vertical velocities could not be calculated with great accuracy. Orography was concluded to have less of an effect in summer than in winter, when winds are stronger.

On the selection of ordinary differential equation models with application to predator-prey dynamical models.

PubMed

Zhang, Xinyu; Cao, Jiguo; Carroll, Raymond J

2015-03-01

We consider model selection and estimation in a context where there are competing ordinary differential equation (ODE) models, and all the models are special cases of a "full" model. We propose a computationally inexpensive approach that employs statistical estimation of the full model, followed by a combination of a least squares approximation (LSA) and the adaptive Lasso. We show the resulting method, here called the LSA method, to be an (asymptotically) oracle model selection method. The finite sample performance of the proposed LSA method is investigated with Monte Carlo simulations, in which we examine the percentage of selecting true ODE models, the efficiency of the parameter estimation compared to simply using the full and true models, and coverage probabilities of the estimated confidence intervals for ODE parameters, all of which have satisfactory performances. Our method is also demonstrated by selecting the best predator-prey ODE to model a lynx and hare population dynamical system among some well-known and biologically interpretable ODE models. © 2014, The International Biometric Society.

Regression equations for estimation of annual peak-streamflow frequency for undeveloped watersheds in Texas using an L-moment-based, PRESS-minimized, residual-adjusted approach

USGS Publications Warehouse

Asquith, William H.; Roussel, Meghan C.

2009-01-01

Annual peak-streamflow frequency estimates are needed for flood-plain management; for objective assessment of flood risk; for cost-effective design of dams, levees, and other flood-control structures; and for design of roads, bridges, and culverts. Annual peak-streamflow frequency represents the peak streamflow for nine recurrence intervals of 2, 5, 10, 25, 50, 100, 200, 250, and 500 years. Common methods for estimation of peak-streamflow frequency for ungaged or unmonitored watersheds are regression equations for each recurrence interval developed for one or more regions; such regional equations are the subject of this report. The method is based on analysis of annual peak-streamflow data from U.S. Geological Survey streamflow-gaging stations (stations). Beginning in 2007, the U.S. Geological Survey, in cooperation with the Texas Department of Transportation and in partnership with Texas Tech University, began a 3-year investigation concerning the development of regional equations to estimate annual peak-streamflow frequency for undeveloped watersheds in Texas. The investigation focuses primarily on 638 stations with 8 or more years of data from undeveloped watersheds and other criteria. The general approach is explicitly limited to the use of L-moment statistics, which are used in conjunction with a technique of multi-linear regression referred to as PRESS minimization. The approach used to develop the regional equations, which was refined during the investigation, is referred to as the 'L-moment-based, PRESS-minimized, residual-adjusted approach'. For the approach, seven unique distributions are fit to the sample L-moments of the data for each of 638 stations and trimmed means of the seven results of the distributions for each recurrence interval are used to define the station specific, peak-streamflow frequency. As a first iteration of regression, nine weighted-least-squares, PRESS-minimized, multi-linear regression equations are computed using the watershed characteristics of drainage area, dimensionless main-channel slope, and mean annual precipitation. The residuals of the nine equations are spatially mapped, and residuals for the 10-year recurrence interval are selected for generalization to 1-degree latitude and longitude quadrangles. The generalized residual is referred to as the OmegaEM parameter and represents a generalized terrain and climate index that expresses peak-streamflow potential not otherwise represented in the three watershed characteristics. The OmegaEM parameter was assigned to each station, and using OmegaEM, nine additional regression equations are computed. Because of favorable diagnostics, the OmegaEM equations are expected to be generally reliable estimators of peak-streamflow frequency for undeveloped and ungaged stream locations in Texas. The mean residual standard error, adjusted R-squared, and percentage reduction of PRESS by use of OmegaEM are 0.30log10, 0.86, and -21 percent, respectively. Inclusion of the OmegaEM parameter provides a substantial reduction in the PRESS statistic of the regression equations and removes considerable spatial dependency in regression residuals. Although the OmegaEM parameter requires interpretation on the part of analysts and the potential exists that different analysts could estimate different values for a given watershed, the authors suggest that typical uncertainty in the OmegaEM estimate might be about +or-0.1010. Finally, given the two ensembles of equations reported herein and those in previous reports, hydrologic design engineers and other analysts have several different methods, which represent different analytical tracks, to make comparisons of peak-streamflow frequency estimates for ungaged watersheds in the study area.

Estimation of evaporation from open water - A review of selected studies, summary of U.S. Army Corps of Engineers data collection and methods, and evaluation of two methods for estimation of evaporation from five reservoirs in Texas

USGS Publications Warehouse

Harwell, Glenn R.

2012-01-01

Organizations responsible for the management of water resources, such as the U.S. Army Corps of Engineers (USACE), are tasked with estimation of evaporation for water-budgeting and planning purposes. The USACE has historically used Class A pan evaporation data (pan data) to estimate evaporation from reservoirs but many USACE Districts have been experimenting with other techniques for an alternative to collecting pan data. The energy-budget method generally is considered the preferred method for accurate estimation of open-water evaporation from lakes and reservoirs. Complex equations to estimate evaporation, such as the Penman, DeBruin-Keijman, and Priestley-Taylor, perform well when compared with energy-budget method estimates when all of the important energy terms are included in the equations and ideal data are collected. However, sometimes nonideal data are collected and energy terms, such as the change in the amount of stored energy and advected energy, are not included in the equations. When this is done, the corresponding errors in evaporation estimates are not quantifiable. Much simpler methods, such as the Hamon method and a method developed by the U.S. Weather Bureau (USWB) (renamed the National Weather Service in 1970), have been shown to provide reasonable estimates of evaporation when compared to energy-budget method estimates. Data requirements for the Hamon and USWB methods are minimal and sometimes perform well with remotely collected data. The Hamon method requires average daily air temperature, and the USWB method requires daily averages of air temperature, relative humidity, wind speed, and solar radiation. Estimates of annual lake evaporation from pan data are frequently within 20 percent of energy-budget method estimates. Results of evaporation estimates from the Hamon method and the USWB method were compared against historical pan data at five selected reservoirs in Texas (Benbrook Lake, Canyon Lake, Granger Lake, Hords Creek Lake, and Sam Rayburn Lake) to evaluate their performance and to develop coefficients to minimize bias for the purpose of estimating reservoir evaporation with accuracies similar to estimates of evaporation obtained from pan data. The modified Hamon method estimates of reservoir evaporation were similar to estimates of reservoir evaporation from pan data for daily, monthly, and annual time periods. The modified Hamon method estimates of annual reservoir evaporation were always within 20 percent of annual reservoir evaporation from pan data. Unmodified and modified USWB method estimates of annual reservoir evaporation were within 20 percent of annual reservoir evaporation from pan data for about 91 percent of the years compared. Average daily differences between modified USWB method estimates and estimates from pan data as a percentage of the average amount of daily evaporation from pan data were within 20 percent for 98 percent of the months. Without any modification to the USWB method, average daily differences as a percentage of the average amount of daily evaporation from pan data were within 20 percent for 73 percent of the months. Use of the unmodified USWB method is appealing because it means estimates of average daily reservoir evaporation can be made from air temperature, relative humidity, wind speed, and solar radiation data collected from remote weather stations without the need to develop site-specific coefficients from historical pan data. Site-specific coefficients would need to be developed for the modified version of the Hamon method.

Methods for estimating flow-duration and annual mean-flow statistics for ungaged streams in Oklahoma

USGS Publications Warehouse

Esralew, Rachel A.; Smith, S. Jerrod

2010-01-01

Flow statistics can be used to provide decision makers with surface-water information needed for activities such as water-supply permitting, flow regulation, and other water rights issues. Flow statistics could be needed at any location along a stream. Most often, streamflow statistics are needed at ungaged sites, where no flow data are available to compute the statistics. Methods are presented in this report for estimating flow-duration and annual mean-flow statistics for ungaged streams in Oklahoma. Flow statistics included the (1) annual (period of record), (2) seasonal (summer-autumn and winter-spring), and (3) 12 monthly duration statistics, including the 20th, 50th, 80th, 90th, and 95th percentile flow exceedances, and the annual mean-flow (mean of daily flows for the period of record). Flow statistics were calculated from daily streamflow information collected from 235 streamflow-gaging stations throughout Oklahoma and areas in adjacent states. A drainage-area ratio method is the preferred method for estimating flow statistics at an ungaged location that is on a stream near a gage. The method generally is reliable only if the drainage-area ratio of the two sites is between 0.5 and 1.5. Regression equations that relate flow statistics to drainage-basin characteristics were developed for the purpose of estimating selected flow-duration and annual mean-flow statistics for ungaged streams that are not near gaging stations on the same stream. Regression equations were developed from flow statistics and drainage-basin characteristics for 113 unregulated gaging stations. Separate regression equations were developed by using U.S. Geological Survey streamflow-gaging stations in regions with similar drainage-basin characteristics. These equations can increase the accuracy of regression equations used for estimating flow-duration and annual mean-flow statistics at ungaged stream locations in Oklahoma. Streamflow-gaging stations were grouped by selected drainage-basin characteristics by using a k-means cluster analysis. Three regions were identified for Oklahoma on the basis of the clustering of gaging stations and a manual delineation of distinguishable hydrologic and geologic boundaries: Region 1 (western Oklahoma excluding the Oklahoma and Texas Panhandles), Region 2 (north- and south-central Oklahoma), and Region 3 (eastern and central Oklahoma). A total of 228 regression equations (225 flow-duration regressions and three annual mean-flow regressions) were developed using ordinary least-squares and left-censored (Tobit) multiple-regression techniques. These equations can be used to estimate 75 flow-duration statistics and annual mean-flow for ungaged streams in the three regions. Drainage-basin characteristics that were statistically significant independent variables in the regression analyses were (1) contributing drainage area; (2) station elevation; (3) mean drainage-basin elevation; (4) channel slope; (5) percentage of forested canopy; (6) mean drainage-basin hillslope; (7) soil permeability; and (8) mean annual, seasonal, and monthly precipitation. The accuracy of flow-duration regression equations generally decreased from high-flow exceedance (low-exceedance probability) to low-flow exceedance (high-exceedance probability) . This decrease may have happened because a greater uncertainty exists for low-flow estimates and low-flow is largely affected by localized geology that was not quantified by the drainage-basin characteristics selected. The standard errors of estimate of regression equations for Region 1 (western Oklahoma) were substantially larger than those standard errors for other regions, especially for low-flow exceedances. These errors may be a result of greater variability in low flow because of increased irrigation activities in this region. Regression equations may not be reliable for sites where the drainage-basin characteristics are outside the range of values of independent vari

Reliable Real-Time Solution of Parametrized Partial Differential Equations: Reduced-Basis Output Bound Methods. Appendix 2

NASA Technical Reports Server (NTRS)

Prudhomme, C.; Rovas, D. V.; Veroy, K.; Machiels, L.; Maday, Y.; Patera, A. T.; Turinici, G.; Zang, Thomas A., Jr. (Technical Monitor)

2002-01-01

We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced basis approximations, Galerkin projection onto a space W(sub N) spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation, relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures, methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage, in which, given a new parameter value, we calculate the output of interest and associated error bound, depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control.

A Calibration to Predict the Concentrations of Impurities in Plutonium Oxide by Prompt Gamma Analysis Revision 2

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

Narlesky, Joshua Edward; Kelly, Elizabeth J.

2015-09-10

This report documents the new PG calibration regression equation. These calibration equations incorporate new data that have become available since revision 1 of “A Calibration to Predict the Concentrations of Impurities in Plutonium Oxide by Prompt Gamma Analysis” was issued [3] The calibration equations are based on a weighted least squares (WLS) approach for the regression. The WLS method gives each data point its proper amount of influence over the parameter estimates. This gives two big advantages, more precise parameter estimates and better and more defensible estimates of uncertainties. The WLS approach makes sense both statistically and experimentally because themore » variances increase with concentration, and there are physical reasons that the higher measurements are less reliable and should be less influential. The new magnesium calibration includes a correction for sodium and separate calibration equation for items with and without chlorine. These additional calibration equations allow for better predictions and smaller uncertainties for sodium in materials with and without chlorine. Chlorine and sodium have separate equations for RICH materials. Again, these equations give better predictions and smaller uncertainties chlorine and sodium for RICH materials.« less

Sample size considerations for paired experimental design with incomplete observations of continuous outcomes.

PubMed

Zhu, Hong; Xu, Xiaohan; Ahn, Chul

2017-01-01

Paired experimental design is widely used in clinical and health behavioral studies, where each study unit contributes a pair of observations. Investigators often encounter incomplete observations of paired outcomes in the data collected. Some study units contribute complete pairs of observations, while the others contribute either pre- or post-intervention observations. Statistical inference for paired experimental design with incomplete observations of continuous outcomes has been extensively studied in literature. However, sample size method for such study design is sparsely available. We derive a closed-form sample size formula based on the generalized estimating equation approach by treating the incomplete observations as missing data in a linear model. The proposed method properly accounts for the impact of mixed structure of observed data: a combination of paired and unpaired outcomes. The sample size formula is flexible to accommodate different missing patterns, magnitude of missingness, and correlation parameter values. We demonstrate that under complete observations, the proposed generalized estimating equation sample size estimate is the same as that based on the paired t-test. In the presence of missing data, the proposed method would lead to a more accurate sample size estimate comparing with the crude adjustment. Simulation studies are conducted to evaluate the finite-sample performance of the generalized estimating equation sample size formula. A real application example is presented for illustration.

Statistical methods for incomplete data: Some results on model misspecification.

PubMed

McIsaac, Michael; Cook, R J

2017-02-01

Inverse probability weighted estimating equations and multiple imputation are two of the most studied frameworks for dealing with incomplete data in clinical and epidemiological research. We examine the limiting behaviour of estimators arising from inverse probability weighted estimating equations, augmented inverse probability weighted estimating equations and multiple imputation when the requisite auxiliary models are misspecified. We compute limiting values for settings involving binary responses and covariates and illustrate the effects of model misspecification using simulations based on data from a breast cancer clinical trial. We demonstrate that, even when both auxiliary models are misspecified, the asymptotic biases of double-robust augmented inverse probability weighted estimators are often smaller than the asymptotic biases of estimators arising from complete-case analyses, inverse probability weighting or multiple imputation. We further demonstrate that use of inverse probability weighting or multiple imputation with slightly misspecified auxiliary models can actually result in greater asymptotic bias than the use of naïve, complete case analyses. These asymptotic results are shown to be consistent with empirical results from simulation studies.

Harris-Benedict equation estimations of energy needs as compared to measured 24-h energy expenditure by indirect calorimetry in people with early to mid-stage Huntington's disease.

PubMed

Gaba, Ann; Zhang, Kuan; Moskowitz, Carol B; Boozer, Carol N; Marder, Karen

2008-10-01

Weight loss and energy metabolism are important clinical research areas in understanding the disease mechanisms in Huntington's disease. Having an accurate method to estimate expected total energy expenditure would likely facilitate the development of studies about these features of the disease. The Harris-Benedict equation is a formula commonly used to estimate basal energy expenditure of individuals, adjusted for height, weight, age and gender. This estimate is then multiplied by a physical activity factor to estimate total daily energy needs to maintain the given weight. Data from 24-h indirect calorimetry was utilized to derive an adjustment formula for the physical activity factor of the Harris-Benedict equation for 13 early to mid-stage Huntington's disease patients. The adjusted activity factor provided the most accurate estimate of energy needs. This adjusted formula can be used in clinical assessments of Huntington's disease patients, as well as in research studies when indirect calorimetry has not been performed.

Quick estimate of oil discovery from gas-condensate reservoirs

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

Sarem, A.M.

1966-10-24

A quick method of estimating the depletion performance of gas-condensate reservoirs is presented by graphical representations. The method is based on correlations reported in the literature and expresses recoverable liquid as function of gas reserves, producing gas-oil ratio, and initial and final reservoir pressures. The amount of recoverable liquid reserves (RLR) under depletion conditions, is estimated from an equation which is given. Where the liquid-reserves are in stock-tank barrels the gas reserves are in Mcf, with the arbitrary constant, N calculated from one graphical representation by dividing fractional oil recovery by the initial gas-oil ratio and multiplying 10U6D for convenience.more » An equation is given for estimating the coefficient C. These factors (N and C) can be determined from the graphical representations. An example calculation is included.« less

A Model for Estimating Current and Future Timber Volume Loss from Stem Decay Caused by Heterobasidion annosum and Other Fungi in Stands of True Fir

Treesearch

Gregory M. Filip

1989-01-01

In 1979, an equation was developed to estimate the percentage of current and future timber volume loss due to stem decay caused by Heterobasidion annosum and other fungi in advance regeneration stands of grand and white fir in eastern Oregon and Washington. Methods for using and testing the equation are presented. Extensive testing in 1988 showed the...

Effective quadrature formula in solving linear integro-differential equations of order two

NASA Astrophysics Data System (ADS)

Eshkuvatov, Z. K.; Kammuji, M.; Long, N. M. A. Nik; Yunus, Arif A. M.

2017-08-01

In this note, we solve general form of Fredholm-Volterra integro-differential equations (IDEs) of order 2 with boundary condition approximately and show that proposed method is effective and reliable. Initially, IDEs is reduced into integral equation of the third kind by using standard integration techniques and identity between multiple and single integrals then truncated Legendre series are used to estimate the unknown function. For the kernel integrals, we have applied Gauss-Legendre quadrature formula and collocation points are chosen as the roots of the Legendre polynomials. Finally, reduce the integral equations of the third kind into the system of algebraic equations and Gaussian elimination method is applied to get approximate solutions. Numerical examples and comparisons with other methods reveal that the proposed method is very effective and dominated others in many cases. General theory of existence of the solution is also discussed.

An Algorithm for Efficient Maximum Likelihood Estimation and Confidence Interval Determination in Nonlinear Estimation Problems

NASA Technical Reports Server (NTRS)

Murphy, Patrick Charles

1985-01-01

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The algorithm was developed for airplane parameter estimation problems but is well suited for most nonlinear, multivariable, dynamic systems. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort. MNRES determines the sensitivities with less computational effort than using either a finite-difference method or integrating the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, thus eliminating algorithm reformulation with each new model and providing flexibility to use model equations in any format that is convenient. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. It is observed that the degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. The CR bounds were found to be close to the bounds determined by the search when the degree of nonlinearity was small. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels for the parameter confidence limits. The primary utility of the measure, however, was found to be in predicting the degree of agreement between Cramer-Rao bounds and search estimates.

Generalized Appended Product Indicator Procedure for Nonlinear Structural Equation Analysis.

ERIC Educational Resources Information Center

Wall, Melanie M.; Amemiya, Yasuo

2001-01-01

Considers the estimation of polynomial structural models and shows a limitation of an existing method. Introduces a new procedure, the generalized appended product indicator procedure, for nonlinear structural equation analysis. Addresses statistical issues associated with the procedure through simulation. (SLD)

Cross-validation of recent and longstanding resting metabolic rate prediction equations

USDA-ARS?s Scientific Manuscript database

Resting metabolic rate (RMR) measurement is time consuming and requires specialized equipment. Prediction equations provide an easy method to estimate RMR; however, their accuracy likely varies across individuals. Understanding the factors that influence predicted RMR accuracy at the individual lev...

Modeling Individual Damped Linear Oscillator Processes with Differential Equations: Using Surrogate Data Analysis to Estimate the Smoothing Parameter

ERIC Educational Resources Information Center

Deboeck, Pascal R.; Boker, Steven M.; Bergeman, C. S.

2008-01-01

Among the many methods available for modeling intraindividual time series, differential equation modeling has several advantages that make it promising for applications to psychological data. One interesting differential equation model is that of the damped linear oscillator (DLO), which can be used to model variables that have a tendency to…

Assessing Glomerular Filtration Rate in Hospitalized Patients: A Comparison Between CKD-EPI and Four Cystatin C-Based Equations

PubMed Central

de la Torre, Judith; Ramos, Natalia; Quiroz, Augusto; Garjau, Maria; Torres, Irina; Azancot, M. Antonia; López, Montserrat; Sobrado, Ana

2011-01-01

Summary Background and objectives A specific method is required for estimating glomerular filtration rate GFR in hospitalized patients. Our objective was to validate the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation and four cystatin C (CysC)–based equations in this setting. Design, setting, participants, & measurements This was an epidemiologic, cross-sectional study in a random sample of hospitalized patients (n = 3114). We studied the accuracy of the CKD-EPI and four CysC-based equations—based on (1) CysC alone or (2) adjusted by gender; (3) age, gender, and race; and (4) age, gender, race, and creatinine, respectively—compared with GFR measured by iohexol clearance (mGFR). Clinical, biochemical, and nutritional data were also collected. Results The CysC equation 3 significantly overestimated the GFR (bias of 7.4 ml/min per 1.73 m2). Most of the error in creatinine-based equations was attributable to calculated muscle mass, which depended on patient's nutritional status. In patients without malnutrition or reduced body surface area, the CKD-EPI equation adequately estimated GFR. Equations based on CysC gave more precise mGFR estimates when malnutrition, extensive reduction of body surface area, or loss of muscle mass were present (biases of 1 and 1.3 ml/min per 1.73 m2 for equations 2 and 4, respectively, versus 5.9 ml/min per 1.73 m2 for CKD-EPI). Conclusions These results suggest that the use of equations based on CysC and gender, or CysC, age, gender, and race, is more appropriate in hospitalized patients to estimate GFR, since these equations are much less dependent on patient's nutritional status or muscle mass than the CKD-EPI equation. PMID:21852668

Comparison of techniques for correction of magnification of pelvic X-rays for hip surgery planning.

PubMed

The, Bertram; Kootstra, Johan W J; Hosman, Anton H; Verdonschot, Nico; Gerritsma, Carina L E; Diercks, Ron L

2007-12-01

The aim of this study was to develop an accurate method for correction of magnification of pelvic x-rays to enhance accuracy of hip surgery planning. All investigated methods aim at estimating the anteroposterior location of the hip joint in supine position to correctly position a reference object for correction of magnification. An existing method-which is currently being used in clinical practice in our clinics-is based on estimating the position of the hip joint by palpation of the greater trochanter. It is only moderately accurate and difficult to execute reliably in clinical practice. To develop a new method, 99 patients who already had a hip implant in situ were included; this enabled determining the true location of the hip joint deducted from the magnification of the prosthesis. Physical examination was used to obtain predictor variables possibly associated with the height of the hip joint. This included a simple dynamic hip joint examination to estimate the position of the center of rotation. Prediction equations were then constructed using regression analysis. The performance of these prediction equations was compared with the performance of the existing protocol. The mean absolute error in predicting the height of the hip joint center using the old method was 20 mm (range -79 mm to +46 mm). This was 11 mm for the new method (-32 mm to +39 mm). The prediction equation is: height (mm) = 34 + 1/2 abdominal circumference (cm). The newly developed prediction equation is a superior method for predicting the height of the hip joint center for correction of magnification of pelvic x-rays. We recommend its implementation in the departments of radiology and orthopedic surgery.

Are traditional body fat equations and anthropometry valid to estimate body fat in children and adolescents living with HIV?

PubMed

Lima, Luiz Rodrigo Augustemak de; Martins, Priscila Custódio; Junior, Carlos Alencar Souza Alves; Castro, João Antônio Chula de; Silva, Diego Augusto Santos; Petroski, Edio Luiz

The aim of this study was to assess the validity of traditional anthropometric equations and to develop predictive equations of total body and trunk fat for children and adolescents living with HIV based on anthropometric measurements. Forty-eight children and adolescents of both sexes (24 boys) aged 7-17 years, living in Santa Catarina, Brazil, participated in the study. Dual-energy X-ray absorptiometry was used as the reference method to evaluate total body and trunk fat. Height, body weight, circumferences and triceps, subscapular, abdominal and calf skinfolds were measured. The traditional equations of Lohman and Slaughter were used to estimate body fat. Multiple regression models were fitted to predict total body fat (Model 1) and trunk fat (Model 2) using a backward selection procedure. Model 1 had an R 2 =0.85 and a standard error of the estimate of 1.43. Model 2 had an R 2 =0.80 and standard error of the estimate=0.49. The traditional equations of Lohman and Slaughter showed poor performance in estimating body fat in children and adolescents living with HIV. The prediction models using anthropometry provided reliable estimates and can be used by clinicians and healthcare professionals to monitor total body and trunk fat in children and adolescents living with HIV. Copyright © 2017 Sociedade Brasileira de Infectologia. Published by Elsevier Editora Ltda. All rights reserved.

Reliable Quantification of the Potential for Equations Based on Spot Urine Samples to Estimate Population Salt Intake: Protocol for a Systematic Review and Meta-Analysis.

PubMed

Huang, Liping; Crino, Michelle; Wu, Jason Hy; Woodward, Mark; Land, Mary-Anne; McLean, Rachael; Webster, Jacqui; Enkhtungalag, Batsaikhan; Nowson, Caryl A; Elliott, Paul; Cogswell, Mary; Toft, Ulla; Mill, Jose G; Furlanetto, Tania W; Ilich, Jasminka Z; Hong, Yet Hoi; Cohall, Damian; Luzardo, Leonella; Noboa, Oscar; Holm, Ellen; Gerbes, Alexander L; Senousy, Bahaa; Pinar Kara, Sonat; Brewster, Lizzy M; Ueshima, Hirotsugu; Subramanian, Srinivas; Teo, Boon Wee; Allen, Norrina; Choudhury, Sohel Reza; Polonia, Jorge; Yasuda, Yoshinari; Campbell, Norm Rc; Neal, Bruce; Petersen, Kristina S

2016-09-21

Methods based on spot urine samples (a single sample at one time-point) have been identified as a possible alternative approach to 24-hour urine samples for determining mean population salt intake. The aim of this study is to identify a reliable method for estimating mean population salt intake from spot urine samples. This will be done by comparing the performance of existing equations against one other and against estimates derived from 24-hour urine samples. The effects of factors such as ethnicity, sex, age, body mass index, antihypertensive drug use, health status, and timing of spot urine collection will be explored. The capacity of spot urine samples to measure change in salt intake over time will also be determined. Finally, we aim to develop a novel equation (or equations) that performs better than existing equations to estimate mean population salt intake. A systematic review and meta-analysis of individual participant data will be conducted. A search has been conducted to identify human studies that report salt (or sodium) excretion based upon 24-hour urine samples and spot urine samples. There were no restrictions on language, study sample size, or characteristics of the study population. MEDLINE via OvidSP (1946-present), Premedline via OvidSP, EMBASE, Global Health via OvidSP (1910-present), and the Cochrane Library were searched, and two reviewers identified eligible studies. The authors of these studies will be invited to contribute data according to a standard format. Individual participant records will be compiled and a series of analyses will be completed to: (1) compare existing equations for estimating 24-hour salt intake from spot urine samples with 24-hour urine samples, and assess the degree of bias according to key demographic and clinical characteristics; (2) assess the reliability of using spot urine samples to measure population changes in salt intake overtime; and (3) develop a novel equation that performs better than existing equations to estimate mean population salt intake. The search strategy identified 538 records; 100 records were obtained for review in full text and 73 have been confirmed as eligible. In addition, 68 abstracts were identified, some of which may contain data eligible for inclusion. Individual participant data will be requested from the authors of eligible studies. Many equations for estimating salt intake from spot urine samples have been developed and validated, although most have been studied in very specific settings. This meta-analysis of individual participant data will enable a much broader understanding of the capacity for spot urine samples to estimate population salt intake.

Empirical Likelihood in Nonignorable Covariate-Missing Data Problems.

PubMed

Xie, Yanmei; Zhang, Biao

2017-04-20

Missing covariate data occurs often in regression analysis, which frequently arises in the health and social sciences as well as in survey sampling. We study methods for the analysis of a nonignorable covariate-missing data problem in an assumed conditional mean function when some covariates are completely observed but other covariates are missing for some subjects. We adopt the semiparametric perspective of Bartlett et al. (Improving upon the efficiency of complete case analysis when covariates are MNAR. Biostatistics 2014;15:719-30) on regression analyses with nonignorable missing covariates, in which they have introduced the use of two working models, the working probability model of missingness and the working conditional score model. In this paper, we study an empirical likelihood approach to nonignorable covariate-missing data problems with the objective of effectively utilizing the two working models in the analysis of covariate-missing data. We propose a unified approach to constructing a system of unbiased estimating equations, where there are more equations than unknown parameters of interest. One useful feature of these unbiased estimating equations is that they naturally incorporate the incomplete data into the data analysis, making it possible to seek efficient estimation of the parameter of interest even when the working regression function is not specified to be the optimal regression function. We apply the general methodology of empirical likelihood to optimally combine these unbiased estimating equations. We propose three maximum empirical likelihood estimators of the underlying regression parameters and compare their efficiencies with other existing competitors. We present a simulation study to compare the finite-sample performance of various methods with respect to bias, efficiency, and robustness to model misspecification. The proposed empirical likelihood method is also illustrated by an analysis of a data set from the US National Health and Nutrition Examination Survey (NHANES).

Development and validation of anthropometric prediction equations for estimation of lean body mass and appendicular lean soft tissue in Indian men and women.

PubMed

Kulkarni, Bharati; Kuper, Hannah; Taylor, Amy; Wells, Jonathan C; Radhakrishna, K V; Kinra, Sanjay; Ben-Shlomo, Yoav; Smith, George Davey; Ebrahim, Shah; Byrne, Nuala M; Hills, Andrew P

2013-10-15

Lean body mass (LBM) and muscle mass remain difficult to quantify in large epidemiological studies due to the unavailability of inexpensive methods. We therefore developed anthropometric prediction equations to estimate the LBM and appendicular lean soft tissue (ALST) using dual-energy X-ray absorptiometry (DXA) as a reference method. Healthy volunteers (n = 2,220; 36% women; age 18-79 yr), representing a wide range of body mass index (14-44 kg/m(2)), participated in this study. Their LBM, including ALST, was assessed by DXA along with anthropometric measurements. The sample was divided into prediction (60%) and validation (40%) sets. In the prediction set, a number of prediction models were constructed using DXA-measured LBM and ALST estimates as dependent variables and a combination of anthropometric indices as independent variables. These equations were cross-validated in the validation set. Simple equations using age, height, and weight explained >90% variation in the LBM and ALST in both men and women. Additional variables (hip and limb circumferences and sum of skinfold thicknesses) increased the explained variation by 5-8% in the fully adjusted models predicting LBM and ALST. More complex equations using all of the above anthropometric variables could predict the DXA-measured LBM and ALST accurately, as indicated by low standard error of the estimate (LBM: 1.47 kg and 1.63 kg for men and women, respectively), as well as good agreement by Bland-Altman analyses (Bland JM, Altman D. Lancet 1: 307-310, 1986). These equations could be a valuable tool in large epidemiological studies assessing these body compartments in Indians and other population groups with similar body composition.

Development and validation of anthropometric prediction equations for estimation of lean body mass and appendicular lean soft tissue in Indian men and women

PubMed Central

Kuper, Hannah; Taylor, Amy; Wells, Jonathan C.; Radhakrishna, K. V.; Kinra, Sanjay; Ben-Shlomo, Yoav; Smith, George Davey; Ebrahim, Shah; Byrne, Nuala M.; Hills, Andrew P.

2013-01-01

Lean body mass (LBM) and muscle mass remain difficult to quantify in large epidemiological studies due to the unavailability of inexpensive methods. We therefore developed anthropometric prediction equations to estimate the LBM and appendicular lean soft tissue (ALST) using dual-energy X-ray absorptiometry (DXA) as a reference method. Healthy volunteers (n = 2,220; 36% women; age 18-79 yr), representing a wide range of body mass index (14–44 kg/m2), participated in this study. Their LBM, including ALST, was assessed by DXA along with anthropometric measurements. The sample was divided into prediction (60%) and validation (40%) sets. In the prediction set, a number of prediction models were constructed using DXA-measured LBM and ALST estimates as dependent variables and a combination of anthropometric indices as independent variables. These equations were cross-validated in the validation set. Simple equations using age, height, and weight explained >90% variation in the LBM and ALST in both men and women. Additional variables (hip and limb circumferences and sum of skinfold thicknesses) increased the explained variation by 5–8% in the fully adjusted models predicting LBM and ALST. More complex equations using all of the above anthropometric variables could predict the DXA-measured LBM and ALST accurately, as indicated by low standard error of the estimate (LBM: 1.47 kg and 1.63 kg for men and women, respectively), as well as good agreement by Bland-Altman analyses (Bland JM, Altman D. Lancet 1: 307–310, 1986). These equations could be a valuable tool in large epidemiological studies assessing these body compartments in Indians and other population groups with similar body composition. PMID:23950165

Simple models for estimating local removals of timber in the northeast

Treesearch

David N. Larsen; David A. Gansner

1975-01-01

Provides a practical method of estimating subregional removals of timber and demonstrates its application to a typical problem. Stepwise multiple regression analysis is used to develop equations for estimating removals of softwood, hardwood, and all timber from selected characteristics of socioeconomic structure.

A method of estimating GPS instrumental biases with a convolution algorithm

NASA Astrophysics Data System (ADS)

Li, Qi; Ma, Guanyi; Lu, Weijun; Wan, Qingtao; Fan, Jiangtao; Wang, Xiaolan; Li, Jinghua; Li, Changhua

2018-03-01

This paper presents a method of deriving the instrumental differential code biases (DCBs) of GPS satellites and dual frequency receivers. Considering that the total electron content (TEC) varies smoothly over a small area, one ionospheric pierce point (IPP) and four more nearby IPPs were selected to build an equation with a convolution algorithm. In addition, unknown DCB parameters were arranged into a set of equations with GPS observations in a day unit by assuming that DCBs do not vary within a day. Then, the DCBs of satellites and receivers were determined by solving the equation set with the least-squares fitting technique. The performance of this method is examined by applying it to 361 days in 2014 using the observation data from 1311 GPS Earth Observation Network (GEONET) receivers. The result was crosswise-compared with the DCB estimated by the mesh method and the IONEX products from the Center for Orbit Determination in Europe (CODE). The DCB values derived by this method agree with those of the mesh method and the CODE products, with biases of 0.091 ns and 0.321 ns, respectively. The convolution method's accuracy and stability were quite good and showed improvements over the mesh method.

Pseudo-time methods for constrained optimization problems governed by PDE

NASA Technical Reports Server (NTRS)

Taasan, Shlomo

1995-01-01

In this paper we present a novel method for solving optimization problems governed by partial differential equations. Existing methods are gradient information in marching toward the minimum, where the constrained PDE is solved once (sometimes only approximately) per each optimization step. Such methods can be viewed as a marching techniques on the intersection of the state and costate hypersurfaces while improving the residuals of the design equations per each iteration. In contrast, the method presented here march on the design hypersurface and at each iteration improve the residuals of the state and costate equations. The new method is usually much less expensive per iteration step since, in most problems of practical interest, the design equation involves much less unknowns that that of either the state or costate equations. Convergence is shown using energy estimates for the evolution equations governing the iterative process. Numerical tests show that the new method allows the solution of the optimization problem in a cost of solving the analysis problems just a few times, independent of the number of design parameters. The method can be applied using single grid iterations as well as with multigrid solvers.

Comparison of semipermeable membrane device (SPMD) and large-volume solid-phase extraction techniques to measure water concentrations of 4,4'-DDT, 4,4'-DDE, and 4,4'-DDD in Lake Chelan, Washington.

PubMed

Ellis, Steven G; Booij, Kees; Kaputa, Mike

2008-07-01

Semipermeable membrane devices (SPMDs) spiked with the performance reference compound PCB29 were deployed 6.1 m above the sediments of Lake Chelan, Washington, for a period of 27 d, to estimate the dissolved concentrations of 4,4'-DDT, 4,4'-DDE, and 4,4'-DDD. Water concentrations were estimated using methods proposed in 2002 and newer equations published in 2006 to determine how the application of the newer equations affects historical SPMD data that used the older method. The estimated concentrations of DDD, DDE, and DDD calculated using the older method were 1.5-2.9 times higher than the newer method. SPMD estimates from both methods were also compared to dissolved and particulate DDT concentrations measured directly by processing large volumes of water through a large-volume solid-phase extraction device (Infiltrex 300). SPMD estimates of DDD+DDE+DDT (SigmaDDT) using the older and newer methods were lower than Infiltrex concentrations by factors of 1.1 and 2.3, respectively. All measurements of DDT were below the Washington State water quality standards for the protection of human health (0.59 ng l(-1)) and aquatic life (1.0 ng l(-1)).

Density of Jatropha curcas Seed Oil and its Methyl Esters: Measurement and Estimations

NASA Astrophysics Data System (ADS)

Veny, Harumi; Baroutian, Saeid; Aroua, Mohamed Kheireddine; Hasan, Masitah; Raman, Abdul Aziz; Sulaiman, Nik Meriam Nik

2009-04-01

Density data as a function of temperature have been measured for Jatropha curcas seed oil, as well as biodiesel jatropha methyl esters at temperatures from above their melting points to 90 ° C. The data obtained were used to validate the method proposed by Spencer and Danner using a modified Rackett equation. The experimental and estimated density values using the modified Rackett equation gave almost identical values with average absolute percent deviations less than 0.03% for the jatropha oil and 0.04% for the jatropha methyl esters. The Janarthanan empirical equation was also employed to predict jatropha biodiesel densities. This equation performed equally well with average absolute percent deviations within 0.05%. Two simple linear equations for densities of jatropha oil and its methyl esters are also proposed in this study.

Methods to estimate annual mean spring discharge to the Snake River between Milner Dam and King Hill, Idaho

USGS Publications Warehouse

Kjelstrom, L.C.

1995-01-01

Many individual springs and groups of springs discharge water from volcanic rocks that form the north canyon wall of the Snake River between Milner Dam and King Hill. Previous estimates of annual mean discharge from these springs have been used to understand the hydrology of the eastern part of the Snake River Plain. Four methods that were used in previous studies or developed to estimate annual mean discharge since 1902 were (1) water-budget analysis of the Snake River; (2) correlation of water-budget estimates with discharge from 10 index springs; (3) determination of the combined discharge from individual springs or groups of springs by using annual discharge measurements of 8 springs, gaging-station records of 4 springs and 3 sites on the Malad River, and regression equations developed from 5 of the measured springs; and (4) a single regression equation that correlates gaging-station records of 2 springs with historical water-budget estimates. Comparisons made among the four methods of estimating annual mean spring discharges from 1951 to 1959 and 1963 to 1980 indicated that differences were about equivalent to a measurement error of 2 to 3 percent. The method that best demonstrates the response of annual mean spring discharge to changes in ground-water recharge and discharge is method 3, which combines the measurements and regression estimates of discharge from individual springs.

Evapotranspiration from areas of native vegetation in west-central Florida

USGS Publications Warehouse

Bidlake, W.R.; Woodham, W.M.; Lopez, M.A.

1993-01-01

A study was made to examine the suitability of three different micrometeorological methods for estimating evapotranspiration from selected areas of native vegetation in west-central Florida and to estimate annual evapotranspiration from those areas. Evapotranspiration was estimated using the energy- balance Bowen ratio and eddy correlation methods. Potential evapotranspiration was computed using the Penman equation. The energy-balance Bowen ratio method was used to estimate diurnal evapotrans- piration at unforested sites and yielded reasonable results; however, measurements indicated that the magnitudes of air temperature and vapor-pressure gradients above the forested sites were too small to obtain reliable evapotranspiration measurements with the energy balance Bowen ratio system. Analysis of the surface energy-balance indicated that sensible and latent heat fluxes computed using standard eddy correlation computation methods did not adequately account for available energy. Eddy correlation data were combined with the equation for the surface energy balance to yield two additional estimates of evapotranspiration. Daily potential evapotranspiration and evapotranspira- tion estimated using the energy-balance Bowen ratio method were not correlated at a unforested, dry prairie site, but they were correlated at a marsh site. Estimates of annual evapotranspiration for sites within the four vegetation types, which were based on energy-balance Bowen ratio and eddy correlation measurements, were 1,010 millimeters for dry prairie sites, 990 millimeters for marsh sites, 1,060 millimeters for pine flatwood sites, and 970 millimeters for a cypress swamp site.

Expected versus Observed Information in SEM with Incomplete Normal and Nonnormal Data

ERIC Educational Resources Information Center

Savalei, Victoria

2010-01-01

Maximum likelihood is the most common estimation method in structural equation modeling. Standard errors for maximum likelihood estimates are obtained from the associated information matrix, which can be estimated from the sample using either expected or observed information. It is known that, with complete data, estimates based on observed or…

Magnitude and Frequency of Floods on Nontidal Streams in Delaware

USGS Publications Warehouse

Ries, Kernell G.; Dillow, Jonathan J.A.

2006-01-01

Reliable estimates of the magnitude and frequency of annual peak flows are required for the economical and safe design of transportation and water-conveyance structures. This report, done in cooperation with the Delaware Department of Transportation (DelDOT) and the Delaware Geological Survey (DGS), presents methods for estimating the magnitude and frequency of floods on nontidal streams in Delaware at locations where streamgaging stations monitor streamflow continuously and at ungaged sites. Methods are presented for estimating the magnitude of floods for return frequencies ranging from 2 through 500 years. These methods are applicable to watersheds exhibiting a full range of urban development conditions. The report also describes StreamStats, a web application that makes it easy to obtain flood-frequency estimates for user-selected locations on Delaware streams. Flood-frequency estimates for ungaged sites are obtained through a process known as regionalization, using statistical regression analysis, where information determined for a group of streamgaging stations within a region forms the basis for estimates for ungaged sites within the region. One hundred and sixteen streamgaging stations in and near Delaware with at least 10 years of non-regulated annual peak-flow data available were used in the regional analysis. Estimates for gaged sites are obtained by combining the station peak-flow statistics (mean, standard deviation, and skew) and peak-flow estimates with regional estimates of skew and flood-frequency magnitudes. Example flood-frequency estimate calculations using the methods presented in the report are given for: (1) ungaged sites, (2) gaged locations, (3) sites upstream or downstream from a gaged location, and (4) sites between gaged locations. Regional regression equations applicable to ungaged sites in the Piedmont and Coastal Plain Physiographic Provinces of Delaware are presented. The equations incorporate drainage area, forest cover, impervious area, basin storage, housing density, soil type A, and mean basin slope as explanatory variables, and have average standard errors of prediction ranging from 28 to 72 percent. Additional regression equations that incorporate drainage area and housing density as explanatory variables are presented for use in defining the effects of urbanization on peak-flow estimates throughout Delaware for the 2-year through 500-year recurrence intervals, along with suggestions for their appropriate use in predicting development-affected peak flows. Additional topics associated with the analyses performed during the study are also discussed, including: (1) the availability and description of more than 30 basin and climatic characteristics considered during the development of the regional regression equations; (2) the treatment of increasing trends in the annual peak-flow series identified at 18 gaged sites, with respect to their relations with maximum 24-hour precipitation and housing density, and their use in the regional analysis; (3) calculation of the 90-percent confidence interval associated with peak-flow estimates from the regional regression equations; and (4) a comparison of flood-frequency estimates at gages used in a previous study, highlighting the effects of various improved analytical techniques.

Statistical comparison of methods for estimating sediment thickness from Horizontal-to-Vertical Spectral Ratio (HVSR) seismic methods: An example from Tylerville, Connecticut, USA

USGS Publications Warehouse

Johnson, Carole D.; Lane, John W.

2016-01-01

Determining sediment thickness and delineating bedrock topography are important for assessing groundwater availability and characterizing contamination sites. In recent years, the horizontal-to-vertical spectral ratio (HVSR) seismic method has emerged as a non-invasive, cost-effective approach for estimating the thickness of unconsolidated sediments above bedrock. Using a three-component seismometer, this method uses the ratio of the average horizontal- and vertical-component amplitude spectrums to produce a spectral ratio curve with a peak at the fundamental resonance frequency. The HVSR method produces clear and repeatable resonance frequency peaks when there is a sharp contrast (>2:1) in acoustic impedance at the sediment/bedrock boundary. Given the resonant frequency, sediment thickness can be determined either by (1) using an estimate of average local sediment shear-wave velocity or by (2) application of a power-law regression equation developed from resonance frequency observations at sites with a range of known depths to bedrock. Two frequently asked questions about the HVSR method are (1) how accurate are the sediment thickness estimates? and (2) how much do sediment thickness/bedrock depth estimates change when using different published regression equations? This paper compares and contrasts different approaches for generating HVSR depth estimates, through analysis of HVSR data acquired in the vicinity of Tylerville, Connecticut, USA.

Iohexol clearance is superior to creatinine-based renal function estimating equations in detecting short-term renal function decline in chronic heart failure

PubMed Central

Cvan Trobec, Katja; Kerec Kos, Mojca; von Haehling, Stephan; Anker, Stefan D.; Macdougall, Iain C.; Ponikowski, Piotr; Lainscak, Mitja

2015-01-01

Aim To compare the performance of iohexol plasma clearance and creatinine-based renal function estimating equations in monitoring longitudinal renal function changes in chronic heart failure (CHF) patients, and to assess the effects of body composition on the equation performance. Methods Iohexol plasma clearance was measured in 43 CHF patients at baseline and after at least 6 months. Simultaneously, renal function was estimated with five creatinine-based equations (four- and six-variable Modification of Diet in Renal Disease, Cockcroft-Gault, Cockcroft-Gault adjusted for lean body mass, Chronic Kidney Disease Epidemiology Collaboration equation) and body composition was assessed using bioimpedance and dual-energy x-ray absorptiometry. Results Over a median follow-up of 7.5 months (range 6-17 months), iohexol clearance significantly declined (52.8 vs 44.4 mL/[min ×1.73 m2], P = 0.001). This decline was significantly higher in patients receiving mineralocorticoid receptor antagonists at baseline (mean decline -22% of baseline value vs -3%, P = 0.037). Mean serum creatinine concentration did not change significantly during follow-up and no creatinine-based renal function estimating equation was able to detect the significant longitudinal decline of renal function determined by iohexol clearance. After accounting for body composition, the accuracy of the equations improved, but not their ability to detect renal function decline. Conclusions Renal function measured with iohexol plasma clearance showed relevant decline in CHF patients, particularly in those treated with mineralocorticoid receptor antagonists. None of the equations for renal function estimation was able to detect these changes. ClinicalTrials.gov registration number NCT01829880 PMID:26718759

Transforming parts of a differential equations system to difference equations as a method for run-time savings in NONMEM.

PubMed

Petersson, K J F; Friberg, L E; Karlsson, M O

2010-10-01

Computer models of biological systems grow more complex as computing power increase. Often these models are defined as differential equations and no analytical solutions exist. Numerical integration is used to approximate the solution; this can be computationally intensive, time consuming and be a large proportion of the total computer runtime. The performance of different integration methods depend on the mathematical properties of the differential equations system at hand. In this paper we investigate the possibility of runtime gains by calculating parts of or the whole differential equations system at given time intervals, outside of the differential equations solver. This approach was tested on nine models defined as differential equations with the goal to reduce runtime while maintaining model fit, based on the objective function value. The software used was NONMEM. In four models the computational runtime was successfully reduced (by 59-96%). The differences in parameter estimates, compared to using only the differential equations solver were less than 12% for all fixed effects parameters. For the variance parameters, estimates were within 10% for the majority of the parameters. Population and individual predictions were similar and the differences in OFV were between 1 and -14 units. When computational runtime seriously affects the usefulness of a model we suggest evaluating this approach for repetitive elements of model building and evaluation such as covariate inclusions or bootstraps.

The Bland-Altman Method Should Not Be Used in Regression Cross-Validation Studies

ERIC Educational Resources Information Center

O'Connor, Daniel P.; Mahar, Matthew T.; Laughlin, Mitzi S.; Jackson, Andrew S.

2011-01-01

The purpose of this study was to demonstrate the bias in the Bland-Altman (BA) limits of agreement method when it is used to validate regression models. Data from 1,158 men were used to develop three regression equations to estimate maximum oxygen uptake (R[superscript 2] = 0.40, 0.61, and 0.82, respectively). The equations were evaluated in a…

Regional regression equations to estimate peak-flow frequency at sites in North Dakota using data through 2009

USGS Publications Warehouse

Williams-Sether, Tara

2015-08-06

Annual peak-flow frequency data from 231 U.S. Geological Survey streamflow-gaging stations in North Dakota and parts of Montana, South Dakota, and Minnesota, with 10 or more years of unregulated peak-flow record, were used to develop regional regression equations for exceedance probabilities of 0.5, 0.20, 0.10, 0.04, 0.02, 0.01, and 0.002 using generalized least-squares techniques. Updated peak-flow frequency estimates for 262 streamflow-gaging stations were developed using data through 2009 and log-Pearson Type III procedures outlined by the Hydrology Subcommittee of the Interagency Advisory Committee on Water Data. An average generalized skew coefficient was determined for three hydrologic zones in North Dakota. A StreamStats web application was developed to estimate basin characteristics for the regional regression equation analysis. Methods for estimating a weighted peak-flow frequency for gaged sites and ungaged sites are presented.

Quantitative Compactness Estimates for Hamilton-Jacobi Equations

NASA Astrophysics Data System (ADS)

Ancona, Fabio; Cannarsa, Piermarco; Nguyen, Khai T.

2016-02-01

We study quantitative compactness estimates in {W^{1,1}_{loc}} for the map {S_t}, {t > 0} that is associated with the given initial data {u_0in Lip (R^N)} for the corresponding solution {S_t u_0} of a Hamilton-Jacobi equation u_t+Hbig(nabla_{x} ubig)=0, qquad t≥ 0,quad xinR^N, with a uniformly convex Hamiltonian {H=H(p)}. We provide upper and lower estimates of order {1/\\varepsilon^N} on the Kolmogorov {\\varepsilon}-entropy in {W^{1,1}} of the image through the map S t of sets of bounded, compactly supported initial data. Estimates of this type are inspired by a question posed by Lax (Course on Hyperbolic Systems of Conservation Laws. XXVII Scuola Estiva di Fisica Matematica, Ravello, 2002) within the context of conservation laws, and could provide a measure of the order of "resolution" of a numerical method implemented for this equation.

Sonographic estimation of fetal weight: comparison of bias, precision and consistency using 12 different formulae.

PubMed

Anderson, N G; Jolley, I J; Wells, J E

2007-08-01

To determine the major sources of error in ultrasonographic assessment of fetal weight and whether they have changed over the last decade. We performed a prospective observational study in 1991 and again in 2000 of a mixed-risk pregnancy population, estimating fetal weight within 7 days of delivery. In 1991, the Rose and McCallum formula was used for 72 deliveries. Inter- and intraobserver agreement was assessed within this group. Bland-Altman measures of agreement from log data were calculated as ratios. We repeated the study in 2000 in 208 consecutive deliveries, comparing predicted and actual weights for 12 published equations using Bland-Altman and percentage error methods. We compared bias (mean percentage error), precision (SD percentage error), and their consistency across the weight ranges. 95% limits of agreement ranged from - 4.4% to + 3.3% for inter- and intraobserver estimates, but were - 18.0% to 24.0% for estimated and actual birth weight. There was no improvement in accuracy between 1991 and 2000. In 2000 only six of the 12 published formulae had overall bias within 7% and precision within 15%. There was greater bias and poorer precision in nearly all equations if the birth weight was < 1,000 g. Observer error is a relatively minor component of the error in estimating fetal weight; error due to the equation is a larger source of error. Improvements in ultrasound technology have not improved the accuracy of estimating fetal weight. Comparison of methods of estimating fetal weight requires statistical methods that can separate out bias, precision and consistency. Estimating fetal weight in the very low birth weight infant is subject to much greater error than it is in larger babies. Copyright (c) 2007 ISUOG. Published by John Wiley & Sons, Ltd.

Double Cross-Validation in Multiple Regression: A Method of Estimating the Stability of Results.

ERIC Educational Resources Information Center

Rowell, R. Kevin

In multiple regression analysis, where resulting predictive equation effectiveness is subject to shrinkage, it is especially important to evaluate result replicability. Double cross-validation is an empirical method by which an estimate of invariance or stability can be obtained from research data. A procedure for double cross-validation is…

Flood-Frequency Estimates for Streams on Kaua`i, O`ahu, Moloka`i, Maui, and Hawai`i, State of Hawai`i

USGS Publications Warehouse

Oki, Delwyn S.; Rosa, Sarah N.; Yeung, Chiu W.

2010-01-01

This study provides an updated analysis of the magnitude and frequency of peak stream discharges in Hawai`i. Annual peak-discharge data collected by the U.S. Geological Survey during and before water year 2008 (ending September 30, 2008) at stream-gaging stations were analyzed. The existing generalized-skew value for the State of Hawai`i was retained, although three methods were used to evaluate whether an update was needed. Regional regression equations were developed for peak discharges with 2-, 5-, 10-, 25-, 50-, 100-, and 500-year recurrence intervals for unregulated streams (those for which peak discharges are not affected to a large extent by upstream reservoirs, dams, diversions, or other structures) in areas with less than 20 percent combined medium- and high-intensity development on Kaua`i, O`ahu, Moloka`i, Maui, and Hawai`i. The generalized-least-squares (GLS) regression equations relate peak stream discharge to quantified basin characteristics (for example, drainage-basin area and mean annual rainfall) that were determined using geographic information system (GIS) methods. Each of the islands of Kaua`i,O`ahu, Moloka`i, Maui, and Hawai`i was divided into two regions, generally corresponding to a wet region and a dry region. Unique peak-discharge regression equations were developed for each region. The regression equations developed for this study have standard errors of prediction ranging from 16 to 620 percent. Standard errors of prediction are greatest for regression equations developed for leeward Moloka`i and southern Hawai`i. In general, estimated 100-year peak discharges from this study are lower than those from previous studies, which may reflect the longer periods of record used in this study. Each regression equation is valid within the range of values of the explanatory variables used to develop the equation. The regression equations were developed using peak-discharge data from streams that are mainly unregulated, and they should not be used to estimate peak discharges in regulated streams. Use of a regression equation beyond its limits will produce peak-discharge estimates with unknown error and should therefore be avoided. Improved estimates of the magnitude and frequency of peak discharges in Hawai`i will require continued operation of existing stream-gaging stations and operation of additional gaging stations for areas such as Moloka`i and Hawai`i, where limited stream-gaging data are available.

Analysis of cohort studies with multivariate and partially observed disease classification data.

PubMed

Chatterjee, Nilanjan; Sinha, Samiran; Diver, W Ryan; Feigelson, Heather Spencer

2010-09-01

Complex diseases like cancers can often be classified into subtypes using various pathological and molecular traits of the disease. In this article, we develop methods for analysis of disease incidence in cohort studies incorporating data on multiple disease traits using a two-stage semiparametric Cox proportional hazards regression model that allows one to examine the heterogeneity in the effect of the covariates by the levels of the different disease traits. For inference in the presence of missing disease traits, we propose a generalization of an estimating equation approach for handling missing cause of failure in competing-risk data. We prove asymptotic unbiasedness of the estimating equation method under a general missing-at-random assumption and propose a novel influence-function-based sandwich variance estimator. The methods are illustrated using simulation studies and a real data application involving the Cancer Prevention Study II nutrition cohort.

An empirical method for approximating stream baseflow time series using groundwater table fluctuations

NASA Astrophysics Data System (ADS)

Meshgi, Ali; Schmitter, Petra; Babovic, Vladan; Chui, Ting Fong May

2014-11-01

Developing reliable methods to estimate stream baseflow has been a subject of interest due to its importance in catchment response and sustainable watershed management. However, to date, in the absence of complex numerical models, baseflow is most commonly estimated using statistically derived empirical approaches that do not directly incorporate physically-meaningful information. On the other hand, Artificial Intelligence (AI) tools such as Genetic Programming (GP) offer unique capabilities to reduce the complexities of hydrological systems without losing relevant physical information. This study presents a simple-to-use empirical equation to estimate baseflow time series using GP so that minimal data is required and physical information is preserved. A groundwater numerical model was first adopted to simulate baseflow for a small semi-urban catchment (0.043 km2) located in Singapore. GP was then used to derive an empirical equation relating baseflow time series to time series of groundwater table fluctuations, which are relatively easily measured and are physically related to baseflow generation. The equation was then generalized for approximating baseflow in other catchments and validated for a larger vegetation-dominated basin located in the US (24 km2). Overall, this study used GP to propose a simple-to-use equation to predict baseflow time series based on only three parameters: minimum daily baseflow of the entire period, area of the catchment and groundwater table fluctuations. It serves as an alternative approach for baseflow estimation in un-gauged systems when only groundwater table and soil information is available, and is thus complementary to other methods that require discharge measurements.

Diffusion phenomenon for linear dissipative wave equations in an exterior domain

NASA Astrophysics Data System (ADS)

Ikehata, Ryo

Under the general condition of the initial data, we will derive the crucial estimates which imply the diffusion phenomenon for the dissipative linear wave equations in an exterior domain. In order to derive the diffusion phenomenon for dissipative wave equations, the time integral method which was developed by Ikehata and Matsuyama (Sci. Math. Japon. 55 (2002) 33) plays an effective role.

Performance of three glomerular filtration rate estimation equations in a population of sub-Saharan Africans with Type 2 diabetes.

PubMed

Agoons, D D; Balti, E V; Kaze, F F; Azabji-Kenfack, M; Ashuntantang, G; Kengne, A P; Sobngwi, E; Mbanya, J C

2016-09-01

We evaluated the performance of the Modification of Diet in Renal Disease (MDRD), Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) and Cockcroft-Gault (CG) equations against creatinine clearance (CrCl) to estimate glomerular filtration rate (GFR) in 51 patients with Type 2 diabetes. The CrCl value was obtained from the average of two consecutive 24-h urine samples. Results were adjusted for body surface area using the Dubois formula. Serum creatinine was measured using the kinetic Jaffe method and was calibrated to standardized levels. Bland-Altman analysis and kappa statistic were used to examine agreement between measured and estimated GFR. Estimates of GFR from the CrCl, MDRD, CKD-EPI and CG equations were similar (overall P = 0.298), and MDRD (r = 0.58; 95% CI: 0.36-0.74), CKD-EPI (r = 0.55; 95% CI: 0.33-0.72) and CG (r = 0.61; 95% CI: 0.39-0.75) showed modest correlation with CrCl (all P < 0.001). Bias was -0.3 for MDRD, 1.7 for CKD-EPI and -5.4 for CG. All three equations showed fair-to-moderate agreement with CrCl (kappa: 0.38-0.51). The c-statistic for all three equations ranged between 0.75 and 0.77 with no significant difference (P = 0.639 for c-statistic comparison). The MDRD equation seems to have a modest advantage over CKD-EPI and CG in estimating GFR and detecting impaired renal function in sub-Saharan African patients with Type 2 diabetes. The overall relatively modest correlation with CrCl, however, suggests the need for context-specific estimators of GFR or context adaptation of existing estimators. © 2015 Diabetes UK.

Are Ethnic and Gender Specific Equations Needed to Derive Fat Free Mass from Bioelectrical Impedance in Children of South Asian, Black African-Caribbean and White European Origin? Results of the Assessment of Body Composition in Children Study

PubMed Central

Nightingale, Claire M.; Rudnicka, Alicja R.; Owen, Christopher G.; Donin, Angela S.; Newton, Sian L.; Furness, Cheryl A.; Howard, Emma L.; Gillings, Rachel D.; Wells, Jonathan C. K.; Cook, Derek G.; Whincup, Peter H.

2013-01-01

Background Bioelectrical impedance analysis (BIA) is a potentially valuable method for assessing lean mass and body fat levels in children from different ethnic groups. We examined the need for ethnic- and gender-specific equations for estimating fat free mass (FFM) from BIA in children from different ethnic groups and examined their effects on the assessment of ethnic differences in body fat. Methods Cross-sectional study of children aged 8–10 years in London Primary schools including 325 South Asians, 250 black African-Caribbeans and 289 white Europeans with measurements of height, weight and arm-leg impedance (Z; Bodystat 1500). Total body water was estimated from deuterium dilution and converted to FFM. Multilevel models were used to derive three types of equation {A: FFM = linear combination(height+weight+Z); B: FFM = linear combination(height2/Z); C: FFM = linear combination(height2/Z+weight)}. Results Ethnicity and gender were important predictors of FFM and improved model fit in all equations. The models of best fit were ethnicity and gender specific versions of equation A, followed by equation C; these provided accurate assessments of ethnic differences in FFM and FM. In contrast, the use of generic equations led to underestimation of both the negative South Asian-white European FFM difference and the positive black African-Caribbean-white European FFM difference (by 0.53 kg and by 0.73 kg respectively for equation A). The use of generic equations underestimated the positive South Asian-white European difference in fat mass (FM) and overestimated the positive black African-Caribbean-white European difference in FM (by 4.7% and 10.1% respectively for equation A). Consistent results were observed when the equations were applied to a large external data set. Conclusions Ethnic- and gender-specific equations for predicting FFM from BIA provide better estimates of ethnic differences in FFM and FM in children, while generic equations can misrepresent these ethnic differences. PMID:24204625

Time-lapse joint AVO inversion using generalized linear method based on exact Zoeppritz equations

NASA Astrophysics Data System (ADS)

Zhi, L.; Gu, H.

2017-12-01

The conventional method of time-lapse AVO (Amplitude Versus Offset) inversion is mainly based on the approximate expression of Zoeppritz equations. Though the approximate expression is concise and convenient to use, it has certain limitations. For example, its application condition is that the difference of elastic parameters between the upper medium and lower medium is little and the incident angle is small. In addition, the inversion of density is not stable. Therefore, we develop the method of time-lapse joint AVO inversion based on exact Zoeppritz equations. In this method, we apply exact Zoeppritz equations to calculate the reflection coefficient of PP wave. And in the construction of objective function for inversion, we use Taylor expansion to linearize the inversion problem. Through the joint AVO inversion of seismic data in baseline survey and monitor survey, we can obtain P-wave velocity, S-wave velocity, density in baseline survey and their time-lapse changes simultaneously. We can also estimate the oil saturation change according to inversion results. Compared with the time-lapse difference inversion, the joint inversion has a better applicability. It doesn't need some assumptions and can estimate more parameters simultaneously. Meanwhile, by using the generalized linear method, the inversion is easily realized and its calculation amount is small. We use the Marmousi model to generate synthetic seismic records to test and analyze the influence of random noise. Without noise, all estimation results are relatively accurate. With the increase of noise, P-wave velocity change and oil saturation change are stable and less affected by noise. S-wave velocity change is most affected by noise. Finally we use the actual field data of time-lapse seismic prospecting to process and the results can prove the availability and feasibility of our method in actual situation.

The use of copulas to practical estimation of multivariate stochastic differential equation mixed effects models

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

Rupšys, P.

A system of stochastic differential equations (SDE) with mixed-effects parameters and multivariate normal copula density function were used to develop tree height model for Scots pine trees in Lithuania. A two-step maximum likelihood parameter estimation method is used and computational guidelines are given. After fitting the conditional probability density functions to outside bark diameter at breast height, and total tree height, a bivariate normal copula distribution model was constructed. Predictions from the mixed-effects parameters SDE tree height model calculated during this research were compared to the regression tree height equations. The results are implemented in the symbolic computational language MAPLE.

Method for rapid estimation of scour at highway bridges based on limited site data

USGS Publications Warehouse

Holnbeck, S.R.; Parrett, Charles

1997-01-01

Limited site data were used to develop a method for rapid estimation of scour at highway bridges. The estimates can be obtained in a matter of hours rather than several days as required by more-detailed methods. Such a method is important because scour assessments are needed to identify scour-critical bridges throughout the United States. Using detailed scour-analysis methods and scour-prediction equations recommended by the Federal Highway Administration, the U.S. Geological Survey, in cooperation with the Montana Department of Transportation, obtained contraction, pier, and abutment scour-depth data for sites from 10 States.The data were used to develop relations between scour depth and hydraulic variables that can be rapidly measured in the field. Relations between scour depth and hydraulic variables, in the form of envelope curves, were based on simpler forms of detailed scour-prediction equations. To apply the rapid-estimation method, a 100-year recurrence interval peak discharge is determined, and bridge- length data are used in the field with graphs relating unit discharge to velocity and velocity to bridge backwater as a basis for estimating flow depths and other hydraulic variables that can then be applied using the envelope curves. The method was tested in the field. Results showed good agreement among individuals involved and with results from more-detailed methods. Although useful for identifying potentially scour-critical bridges, themethod does not replace more-detailed methods used for design purposes. Use of the rapid- estimation method should be limited to individuals having experience in bridge scour, hydraulics, and flood hydrology, and some training in use of the method.

Score Estimating Equations from Embedded Likelihood Functions under Accelerated Failure Time Model

PubMed Central

NING, JING; QIN, JING; SHEN, YU

2014-01-01

SUMMARY The semiparametric accelerated failure time (AFT) model is one of the most popular models for analyzing time-to-event outcomes. One appealing feature of the AFT model is that the observed failure time data can be transformed to identically independent distributed random variables without covariate effects. We describe a class of estimating equations based on the score functions for the transformed data, which are derived from the full likelihood function under commonly used semiparametric models such as the proportional hazards or proportional odds model. The methods of estimating regression parameters under the AFT model can be applied to traditional right-censored survival data as well as more complex time-to-event data subject to length-biased sampling. We establish the asymptotic properties and evaluate the small sample performance of the proposed estimators. We illustrate the proposed methods through applications in two examples. PMID:25663727

Modeling individualized coefficient alpha to measure quality of test score data.

PubMed

Liu, Molei; Hu, Ming; Zhou, Xiao-Hua

2018-05-23

Individualized coefficient alpha is defined. It is item and subject specific and is used to measure the quality of test score data with heterogenicity among the subjects and items. A regression model is developed based on 3 sets of generalized estimating equations. The first set of generalized estimating equation models the expectation of the responses, the second set models the response's variance, and the third set is proposed to estimate the individualized coefficient alpha, defined and used to measure individualized internal consistency of the responses. We also use different techniques to extend our method to handle missing data. Asymptotic property of the estimators is discussed, based on which inference on the coefficient alpha is derived. Performance of our method is evaluated through simulation study and real data analysis. The real data application is from a health literacy study in Hunan province of China. Copyright © 2018 John Wiley & Sons, Ltd.

Optimal estimation of spatially variable recharge and transmissivity fields under steady-state groundwater flow. Part 1. Theory

NASA Astrophysics Data System (ADS)

Graham, Wendy D.; Tankersley, Claude D.

1994-05-01

Stochastic methods are used to analyze two-dimensional steady groundwater flow subject to spatially variable recharge and transmissivity. Approximate partial differential equations are developed for the covariances and cross-covariances between the random head, transmissivity and recharge fields. Closed-form solutions of these equations are obtained using Fourier transform techniques. The resulting covariances and cross-covariances can be incorporated into a Bayesian conditioning procedure which provides optimal estimates of the recharge, transmissivity and head fields given available measurements of any or all of these random fields. Results show that head measurements contain valuable information for estimating the random recharge field. However, when recharge is treated as a spatially variable random field, the value of head measurements for estimating the transmissivity field can be reduced considerably. In a companion paper, the method is applied to a case study of the Upper Floridan Aquifer in NE Florida.

Methods for estimating selected spring and fall low-flow frequency statistics for ungaged stream sites in Iowa, based on data through June 2014

USGS Publications Warehouse

Eash, David A.; Barnes, Kimberlee K.; O'Shea, Padraic S.

2016-09-19

A statewide study was led to develop regression equations for estimating three selected spring and three selected fall low-flow frequency statistics for ungaged stream sites in Iowa. The estimation equations developed for the six low-flow frequency statistics include spring (April through June) 1-, 7-, and 30-day mean low flows for a recurrence interval of 10 years and fall (October through December) 1-, 7-, and 30-day mean low flows for a recurrence interval of 10 years. Estimates of the three selected spring statistics are provided for 241 U.S. Geological Survey continuous-record streamgages, and estimates of the three selected fall statistics are provided for 238 of these streamgages, using data through June 2014. Because only 9 years of fall streamflow record were available, three streamgages included in the development of the spring regression equations were not included in the development of the fall regression equations. Because of regulation, diversion, or urbanization, 30 of the 241 streamgages were not included in the development of the regression equations. The study area includes Iowa and adjacent areas within 50 miles of the Iowa border. Because trend analyses indicated statistically significant positive trends when considering the period of record for most of the streamgages, the longest, most recent period of record without a significant trend was determined for each streamgage for use in the study. Geographic information system software was used to measure 63 selected basin characteristics for each of the 211streamgages used to develop the regional regression equations. The study area was divided into three low-flow regions that were defined in a previous study for the development of regional regression equations.Because several streamgages included in the development of regional regression equations have estimates of zero flow calculated from observed streamflow for selected spring and fall low-flow frequency statistics, the final equations for the three low-flow regions were developed using two types of regression analyses—left-censored and generalized-least-squares regression analyses. A total of 211 streamgages were included in the development of nine spring regression equations—three equations for each of the three low-flow regions. A total of 208 streamgages were included in the development of nine fall regression equations—three equations for each of the three low-flow regions. A censoring threshold was used to develop 15 left-censored regression equations to estimate the three fall low-flow frequency statistics for each of the three low-flow regions and to estimate the three spring low-flow frequency statistics for the southern and northwest regions. For the northeast region, generalized-least-squares regression was used to develop three equations to estimate the three spring low-flow frequency statistics. For the northeast region, average standard errors of prediction range from 32.4 to 48.4 percent for the spring equations and average standard errors of estimate range from 56.4 to 73.8 percent for the fall equations. For the northwest region, average standard errors of estimate range from 58.9 to 62.1 percent for the spring equations and from 83.2 to 109.4 percent for the fall equations. For the southern region, average standard errors of estimate range from 43.2 to 64.0 percent for the spring equations and from 78.1 to 78.7 percent for the fall equations.The regression equations are applicable only to stream sites in Iowa with low flows not substantially affected by regulation, diversion, or urbanization and with basin characteristics within the range of those used to develop the equations. The regression equations will be implemented within the U.S. Geological Survey StreamStats Web-based geographic information system application. StreamStats allows users to click on any ungaged stream site and compute estimates of the six selected spring and fall low-flow statistics; in addition, 90-percent prediction intervals and the measured basin characteristics for the ungaged site are provided. StreamStats also allows users to click on any Iowa streamgage to obtain computed estimates for the six selected spring and fall low-flow statistics.

MIXED MODEL AND ESTIMATING EQUATION APPROACHES FOR ZERO INFLATION IN CLUSTERED BINARY RESPONSE DATA WITH APPLICATION TO A DATING VIOLENCE STUDY1

PubMed Central

Fulton, Kara A.; Liu, Danping; Haynie, Denise L.; Albert, Paul S.

2016-01-01

The NEXT Generation Health study investigates the dating violence of adolescents using a survey questionnaire. Each student is asked to affirm or deny multiple instances of violence in his/her dating relationship. There is, however, evidence suggesting that students not in a relationship responded to the survey, resulting in excessive zeros in the responses. This paper proposes likelihood-based and estimating equation approaches to analyze the zero-inflated clustered binary response data. We adopt a mixed model method to account for the cluster effect, and the model parameters are estimated using a maximum-likelihood (ML) approach that requires a Gaussian–Hermite quadrature (GHQ) approximation for implementation. Since an incorrect assumption on the random effects distribution may bias the results, we construct generalized estimating equations (GEE) that do not require the correct specification of within-cluster correlation. In a series of simulation studies, we examine the performance of ML and GEE methods in terms of their bias, efficiency and robustness. We illustrate the importance of properly accounting for this zero inflation by reanalyzing the NEXT data where this issue has previously been ignored. PMID:26937263

Performance of the modified Poisson regression approach for estimating relative risks from clustered prospective data.

PubMed

Yelland, Lisa N; Salter, Amy B; Ryan, Philip

2011-10-15

Modified Poisson regression, which combines a log Poisson regression model with robust variance estimation, is a useful alternative to log binomial regression for estimating relative risks. Previous studies have shown both analytically and by simulation that modified Poisson regression is appropriate for independent prospective data. This method is often applied to clustered prospective data, despite a lack of evidence to support its use in this setting. The purpose of this article is to evaluate the performance of the modified Poisson regression approach for estimating relative risks from clustered prospective data, by using generalized estimating equations to account for clustering. A simulation study is conducted to compare log binomial regression and modified Poisson regression for analyzing clustered data from intervention and observational studies. Both methods generally perform well in terms of bias, type I error, and coverage. Unlike log binomial regression, modified Poisson regression is not prone to convergence problems. The methods are contrasted by using example data sets from 2 large studies. The results presented in this article support the use of modified Poisson regression as an alternative to log binomial regression for analyzing clustered prospective data when clustering is taken into account by using generalized estimating equations.

Why Might Relative Fit Indices Differ between Estimators?

ERIC Educational Resources Information Center

Weng, Li-Jen; Cheng, Chung-Ping

1997-01-01

Relative fit indices using the null model as the reference point in computation may differ across estimation methods, as this article illustrates by comparing maximum likelihood, ordinary least squares, and generalized least squares estimation in structural equation modeling. The illustration uses a covariance matrix for six observed variables…

Brute force meets Bruno force in parameter optimisation: introduction of novel constraints for parameter accuracy improvement by symbolic computation.

PubMed

Nakatsui, M; Horimoto, K; Lemaire, F; Ürgüplü, A; Sedoglavic, A; Boulier, F

2011-09-01

Recent remarkable advances in computer performance have enabled us to estimate parameter values by the huge power of numerical computation, the so-called 'Brute force', resulting in the high-speed simultaneous estimation of a large number of parameter values. However, these advancements have not been fully utilised to improve the accuracy of parameter estimation. Here the authors review a novel method for parameter estimation using symbolic computation power, 'Bruno force', named after Bruno Buchberger, who found the Gröbner base. In the method, the objective functions combining the symbolic computation techniques are formulated. First, the authors utilise a symbolic computation technique, differential elimination, which symbolically reduces an equivalent system of differential equations to a system in a given model. Second, since its equivalent system is frequently composed of large equations, the system is further simplified by another symbolic computation. The performance of the authors' method for parameter accuracy improvement is illustrated by two representative models in biology, a simple cascade model and a negative feedback model in comparison with the previous numerical methods. Finally, the limits and extensions of the authors' method are discussed, in terms of the possible power of 'Bruno force' for the development of a new horizon in parameter estimation.

Development and validation of a predictive equation for lean body mass in children and adolescents.

PubMed

Foster, Bethany J; Platt, Robert W; Zemel, Babette S

2012-05-01

Lean body mass (LBM) is not easy to measure directly in the field or clinical setting. Equations to predict LBM from simple anthropometric measures, which account for the differing contributions of fat and lean to body weight at different ages and levels of adiposity, would be useful to both human biologists and clinicians. To develop and validate equations to predict LBM in children and adolescents across the entire range of the adiposity spectrum. Dual energy X-ray absorptiometry was used to measure LBM in 836 healthy children (437 females) and linear regression was used to develop sex-specific equations to estimate LBM from height, weight, age, body mass index (BMI) for age z-score and population ancestry. Equations were validated using bootstrapping methods and in a local independent sample of 332 children and in national data collected by NHANES. The mean difference between measured and predicted LBM was - 0.12% (95% limits of agreement - 11.3% to 8.5%) for males and - 0.14% ( - 11.9% to 10.9%) for females. Equations performed equally well across the entire adiposity spectrum, as estimated by BMI z-score. Validation indicated no over-fitting. LBM was predicted within 5% of measured LBM in the validation sample. The equations estimate LBM accurately from simple anthropometric measures.

ZZ-Type a posteriori error estimators for adaptive boundary element methods on a curve☆

PubMed Central

Feischl, Michael; Führer, Thomas; Karkulik, Michael; Praetorius, Dirk

2014-01-01

In the context of the adaptive finite element method (FEM), ZZ-error estimators named after Zienkiewicz and Zhu (1987) [52] are mathematically well-established and widely used in practice. In this work, we propose and analyze ZZ-type error estimators for the adaptive boundary element method (BEM). We consider weakly singular and hyper-singular integral equations and prove, in particular, convergence of the related adaptive mesh-refining algorithms. Throughout, the theoretical findings are underlined by numerical experiments. PMID:24748725

The novel application of artificial neural network on bioelectrical impedance analysis to assess the body composition in elderly

PubMed Central

2013-01-01

Background This study aims to improve accuracy of Bioelectrical Impedance Analysis (BIA) prediction equations for estimating fat free mass (FFM) of the elderly by using non-linear Back Propagation Artificial Neural Network (BP-ANN) model and to compare the predictive accuracy with the linear regression model by using energy dual X-ray absorptiometry (DXA) as reference method. Methods A total of 88 Taiwanese elderly adults were recruited in this study as subjects. Linear regression equations and BP-ANN prediction equation were developed using impedances and other anthropometrics for predicting the reference FFM measured by DXA (FFMDXA) in 36 male and 26 female Taiwanese elderly adults. The FFM estimated by BIA prediction equations using traditional linear regression model (FFMLR) and BP-ANN model (FFMANN) were compared to the FFMDXA. The measuring results of an additional 26 elderly adults were used to validate than accuracy of the predictive models. Results The results showed the significant predictors were impedance, gender, age, height and weight in developed FFMLR linear model (LR) for predicting FFM (coefficient of determination, r2 = 0.940; standard error of estimate (SEE) = 2.729 kg; root mean square error (RMSE) = 2.571kg, P < 0.001). The above predictors were set as the variables of the input layer by using five neurons in the BP-ANN model (r2 = 0.987 with a SD = 1.192 kg and relatively lower RMSE = 1.183 kg), which had greater (improved) accuracy for estimating FFM when compared with linear model. The results showed a better agreement existed between FFMANN and FFMDXA than that between FFMLR and FFMDXA. Conclusion When compared the performance of developed prediction equations for estimating reference FFMDXA, the linear model has lower r2 with a larger SD in predictive results than that of BP-ANN model, which indicated ANN model is more suitable for estimating FFM. PMID:23388042

Evaluation of Soil Loss and Erosion Control Measures on Ranges and Range Structures at Installations in Temperate Climates

DTIC Science & Technology

2006-06-01

Soil Loss Equation ( USLE ) and the Revised Universal Soil Loss Equation (RUSLE) continue to be widely accepted methods for estimating sediment loss...range areas. Therefore, a generalized design methodology using the Universal Soil Loss Equation ( USLE ) is presented to accommodate the variations...constructed use the slope most suitable to the area topography (3:1 or 4:1). Step 4: Using the Universal Soil Loss equation, USLE , find the values of A

Estimation of Organic Vapor Breakthrough in Humidified Activated Carbon Beds: -Application of Wheeler-Jonas Equation, NIOSH MultiVapor™ and RBT (Relative Breakthrough Time)

PubMed Central

Abiko, Hironobu; Furuse, Mitsuya; Takano, Tsuguo

2016-01-01

Objectives: In the use of activated carbon beds as adsorbents for various types of organic vapor in respirator gas filters, water adsorption of the bed and test gas humidity are expected to alter the accuracy in the estimation of breakthrough data. There is increasing interest in the effects of moisture on estimation methods, and this study has investigated the effects with actual breakthrough data. Methods: We prepared several activated carbon beds preconditioned by equilibration with moisture at different relative humidities (RH=40%-70%) and a constant temperature of 20°C. Then, we measured breakthrough curves in the early region of breakthrough time for 10 types of organic vapor, and investigated the effects of moisture on estimation using the Wheeler-Jonas equation, the simulation software NIOSH MultiVapor™ 2.2.3, and RBT (Relative Breakthrough Time) proposed by Tanaka et al. Results: The Wheeler-Jonas equation showed good accordance with breakthrough curves at all RH in this study. However, the correlation coefficient decreased gradually with increasing RH regardless of type of organic vapor. Estimation of breakthrough time by MultiVapor showed good accordance with experimental data at RH=50%. In contrast, it showed discordance at high RH (>50%). RBTs reported previously were consistent with experimental data at RH=50%. On the other hand, the values of RBT changed markedly with increasing RH. Conclusions: The results of each estimation method showed good accordance with experimental data under comparatively dry conditions (RH≤50%). However, there were discrepancies under high humidified conditions, and further studies are warranted. PMID:27725483

Solutions for the diurnally forced advection-diffusion equation to estimate bulk fluid velocity and diffusivity in streambeds from temperature time series

NASA Astrophysics Data System (ADS)

Luce, C.; Tonina, D.; Gariglio, F. P.; Applebee, R.

2012-12-01

Differences in the diurnal variations of temperature at different depths in streambed sediments are commonly used for estimating vertical fluxes of water in the streambed. We applied spatial and temporal rescaling of the advection-diffusion equation to derive two new relationships that greatly extend the kinds of information that can be derived from streambed temperature measurements. The first equation provides a direct estimate of the Peclet number from the amplitude decay and phase delay information. The analytical equation is explicit (e.g. no numerical root-finding is necessary), and invertable. The thermal front velocity can be estimated from the Peclet number when the thermal diffusivity is known. The second equation allows for an independent estimate of the thermal diffusivity directly from the amplitude decay and phase delay information. Several improvements are available with the new information. The first equation uses a ratio of the amplitude decay and phase delay information; thus Peclet number calculations are independent of depth. The explicit form also makes it somewhat faster and easier to calculate estimates from a large number of sensors or multiple positions along one sensor. Where current practice requires a priori estimation of streambed thermal diffusivity, the new approach allows an independent calculation, improving precision of estimates. Furthermore, when many measurements are made over space and time, expectations of the spatial correlation and temporal invariance of thermal diffusivity are valuable for validation of measurements. Finally, the closed-form explicit solution allows for direct calculation of propagation of uncertainties in error measurements and parameter estimates, providing insight about error expectations for sensors placed at different depths in different environments as a function of surface temperature variation amplitudes. The improvements are expected to increase the utility of temperature measurement methods for studying groundwater-surface water interactions across space and time scales. We discuss the theoretical implications of the new solutions supported by examples with data for illustration and validation.

Validity of Bioelectrical Impedance Measurement in Predicting Fat-Free Mass of Chinese Children and Adolescents

PubMed Central

Wang, Lin; Hui, Stanley Sai-chuen; Wong, Stephen Heung-sang

2014-01-01

Background The current study aimed to examine the validity of various published bioelectrical impedance analysis (BIA) equations in estimating FFM among Chinese children and adolescents and to develop BIA equations for the estimation of fat-free mass (FFM) appropriate for Chinese children and adolescents. Material/Methods A total of 255 healthy Chinese children and adolescents aged 9 to 19 years old (127 males and 128 females) from Tianjin, China, participated in the BIA measurement at 50 kHz between the hand and the foot. The criterion measure of FFM was also employed using dual-energy X-ray absorptiometry (DEXA). FFM estimated from 24 published BIA equations was cross-validated against the criterion measure from DEXA. Multiple linear regression was conducted to examine alternative BIA equation for the studied population. Results FFM estimated from the 24 published BIA equations yielded high correlations with the directly measured FFM from DEXA. However, none of the 24 equations was statistically equivalent with the DEXA-measured FFM. Using multiple linear regression and cross-validation against DEXA measurement, an alternative prediction equation was determined as follows: FFM (kg)=1.613+0.742×height (cm)2/impedance (Ω)+0.151×body weight (kg); R2=0.95; SEE=2.45kg; CV=6.5, 93.7% of the residuals of all the participants fell within the 95% limits of agreement. Conclusions BIA was highly correlated with FFM in Chinese children and adolescents. When the new developed BIA equations are applied, BIA can provide a practical and valid measurement of body composition in Chinese children and adolescents. PMID:25398209

An effective solution to the nonlinear, nonstationary Navier-Stokes equations for two dimensions

NASA Technical Reports Server (NTRS)

Gabrielsen, R. E.

1975-01-01

A sequence of approximate solutions for the nonlinear, nonstationary Navier-Stokes equations for a two-dimensional domain, from which explicit error estimates and rates of convergence are obtained, is described. This sequence of approximate solutions is based primarily on the Newton-Kantorovich method.

A Leap-Frog Discontinuous Galerkin Method for the Time-Domain Maxwell's Equations in Metamaterials

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

Li, J., Waters, J. W., Machorro, E. A.

2012-06-01

Numerical simulation of metamaterials play a very important role in the design of invisibility cloak, and sub-wavelength imaging. In this paper, we propose a leap-frog discontinuous Galerkin method to solve the time-dependent Maxwell’s equations in metamaterials. Conditional stability and error estimates are proved for the scheme. The proposed algorithm is implemented and numerical results supporting the analysis are provided.

A robust and accurate numerical method for transcritical turbulent flows at supercritical pressure with an arbitrary equation of state

NASA Astrophysics Data System (ADS)

Kawai, Soshi; Terashima, Hiroshi; Negishi, Hideyo

2015-11-01

This paper addresses issues in high-fidelity numerical simulations of transcritical turbulent flows at supercritical pressure. The proposed strategy builds on a tabulated look-up table method based on REFPROP database for an accurate estimation of non-linear behaviors of thermodynamic and fluid transport properties at the transcritical conditions. Based on the look-up table method we propose a numerical method that satisfies high-order spatial accuracy, spurious-oscillation-free property, and capability of capturing the abrupt variation in thermodynamic properties across the transcritical contact surface. The method introduces artificial mass diffusivity to the continuity and momentum equations in a physically-consistent manner in order to capture the steep transcritical thermodynamic variations robustly while maintaining spurious-oscillation-free property in the velocity field. The pressure evolution equation is derived from the full compressible Navier-Stokes equations and solved instead of solving the total energy equation to achieve the spurious pressure oscillation free property with an arbitrary equation of state including the present look-up table method. Flow problems with and without physical diffusion are employed for the numerical tests to validate the robustness, accuracy, and consistency of the proposed approach.

A robust and accurate numerical method for transcritical turbulent flows at supercritical pressure with an arbitrary equation of state

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

Kawai, Soshi, E-mail: kawai@cfd.mech.tohoku.ac.jp; Terashima, Hiroshi; Negishi, Hideyo

2015-11-01

This paper addresses issues in high-fidelity numerical simulations of transcritical turbulent flows at supercritical pressure. The proposed strategy builds on a tabulated look-up table method based on REFPROP database for an accurate estimation of non-linear behaviors of thermodynamic and fluid transport properties at the transcritical conditions. Based on the look-up table method we propose a numerical method that satisfies high-order spatial accuracy, spurious-oscillation-free property, and capability of capturing the abrupt variation in thermodynamic properties across the transcritical contact surface. The method introduces artificial mass diffusivity to the continuity and momentum equations in a physically-consistent manner in order to capture themore » steep transcritical thermodynamic variations robustly while maintaining spurious-oscillation-free property in the velocity field. The pressure evolution equation is derived from the full compressible Navier–Stokes equations and solved instead of solving the total energy equation to achieve the spurious pressure oscillation free property with an arbitrary equation of state including the present look-up table method. Flow problems with and without physical diffusion are employed for the numerical tests to validate the robustness, accuracy, and consistency of the proposed approach.« less

Equations and charts for the rapid estimation of hinge-moment and effectiveness parameters for trailing-edge controls having leading and trailing edges swept ahead of the Mach lines

NASA Technical Reports Server (NTRS)

Goin, Kennith L

1951-01-01

Existing conical-flow solutions have been used to calculate the hinge-moments and effectiveness parameters of trailing-edge controls having leading and trailing edges swept ahead of the Mach lines and having streamwise root and tip chords. Equations and detailed charts are presented for the rapid estimation of these parameters. Also included is an approximate method by which these parameters may be corrected for airfoil-section thickness.

Application of mathematical model methods for optimization tasks in construction materials technology

NASA Astrophysics Data System (ADS)

Fomina, E. V.; Kozhukhova, N. I.; Sverguzova, S. V.; Fomin, A. E.

2018-05-01

In this paper, the regression equations method for design of construction material was studied. Regression and polynomial equations representing the correlation between the studied parameters were proposed. The logic design and software interface of the regression equations method focused on parameter optimization to provide the energy saving effect at the stage of autoclave aerated concrete design considering the replacement of traditionally used quartz sand by coal mining by-product such as argillite. The mathematical model represented by a quadric polynomial for the design of experiment was obtained using calculated and experimental data. This allowed the estimation of relationship between the composition and final properties of the aerated concrete. The surface response graphically presented in a nomogram allowed the estimation of concrete properties in response to variation of composition within the x-space. The optimal range of argillite content was obtained leading to a reduction of raw materials demand, development of target plastic strength of aerated concrete as well as a reduction of curing time before autoclave treatment. Generally, this method allows the design of autoclave aerated concrete with required performance without additional resource and time costs.

A Comparison of Limited-Information and Full-Information Methods in M"plus" for Estimating Item Response Theory Parameters for Nonnormal Populations

ERIC Educational Resources Information Center

DeMars, Christine E.

2012-01-01

In structural equation modeling software, either limited-information (bivariate proportions) or full-information item parameter estimation routines could be used for the 2-parameter item response theory (IRT) model. Limited-information methods assume the continuous variable underlying an item response is normally distributed. For skewed and…

Impact of Violation of the Missing-at-Random Assumption on Full-Information Maximum Likelihood Method in Multidimensional Adaptive Testing

ERIC Educational Resources Information Center

Han, Kyung T.; Guo, Fanmin

2014-01-01

The full-information maximum likelihood (FIML) method makes it possible to estimate and analyze structural equation models (SEM) even when data are partially missing, enabling incomplete data to contribute to model estimation. The cornerstone of FIML is the missing-at-random (MAR) assumption. In (unidimensional) computerized adaptive testing…

Uniqueness of solutions for Keller-Segel system of porous medium type coupled to fluid equations

NASA Astrophysics Data System (ADS)

Bae, Hantaek; Kang, Kyungkeun; Kim, Seick

2018-04-01

We prove the uniqueness of Hölder continuous weak solutions via duality argument and vanishing viscosity method for the Keller-Segel system of porous medium type equations coupled to the Stokes system in dimensions three. An important step is the estimate of the Green function of parabolic equations with lower order terms of variable coefficients, which seems to be of independent interest.

Research and Development of Methods for Estimating Physicochemical Properties of Organic Compounds of Environmental Concern

DTIC Science & Technology

1979-02-01

coefficient (at equilibrium) when hysteresis is apparent. 6. Coefficient n in Freundlich equation for 1/n soil or sediment adsorption isotherms ýX - KC . 7...Biodegradation Chemical structures cal clasaes (e.g., Diffusion Correlations phenols). General Diffusion coefficients Equations terms for organic...OF THE FATE AND TRANSPORT OF ORGANIC CHEMICALS Adsorption coefficients: K, n* from Freundlich equation + Desorption coefficients: K’*, n’* from

[Compatible biomass models of natural spruce (Picea asperata)].

PubMed

Wang, Jin Chi; Deng, Hua Feng; Huang, Guo Sheng; Wang, Xue Jun; Zhang, Lu

2017-10-01

By using nonlinear measurement error method, the compatible tree volume and above ground biomass equations were established based on the volume and biomass data of 150 sampling trees of natural spruce (Picea asperata). Two approaches, controlling directly under total aboveground biomass and controlling jointly from level to level, were used to design the compatible system for the total aboveground biomass and the biomass of four components (stem, bark, branch and foliage), and the total ground biomass could be estimated independently or estimated simultaneously in the system. The results showed that the R 2 of the one variable and bivariate compatible tree volume and aboveground biomass equations were all above 0.85, and the maximum value reached 0.99. The prediction effect of the volume equations could be improved significantly when tree height was included as predictor, while it was not significant in biomass estimation. For the compatible biomass systems, the one variable model based on controlling jointly from level to level was better than the model using controlling directly under total above ground biomass, but the bivariate models of the two methods were similar. Comparing the imitative effects of the one variable and bivariate compatible biomass models, the results showed that the increase of explainable variables could significantly improve the fitness of branch and foliage biomass, but had little effect on other components. Besides, there was almost no difference between the two methods of estimation based on the comparison.

Spinodal Decomposition for the Cahn-Hilliard Equation in Higher Dimensions.Part I: Probability and Wavelength Estimate

NASA Astrophysics Data System (ADS)

Maier-Paape, Stanislaus; Wanner, Thomas

This paper is the first in a series of two papers addressing the phenomenon of spinodal decomposition for the Cahn-Hilliard equation where , is a bounded domain with sufficiently smooth boundary, and f is cubic-like, for example f(u) =u-u3. We will present the main ideas of our approach and explain in what way our method differs from known results in one space dimension due to Grant [26]. Furthermore, we derive certain probability and wavelength estimates. The probability estimate is needed to understand why in a neighborhood of a homogeneous equilibrium u0≡μ of the Cahn-Hilliard equation, with mass μ in the spinodal region, a strongly unstable manifold has dominating effects. This is demonstrated for the linearized equation, but will be essential for the nonlinear setting in the second paper [37] as well. Moreover, we introduce the notion of a characteristic wavelength for the strongly unstable directions.

Estimation of Glomerular Filtration Rate Based on Serum Cystatin C versus Creatinine in a Uruguayan Population

PubMed Central

Lujambio, Inés; Sottolano, Mariana; Robaina, Sebastián; Carusso, Florencia; da Rosa, Alicia; Ríos, Ana Carina; Olascoaga, Alicia; Gadola, Liliana; Noboa, Oscar; Staessen, Jan A.; Boggia, José

2014-01-01

Background. Estimation of glomerular filtration rate (eGFR) from biomarkers has evolved and multiple equations are available to estimate renal function at bedside. Methods. In a random sample of 119 Uruguayans (54.5% women; 56.2 years (mean)), we used Bland and Altman's method and Cohen's kappa statistic to assess concordance on a continuous or categorical (eGFR < 60 versus ≥60 mL/min/1.73 m2) scale between eGFRcys (reference) and eGFR derived from serum creatinine according to the Modification of Diet in Renal Disease (eGFRmdrd) or the Chronic Kidney Disease Epidemiology Collaboration equations (eGFRepi) or from both serum cystatin C and creatinine (eGFRmix). Results. In all participants, eGFRmdrd, eGFRepi, and eGFRmix were, respectively, 9.7, 11.5, and 5.6 mL/min/1.73 m2 higher (P < 0.0001) than eGFRcys. The prevalence of eGFR <60 mL/min/1.73 m2 was the highest for eGFRcys (21.8%), intermediate for eGFRmix (11.8%), and the lowest for eGFRmdrd (5.9%) and eGFRepi (3.4%). Using eGFRcys as reference, we found only fair agreement with the equations based on creatinine (Cohen's kappa statistic 0.15 to 0.23). Conclusion. Using different equations we reached clinically significant differences in the estimation of renal function. eGFRcys provides lower estimates, resulting in higher prevalence of eGFR <60 mL/min/1.73 m2. PMID:25215234

Estimates of monthly streamflow characteristics at selected sites in the upper Missouri River basin, Montana, base period water years 1937-86

USGS Publications Warehouse

Parrett, Charles; Johnson, D.R.; Hull, J.A.

1989-01-01

Estimates of streamflow characteristics (monthly mean flow that is exceeded 90, 80, 50, and 20 percent of the time for all years of record and mean monthly flow) were made and are presented in tabular form for 312 sites in the Missouri River basin in Montana. Short-term gaged records were extended to the base period of water years 1937-86, and were used to estimate monthly streamflow characteristics at 100 sites. Data from 47 gaged sites were used in regression analysis relating the streamflow characteristics to basin characteristics and to active-channel width. The basin-characteristics equations, with standard errors of 35% to 97%, were used to estimate streamflow characteristics at 179 ungaged sites. The channel-width equations, with standard errors of 36% to 103%, were used to estimate characteristics at 138 ungaged sites. Streamflow measurements were correlated with concurrent streamflows at nearby gaged sites to estimate streamflow characteristics at 139 ungaged sites. In a test using 20 pairs of gages, the standard errors ranged from 31% to 111%. At 139 ungaged sites, the estimates from two or more of the methods were weighted and combined in accordance with the variance of individual methods. When estimates from three methods were combined the standard errors ranged from 24% to 63 %. A drainage-area-ratio adjustment method was used to estimate monthly streamflow characteristics at seven ungaged sites. The reliability of the drainage-area-ratio adjustment method was estimated to be about equal to that of the basin-characteristics method. The estimate were checked for reliability. Estimates of monthly streamflow characteristics from gaged records were considered to be most reliable, and estimates at sites with actual flow record from 1937-86 were considered to be completely reliable (zero error). Weighted-average estimates were considered to be the most reliable estimates made at ungaged sites. (USGS)

Estimating mean change in population salt intake using spot urine samples.

PubMed

Petersen, Kristina S; Wu, Jason H Y; Webster, Jacqui; Grimes, Carley; Woodward, Mark; Nowson, Caryl A; Neal, Bruce

2017-10-01

Spot urine samples are easier to collect than 24-h urine samples and have been used with estimating equations to derive the mean daily salt intake of a population. Whether equations using data from spot urine samples can also be used to estimate change in mean daily population salt intake over time is unknown. We compared estimates of change in mean daily population salt intake based upon 24-h urine collections with estimates derived using equations based on spot urine samples. Paired and unpaired 24-h urine samples and spot urine samples were collected from individuals in two Australian populations, in 2011 and 2014. Estimates of change in daily mean population salt intake between 2011 and 2014 were obtained directly from the 24-h urine samples and by applying established estimating equations (Kawasaki, Tanaka, Mage, Toft, INTERSALT) to the data from spot urine samples. Differences between 2011 and 2014 were calculated using mixed models. A total of 1000 participants provided a 24-h urine sample and a spot urine sample in 2011, and 1012 did so in 2014 (paired samples n = 870; unpaired samples n = 1142). The participants were community-dwelling individuals living in the State of Victoria or the town of Lithgow in the State of New South Wales, Australia, with a mean age of 55 years in 2011. The mean (95% confidence interval) difference in population salt intake between 2011 and 2014 determined from the 24-h urine samples was -0.48g/day (-0.74 to -0.21; P < 0.001). The corresponding result estimated from the spot urine samples was -0.24 g/day (-0.42 to -0.06; P = 0.01) using the Tanaka equation, -0.42 g/day (-0.70 to -0.13; p = 0.004) using the Kawasaki equation, -0.51 g/day (-1.00 to -0.01; P = 0.046) using the Mage equation, -0.26 g/day (-0.42 to -0.10; P = 0.001) using the Toft equation, -0.20 g/day (-0.32 to -0.09; P = 0.001) using the INTERSALT equation and -0.27 g/day (-0.39 to -0.15; P < 0.001) using the INTERSALT equation with potassium. There was no evidence that the changes detected by the 24-h collections and estimating equations were different (all P > 0.058). Separate analysis of the unpaired and paired data showed that detection of change by the estimating equations was observed only in the paired data. All the estimating equations based upon spot urine samples identified a similar change in daily salt intake to that detected by the 24-h urine samples. Methods based upon spot urine samples may provide an approach to measuring change in mean population salt intake, although further investigation in larger and more diverse population groups is required. © The Author 2016; all rights reserved. Published by Oxford University Press on behalf of the International Epidemiological Association

Gibbs Sampler-Based λ-Dynamics and Rao-Blackwell Estimator for Alchemical Free Energy Calculation.

PubMed

Ding, Xinqiang; Vilseck, Jonah Z; Hayes, Ryan L; Brooks, Charles L

2017-06-13

λ-dynamics is a generalized ensemble method for alchemical free energy calculations. In traditional λ-dynamics, the alchemical switch variable λ is treated as a continuous variable ranging from 0 to 1 and an empirical estimator is utilized to approximate the free energy. In the present article, we describe an alternative formulation of λ-dynamics that utilizes the Gibbs sampler framework, which we call Gibbs sampler-based λ-dynamics (GSLD). GSLD, like traditional λ-dynamics, can be readily extended to calculate free energy differences between multiple ligands in one simulation. We also introduce a new free energy estimator, the Rao-Blackwell estimator (RBE), for use in conjunction with GSLD. Compared with the current empirical estimator, the advantage of RBE is that RBE is an unbiased estimator and its variance is usually smaller than the current empirical estimator. We also show that the multistate Bennett acceptance ratio equation or the unbinned weighted histogram analysis method equation can be derived using the RBE. We illustrate the use and performance of this new free energy computational framework by application to a simple harmonic system as well as relevant calculations of small molecule relative free energies of solvation and binding to a protein receptor. Our findings demonstrate consistent and improved performance compared with conventional alchemical free energy methods.

Computed statistics at streamgages, and methods for estimating low-flow frequency statistics and development of regional regression equations for estimating low-flow frequency statistics at ungaged locations in Missouri

USGS Publications Warehouse

Southard, Rodney E.

2013-01-01

The weather and precipitation patterns in Missouri vary considerably from year to year. In 2008, the statewide average rainfall was 57.34 inches and in 2012, the statewide average rainfall was 30.64 inches. This variability in precipitation and resulting streamflow in Missouri underlies the necessity for water managers and users to have reliable streamflow statistics and a means to compute select statistics at ungaged locations for a better understanding of water availability. Knowledge of surface-water availability is dependent on the streamflow data that have been collected and analyzed by the U.S. Geological Survey for more than 100 years at approximately 350 streamgages throughout Missouri. The U.S. Geological Survey, in cooperation with the Missouri Department of Natural Resources, computed streamflow statistics at streamgages through the 2010 water year, defined periods of drought and defined methods to estimate streamflow statistics at ungaged locations, and developed regional regression equations to compute selected streamflow statistics at ungaged locations. Streamflow statistics and flow durations were computed for 532 streamgages in Missouri and in neighboring States of Missouri. For streamgages with more than 10 years of record, Kendall’s tau was computed to evaluate for trends in streamflow data. If trends were detected, the variable length method was used to define the period of no trend. Water years were removed from the dataset from the beginning of the record for a streamgage until no trend was detected. Low-flow frequency statistics were then computed for the entire period of record and for the period of no trend if 10 or more years of record were available for each analysis. Three methods are presented for computing selected streamflow statistics at ungaged locations. The first method uses power curve equations developed for 28 selected streams in Missouri and neighboring States that have multiple streamgages on the same streams. Statistical estimates on one of these streams can be calculated at an ungaged location that has a drainage area that is between 40 percent of the drainage area of the farthest upstream streamgage and within 150 percent of the drainage area of the farthest downstream streamgage along the stream of interest. The second method may be used on any stream with a streamgage that has operated for 10 years or longer and for which anthropogenic effects have not changed the low-flow characteristics at the ungaged location since collection of the streamflow data. A ratio of drainage area of the stream at the ungaged location to the drainage area of the stream at the streamgage was computed to estimate the statistic at the ungaged location. The range of applicability is between 40- and 150-percent of the drainage area of the streamgage, and the ungaged location must be located on the same stream as the streamgage. The third method uses regional regression equations to estimate selected low-flow frequency statistics for unregulated streams in Missouri. This report presents regression equations to estimate frequency statistics for the 10-year recurrence interval and for the N-day durations of 1, 2, 3, 7, 10, 30, and 60 days. Basin and climatic characteristics were computed using geographic information system software and digital geospatial data. A total of 35 characteristics were computed for use in preliminary statewide and regional regression analyses based on existing digital geospatial data and previous studies. Spatial analyses for geographical bias in the predictive accuracy of the regional regression equations defined three low-flow regions with the State representing the three major physiographic provinces in Missouri. Region 1 includes the Central Lowlands, Region 2 includes the Ozark Plateaus, and Region 3 includes the Mississippi Alluvial Plain. A total of 207 streamgages were used in the regression analyses for the regional equations. Of the 207 U.S. Geological Survey streamgages, 77 were located in Region 1, 120 were located in Region 2, and 10 were located in Region 3. Streamgages located outside of Missouri were selected to extend the range of data used for the independent variables in the regression analyses. Streamgages included in the regression analyses had 10 or more years of record and were considered to be affected minimally by anthropogenic activities or trends. Regional regression analyses identified three characteristics as statistically significant for the development of regional equations. For Region 1, drainage area, longest flow path, and streamflow-variability index were statistically significant. The range in the standard error of estimate for Region 1 is 79.6 to 94.2 percent. For Region 2, drainage area and streamflow variability index were statistically significant, and the range in the standard error of estimate is 48.2 to 72.1 percent. For Region 3, drainage area and streamflow-variability index also were statistically significant with a range in the standard error of estimate of 48.1 to 96.2 percent. Limitations on the use of estimating low-flow frequency statistics at ungaged locations are dependent on the method used. The first method outlined for use in Missouri, power curve equations, were developed to estimate the selected statistics for ungaged locations on 28 selected streams with multiple streamgages located on the same stream. A second method uses a drainage-area ratio to compute statistics at an ungaged location using data from a single streamgage on the same stream with 10 or more years of record. Ungaged locations on these streams may use the ratio of the drainage area at an ungaged location to the drainage area at a streamgage location to scale the selected statistic value from the streamgage location to the ungaged location. This method can be used if the drainage area of the ungaged location is within 40 to 150 percent of the streamgage drainage area. The third method is the use of the regional regression equations. The limits for the use of these equations are based on the ranges of the characteristics used as independent variables and that streams must be affected minimally by anthropogenic activities.

Prediction of Sublimation Pressures of Low Volatility Solids

NASA Astrophysics Data System (ADS)

Drake, Bruce Douglas

Sublimation pressures are required for solid-vapor phase equilibrium models in design of processes such as supercritical fluid extraction, sublimation purification and vapor epitaxy. The objective of this work is to identify and compare alternative methods for predicting sublimation pressures. A bibliography of recent sublimation data is included. Corresponding states methods based on the triple point (rather than critical point) are examined. A modified Trouton's rule is the preferred method for estimating triple point pressure in the absence of any sublimation data. Only boiling and melting temperatures are required. Typical error in log_{10} P _{rm triple} is 0.3. For lower temperature estimates, the slope of the sublimation curve is predicted by a correlation based on molar volume. Typical error is 10% of slope. Molecular dynamics methods for surface modeling are tested as estimators of vapor pressure. The time constants of the vapor and solid phases are too different to allow the vapor to come to thermal equilibrium with the solid. The method shows no advantages in prediction of sublimation pressure but provides insight into appropriate models and experimental methods for sublimation. Density-dependent augmented van der Waals equations of state based on hard-sphere distribution functions are examined. The perturbation term is almost linear and is well fit by a simple quadratic. Use of the equation provides reasonable fitting of sublimation pressures from one data point. Order-of-magnitude estimation is possible from melting temperature and solid molar volume. The inverse -12 fluid is used to develop an additional equation of state. Sublimation pressure results, including quality of pressure predictions, are similar to the hard-sphere results. Three-body (Axilrod -Teller) interactions are used to improve results.

Methods for estimating magnitude and frequency of peak flows for small watersheds in Utah.

DOT National Transportation Integrated Search

2010-06-01

Determining discharge in a stream is important to the design of culverts, bridges, and other structures pertaining to : transportation systems. Currently in Utah regression equations exist to estimate recurrence flood year discharges for : rural wate...

Transport parameter estimation from lymph measurements and the Patlak equation.

PubMed

Watson, P D; Wolf, M B

1992-01-01

Two methods of estimating protein transport parameters for plasma-to-lymph transport data are presented. Both use IBM-compatible computers to obtain least-squares parameters for the solvent drag reflection coefficient and the permeability-surface area product using the Patlak equation. A matrix search approach is described, and the speed and convenience of this are compared with a commercially available gradient method. The results from both of these methods were different from those of a method reported by Reed, Townsley, and Taylor [Am. J. Physiol. 257 (Heart Circ. Physiol. 26): H1037-H1041, 1989]. It is shown that the Reed et al. method contains a systematic error. It is also shown that diffusion always plays an important role for transmembrane transport at the exit end of a membrane channel under all conditions of lymph flow rate and that the statement that diffusion becomes zero at high lymph flow rate depends on a mathematical definition of diffusion.

Chandrasekhar-type algorithms for fast recursive estimation in linear systems with constant parameters

NASA Technical Reports Server (NTRS)

Choudhury, A. K.; Djalali, M.

1975-01-01

In this recursive method proposed, the gain matrix for the Kalman filter and the convariance of the state vector are computed not via the Riccati equation, but from certain other equations. These differential equations are of Chandrasekhar-type. The 'invariant imbedding' idea resulted in the reduction of the basic boundary value problem of transport theory to an equivalent initial value system, a significant computational advance. Initial value experience showed that there is some computational savings in the method and the loss of positive definiteness of the covariance matrix is less vulnerable.

Estimating Dynamical Systems: Derivative Estimation Hints from Sir Ronald A. Fisher

ERIC Educational Resources Information Center

Deboeck, Pascal R.

2010-01-01

The fitting of dynamical systems to psychological data offers the promise of addressing new and innovative questions about how people change over time. One method of fitting dynamical systems is to estimate the derivatives of a time series and then examine the relationships between derivatives using a differential equation model. One common…

What to Do about Zero Frequency Cells when Estimating Polychoric Correlations

ERIC Educational Resources Information Center

Savalei, Victoria

2011-01-01

Categorical structural equation modeling (SEM) methods that fit the model to estimated polychoric correlations have become popular in the social sciences. When population thresholds are high in absolute value, contingency tables in small samples are likely to contain zero frequency cells. Such cells make the estimation of the polychoric…

[Quantitative estimation of vegetation cover and management factor in USLE and RUSLE models by using remote sensing data: a review].

PubMed

Wu, Chang-Guang; Li, Sheng; Ren, Hua-Dong; Yao, Xiao-Hua; Huang, Zi-Jie

2012-06-01

Soil loss prediction models such as universal soil loss equation (USLE) and its revised universal soil loss equation (RUSLE) are the useful tools for risk assessment of soil erosion and planning of soil conservation at regional scale. To make a rational estimation of vegetation cover and management factor, the most important parameters in USLE or RUSLE, is particularly important for the accurate prediction of soil erosion. The traditional estimation based on field survey and measurement is time-consuming, laborious, and costly, and cannot rapidly extract the vegetation cover and management factor at macro-scale. In recent years, the development of remote sensing technology has provided both data and methods for the estimation of vegetation cover and management factor over broad geographic areas. This paper summarized the research findings on the quantitative estimation of vegetation cover and management factor by using remote sensing data, and analyzed the advantages and the disadvantages of various methods, aimed to provide reference for the further research and quantitative estimation of vegetation cover and management factor at large scale.

Evaluation of Methods Used for Estimating Selected Streamflow Statistics, and Flood Frequency and Magnitude, for Small Basins in North Coastal California

USGS Publications Warehouse

Mann, Michael P.; Rizzardo, Jule; Satkowski, Richard

2004-01-01

Accurate streamflow statistics are essential to water resource agencies involved in both science and decision-making. When long-term streamflow data are lacking at a site, estimation techniques are often employed to generate streamflow statistics. However, procedures for accurately estimating streamflow statistics often are lacking. When estimation procedures are developed, they often are not evaluated properly before being applied. Use of unevaluated or underevaluated flow-statistic estimation techniques can result in improper water-resources decision-making. The California State Water Resources Control Board (SWRCB) uses two key techniques, a modified rational equation and drainage basin area-ratio transfer, to estimate streamflow statistics at ungaged locations. These techniques have been implemented to varying degrees, but have not been formally evaluated. For estimating peak flows at the 2-, 5-, 10-, 25-, 50-, and 100-year recurrence intervals, the SWRCB uses the U.S. Geological Surveys (USGS) regional peak-flow equations. In this study, done cooperatively by the USGS and SWRCB, the SWRCB estimated several flow statistics at 40 USGS streamflow gaging stations in the north coast region of California. The SWRCB estimates were made without reference to USGS flow data. The USGS used the streamflow data provided by the 40 stations to generate flow statistics that could be compared with SWRCB estimates for accuracy. While some SWRCB estimates compared favorably with USGS statistics, results were subject to varying degrees of error over the region. Flow-based estimation techniques generally performed better than rain-based methods, especially for estimation of December 15 to March 31 mean daily flows. The USGS peak-flow equations also performed well, but tended to underestimate peak flows. The USGS equations performed within reported error bounds, but will require updating in the future as peak-flow data sets grow larger. Little correlation was discovered between estimation errors and geographic locations or various basin characteristics. However, for 25-percentile year mean-daily-flow estimates for December 15 to March 31, the greatest estimation errors were at east San Francisco Bay area stations with mean annual precipitation less than or equal to 30 inches, and estimated 2-year/24-hour rainfall intensity less than 3 inches.

Oscillations and Rolling for Duffing's Equation

NASA Astrophysics Data System (ADS)

Aref'eva, I. Ya.; Piskovskiy, E. V.; Volovich, I. V.

2013-01-01

The Duffing equation has been used to model nonlinear dynamics not only in mechanics and electronics but also in biology and in neurology for the brain process modeling. Van der Pol's method is often used in nonlinear dynamics to improve perturbation theory results when describing small oscillations. However, in some other problems of nonlinear dynamics particularly in case of Duffing-Higgs equation in field theory, for the Einsten-Friedmann equations in cosmology and for relaxation processes in neurology not only small oscillations regime is of interest but also the regime of slow rolling. In the present work a method for approximate solution to nonlinear dynamics equations in the rolling regime is developed. It is shown that in order to improve perturbation theory in the rolling regime it turns out to be effective to use an expansion in hyperbolic functions instead of trigonometric functions as it is done in van der Pol's method in case of small oscillations. In particular the Duffing equation in the rolling regime is investigated using solution expressed in terms of elliptic functions. Accuracy of obtained approximation is estimated. The Duffing equation with dissipation is also considered.

Stature in archeological samples from central Italy: methodological issues and diachronic changes.

PubMed

Giannecchini, Monica; Moggi-Cecchi, Jacopo

2008-03-01

Stature reconstructions from skeletal remains are usually obtained through regression equations based on the relationship between height and limb bone length. Different equations have been employed to reconstruct stature in skeletal samples, but this is the first study to provide a systematic analysis of the reliability of the different methods for Italian historical samples. Aims of this article are: 1) to analyze the reliability of different regression methods to estimate stature for populations living in Central Italy from the Iron Age to Medieval times; 2) to search for trends in stature over this time period by applying the most reliable regression method. Long bone measurements were collected from 1,021 individuals (560 males, 461 females), from 66 archeological sites for males and 54 for females. Three time periods were identified: Iron Age, Roman period, and Medieval period. To determine the most appropriate equation to reconstruct stature the Delta parameter of Gini (Memorie di metodologia statistica. Milano: Giuffre A. 1939), in which stature estimates derived from different limb bones are compared, was employed. The equations proposed by Pearson (Philos Trans R Soc London 192 (1899) 169-244) and Trotter and Gleser for Afro-Americans (Am J Phys Anthropol 10 (1952) 463-514; Am J Phys Anthropol 47 (1977) 355-356) provided the most consistent estimates when applied to our sample. We then used the equation by Pearson for further analyses. Results indicate a reduction in stature in the transition from the Iron Age to the Roman period, and a subsequent increase in the transition from the Roman period to the Medieval period. Changes of limb lengths over time were more pronounced in the distal than in the proximal elements in both limbs. 2007 Wiley-Liss, Inc.

A new experimental method for determining local airloads on rotor blades in forward flight

NASA Astrophysics Data System (ADS)

Berton, E.; Maresca, C.; Favier, D.

This paper presents a new approach for determining local airloads on helicopter rotor blade sections in forward flight. The method is based on the momentum equation in which all the terms are expressed by means of the velocity field measured by a laser Doppler velocimeter. The relative magnitude of the different terms involved in the momentum and Bernoulli equations is estimated and the results are encouraging.

Space-dependent perfusion coefficient estimation in a 2D bioheat transfer problem

NASA Astrophysics Data System (ADS)

Bazán, Fermín S. V.; Bedin, Luciano; Borges, Leonardo S.

2017-05-01

In this work, a method for estimating the space-dependent perfusion coefficient parameter in a 2D bioheat transfer model is presented. In the method, the bioheat transfer model is transformed into a time-dependent semidiscrete system of ordinary differential equations involving perfusion coefficient values as parameters, and the estimation problem is solved through a nonlinear least squares technique. In particular, the bioheat problem is solved by the method of lines based on a highly accurate pseudospectral approach, and perfusion coefficient values are estimated by the regularized Gauss-Newton method coupled with a proper regularization parameter. The performance of the method on several test problems is illustrated numerically.

Alpha models for rotating Navier-Stokes equations in geophysics with nonlinear dispersive regularization

NASA Astrophysics Data System (ADS)

Kim, Bong-Sik

Three dimensional (3D) Navier-Stokes-alpha equations are considered for uniformly rotating geophysical fluid flows (large Coriolis parameter f = 2O). The Navier-Stokes-alpha equations are a nonlinear dispersive regularization of usual Navier-Stokes equations obtained by Lagrangian averaging. The focus is on the existence and global regularity of solutions of the 3D rotating Navier-Stokes-alpha equations and the uniform convergence of these solutions to those of the original 3D rotating Navier-Stokes equations for large Coriolis parameters f as alpha → 0. Methods are based on fast singular oscillating limits and results are obtained for periodic boundary conditions for all domain aspect ratios, including the case of three wave resonances which yields nonlinear "2½-dimensional" limit resonant equations for f → 0. The existence and global regularity of solutions of limit resonant equations is established, uniformly in alpha. Bootstrapping from global regularity of the limit equations, the existence of a regular solution of the full 3D rotating Navier-Stokes-alpha equations for large f for an infinite time is established. Then, the uniform convergence of a regular solution of the 3D rotating Navier-Stokes-alpha equations (alpha ≠ 0) to the one of the original 3D rotating NavierStokes equations (alpha = 0) for f large but fixed as alpha → 0 follows; this implies "shadowing" of trajectories of the limit dynamical systems by those of the perturbed alpha-dynamical systems. All the estimates are uniform in alpha, in contrast with previous estimates in the literature which blow up as alpha → 0. Finally, the existence of global attractors as well as exponential attractors is established for large f and the estimates are uniform in alpha.

Working covariance model selection for generalized estimating equations.

PubMed

Carey, Vincent J; Wang, You-Gan

2011-11-20

We investigate methods for data-based selection of working covariance models in the analysis of correlated data with generalized estimating equations. We study two selection criteria: Gaussian pseudolikelihood and a geodesic distance based on discrepancy between model-sensitive and model-robust regression parameter covariance estimators. The Gaussian pseudolikelihood is found in simulation to be reasonably sensitive for several response distributions and noncanonical mean-variance relations for longitudinal data. Application is also made to a clinical dataset. Assessment of adequacy of both correlation and variance models for longitudinal data should be routine in applications, and we describe open-source software supporting this practice. Copyright © 2011 John Wiley & Sons, Ltd.

Robust Maneuvering Envelope Estimation Based on Reachability Analysis in an Optimal Control Formulation

NASA Technical Reports Server (NTRS)

Lombaerts, Thomas; Schuet, Stefan R.; Wheeler, Kevin; Acosta, Diana; Kaneshige, John

2013-01-01

This paper discusses an algorithm for estimating the safe maneuvering envelope of damaged aircraft. The algorithm performs a robust reachability analysis through an optimal control formulation while making use of time scale separation and taking into account uncertainties in the aerodynamic derivatives. Starting with an optimal control formulation, the optimization problem can be rewritten as a Hamilton- Jacobi-Bellman equation. This equation can be solved by level set methods. This approach has been applied on an aircraft example involving structural airframe damage. Monte Carlo validation tests have confirmed that this approach is successful in estimating the safe maneuvering envelope for damaged aircraft.

Petrophysical approach for S-wave velocity prediction based on brittleness index and total organic carbon of shale gas reservoir: A case study from Horn River Basin, Canada

NASA Astrophysics Data System (ADS)

Kim, Taeyoun; Hwang, Seho; Jang, Seonghyung

2017-01-01

When finding the "sweet spot" of a shale gas reservoir, it is essential to estimate the brittleness index (BI) and total organic carbon (TOC) of the formation. Particularly, the BI is one of the key factors in determining the crack propagation and crushing efficiency for hydraulic fracturing. There are several methods for estimating the BI of a formation, but most of them are empirical equations that are specific to particular rock types. We estimated the mineralogical BI based on elemental capture spectroscopy (ECS) log and elastic BI based on well log data, and we propose a new method for predicting S-wave velocity (VS) using mineralogical BI and elastic BI. The TOC is related to the gas content of shale gas reservoirs. Since it is difficult to perform core analysis for all intervals of shale gas reservoirs, we make empirical equations for the Horn River Basin, Canada, as well as TOC log using a linear relation between core-tested TOC and well log data. In addition, two empirical equations have been suggested for VS prediction based on density and gamma ray log used for TOC analysis. By applying the empirical equations proposed from the perspective of BI and TOC to another well log data and then comparing predicted VS log with real VS log, the validity of empirical equations suggested in this paper has been tested.

Estimation of Fat-free Mass at Discharge in Preterm Infants Fed With Optimized Feeding Regimen.

PubMed

Larcade, Julie; Pradat, Pierre; Buffin, Rachel; Leick-Courtois, Charline; Jourdes, Emilie; Picaud, Jean-Charles

2017-01-01

The purpose of the present study was to validate a previously calculated equation (E1) that estimates infant fat-free mass (FFM) at discharge using data from a population of preterm infants receiving an optimized feeding regimen. Preterm infants born before 33 weeks of gestation between April 2014 and November 2015 in the tertiary care unit of Croix-Rousse Hospital in Lyon, France, were included in the study. At discharge, FFM was assessed by air displacement plethysmography (PEA POD) and was compared with FFM estimated by E1. FFM was estimated using a multiple linear regression model. Data on 155 preterm infants were collected. There was a strong correlation between the FFM estimated by E1 and FFM assessed by the PEA POD (r = 0.939). E1, however, underestimated the FFM (average difference: -197 g), and this underestimation increased as FFM increased. A new, more predictive equation is proposed (r = 0.950, average difference: -12 g). Although previous estimation methods were useful for estimating FFM at discharge, an equation adapted to present populations of preterm infants with "modern" neonatal care and nutritional practices is required for accuracy.

Evaluation of an Approximate Method for Synthesizing Covariance Matrices for Use in Meta-Analytic SEM

ERIC Educational Resources Information Center

Beretvas, S. Natasha; Furlow, Carolyn F.

2006-01-01

Meta-analytic structural equation modeling (MA-SEM) is increasingly being used to assess model-fit for variables' interrelations synthesized across studies. MA-SEM researchers have analyzed synthesized correlation matrices using structural equation modeling (SEM) estimation that is designed for covariance matrices. This can produce incorrect…

Reliability of tanoak volume equations when applied to different areas

Treesearch

Norman H. Pillsbury; Philip M. McDonald; Victor Simon

1995-01-01

Tree volume equations for tanoak (Lithocarpus densiflorus) were developed for seven stands throughout its natural range and compared by a volume prediction and a parameter difference method. The objective was to test if volume estimates from a species growing in a local, relatively uniform habitat could be applied more widely. Results indicated...

Simplified Equations to Estimate Flushline Diameter for Subsurface Drip Irrigation Systems

USDA-ARS?s Scientific Manuscript database

A formulation of the Hazen-Williams equation is typically used to determine the diameter of the common flushline that is often used at the distal end of subsurface drip irrigation systems to aid in joint flushing of a group of driplines. Although this method is accurate, its usage is not intuitive a...

Equations for estimating bankfull channel geometry and discharge for streams in Massachusetts

USGS Publications Warehouse

Bent, Gardner C.; Waite, Andrew M.

2013-01-01

Regression equations were developed for estimating bankfull geometry—width, mean depth, cross-sectional area—and discharge for streams in Massachusetts. The equations provide water-resource and conservation managers with methods for estimating bankfull characteristics at specific stream sites in Massachusetts. This information can be used for the adminstration of the Commonwealth of Massachusetts Rivers Protection Act of 1996, which establishes a protected riverfront area extending from the mean annual high-water line corresponding to the elevation of bankfull discharge along each side of a perennial stream. Additionally, information on bankfull channel geometry and discharge are important to Federal, State, and local government agencies and private organizations involved in stream assessment and restoration projects. Regression equations are based on data from stream surveys at 33 sites (32 streamgages and 1 crest-stage gage operated by the U.S. Geological Survey) in and near Massachusetts. Drainage areas of the 33 sites ranged from 0.60 to 329 square miles (mi2). At 27 of the 33 sites, field data were collected and analyses were done to determine bankfull channel geometry and discharge as part of the present study. For 6 of the 33 sites, data on bankfull channel geometry and discharge were compiled from other studies done by the U.S. Geological Survey, Natural Resources Conservation Service of the U.S. Department of Agriculture, and the Vermont Department of Environmental Conservation. Similar techniques were used for field data collection and analysis for bankfull channel geometry and discharge at all 33 sites. Recurrence intervals of the bankfull discharge, which represent the frequency with which a stream fills its channel, averaged 1.53 years (median value 1.34 years) at the 33 sites. Simple regression equations were developed for bankfull width, mean depth, cross-sectional area, and discharge using drainage area, which is the most significant explanatory variable in estimating these bankfull characteristics. The use of drainage area as an explanatory variable is also the most commonly published method for estimating these bankfull characteristics. Regional curves (graphic plots) of bankfull channel geometry and discharge by drainage area are presented. The regional curves are based on the simple regression equations and can be used to estimate bankfull characteristics from drainage area. Multiple regression analysis, which includes basin characteristics in addition to drainage area, also was used to develop equations. Variability in bankfull width, mean depth, cross-sectional area, and discharge was more fully explained by the multiple regression equations that include mean-basin slope and drainage area than was explained by equations based on drainage area alone. The Massachusetts regional curves and equations developed in this study are similar, in terms of values of slopes and intercepts, to those developed for other parts of the northeastern United States. Limitations associated with site selection and development of the equations resulted in some constraints for the application of equations and regional curves presented in this report. The curves and equations are applicable to stream sites that have (1) less than about 25 percent of their drainage basin area occupied by urban land use (commercial, industrial, transportation, and high-density residential), (2) little to no streamflow regulation, especially from flood-control structures, (3) drainage basin areas greater than 0.60 mi2 and less than 329 mi2, and (4) a mean basin slope greater than 2.2 percent and less than 23.9 percent. The equations may not be applicable where streams flow through extensive wetlands. The equations also may not apply in areas of Cape Cod and the Islands and the area of southeastern Massachusetts close to Cape Cod with extensive areas of coarse-grained glacial deposits where none of the study sites are located. Regardless of the setting, the regression equations are not intended for use as the sole method of estimating bankfull characteristics; however, they may supplement field identification of the bankfull channel when used in conjunction with field verified bankfull indicators, flood-frequency analysis, or other supporting evidence.

Validation of Field Methods to Assess Body Fat Percentage in Elite Youth Soccer Players.

PubMed

Munguia-Izquierdo, Diego; Suarez-Arrones, Luis; Di Salvo, Valter; Paredes-Hernandez, Victor; Alcazar, Julian; Ara, Ignacio; Kreider, Richard; Mendez-Villanueva, Alberto

2018-05-01

This study determined the most effective field method for quantifying body fat percentage in male elite youth soccer players and developed prediction equations based on anthropometric variables. Forty-four male elite-standard youth soccer players aged 16.3-18.0 years underwent body fat percentage assessments, including bioelectrical impedance analysis and the calculation of various skinfold-based prediction equations. Dual X-ray absorptiometry provided a criterion measure of body fat percentage. Correlation coefficients, bias, limits of agreement, and differences were used as validity measures, and regression analyses were used to develop soccer-specific prediction equations. The equations from Sarria et al. (1998) and Durnin & Rahaman (1967) reached very large correlations and the lowest biases, and they reached neither the practically worthwhile difference nor the substantial difference between methods. The new youth soccer-specific skinfold equation included a combination of triceps and supraspinale skinfolds. None of the practical methods compared in this study are adequate for estimating body fat percentage in male elite youth soccer players, except for the equations from Sarria et al. (1998) and Durnin & Rahaman (1967). The new youth soccer-specific equation calculated in this investigation is the only field method specifically developed and validated in elite male players, and it shows potentially good predictive power. © Georg Thieme Verlag KG Stuttgart · New York.

Entropy Splitting for High Order Numerical Simulation of Vortex Sound at Low Mach Numbers

NASA Technical Reports Server (NTRS)

Mueller, B.; Yee, H. C.; Mansour, Nagi (Technical Monitor)

2001-01-01

A method of minimizing numerical errors, and improving nonlinear stability and accuracy associated with low Mach number computational aeroacoustics (CAA) is proposed. The method consists of two levels. From the governing equation level, we condition the Euler equations in two steps. The first step is to split the inviscid flux derivatives into a conservative and a non-conservative portion that satisfies a so called generalized energy estimate. This involves the symmetrization of the Euler equations via a transformation of variables that are functions of the physical entropy. Owing to the large disparity of acoustic and stagnation quantities in low Mach number aeroacoustics, the second step is to reformulate the split Euler equations in perturbation form with the new unknowns as the small changes of the conservative variables with respect to their large stagnation values. From the numerical scheme level, a stable sixth-order central interior scheme with a third-order boundary schemes that satisfies the discrete analogue of the integration-by-parts procedure used in the continuous energy estimate (summation-by-parts property) is employed.

August Median Streamflow on Ungaged Streams in Eastern Aroostook County, Maine

USGS Publications Warehouse

Lombard, Pamela J.; Tasker, Gary D.; Nielsen, Martha G.

2003-01-01

Methods for estimating August median streamflow were developed for ungaged, unregulated streams in the eastern part of Aroostook County, Maine, with drainage areas from 0.38 to 43 square miles and mean basin elevations from 437 to 1,024 feet. Few long-term, continuous-record streamflow-gaging stations with small drainage areas were available from which to develop the equations; therefore, 24 partial-record gaging stations were established in this investigation. A mathematical technique for estimating a standard low-flow statistic, August median streamflow, at partial-record stations was applied by relating base-flow measurements at these stations to concurrent daily flows at nearby long-term, continuous-record streamflow- gaging stations (index stations). Generalized least-squares regression analysis (GLS) was used to relate estimates of August median streamflow at gaging stations to basin characteristics at these same stations to develop equations that can be applied to estimate August median streamflow on ungaged streams. GLS accounts for varying periods of record at the gaging stations and the cross correlation of concurrent streamflows among gaging stations. Twenty-three partial-record stations and one continuous-record station were used for the final regression equations. The basin characteristics of drainage area and mean basin elevation are used in the calculated regression equation for ungaged streams to estimate August median flow. The equation has an average standard error of prediction from -38 to 62 percent. A one-variable equation uses only drainage area to estimate August median streamflow when less accuracy is acceptable. This equation has an average standard error of prediction from -40 to 67 percent. Model error is larger than sampling error for both equations, indicating that additional basin characteristics could be important to improved estimates of low-flow statistics. Weighted estimates of August median streamflow, which can be used when making estimates at partial-record or continuous-record gaging stations, range from 0.03 to 11.7 cubic feet per second or from 0.1 to 0.4 cubic feet per second per square mile. Estimates of August median streamflow on ungaged streams in the eastern part of Aroostook County, within the range of acceptable explanatory variables, range from 0.03 to 30 cubic feet per second or 0.1 to 0.7 cubic feet per second per square mile. Estimates of August median streamflow per square mile of drainage area generally increase as mean elevation and drainage area increase.

A model and variance reduction method for computing statistical outputs of stochastic elliptic partial differential equations

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

Vidal-Codina, F., E-mail: fvidal@mit.edu; Nguyen, N.C., E-mail: cuongng@mit.edu; Giles, M.B., E-mail: mike.giles@maths.ox.ac.uk

We present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the hybridizable discontinuous Galerkin (HDG) discretization of elliptic partial differential equations (PDEs), which allows us to obtain high-order accurate solutions of the governing PDE; (2) the reduced basis method for a new HDG discretization of the underlying PDE to enable real-time solution of the parameterized PDE in the presence of stochastic parameters; and (3) a multilevel variance reduction method that exploits the statistical correlation among the different reduced basismore » approximations and the high-fidelity HDG discretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the reduced basis approximations. Furthermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the reduced basis approximations and the sizes of Monte Carlo samples to achieve a given error tolerance. We provide numerical examples to demonstrate the performance of the proposed method.« less

Estimating peak discharges, flood volumes, and hydrograph shapes of small ungaged urban streams in Ohio

USGS Publications Warehouse

Sherwood, J.M.

1986-01-01

Methods are presented for estimating peak discharges, flood volumes and hydrograph shapes of small (less than 5 sq mi) urban streams in Ohio. Examples of how to use the various regression equations and estimating techniques also are presented. Multiple-regression equations were developed for estimating peak discharges having recurrence intervals of 2, 5, 10, 25, 50, and 100 years. The significant independent variables affecting peak discharge are drainage area, main-channel slope, average basin-elevation index, and basin-development factor. Standard errors of regression and prediction for the peak discharge equations range from +/-37% to +/-41%. An equation also was developed to estimate the flood volume of a given peak discharge. Peak discharge, drainage area, main-channel slope, and basin-development factor were found to be the significant independent variables affecting flood volumes for given peak discharges. The standard error of regression for the volume equation is +/-52%. A technique is described for estimating the shape of a runoff hydrograph by applying a specific peak discharge and the estimated lagtime to a dimensionless hydrograph. An equation for estimating the lagtime of a basin was developed. Two variables--main-channel length divided by the square root of the main-channel slope and basin-development factor--have a significant effect on basin lagtime. The standard error of regression for the lagtime equation is +/-48%. The data base for the study was established by collecting rainfall-runoff data at 30 basins distributed throughout several metropolitan areas of Ohio. Five to eight years of data were collected at a 5-min record interval. The USGS rainfall-runoff model A634 was calibrated for each site. The calibrated models were used in conjunction with long-term rainfall records to generate a long-term streamflow record for each site. Each annual peak-discharge record was fitted to a Log-Pearson Type III frequency curve. Multiple-regression techniques were then used to analyze the peak discharge data as a function of the basin characteristics of the 30 sites. (Author 's abstract)

Evaluation of drainage-area ratio method used to estimate streamflow for the Red River of the North Basin, North Dakota and Minnesota

USGS Publications Warehouse

Emerson, Douglas G.; Vecchia, Aldo V.; Dahl, Ann L.

2005-01-01

The drainage-area ratio method commonly is used to estimate streamflow for sites where no streamflow data were collected. To evaluate the validity of the drainage-area ratio method and to determine if an improved method could be developed to estimate streamflow, a multiple-regression technique was used to determine if drainage area, main channel slope, and precipitation were significant variables for estimating streamflow in the Red River of the North Basin. A separate regression analysis was performed for streamflow for each of three seasons-- winter, spring, and summer. Drainage area and summer precipitation were the most significant variables. However, the regression equations generally overestimated streamflows for North Dakota stations and underestimated streamflows for Minnesota stations. To correct the bias in the residuals for the two groups of stations, indicator variables were included to allow both the intercept and the coefficient for the logarithm of drainage area to depend on the group. Drainage area was the only significant variable in the revised regression equations. The exponents for the drainage-area ratio were 0.85 for the winter season, 0.91 for the spring season, and 1.02 for the summer season.

Causal mediation analysis with a latent mediator.

PubMed

Albert, Jeffrey M; Geng, Cuiyu; Nelson, Suchitra

2016-05-01

Health researchers are often interested in assessing the direct effect of a treatment or exposure on an outcome variable, as well as its indirect (or mediation) effect through an intermediate variable (or mediator). For an outcome following a nonlinear model, the mediation formula may be used to estimate causally interpretable mediation effects. This method, like others, assumes that the mediator is observed. However, as is common in structural equations modeling, we may wish to consider a latent (unobserved) mediator. We follow a potential outcomes framework and assume a generalized structural equations model (GSEM). We provide maximum-likelihood estimation of GSEM parameters using an approximate Monte Carlo EM algorithm, coupled with a mediation formula approach to estimate natural direct and indirect effects. The method relies on an untestable sequential ignorability assumption; we assess robustness to this assumption by adapting a recently proposed method for sensitivity analysis. Simulation studies show good properties of the proposed estimators in plausible scenarios. Our method is applied to a study of the effect of mother education on occurrence of adolescent dental caries, in which we examine possible mediation through latent oral health behavior. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

A multiple linear regression analysis of hot corrosion attack on a series of nickel base turbine alloys

NASA Technical Reports Server (NTRS)

Barrett, C. A.

1985-01-01

Multiple linear regression analysis was used to determine an equation for estimating hot corrosion attack for a series of Ni base cast turbine alloys. The U transform (i.e., 1/sin (% A/100) to the 1/2) was shown to give the best estimate of the dependent variable, y. A complete second degree equation is described for the centered" weight chemistries for the elements Cr, Al, Ti, Mo, W, Cb, Ta, and Co. In addition linear terms for the minor elements C, B, and Zr were added for a basic 47 term equation. The best reduced equation was determined by the stepwise selection method with essentially 13 terms. The Cr term was found to be the most important accounting for 60 percent of the explained variability hot corrosion attack.

77 FR 51477 - 2012 Technical Corrections, Clarifying and Other Amendments to the Greenhouse Gas Reporting Rule...

Federal Register 2010, 2011, 2012, 2013, 2014

2012-08-24

... Equation W-7 to allow for reporters to use alternative methods such as engineering estimates based on best... requirement in 40 CFR 98.236 for reporting of ``annual throughput as determined by engineering estimate based...

[Theory, method and application of method R on estimation of (co)variance components].

PubMed

Liu, Wen-Zhong

2004-07-01

Theory, method and application of Method R on estimation of (co)variance components were reviewed in order to make the method be reasonably used. Estimation requires R values,which are regressions of predicted random effects that are calculated using complete dataset on predicted random effects that are calculated using random subsets of the same data. By using multivariate iteration algorithm based on a transformation matrix,and combining with the preconditioned conjugate gradient to solve the mixed model equations, the computation efficiency of Method R is much improved. Method R is computationally inexpensive,and the sampling errors and approximate credible intervals of estimates can be obtained. Disadvantages of Method R include a larger sampling variance than other methods for the same data,and biased estimates in small datasets. As an alternative method, Method R can be used in larger datasets. It is necessary to study its theoretical properties and broaden its application range further.

Evaluation of various equations for estimating renal function in elderly Chinese patients with type 2 diabetes mellitus

PubMed Central

Guo, Mei; Niu, Jian-Ying; Ye, Xian-Wu; Han, Xiao-Jie; Zha, Ying; Hong, Yang; Fang, Hong; Gu, Yong

2017-01-01

Background The clinical assessment of kidney function based on the estimated glomerular filtration rate (GFR) in older patients remains controversial. This study evaluated the concordance and feasibility of using various creatinine-based equations for estimating GFR in elderly Chinese patients with type 2 diabetes mellitus (T2DM). Methods A cross-sectional analytical study was conducted in 21,723 older diabetic patients (≥60 years) based on electronic health records (EHR) for Minhang District, Shanghai, China. The concordance of chronic kidney disease (CKD) classification among different creatinine-based equations was assessed based on Kappa values, intraclass correlation coefficient (ICC) statistics, and the eGFR agreement between the equations was tested using Bland–Altman plots. The GFR was estimated using the Cockcroft–Gault (CG), Berlin Initiative Study 1 (BIS1), simplified Modification of Diet in Renal Disease (MDRD), MDRD modified for Chinese populations (mMDRD), chronic kidney disease epidemiology collaboration (CKD-EPI), CKD-EPI in Asians (CKD-EPI-Asia), and Ruijin equations. Results Overall, the proportion of CKD stages 3–5 (eGFR <60 mL/min/1.73 m2) was calculated as 28.9%, 39.1%, 11.8%, 8.4%, 14.3%, 11.5%, and 12.7% by the eGFRCG, eGFRBIS1, eGFRMDRD, eGFRmMDRD, eGFRCKD-EPI, eGFRCKD-EPI-Asia, and eGFRRuijin equations, respectively. The concordance of albuminuria and decreased eGFR based on the different equations was poor by both the Kappa (<0.2) and ICC (<0.4) statistics. The CKD-EPI-Asia equation resulted in excellent concordance with the CKD-EPI (ICC =0.931), MDRD (ICC =0.963), mMDRD (ICC =0.892), and Ruijin (ICC =0.956) equations for the classification of CKD stages, whereas the BIS1 equation exhibited good concordance with the CG equation (ICC =0.809). In addition, significant differences were observed for CKD stage 1 among all these equations. Conclusion Accurate GFR values are difficult to estimate using creatinine-based equations in older diabetic patients. Kidney function is complex, and the staff need to be aware of the individualized consideration of other risk factors or markers of reduced renal function in clinical practice. PMID:29070944

Methods for estimating magnitude and frequency of floods in Montana based on data through 1983

USGS Publications Warehouse

Omang, R.J.; Parrett, Charles; Hull, J.A.

1986-01-01

Equations are presented for estimating flood magnitudes for ungaged sites in Montana based on data through 1983. The State was divided into eight regions based on hydrologic conditions, and separate multiple regression equations were developed for each region. These equations relate annual flood magnitudes and frequencies to basin characteristics and are applicable only to natural flow streams. In three of the regions, equations also were developed relating flood magnitudes and frequencies to basin characteristics and channel geometry measurements. The standard errors of estimate for an exceedance probability of 1% ranged from 39% to 87%. Techniques are described for estimating annual flood magnitude and flood frequency information at ungaged sites based on data from gaged sites on the same stream. Included are curves relating flood frequency information to drainage area for eight major streams in the State. Maximum known flood magnitudes in Montana are compared with estimated 1 %-chance flood magnitudes and with maximum known floods in the United States. Values of flood magnitudes for selected exceedance probabilities and values of significant basin characteristics and channel geometry measurements for all gaging stations used in the analysis are tabulated. Included are 375 stations in Montana and 28 nearby stations in Canada and adjoining States. (Author 's abstract)

On the Analysis of Multistep-Out-of-Grid Method for Celestial Mechanics Tasks

NASA Astrophysics Data System (ADS)

Olifer, L.; Choliy, V.

2016-09-01

Occasionally, there is a necessity in high-accurate prediction of celestial body trajectory. The most common way to do that is to solve Kepler's equation analytically or to use Runge-Kutta or Adams integrators to solve equation of motion numerically. For low-orbit satellites, there is a critical need in accounting geopotential and another forces which influence motion. As the result, the right side of equation of motion becomes much bigger, and classical integrators will not be quite effective. On the other hand, there is a multistep-out-of-grid (MOG) method which combines Runge-Kutta and Adams methods. The MOG method is based on using m on-grid values of the solution and n × m off-grid derivative estimations. Such method could provide stable integrators of maximum possible order, O (hm+mn+n-1). The main subject of this research was to implement and analyze the MOG method for solving satellite equation of motion with taking into account Earth geopotential model (ex. EGM2008 (Pavlis at al., 2008)) and with possibility to add other perturbations such as atmospheric drag or solar radiation pressure. Simulations were made for satellites on low orbit and with various eccentricities (from 0.1 to 0.9). Results of the MOG integrator were compared with results of Runge-Kutta and Adams integrators. It was shown that the MOG method has better accuracy than classical ones of the same order and less right-hand value estimations when is working on high orders. That gives it some advantage over "classical" methods.

Non-invasive pressure difference estimation from PC-MRI using the work-energy equation

PubMed Central

Donati, Fabrizio; Figueroa, C. Alberto; Smith, Nicolas P.; Lamata, Pablo; Nordsletten, David A.

2015-01-01

Pressure difference is an accepted clinical biomarker for cardiovascular disease conditions such as aortic coarctation. Currently, measurements of pressure differences in the clinic rely on invasive techniques (catheterization), prompting development of non-invasive estimates based on blood flow. In this work, we propose a non-invasive estimation procedure deriving pressure difference from the work-energy equation for a Newtonian fluid. Spatial and temporal convergence is demonstrated on in silico Phase Contrast Magnetic Resonance Image (PC-MRI) phantoms with steady and transient flow fields. The method is also tested on an image dataset generated in silico from a 3D patient-specific Computational Fluid Dynamics (CFD) simulation and finally evaluated on a cohort of 9 subjects. The performance is compared to existing approaches based on steady and unsteady Bernoulli formulations as well as the pressure Poisson equation. The new technique shows good accuracy, robustness to noise, and robustness to the image segmentation process, illustrating the potential of this approach for non-invasive pressure difference estimation. PMID:26409245

Estimation of true serum thyroglobulin concentration using simultaneous measurement of serum antithyroglobulin antibody.

PubMed

Ahn, Byeong-Cheol; Lee, Won Kee; Jeong, Shin Young; Lee, Sang-Woo; Lee, Jaetae

2013-01-01

We investigated the analytical interference of antithyroglobulin antibody (TgAb) to thyroglobulin (Tg) measurement and tried to convert measured Tg concentration to true Tg concentration using a mathematical equation which includes a concentration of TgAb. Methods. Tg was measured by immunoradiometric assay and TgAb by radioimmunoassy. Experimental samples were produced by mixing Tg and TgAb standard solutions or mixing patients' serum with high Tg or high TgAb. Mathematical equations for prediction of expected Tg concentration with measured Tg and TgAb concentrations were deduced. The Tg concentration calculated using the equations was compared with the expected Tg concentration. Results. Measured Tg concentrations of samples having high TgAb were significantly lower than their expected Tg concentration. Magnitude of TgAb interference with the Tg assay showed a positive correlation with concentration of TgAb. Mathematical equations for estimation of expected Tg concentration using measured Tg and TgAb concentrations were successfully deduced and the calculated Tg concentration showed excellent correlation with expected Tg concentration. Conclusions. A mathematic equation for estimation of true Tg concentration using measured Tg and TgAb concentration was deduced. Tg concentration calculated by use of the equation might be more valuable than measured Tg concentration in patients with differentiated thyroid cancer.

Improved Estimates of Thermodynamic Parameters

NASA Technical Reports Server (NTRS)

Lawson, D. D.

1982-01-01

Techniques refined for estimating heat of vaporization and other parameters from molecular structure. Using parabolic equation with three adjustable parameters, heat of vaporization can be used to estimate boiling point, and vice versa. Boiling points and vapor pressures for some nonpolar liquids were estimated by improved method and compared with previously reported values. Technique for estimating thermodynamic parameters should make it easier for engineers to choose among candidate heat-exchange fluids for thermochemical cycles.

Reference breast temperature: proposal of an equation

PubMed Central

de Souza, Gladis Aparecida Galindo Reisemberger; Brioschi, Marcos Leal; Vargas, José Viriato Coelho; Morais, Keli Cristiane Correia; Dalmaso, Carlos; Neves, Eduardo Borba

2015-01-01

ABSTRACT Objective To develop an equation to estimate the breast reference temperature according to the variation of room and core body temperatures. Methods Four asymptomatic women were evaluated for three consecutive menstrual cycles. Using thermography, the temperature of breasts and eyes was measured as indirect reference of core body and room temperatures. To analyze the thermal behavior of the breasts during the cycle, the core body and room temperatures were normalized by means of a mathematical equation. Results We performed 180 observations and the core temperature had the highest correlation with the breast temperature, followed by room temperature. The proposed prediction model could explain 45.3% of the breast temperature variation, with variable room temperature variable; it can be accepted as a way to estimate the reference breast temperature at different room temperatures. Conclusion The average breast temperature in healthy women had a direct relation with the core and room temperature and can be estimated mathematically. It is suggested that an equation could be used in clinical practice to estimate the normal breast reference temperature in young women, regardless of the day of the cycle, therefore assisting in evaluation of anatomical studies. PMID:26761549

Stability and error estimation for Component Adaptive Grid methods

NASA Technical Reports Server (NTRS)

Oliger, Joseph; Zhu, Xiaolei

1994-01-01

Component adaptive grid (CAG) methods for solving hyperbolic partial differential equations (PDE's) are discussed in this paper. Applying recent stability results for a class of numerical methods on uniform grids. The convergence of these methods for linear problems on component adaptive grids is established here. Furthermore, the computational error can be estimated on CAG's using the stability results. Using these estimates, the error can be controlled on CAG's. Thus, the solution can be computed efficiently on CAG's within a given error tolerance. Computational results for time dependent linear problems in one and two space dimensions are presented.

Wavelet and adaptive methods for time dependent problems and applications in aerosol dynamics

NASA Astrophysics Data System (ADS)

Guo, Qiang

Time dependent partial differential equations (PDEs) are widely used as mathematical models of environmental problems. Aerosols are now clearly identified as an important factor in many environmental aspects of climate and radiative forcing processes, as well as in the health effects of air quality. The mathematical models for the aerosol dynamics with respect to size distribution are nonlinear partial differential and integral equations, which describe processes of condensation, coagulation and deposition. Simulating the general aerosol dynamic equations on time, particle size and space exhibits serious difficulties because the size dimension ranges from a few nanometer to several micrometer while the spatial dimension is usually described with kilometers. Therefore, it is an important and challenging task to develop efficient techniques for solving time dependent dynamic equations. In this thesis, we develop and analyze efficient wavelet and adaptive methods for the time dependent dynamic equations on particle size and further apply them to the spatial aerosol dynamic systems. Wavelet Galerkin method is proposed to solve the aerosol dynamic equations on time and particle size due to the fact that aerosol distribution changes strongly along size direction and the wavelet technique can solve it very efficiently. Daubechies' wavelets are considered in the study due to the fact that they possess useful properties like orthogonality, compact support, exact representation of polynomials to a certain degree. Another problem encountered in the solution of the aerosol dynamic equations results from the hyperbolic form due to the condensation growth term. We propose a new characteristic-based fully adaptive multiresolution numerical scheme for solving the aerosol dynamic equation, which combines the attractive advantages of adaptive multiresolution technique and the characteristics method. On the aspect of theoretical analysis, the global existence and uniqueness of solutions of continuous time wavelet numerical methods for the nonlinear aerosol dynamics are proved by using Schauder's fixed point theorem and the variational technique. Optimal error estimates are derived for both continuous and discrete time wavelet Galerkin schemes. We further derive reliable and efficient a posteriori error estimate which is based on stable multiresolution wavelet bases and an adaptive space-time algorithm for efficient solution of linear parabolic differential equations. The adaptive space refinement strategies based on the locality of corresponding multiresolution processes are proved to converge. At last, we develop efficient numerical methods by combining the wavelet methods proposed in previous parts and the splitting technique to solve the spatial aerosol dynamic equations. Wavelet methods along the particle size direction and the upstream finite difference method along the spatial direction are alternately used in each time interval. Numerical experiments are taken to show the effectiveness of our developed methods.

Computational tools for fitting the Hill equation to dose-response curves.

PubMed

Gadagkar, Sudhindra R; Call, Gerald B

2015-01-01

Many biological response curves commonly assume a sigmoidal shape that can be approximated well by means of the 4-parameter nonlinear logistic equation, also called the Hill equation. However, estimation of the Hill equation parameters requires access to commercial software or the ability to write computer code. Here we present two user-friendly and freely available computer programs to fit the Hill equation - a Solver-based Microsoft Excel template and a stand-alone GUI-based "point and click" program, called HEPB. Both computer programs use the iterative method to estimate two of the Hill equation parameters (EC50 and the Hill slope), while constraining the values of the other two parameters (the minimum and maximum asymptotes of the response variable) to fit the Hill equation to the data. In addition, HEPB draws the prediction band at a user-defined confidence level, and determines the EC50 value for each of the limits of this band to give boundary values that help objectively delineate sensitive, normal and resistant responses to the drug being tested. Both programs were tested by analyzing twelve datasets that varied widely in data values, sample size and slope, and were found to yield estimates of the Hill equation parameters that were essentially identical to those provided by commercial software such as GraphPad Prism and nls, the statistical package in the programming language R. The Excel template provides a means to estimate the parameters of the Hill equation and plot the regression line in a familiar Microsoft Office environment. HEPB, in addition to providing the above results, also computes the prediction band for the data at a user-defined level of confidence, and determines objective cut-off values to distinguish among response types (sensitive, normal and resistant). Both programs are found to yield estimated values that are essentially the same as those from standard software such as GraphPad Prism and the R-based nls. Furthermore, HEPB also has the option to simulate 500 response values based on the range of values of the dose variable in the original data and the fit of the Hill equation to that data. Copyright © 2014. Published by Elsevier Inc.

Estimating vapor pressures of pure liquids

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

Haraburda, S.S.

1996-03-01

Calculating the vapor pressures for pure liquid chemicals is a key step in designing equipment for separation of liquid mixtures. Here is a useful way to develop an equation for predicting vapor pressures over a range of temperatures. The technique uses known vapor pressure points for different temperatures. Although a vapor-pressure equation is being showcased in this article, the basic method has much broader applicability -- in fact, users can apply it to develop equations for any temperature-dependent model. The method can be easily adapted for use in software programs for mathematics evaluation, minimizing the need for any programming. Themore » model used is the Antoine equation, which typically provides a good correlation with experimental or measured data.« less

[Consensus document: recommendations for the use of equations to estimate glomerular filtration rate in children].

PubMed

Montañés Bermúdez, R; Gràcia Garcia, S; Fraga Rodríguez, G M; Escribano Subias, J; Diez de Los Ríos Carrasco, M J; Alonso Melgar, A; García Nieto, V

2014-05-01

The appearance of the K/DOQI guidelines in 2002 on the definition, evaluation and staging of chronic kidney disease (CKD) have led to a major change in how to assess renal function in adults and children. These guidelines, recently updated, recommended that the study of renal function is based, not only on measuring the serum creatinine concentration, but this must be accompanied by the estimation of glomerular filtration rate (GFR) obtained by an equation. However, the implementation of this recommendation in the clinical laboratory reports in the paediatric population has been negligible. Numerous studies have appeared in recent years on the importance of screening and monitoring of patients with CKD, the emergence of new equations for estimating GFR, and advances in clinical laboratories regarding the methods for measuring plasma creatinine and cystatin C, determined by the collaboration between the departments of paediatrics and clinical laboratories to establish recommendations based on the best scientific evidence on the use of equations to estimate GFR in this population. The purpose of this document is to provide recommendations on the evaluation of renal function and the use of equations to estimate GFR in children from birth to 18 years of age. The recipients of these recommendations are paediatricians, nephrologists, clinical biochemistry, clinical analysts, and all health professionals involved in the study and evaluation of renal function in this group of patients. Copyright © 2013 Asociación Española de Pediatría. Published by Elsevier Espana. All rights reserved.

Adjustment of regional regression equations for urban storm-runoff quality using at-site data

USGS Publications Warehouse

Barks, C.S.

1996-01-01

Regional regression equations have been developed to estimate urban storm-runoff loads and mean concentrations using a national data base. Four statistical methods using at-site data to adjust the regional equation predictions were developed to provide better local estimates. The four adjustment procedures are a single-factor adjustment, a regression of the observed data against the predicted values, a regression of the observed values against the predicted values and additional local independent variables, and a weighted combination of a local regression with the regional prediction. Data collected at five representative storm-runoff sites during 22 storms in Little Rock, Arkansas, were used to verify, and, when appropriate, adjust the regional regression equation predictions. Comparison of observed values of stormrunoff loads and mean concentrations to the predicted values from the regional regression equations for nine constituents (chemical oxygen demand, suspended solids, total nitrogen as N, total ammonia plus organic nitrogen as N, total phosphorus as P, dissolved phosphorus as P, total recoverable copper, total recoverable lead, and total recoverable zinc) showed large prediction errors ranging from 63 percent to more than several thousand percent. Prediction errors for 6 of the 18 regional regression equations were less than 100 percent and could be considered reasonable for water-quality prediction equations. The regression adjustment procedure was used to adjust five of the regional equation predictions to improve the predictive accuracy. For seven of the regional equations the observed and the predicted values are not significantly correlated. Thus neither the unadjusted regional equations nor any of the adjustments were appropriate. The mean of the observed values was used as a simple estimator when the regional equation predictions and adjusted predictions were not appropriate.

On the implementation of an accurate and efficient solver for convection-diffusion equations

NASA Astrophysics Data System (ADS)

Wu, Chin-Tien

In this dissertation, we examine several different aspects of computing the numerical solution of the convection-diffusion equation. The solution of this equation often exhibits sharp gradients due to Dirichlet outflow boundaries or discontinuities in boundary conditions. Because of the singular-perturbed nature of the equation, numerical solutions often have severe oscillations when grid sizes are not small enough to resolve sharp gradients. To overcome such difficulties, the streamline diffusion discretization method can be used to obtain an accurate approximate solution in regions where the solution is smooth. To increase accuracy of the solution in the regions containing layers, adaptive mesh refinement and mesh movement based on a posteriori error estimations can be employed. An error-adapted mesh refinement strategy based on a posteriori error estimations is also proposed to resolve layers. For solving the sparse linear systems that arise from discretization, goemetric multigrid (MG) and algebraic multigrid (AMG) are compared. In addition, both methods are also used as preconditioners for Krylov subspace methods. We derive some convergence results for MG with line Gauss-Seidel smoothers and bilinear interpolation. Finally, while considering adaptive mesh refinement as an integral part of the solution process, it is natural to set a stopping tolerance for the iterative linear solvers on each mesh stage so that the difference between the approximate solution obtained from iterative methods and the finite element solution is bounded by an a posteriori error bound. Here, we present two stopping criteria. The first is based on a residual-type a posteriori error estimator developed by Verfurth. The second is based on an a posteriori error estimator, using local solutions, developed by Kay and Silvester. Our numerical results show the refined mesh obtained from the iterative solution which satisfies the second criteria is similar to the refined mesh obtained from the finite element solution.

Numerical scheme approximating solution and parameters in a beam equation

NASA Astrophysics Data System (ADS)

Ferdinand, Robert R.

2003-12-01

We present a mathematical model which describes vibration in a metallic beam about its equilibrium position. This model takes the form of a nonlinear second-order (in time) and fourth-order (in space) partial differential equation with boundary and initial conditions. A finite-element Galerkin approximation scheme is used to estimate model solution. Infinite-dimensional model parameters are then estimated numerically using an inverse method procedure which involves the minimization of a least-squares cost functional. Numerical results are presented and future work to be done is discussed.

Methods for estimating magnitude and frequency of 1-, 3-, 7-, 15-, and 30-day flood-duration flows in Arizona

USGS Publications Warehouse

Kennedy, Jeffrey R.; Paretti, Nicholas V.; Veilleux, Andrea G.

2014-01-01

Regression equations, which allow predictions of n-day flood-duration flows for selected annual exceedance probabilities at ungaged sites, were developed using generalized least-squares regression and flood-duration flow frequency estimates at 56 streamgaging stations within a single, relatively uniform physiographic region in the central part of Arizona, between the Colorado Plateau and Basin and Range Province, called the Transition Zone. Drainage area explained most of the variation in the n-day flood-duration annual exceedance probabilities, but mean annual precipitation and mean elevation were also significant variables in the regression models. Standard error of prediction for the regression equations varies from 28 to 53 percent and generally decreases with increasing n-day duration. Outside the Transition Zone there are insufficient streamgaging stations to develop regression equations, but flood-duration flow frequency estimates are presented at select streamgaging stations.

[Progress on Individual Stature Estimation in Forensic Medicine].

PubMed

Wu, Rong-qi; Huang, Li-na; Chen, Xin

2015-12-01

Individual stature estimation is one of the most important contents of forensic anthropology. Currently, it has been used that the regression equations established by the data collected by direct measurement or radiological techniques in a certain group of limbs, irregular bones, and anatomic landmarks. Due to the impact of population mobility, human physical improvement, racial and geographic differences, estimation of individual stature should be a regular study. This paper reviews the different methods of stature estimation, briefly describes the advantages and disadvantages of each method, and prospects a new research direction.

Magnitude and frequency of floods in Arkansas

USGS Publications Warehouse

Hodge, Scott A.; Tasker, Gary D.

1995-01-01

Methods are presented for estimating the magnitude and frequency of peak discharges of streams in Arkansas. Regression analyses were developed in which a stream's physical and flood characteristics were related. Four sets of regional regression equations were derived to predict peak discharges with selected recurrence intervals of 2, 5, 10, 25, 50, 100, and 500 years on streams draining less than 7,770 square kilometers. The regression analyses indicate that size of drainage area, main channel slope, mean basin elevation, and the basin shape factor were the most significant basin characteristics that affect magnitude and frequency of floods. The region of influence method is included in this report. This method is still being improved and is to be considered only as a second alternative to the standard method of producing regional regression equations. This method estimates unique regression equations for each recurrence interval for each ungaged site. The regression analyses indicate that size of drainage area, main channel slope, mean annual precipitation, mean basin elevation, and the basin shape factor were the most significant basin and climatic characteristics that affect magnitude and frequency of floods for this method. Certain recommendations on the use of this method are provided. A method is described for estimating the magnitude and frequency of peak discharges of streams for urban areas in Arkansas. The method is from a nationwide U.S. Geeological Survey flood frequency report which uses urban basin characteristics combined with rural discharges to estimate urban discharges. Annual peak discharges from 204 gaging stations, with drainage areas less than 7,770 square kilometers and at least 10 years of unregulated record, were used in the analysis. These data provide the basis for this analysis and are published in the Appendix of this report as supplemental data. Large rivers such as the Red, Arkansas, White, Black, St. Francis, Mississippi, and Ouachita Rivers have floodflow characteristics that differ from those of smaller tributary streams and were treated individually. Regional regression equations are not applicable to these large rivers. The magnitude and frequency of floods along these rivers are based on specific station data. This section is provided in the Appendix and has not been updated since the last Arkansas flood frequency report (1987b), but is included at the request of the cooperator.

Method for estimating spatially variable seepage loss and hydraulic conductivity in intermittent and ephemeral streams

USGS Publications Warehouse

Niswonger, R.G.; Prudic, David E.; Fogg, G.E.; Stonestrom, David A.; Buckland, E.M.

2008-01-01

A method is presented for estimating seepage loss and streambed hydraulic conductivity along intermittent and ephemeral streams using streamflow front velocities in initially dry channels. The method uses the kinematic wave equation for routing streamflow in channels coupled to Philip's equation for infiltration. The coupled model considers variations in seepage loss both across and along the channel. Water redistribution in the unsaturated zone is also represented in the model. Sensitivity of the streamflow front velocity to parameters used for calculating seepage loss and for routing streamflow shows that the streambed hydraulic conductivity has the greatest sensitivity for moderate to large seepage loss rates. Channel roughness, geometry, and slope are most important for low seepage loss rates; however, streambed hydraulic conductivity is still important for values greater than 0.008 m/d. Two example applications are presented to demonstrate the utility of the method.

GFR Estimation: From Physiology to Public Health

PubMed Central

Levey, Andrew S.; Inker, Lesley A.; Coresh, Josef

2014-01-01

Estimating glomerular filtration rate (GFR) is essential for clinical practice, research, and public health. Appropriate interpretation of estimated GFR (eGFR) requires understanding the principles of physiology, laboratory medicine, epidemiology and biostatistics used in the development and validation of GFR estimating equations. Equations developed in diverse populations are less biased at higher GFR than equations developed in CKD populations and are more appropriate for general use. Equations that include multiple endogenous filtration markers are more precise than equations including a single filtration marker. The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equations are the most accurate GFR estimating equations that have been evaluated in large, diverse populations and are applicable for general clinical use. The 2009 CKD-EPI creatinine equation is more accurate in estimating GFR and prognosis than the 2006 Modification of Diet in Renal Disease (MDRD) Study equation and provides lower estimates of prevalence of decreased eGFR. It is useful as a “first” test for decreased eGFR and should replace the MDRD Study equation for routine reporting of serum creatinine–based eGFR by clinical laboratories. The 2012 CKD-EPI cystatin C equation is as accurate as the 2009 CKD-EPI creatinine equation in estimating eGFR, does not require specification of race, and may be more accurate in patients with decreased muscle mass. The 2012 CKD-EPI creatinine–cystatin C equation is more accurate than the 2009 CKD-EPI creatinine and 2012 CKD-EPI cystatin C equations and is useful as a confirmatory test for decreased eGFR as determined by an equation based on serum creatinine. Further improvement in GFR estimating equations will require development in more broadly representative populations, including diverse racial and ethnic groups, use of multiple filtration markers, and evaluation using statistical techniques to compare eGFR to “true GFR”. PMID:24485147

SU-E-T-598: Parametric Equation for Quick and Reliable Estimate of Stray Neutron Doses in Proton Therapy and Application for Intracranial Tumor Treatments

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

Bonfrate, A; Farah, J; Sayah, R

2015-06-15

Purpose: Development of a parametric equation suitable for a daily use in routine clinic to provide estimates of stray neutron doses in proton therapy. Methods: Monte Carlo (MC) calculations using the UF-NCI 1-year-old phantom were exercised to determine the variation of stray neutron doses as a function of irradiation parameters while performing intracranial treatments. This was done by individually changing the proton beam energy, modulation width, collimator aperture and thickness, compensator thickness and the air gap size while their impact on neutron doses were put into a single equation. The variation of neutron doses with distance from the target volumemore » was also included in it. Then, a first step consisted in establishing the fitting coefficients by using 221 learning data which were neutron absorbed doses obtained with MC simulations while a second step consisted in validating the final equation. Results: The variation of stray neutron doses with irradiation parameters were fitted with linear, polynomial, etc. model while a power-law model was used to fit the variation of stray neutron doses with the distance from the target volume. The parametric equation fitted well MC simulations while establishing fitting coefficients as the discrepancies on the estimate of neutron absorbed doses were within 10%. The discrepancy can reach ∼25% for the bladder, the farthest organ from the target volume. Finally, the validation showed results in compliance with MC calculations since the discrepancies were also within 10% for head-and-neck and thoracic organs while they can reach ∼25%, again for pelvic organs. Conclusion: The parametric equation presents promising results and will be validated for other target sites as well as other facilities to go towards a universal method.« less

Effects of Serum Creatinine Calibration on Estimated Renal Function in African Americans: the Jackson Heart Study

PubMed Central

Wang, Wei; Young, Bessie A.; Fülöp, Tibor; de Boer, Ian H.; Boulware, L. Ebony; Katz, Ronit; Correa, Adolfo; Griswold, Michael E.

2015-01-01

Background The calibration to Isotope Dilution Mass Spectroscopy (IDMS) traceable creatinine is essential for valid use of the new Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation to estimate the glomerular filtration rate (GFR). Methods For 5,210 participants in the Jackson Heart Study (JHS), serum creatinine was measured with a multipoint enzymatic spectrophotometric assay at the baseline visit (2000–2004) and re-measured using the Roche enzymatic method, traceable to IDMS in a subset of 206 subjects. The 200 eligible samples (6 were excluded, 1 for failure of the re-measurement and 5 for outliers) were divided into three disjoint sets - training, validation, and test - to select a calibration model, estimate true errors, and assess performance of the final calibration equation. The calibration equation was applied to serum creatinine measurements of 5,210 participants to estimate GFR and the prevalence of CKD. Results The selected Deming regression model provided a slope of 0.968 (95% Confidence Interval (CI), 0.904 to 1.053) and intercept of −0.0248 (95% CI, −0.0862 to 0.0366) with R squared 0.9527. Calibrated serum creatinine showed high agreement with actual measurements when applying to the unused test set (concordance correlation coefficient 0.934, 95% CI, 0.894 to 0.960). The baseline prevalence of CKD in the JHS (2000–2004) was 6.30% using calibrated values, compared with 8.29% using non-calibrated serum creatinine with the CKD-EPI equation (P < 0.001). Conclusions A Deming regression model was chosen to optimally calibrate baseline serum creatinine measurements in the JHS and the calibrated values provide a lower CKD prevalence estimate. PMID:25806862

Comparison of bioimpedance methods for estimating total body water and intracellular water changes during hemodialysis.

PubMed

Dou, Yanna; Liu, Li; Cheng, Xuyang; Cao, Liyun; Zuo, Li

2011-10-01

The accurate assessment of body fluid volume is important in many clinical situations. Hannan et al. proposed a single-frequency bioimpedance equation (HE) to calculate extracellular water (ECW) and total body water (TBW). There are two equations based on the bioimpedance spectroscopy (BIS) method for the evaluation of body fluid volume: Xitron equations (XE) and body composition spectroscopy equations (BCSE). The aim of the study was to compare the accuracy of these three equations in body fluid volume point estimation in maintenance hemodialysis (MHD) patients. The BIS method was performed in MHD patients before and after a hemodialysis (HD) session. TBW, ECW and intracellular water (ICW) were calculated by XE, BCSE and HE, respectively. Hydration status (HS) was calculated using inputs of XE, BCSE and HE. ICW before dialysis was compared to ICW after dialysis. The change of TBW and HS using different equations was compared to actual ultrafiltration volume (AUV) that was calculated as weight difference of pre- to postdialysis. Fifty MHD patients (27 females) were included in the study. Significant changes in ICW were observed using the XE and HE method with ultrafiltration (XE: 15.51 ± 5.07 versus 16.17 ± 5.34 L, P < 0.01; HE: 17.40 ± 5.13 versus 16.55 ± 4.71 L, P < 0.01). However, no significant ICW change was observed using BCSE (17.47 ± 4.35 versus 17.54 ± 4.36 L, P > 0.05). ΔTBW_XE and ΔTBW_HE were significantly different from AUV (XE 1.76 ± 0.89 versus 2.46 ± 0.89 L, P < 0.01; HE 4.16 ± 1.36 versus 2.46 ± 0.89 L, P < 0.01); however, ΔTBW_BCSE was much closer to AUV (2.27 ± 0.90 versus 2.46 ± 0.89 L, P = 0.129). The change of HS using inputs of BCSE was also closer to AUV (2.41 ± 0.86 versus 2.46 ± 0.89 L, P = 1.0). Our study indicated that BCSE provided a better point estimation of ICW and TBW.

Time-lapse joint AVO inversion using generalized linear method based on exact Zoeppritz equations

NASA Astrophysics Data System (ADS)

Zhi, Longxiao; Gu, Hanming

2018-03-01

The conventional method of time-lapse AVO (Amplitude Versus Offset) inversion is mainly based on the approximate expression of Zoeppritz equations. Though the approximate expression is concise and convenient to use, it has certain limitations. For example, its application condition is that the difference of elastic parameters between the upper medium and lower medium is little and the incident angle is small. In addition, the inversion of density is not stable. Therefore, we develop the method of time-lapse joint AVO inversion based on exact Zoeppritz equations. In this method, we apply exact Zoeppritz equations to calculate the reflection coefficient of PP wave. And in the construction of objective function for inversion, we use Taylor series expansion to linearize the inversion problem. Through the joint AVO inversion of seismic data in baseline survey and monitor survey, we can obtain the P-wave velocity, S-wave velocity, density in baseline survey and their time-lapse changes simultaneously. We can also estimate the oil saturation change according to inversion results. Compared with the time-lapse difference inversion, the joint inversion doesn't need certain assumptions and can estimate more parameters simultaneously. It has a better applicability. Meanwhile, by using the generalized linear method, the inversion is easily implemented and its calculation cost is small. We use the theoretical model to generate synthetic seismic records to test and analyze the influence of random noise. The results can prove the availability and anti-noise-interference ability of our method. We also apply the inversion to actual field data and prove the feasibility of our method in actual situation.

Estimated Glomerular Filtration Rate; Laboratory Implementation and Current Global Status.

PubMed

Miller, W Greg; Jones, Graham R D

2018-01-01

In 2002, the Kidney Disease Outcomes Quality Initiative guidelines for identifying and treating CKD recommended that clinical laboratories report estimated glomerular filtration rate (eGFR) with every creatinine result to assist clinical practitioners to identify people with early-stage CKD. At that time, the original Modification of Diet in Renal Disease (MDRD) Study equation based on serum creatinine measurements was recommended for calculating eGFR. Because the MDRD Study equation was developed using a nonstandardized creatinine method, a Laboratory Working Group of the National Kidney Disease Education program was formed and implemented standardized calibration traceability for all creatinine methods from global manufacturers by approximately 2010. A modified MDRD Study equation for use with standardized creatinine was developed. The Chronic Kidney Disease Epidemiology Collaboration developed a new equation in 2009 that was more accurate than the MDRD Study equation at values above 60 mL/min/1.73 m 2 . As of 2017, reporting eGFR with creatinine is almost universal in many countries. A reference system for cystatin C became available in 2010, and manufacturers are in the process to standardize cystatin C assays. Equations for eGFR based on standardized cystatin C alone and with creatinine are now available from the Chronic Kidney Disease Epidemiology Collaboration and other groups. Copyright © 2017 National Kidney Foundation, Inc. Published by Elsevier Inc. All rights reserved.

Investigation of Convection and Pressure Treatment with Splitting Techniques

NASA Technical Reports Server (NTRS)

Thakur, Siddharth; Shyy, Wei; Liou, Meng-Sing

1995-01-01

Treatment of convective and pressure fluxes in the Euler and Navier-Stokes equations using splitting formulas for convective velocity and pressure is investigated. Two schemes - controlled variation scheme (CVS) and advection upstream splitting method (AUSM) - are explored for their accuracy in resolving sharp gradients in flows involving moving or reflecting shock waves as well as a one-dimensional combusting flow with a strong heat release source term. For two-dimensional compressible flow computations, these two schemes are implemented in one of the pressure-based algorithms, whose very basis is the separate treatment of convective and pressure fluxes. For the convective fluxes in the momentum equations as well as the estimation of mass fluxes in the pressure correction equation (which is derived from the momentum and continuity equations) of the present algorithm, both first- and second-order (with minmod limiter) flux estimations are employed. Some issues resulting from the conventional use in pressure-based methods of a staggered grid, for the location of velocity components and pressure, are also addressed. Using the second-order fluxes, both CVS and AUSM type schemes exhibit sharp resolution. Overall, the combination of upwinding and splitting for the convective and pressure fluxes separately exhibits robust performance for a variety of flows and is particularly amenable for adoption in pressure-based methods.

Performance of Predictive Equations Specifically Developed to Estimate Resting Energy Expenditure in Ventilated Critically Ill Children.

PubMed

Jotterand Chaparro, Corinne; Taffé, Patrick; Moullet, Clémence; Laure Depeyre, Jocelyne; Longchamp, David; Perez, Marie-Hélène; Cotting, Jacques

2017-05-01

To determine, based on indirect calorimetry measurements, the biases of predictive equations specifically developed recently for estimating resting energy expenditure (REE) in ventilated critically ill children, or developed for healthy populations but used in critically ill children. A secondary analysis study was performed using our data on REE measured in a previous prospective study on protein and energy needs in pediatric intensive care unit. We included 75 ventilated critically ill children (median age, 21 months) in whom 407 indirect calorimetry measurements were performed. Fifteen predictive equations were used to estimate REE: the equations of White, Meyer, Mehta, Schofield, Henry, the World Health Organization, Fleisch, and Harris-Benedict and the tables of Talbot. Their differential and proportional biases (with 95% CIs) were computed and the bias plotted in graphs. The Bland-Altman method was also used. Most equations underestimated and overestimated REE between 200 and 1000 kcal/day. The equations of Mehta, Schofield, and Henry and the tables of Talbot had a bias ≤10%, but the 95% CI was large and contained values by far beyond ±10% for low REE values. Other specific equations for critically ill children had even wider biases. In ventilated critically ill children, none of the predictive equations tested met the performance criteria for the entire range of REE between 200 and 1000 kcal/day. Even the equations with the smallest bias may entail a risk of underfeeding or overfeeding, especially in the youngest children. Indirect calorimetry measurement must be preferred. Copyright © 2016 Elsevier Inc. All rights reserved.

Comparison of methods for estimating ground-water recharge and base flow at a small watershed underlain by fractured bedrock in the Eastern United States

USGS Publications Warehouse

Risser, Dennis W.; Gburek, William J.; Folmar, Gordon J.

2005-01-01

This study by the U.S. Geological Survey (USGS), in cooperation with the Agricultural Research Service (ARS), U.S. Department of Agriculture, compared multiple methods for estimating ground-water recharge and base flow (as a proxy for recharge) at sites in east-central Pennsylvania underlain by fractured bedrock and representative of a humid-continental climate. This study was one of several within the USGS Ground-Water Resources Program designed to provide an improved understanding of methods for estimating recharge in the eastern United States. Recharge was estimated on a monthly and annual basis using four methods?(1) unsaturated-zone drainage collected in gravity lysimeters, (2) daily water balance, (3) water-table fluctuations in wells, and (4) equations of Rorabaugh. Base flow was estimated by streamflow-hydrograph separation using the computer programs PART and HYSEP. Estimates of recharge and base flow were compared for an 8-year period (1994-2001) coinciding with operation of the gravity lysimeters at an experimental recharge site (Masser Recharge Site) and a longer 34-year period (1968-2001), for which climate and streamflow data were available on a 2.8-square-mile watershed (WE-38 watershed). Estimates of mean-annual recharge at the Masser Recharge Site and WE-38 watershed for 1994-2001 ranged from 9.9 to 14.0 inches (24 to 33 percent of precipitation). Recharge, in inches, from the various methods was: unsaturated-zone drainage, 12.2; daily water balance, 12.3; Rorabaugh equations with PULSE, 10.2, or RORA, 14.0; and water-table fluctuations, 9.9. Mean-annual base flow from streamflow-hydrograph separation ranged from 9.0 to 11.6 inches (21-28 percent of precipitation). Base flow, in inches, from the various methods was: PART, 10.7; HYSEP Local Minimum, 9.0; HYSEP Sliding Interval, 11.5; and HYSEP Fixed Interval, 11.6. Estimating recharge from multiple methods is useful, but the inherent differences of the methods must be considered when comparing results. For example, although unsaturated-zone drainage from the gravity lysimeters provided the most direct measure of potential recharge, it does not incorporate spatial variability that is contained in watershed-wide estimates of net recharge from the Rorabaugh equations or base flow from streamflow-hydrograph separation. This study showed that water-level fluctuations, in particular, should be used with caution to estimate recharge in low-storage fractured-rock aquifers because of the variability of water-level response among wells and sensitivity of recharge to small errors in estimating specific yield. To bracket the largest range of plausible recharge, results from this study indicate that recharge derived from RORA should be compared with base flow from the Local-Minimum version of HYSEP.

Techniques for Estimating the Magnitude and Frequency of Peak Flows on Small Streams in Minnesota Based on Data through Water Year 2005

USGS Publications Warehouse

Lorenz, David L.; Sanocki, Chris A.; Kocian, Matthew J.

2010-01-01

Knowledge of the peak flow of floods of a given recurrence interval is essential for regulation and planning of water resources and for design of bridges, culverts, and dams along Minnesota's rivers and streams. Statistical techniques are needed to estimate peak flow at ungaged sites because long-term streamflow records are available at relatively few places. Because of the need to have up-to-date peak-flow frequency information in order to estimate peak flows at ungaged sites, the U.S. Geological Survey (USGS) conducted a peak-flow frequency study in cooperation with the Minnesota Department of Transportation and the Minnesota Pollution Control Agency. Estimates of peak-flow magnitudes for 1.5-, 2-, 5-, 10-, 25-, 50-, 100-, and 500-year recurrence intervals are presented for 330 streamflow-gaging stations in Minnesota and adjacent areas in Iowa and South Dakota based on data through water year 2005. The peak-flow frequency information was subsequently used in regression analyses to develop equations relating peak flows for selected recurrence intervals to various basin and climatic characteristics. Two statistically derived techniques-regional regression equation and region of influence regression-can be used to estimate peak flow on ungaged streams smaller than 3,000 square miles in Minnesota. Regional regression equations were developed for selected recurrence intervals in each of six regions in Minnesota: A (northwestern), B (north central and east central), C (northeastern), D (west central and south central), E (southwestern), and F (southeastern). The regression equations can be used to estimate peak flows at ungaged sites. The region of influence regression technique dynamically selects streamflow-gaging stations with characteristics similar to a site of interest. Thus, the region of influence regression technique allows use of a potentially unique set of gaging stations for estimating peak flow at each site of interest. Two methods of selecting streamflow-gaging stations, similarity and proximity, can be used for the region of influence regression technique. The regional regression equation technique is the preferred technique as an estimate of peak flow in all six regions for ungaged sites. The region of influence regression technique is not appropriate for regions C, E, and F because the interrelations of some characteristics of those regions do not agree with the interrelations throughout the rest of the State. Both the similarity and proximity methods for the region of influence technique can be used in the other regions (A, B, and D) to provide additional estimates of peak flow. The peak-flow-frequency estimates and basin characteristics for selected streamflow-gaging stations and regional peak-flow regression equations are included in this report.

Regression analysis of clustered failure time data with informative cluster size under the additive transformation models.

PubMed

Chen, Ling; Feng, Yanqin; Sun, Jianguo

2017-10-01

This paper discusses regression analysis of clustered failure time data, which occur when the failure times of interest are collected from clusters. In particular, we consider the situation where the correlated failure times of interest may be related to cluster sizes. For inference, we present two estimation procedures, the weighted estimating equation-based method and the within-cluster resampling-based method, when the correlated failure times of interest arise from a class of additive transformation models. The former makes use of the inverse of cluster sizes as weights in the estimating equations, while the latter can be easily implemented by using the existing software packages for right-censored failure time data. An extensive simulation study is conducted and indicates that the proposed approaches work well in both the situations with and without informative cluster size. They are applied to a dental study that motivated this study.

Modeling Latent Interactions at Level 2 in Multilevel Structural Equation Models: An Evaluation of Mean-Centered and Residual-Centered Unconstrained Approaches

ERIC Educational Resources Information Center

Leite, Walter L.; Zuo, Youzhen

2011-01-01

Among the many methods currently available for estimating latent variable interactions, the unconstrained approach is attractive to applied researchers because of its relatively easy implementation with any structural equation modeling (SEM) software. Using a Monte Carlo simulation study, we extended and evaluated the unconstrained approach to…

Additivity and maximum likelihood estimation of nonlinear component biomass models

Treesearch

David L.R. Affleck

2015-01-01

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

A Note on the Use of Missing Auxiliary Variables in Full Information Maximum Likelihood-Based Structural Equation Models

ERIC Educational Resources Information Center

Enders, Craig K.

2008-01-01

Recent missing data studies have argued in favor of an "inclusive analytic strategy" that incorporates auxiliary variables into the estimation routine, and Graham (2003) outlined methods for incorporating auxiliary variables into structural equation analyses. In practice, the auxiliary variables often have missing values, so it is reasonable to…

Assessing Fat Mass of Adolescent Swimmers Using Anthropometric Equations: A DXA Validation Study

ERIC Educational Resources Information Center

Lozano-Berges, Gabriel; Gómez-Bruton, Alejandro; Matute-Llorente, Ángel; Julián-Almárcegui, Cristina; Gómez-Cabello, Alba; González-Agüero, Alejandro; Casajús, José A.; Vicente-Rodríguez, Germán

2017-01-01

Purpose: The aim of the present study was to determine which of the published anthropometric equations is the most appropriate to estimate body-fat percentage (BF%) in adolescent swimmers. Method: Eighty-eight swimmers (45 boys, 43 girls) participated in this study. Following the recommendations of the International Society of the Advancement of…

Estimation of Flood Discharges at Selected Recurrence Intervals for Streams in New Hampshire

USGS Publications Warehouse

Olson, Scott A.

2009-01-01

This report provides estimates of flood discharges at selected recurrence intervals for streamgages in and adjacent to New Hampshire and equations for estimating flood discharges at recurrence intervals of 2-, 5-, 10-, 25-, 50-, 100-, and 500-years for ungaged, unregulated, rural streams in New Hampshire. The equations were developed using generalized least-squares regression. Flood-frequency and drainage-basin characteristics from 117 streamgages were used in developing the equations. The drainage-basin characteristics used as explanatory variables in the regression equations include drainage area, mean April precipitation, percentage of wetland area, and main channel slope. The average standard error of prediction for estimating the 2-, 5-, 10-, 25-, 50-, 100-, and 500-year recurrence interval flood discharges with these equations are 30.0, 30.8, 32.0, 34.2, 36.0, 38.1, and 43.4 percent, respectively. Flood discharges at selected recurrence intervals for selected streamgages were computed following the guidelines in Bulletin 17B of the U.S. Interagency Advisory Committee on Water Data. To determine the flood-discharge exceedence probabilities at streamgages in New Hampshire, a new generalized skew coefficient map covering the State was developed. The standard error of the data on new map is 0.298. To improve estimates of flood discharges at selected recurrence intervals for 20 streamgages with short-term records (10 to 15 years), record extension using the two-station comparison technique was applied. The two-station comparison method uses data from a streamgage with long-term record to adjust the frequency characteristics at a streamgage with a short-term record. A technique for adjusting a flood-discharge frequency curve computed from a streamgage record with results from the regression equations is described in this report. Also, a technique is described for estimating flood discharge at a selected recurrence interval for an ungaged site upstream or downstream from a streamgage using a drainage-area adjustment. The final regression equations and the flood-discharge frequency data used in this study will be available in StreamStats. StreamStats is a World Wide Web application providing automated regression-equation solutions for user-selected sites on streams.

Magnetic dipole moment determination by near-field analysis

NASA Technical Reports Server (NTRS)

Eichhorn, W. L.

1972-01-01

A method for determining the magnetic moment of a spacecraft from magnetic field data taken in a limited region of space close to the spacecraft. The spacecraft's magnetic field equations are derived from first principles. With measurements of this field restricted to certain points in space, the near-field equations for the spacecraft are derived. These equations are solved for the dipole moment by a least squares procedure. A method by which one can estimate the magnitude of the error in the calculations is also presented. This technique was thoroughly tested on a computer. The test program is described and evaluated, and partial results are presented.

Chirped or time modulated excitation compared to short pulses for photoacoustic imaging in acoustic attenuating media

NASA Astrophysics Data System (ADS)

Burgholzer, P.; Motz, C.; Lang, O.; Berer, T.; Huemer, M.

2018-02-01

In photoacoustic imaging, optically generated acoustic waves transport the information about embedded structures to the sample surface. Usually, short laser pulses are used for the acoustic excitation. Acoustic attenuation increases for higher frequencies, which reduces the bandwidth and limits the spatial resolution. One could think of more efficient waveforms than single short pulses, such as pseudo noise codes, chirped, or harmonic excitation, which could enable a higher information-transfer from the samples interior to its surface by acoustic waves. We used a linear state space model to discretize the wave equation, such as the Stoke's equation, but this method could be used for any other linear wave equation. Linear estimators and a non-linear function inversion were applied to the measured surface data, for onedimensional image reconstruction. The proposed estimation method allows optimizing the temporal modulation of the excitation laser such that the accuracy and spatial resolution of the reconstructed image is maximized. We have restricted ourselves to one-dimensional models, as for higher dimensions the one-dimensional reconstruction, which corresponds to the acoustic wave without attenuation, can be used as input for any ultrasound imaging method, such as back-projection or time-reversal method.

Vanishing Viscosity Approach to the Compressible Euler Equations for Transonic Nozzle and Spherically Symmetric Flows

NASA Astrophysics Data System (ADS)

Chen, Gui-Qiang G.; Schrecker, Matthew R. I.

2018-04-01

We are concerned with globally defined entropy solutions to the Euler equations for compressible fluid flows in transonic nozzles with general cross-sectional areas. Such nozzles include the de Laval nozzles and other more general nozzles whose cross-sectional area functions are allowed at the nozzle ends to be either zero (closed ends) or infinity (unbounded ends). To achieve this, in this paper, we develop a vanishing viscosity method to construct globally defined approximate solutions and then establish essential uniform estimates in weighted L p norms for the whole range of physical adiabatic exponents γ\\in (1, ∞) , so that the viscosity approximate solutions satisfy the general L p compensated compactness framework. The viscosity method is designed to incorporate artificial viscosity terms with the natural Dirichlet boundary conditions to ensure the uniform estimates. Then such estimates lead to both the convergence of the approximate solutions and the existence theory of globally defined finite-energy entropy solutions to the Euler equations for transonic flows that may have different end-states in the class of nozzles with general cross-sectional areas for all γ\\in (1, ∞) . The approach and techniques developed here apply to other problems with similar difficulties. In particular, we successfully apply them to construct globally defined spherically symmetric entropy solutions to the Euler equations for all γ\\in (1, ∞).

Effects of correcting missing daily feed intake values on the genetic parameters and estimated breeding values for feeding traits in pigs.

PubMed

Ito, Tetsuya; Fukawa, Kazuo; Kamikawa, Mai; Nikaidou, Satoshi; Taniguchi, Masaaki; Arakawa, Aisaku; Tanaka, Genki; Mikawa, Satoshi; Furukawa, Tsutomu; Hirose, Kensuke

2018-01-01

Daily feed intake (DFI) is an important consideration for improving feed efficiency, but measurements using electronic feeder systems contain many missing and incorrect values. Therefore, we evaluated three methods for correcting missing DFI data (quadratic, orthogonal polynomial, and locally weighted (Loess) regression equations) and assessed the effects of these missing values on the genetic parameters and the estimated breeding values (EBV) for feeding traits. DFI records were obtained from 1622 Duroc pigs, comprising 902 individuals without missing DFI and 720 individuals with missing DFI. The Loess equation was the most suitable method for correcting the missing DFI values in 5-50% randomly deleted datasets among the three equations. Both variance components and heritability for the average DFI (ADFI) did not change because of the missing DFI proportion and Loess correction. In terms of rank correlation and information criteria, Loess correction improved the accuracy of EBV for ADFI compared to randomly deleted cases. These findings indicate that the Loess equation is useful for correcting missing DFI values for individual pigs and that the correction of missing DFI values could be effective for the estimation of breeding values and genetic improvement using EBV for feeding traits. © 2017 The Authors. Animal Science Journal published by John Wiley & Sons Australia, Ltd on behalf of Japanese Society of Animal Science.

Energy estimation of inclined air showers with help of detector responses

NASA Astrophysics Data System (ADS)

Dedenko, L. G.; Fedorova, G. F.; Fedunin, E. Yu.; Glushkov, A. V.; Kolosov, V. A.; Podgrudkov, D. A.; Pravdin, M. I.; Roganova, T. M.; Sleptsov, I. E.

2004-11-01

The method of groups of muons have been suggested to estimate the detector responses for the inclined giant air shower in terms of quark-gluon string model with the geomagnetic field taken into account. Groups are average numbers of muons of positive or negative sign in small intervals of energy, height production and direction of motion in the atmosphere estimated with help of transport equations. For every group a relativistic equation of motion has been solved with geomagnetic field and ionization losses taken into account. The response of a detector and arrival time for every group which strike a detector has been estimated. The energy of the inclined giant air shower estimated with help of calculated responses and the data observed at the Yakutsk array happens to be above 10 20 eV.

New non-linear model of groundwater recharge: Inclusion of memory, heterogeneity and visco-elasticity

NASA Astrophysics Data System (ADS)

Spannenberg, Jescica; Atangana, Abdon; Vermeulen, P. D.

2017-09-01

Fractional differentiation has adequate use for investigating real world scenarios related to geological formations associated with elasticity, heterogeneity, viscoelasticity, and the memory effect. Since groundwater systems exist in these geological formations, modelling groundwater recharge as a real world scenario is a challenging task to do because existing recharge estimation methods are governed by linear equations which make use of constant field parameters. This is inadequate because in reality these parameters are a function of both space and time. This study therefore concentrates on modifying the recharge equation governing the EARTH model, by application of the Eton approach. Accordingly, this paper presents a modified equation which is non-linear, and accounts for parameters in a way that it is a function of both space and time. To be more specific, herein, recharge and drainage resistance which are parameters within the equation, became a function of both space and time. Additionally, the study entailed solving the non-linear equation using an iterative method as well as numerical solutions by means of the Crank-Nicolson scheme. The numerical solutions were used alongside the Riemann-Liouville, Caputo-Fabrizio, and Atangana-Baleanu derivatives, so that account was taken for elasticity, heterogeneity, viscoelasticity, and the memory effect. In essence, this paper presents a more adequate model for recharge estimation.

GEE-Smoothing Spline in Semiparametric Model with Correlated Nominal Data

NASA Astrophysics Data System (ADS)

Ibrahim, Noor Akma; Suliadi

2010-11-01

In this paper we propose GEE-Smoothing spline in the estimation of semiparametric models with correlated nominal data. The method can be seen as an extension of parametric generalized estimating equation to semiparametric models. The nonparametric component is estimated using smoothing spline specifically the natural cubic spline. We use profile algorithm in the estimation of both parametric and nonparametric components. The properties of the estimators are evaluated using simulation studies.

Correction of bias in belt transect studies of immotile objects

USGS Publications Warehouse

Anderson, D.R.; Pospahala, R.S.

1970-01-01

Unless a correction is made, population estimates derived from a sample of belt transects will be biased if a fraction of, the individuals on the sample transects are not counted. An approach, useful for correcting this bias when sampling immotile populations using transects of a fixed width, is presented. The method assumes that a searcher's ability to find objects near the center of the transect is nearly perfect. The method utilizes a mathematical equation, estimated from the data, to represent the searcher's inability to find all objects at increasing distances from the center of the transect. An example of the analysis of data, formation of the equation, and application is presented using waterfowl nesting data collected in Colorado.

Lead burdens and behavioral impairments of the lined shore crab Pachygrapsus crassipes

USGS Publications Warehouse

Hui, Clifford A.

2002-01-01

Unless a correction is made, population estimates derived from a sample of belt transects will be biased if a fraction of, the individuals on the sample transects are not counted. An approach, useful for correcting this bias when sampling immotile populations using transects of a fixed width, is presented. The method assumes that a searcher's ability to find objects near the center of the transect is nearly perfect. The method utilizes a mathematical equation, estimated from the data, to represent the searcher's inability to find all objects at increasing distances from the center of the transect. An example of the analysis of data, formation of the equation, and application is presented using waterfowl nesting data collected in Colorado.

Tray estimates for low reflux

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

Barna, B.A.; Ginn, R.F.

1985-05-01

In computer programs which perform shortcut calculations for multicomponent distillation, the Gilliland correlation continues to be used even though errors of up to 60% (compared with rigorous plate-to-plate calculations) were shown by Erbar and Maddox. Average absolute differences were approximately 30% for Gilliland's correlation versus 4% for the Erbar-Maddox method. The reason the Gilliland correlation continues to be used appears to be due to the availability of an equation by Eduljee which facilitates the correlation's use in computer program. A new equation is presented in this paper that represents the Erbar-Maddox correlation of trays with reflux for multicomponent distillation. Atmore » low reflux ratios, results show more trays are needed than would be estimated by Gilliland's method.« less

Simulation of groundwater flow and streamflow depletion in the Branch Brook, Merriland River, and parts of the Mousam River watersheds in southern Maine

USGS Publications Warehouse

Nielsen, Martha G.; Locke, Daniel B.

2015-01-01

The study evaluated two different methods of calculating in-stream flow requirements for Branch Brook and the Merriland River—a set of statewide equations used to calculate monthly median flows and the MOVE.1 record-extension technique used on site-specific streamflow measurements. The August median in-stream flow requirement in the Merriland River was calculated as 7.18 ft3/s using the statewide equations but was 3.07 ft3/s using the MOVE.1 analysis. In Branch Brook, the August median in-stream flow requirements were calculated as 20.3 ft3/s using the statewide equations and 11.8 ft3/s using the MOVE.1 analysis. In each case, using site-specific data yields an estimate of in-stream flow that is much lower than an estimate the statewide equations provide.

Validity of bioelectrical impedance analysis in estimation of fat-free mass in colorectal cancer patients.

PubMed

Ræder, Hanna; Kværner, Ane Sørlie; Henriksen, Christine; Florholmen, Geir; Henriksen, Hege Berg; Bøhn, Siv Kjølsrud; Paur, Ingvild; Smeland, Sigbjørn; Blomhoff, Rune

2018-02-01

Bioelectrical impedance analysis (BIA) is an accessible and cheap method to measure fat-free mass (FFM). However, BIA estimates are subject to uncertainty in patient populations with altered body composition and hydration. The aim of the current study was to validate a whole-body and a segmental BIA device against dual-energy X-ray absorptiometry (DXA) in colorectal cancer (CRC) patients, and to investigate the ability of different empiric equations for BIA to predict DXA FFM (FFM DXA ). Forty-three non-metastatic CRC patients (aged 50-80 years) were enrolled in this study. Whole-body and segmental BIA FFM estimates (FFM whole-bodyBIA , FFM segmentalBIA ) were calculated using 14 empiric equations, including the equations from the manufacturers, before comparison to FFM DXA estimates. Strong linear relationships were observed between FFM BIA and FFM DXA estimates for all equations (R 2  = 0.94-0.98 for both devices). However, there were large discrepancies in FFM estimates depending on the equations used with mean differences in the ranges -6.5-6.8 kg and -11.0-3.4 kg for whole-body and segmental BIA, respectively. For whole-body BIA, 77% of BIA derived FFM estimates were significantly different from FFM DXA , whereas for segmental BIA, 85% were significantly different. For whole-body BIA, the Schols* equation gave the highest agreement with FFM DXA with mean difference ±SD of -0.16 ± 1.94 kg (p = 0.582). The manufacturer's equation gave a small overestimation of FFM with 1.46 ± 2.16 kg (p < 0.001) with a tendency towards proportional bias (r = 0.28, p = 0.066). For segmental BIA, the Heitmann* equation gave the highest agreement with FFM DXA (0.17 ± 1.83 kg (p = 0.546)). Using the manufacturer's equation, no difference in FFM estimates was observed (-0.34 ± 2.06 kg (p = 0.292)), however, a clear proportional bias was detected (r = 0.69, p < 0.001). Both devices demonstrated acceptable ability to detect low FFM compared to DXA using the optimal equation. In a population of non-metastatic CRC patients, mostly consisting of Caucasian adults and with a wide range of body composition measures, both the whole-body BIA and segmental BIA device provide FFM estimates that are comparable to FFM DXA on a group level when the appropriate equations are applied. At the individual level (i.e. in clinical practice) BIA may be a valuable tool to identify patients with low FFM as part of a malnutrition diagnosis. Copyright © 2017 The Author(s). Published by Elsevier Ltd.. All rights reserved.

Methods for estimating the magnitude and frequency of peak streamflows at ungaged sites in and near the Oklahoma Panhandle

USGS Publications Warehouse

Smith, S. Jerrod; Lewis, Jason M.; Graves, Grant M.

2015-09-28

Generalized-least-squares multiple-linear regression analysis was used to formulate regression relations between peak-streamflow frequency statistics and basin characteristics. Contributing drainage area was the only basin characteristic determined to be statistically significant for all percentage of annual exceedance probabilities and was the only basin characteristic used in regional regression equations for estimating peak-streamflow frequency statistics on unregulated streams in and near the Oklahoma Panhandle. The regression model pseudo-coefficient of determination, converted to percent, for the Oklahoma Panhandle regional regression equations ranged from about 38 to 63 percent. The standard errors of prediction and the standard model errors for the Oklahoma Panhandle regional regression equations ranged from about 84 to 148 percent and from about 76 to 138 percent, respectively. These errors were comparable to those reported for regional peak-streamflow frequency regression equations for the High Plains areas of Texas and Colorado. The root mean square errors for the Oklahoma Panhandle regional regression equations (ranging from 3,170 to 92,000 cubic feet per second) were less than the root mean square errors for the Oklahoma statewide regression equations (ranging from 18,900 to 412,000 cubic feet per second); therefore, the Oklahoma Panhandle regional regression equations produce more accurate peak-streamflow statistic estimates for the irrigated period of record in the Oklahoma Panhandle than do the Oklahoma statewide regression equations. The regression equations developed in this report are applicable to streams that are not substantially affected by regulation, impoundment, or surface-water withdrawals. These regression equations are intended for use for stream sites with contributing drainage areas less than or equal to about 2,060 square miles, the maximum value for the independent variable used in the regression analysis.

Differential reactivities of four homogeneous assays for LDL-cholesterol in serum to intermediate-density lipoproteins and small dense LDL: comparisons with the Friedewald equation.

PubMed

Yamashita, Shizuya; Kawase, Ryota; Nakaoka, Hajime; Nakatani, Kazuhiro; Inagaki, Miwako; Yuasa-Kawase, Miyako; Tsubakio-Yamamoto, Kazumi; Sandoval, Jose C; Masuda, Daisaku; Ohama, Tohru; Nakagawa-Toyama, Yumiko; Matsuyama, Akifumi; Nishida, Makoto; Ishigami, Masato

2009-12-01

In routine clinical laboratory testing and numerous epidemiological studies, LDL-cholesterol (LDL-C) has been estimated commonly using the Friedewald equation. We investigated the relationship between the Friedewald equation and 4 homogeneous assays for LDL-C. LDL-C was determined by 4 homogeneous assays [liquid selective detergent method: LDL-C (L), selective solubilization method: LDL-C (S), elimination method: LDL-C (E), and enzyme selective protecting method: LDL-C (P)]. Samples with discrepancies between the Friedewald equation and the 4 homogeneous assays for LDL-C were subjected to polyacrylamide gel electrophoresis and the beta-quantification method. The correlations between the Friedewald equation and the 4 homogeneous LDL-C assays were as follows: LDL-C (L) (r=0.962), LDL-C (S) (r=0.986), LDL-C (E) (r=0.946) and LDL-C (P) (r=0.963). Discrepancies were observed in sera from type III hyperlipoproteinemia patients and in sera containing large amounts of midband and small dense LDL on polyacrylamide gel electrophoresis. LDL-C (S) was most strongly correlated with the beta-quantification method even in sera from patients with type III hyperlipoproteinemia. Of the 4 homogeneous assays for LDL-C, LDL-C (S) exhibited the closest correlation with the Friedewald equation and the beta-quantification method, thus reflecting the current clinical databases for coronary heart disease.

A specific prediction equation is necessary to estimate peak oxygen uptake in obese patients with metabolic syndrome.

PubMed

Debeaumont, D; Tardif, C; Folope, V; Castres, I; Lemaitre, F; Tourny, C; Dechelotte, P; Thill, C; Darmon, A; Coquart, J B

2016-06-01

The aims were to: (1) compare peak oxygen uptake ([Formula: see text]peak) predicted from four standard equations to actual [Formula: see text]peak measured from a cardiopulmonary exercise test (CPET) in obese patients with metabolic syndrome (MetS), and (2) develop a new equation to accurately estimate [Formula: see text]peak in obese women with MetS. Seventy-five obese patients with MetS performed a CPET. Anthropometric data were also collected for each participant. [Formula: see text]peak was predicted from four prediction equations (from Riddle et al., Hansen et al., Wasserman et al. or Gläser et al.) and then compared with the actual [Formula: see text]peak measured during the CPET. The accuracy of the predictions was determined with the Bland-Altman method. When accuracy was low, a new prediction equation including anthropometric variables was proposed. [Formula: see text]peak predicted from the equation of Wasserman et al. was not significantly different from actual [Formula: see text]peak in women. Moreover, a significant correlation was found between the predicted and actual values (p < 0.001, r = 0.69). In men, no significant difference was noted between actual [Formula: see text]peak and [Formula: see text]peak predicted from the prediction equation of Gläser et al., and these two values were also correlated (p = 0.03, r = 0.44). However, the LoA95% was wide, whatever the prediction equation or gender. Regression analysis suggested a new prediction equation derived from age and height for obese women with MetS. The methods of Wasserman et al. and Gläser et al. are valid to predict [Formula: see text]peak in obese women and men with MetS, respectively. However, the accuracy of the predictions was low for both methods. Consequently, a new prediction equation including age and height was developed for obese women with MetS. However, new prediction equation remains to develop in obese men with MetS.

Seismic gradiometry using ambient seismic noise in an anisotropic Earth

NASA Astrophysics Data System (ADS)

de Ridder, S. A. L.; Curtis, A.

2017-05-01

We introduce a wavefield gradiometry technique to estimate both isotropic and anisotropic local medium characteristics from short recordings of seismic signals by inverting a wave equation. The method exploits the information in the spatial gradients of a seismic wavefield that are calculated using dense deployments of seismic arrays. The application of the method uses the surface wave energy in the ambient seismic field. To estimate isotropic and anisotropic medium properties we invert an elliptically anisotropic wave equation. The spatial derivatives of the recorded wavefield are evaluated by calculating finite differences over nearby recordings, which introduces a systematic anisotropic error. A two-step approach corrects this error: finite difference stencils are first calibrated, then the output of the wave-equation inversion is corrected using the linearized impulse response to the inverted velocity anomaly. We test the procedure on ambient seismic noise recorded in a large and dense ocean bottom cable array installed over Ekofisk field. The estimated azimuthal anisotropy forms a circular geometry around the production-induced subsidence bowl. This conforms with results from studies employing controlled sources, and with interferometry correlating long records of seismic noise. Yet in this example, the results were obtained using only a few minutes of ambient seismic noise.

Estimating Aeroheating of a 3D Body Using a 2D Flow Solver

NASA Technical Reports Server (NTRS)

Scott, Carl D.; Brykina, Irina G.

2005-01-01

A method for rapidly estimating the aeroheating, shear stress, and other properties of hypersonic flow about a three-dimensional (3D) blunt body has been devised. First, the geometry of the body is specified in Cartesian coordinates. The surface of the body is then described by its derivatives, coordinates, and principal curvatures. Next, previously relatively simple equations are used to find, for each desired combination of angle of attack and meridional angle, a scaling factor and the shape of an equivalent axisymmetric body. These factors and equivalent shapes are entered as inputs into a previously developed computer program that solves the two-dimensional (2D) equations of flow in a non-equilibrium viscous shock layer (VSL) about an axisymmetric body. The coordinates in the output of the VSL code are transformed back to the Cartesian coordinates of the 3D body, so that computed flow quantities can be registered with locations in the 3D flow field of interest. In tests in which the 3D bodies were elliptic paraboloids, the estimates obtained by use of this method were found to agree well with solutions of 3D, finite-rate-chemistry, thin-VSL equations for a catalytic body.

Regional ground-water evapotranspiration and ground-water budgets, Great Basin, Nevada

USGS Publications Warehouse

Nichols, William D.

2000-01-01

PART A: Ground-water evapotranspiration data from five sites in Nevada and seven sites in Owens Valley, California, were used to develop equations for estimating ground-water evapotranspiration as a function of phreatophyte plant cover or as a function of the depth to ground water. Equations are given for estimating mean daily seasonal and annual ground-water evapotranspiration. The equations that estimate ground-water evapotranspiration as a function of plant cover can be used to estimate regional-scale ground-water evapotranspiration using vegetation indices derived from satellite data for areas where the depth to ground water is poorly known. Equations that estimate ground-water evapotranspiration as a function of the depth to ground water can be used where the depth to ground water is known, but for which information on plant cover is lacking. PART B: Previous ground-water studies estimated groundwater evapotranspiration by phreatophytes and bare soil in Nevada on the basis of results of field studies published in 1912 and 1932. More recent studies of evapotranspiration by rangeland phreatophytes, using micrometeorological methods as discussed in Chapter A of this report, provide new data on which to base estimates of ground-water evapotranspiration. An approach correlating ground-water evapotranspiration with plant cover is used in conjunction with a modified soil-adjusted vegetation index derived from Landsat data to develop a method for estimating the magnitude and distribution of ground-water evapotranspiration at a regional scale. Large areas of phreatophytes near Duckwater and Lockes in Railroad Valley are believed to subsist on ground water discharged from nearby regional springs. Ground-water evapotranspiration by the Duckwater phreatophytes of about 11,500 acre-feet estimated by the method described in this report compares well with measured discharge of about 13,500 acre-feet from the springs near Duckwater. Measured discharge from springs near Lockes was about 2,400 acre-feet; estimated ground-water evapotranspiration using the proposed method was about 2,450 acre-feet. PART C: Previous estimates of ground-water budgets in Nevada were based on methods and data that now are more than 60 years old. Newer methods, data, and technologies were used in the present study to estimate ground-water recharge from precipitation and ground-water discharge by evapotranspiration by phreatophytes for 16 contiguous valleys in eastern Nevada. Annual ground-water recharge to these valleys was estimated to be about 855,000 acre-feet and annual ground-water evapotranspiration was estimated to be about 790,000 acrefeet; both are a little more than two times greater than previous estimates. The imbalance of recharge over evapotranspiration represents recharge that either (1) leaves the area as interbasin flow or (2) is derived from precipitation that falls on terrain within the topographic boundary of the study area but contributes to discharge from hydrologic systems that lie outside these topographic limits. A vegetation index derived from Landsat-satellite data was used to estimate phreatophyte plant cover on the floors of the 16 valleys. The estimated phreatophyte plant cover then was used to estimate annual ground-water evapotranspiration. Detailed estimates of summer, winter, and annual ground-water evapotranspiration for areas with different ranges of phreatophyte plant cover were prepared for each valley. The estimated ground-water discharge from 15 valleys, combined with independent estimates of interbasin ground-water flow into or from a valley, were used to calculate the percentage of recharge derived from precipitation within the topographic boundary of each valley. These percentages then were used to estimate ground-water recharge from precipitation within each valley. Ground-water budgets for all 16 valleys were based on the estimated recharge from precipitation and estimated evapotranspiration. Any imba

Mixed Effects Modeling Using Stochastic Differential Equations: Illustrated by Pharmacokinetic Data of Nicotinic Acid in Obese Zucker Rats.

PubMed

Leander, Jacob; Almquist, Joachim; Ahlström, Christine; Gabrielsson, Johan; Jirstrand, Mats

2015-05-01

Inclusion of stochastic differential equations in mixed effects models provides means to quantify and distinguish three sources of variability in data. In addition to the two commonly encountered sources, measurement error and interindividual variability, we also consider uncertainty in the dynamical model itself. To this end, we extend the ordinary differential equation setting used in nonlinear mixed effects models to include stochastic differential equations. The approximate population likelihood is derived using the first-order conditional estimation with interaction method and extended Kalman filtering. To illustrate the application of the stochastic differential mixed effects model, two pharmacokinetic models are considered. First, we use a stochastic one-compartmental model with first-order input and nonlinear elimination to generate synthetic data in a simulated study. We show that by using the proposed method, the three sources of variability can be successfully separated. If the stochastic part is neglected, the parameter estimates become biased, and the measurement error variance is significantly overestimated. Second, we consider an extension to a stochastic pharmacokinetic model in a preclinical study of nicotinic acid kinetics in obese Zucker rats. The parameter estimates are compared between a deterministic and a stochastic NiAc disposition model, respectively. Discrepancies between model predictions and observations, previously described as measurement noise only, are now separated into a comparatively lower level of measurement noise and a significant uncertainty in model dynamics. These examples demonstrate that stochastic differential mixed effects models are useful tools for identifying incomplete or inaccurate model dynamics and for reducing potential bias in parameter estimates due to such model deficiencies.

Temporal variations of potential fecundity of southern blue whiting (Micromesistius australis australis) in the Southeast Pacific

NASA Astrophysics Data System (ADS)

Flores, Andrés; Wiff, Rodrigo; Díaz, Eduardo; Carvajal, Bernardita

2017-08-01

Fecundity is a key aspect of fish species reproductive biology because it relates directly to total egg production. Yet, despite such importance, fecundity estimates are lacking or scarce for several fish species. The gravimetric method is the most-used one to estimate fecundity by essentially scaling up the oocyte density to the ovary weight. It is a relatively simple and precise technique, but also time consuming because it requires counting all oocytes in an ovary subsample. The auto-diametric method, on the other hand, is relatively new for estimating fecundity, representing a rapid alternative, because it requires only an estimation of mean oocyte density from mean oocyte diameter. Using the extensive database available from commercial fishery and design surveys for southern blue whiting Micromesistius australis australis in the Southeast Pacific, we compared estimates of fecundity using both gravimetric and auto-diametric methods. Temporal variations in potential fecundity from the auto-diametric method were evaluated using generalised linear models considering predictors from maternal characteristics such as female size, condition factor, oocyte size, and gonadosomatic index. A global and time-invariant auto-diametric equation was evaluated using a simulation procedure based on non-parametric bootstrap. Results indicated there were not significant differences regarding fecundity estimates between the gravimetric and auto-diametric method (p > 0.05). Simulation showed the application of a global equation is unbiased and sufficiently precise to estimate time-invariant fecundity of this species. Temporal variations on fecundity were explained by maternal characteristic, revealing signals of fecundity down-regulation. We discuss how oocyte size and nutritional condition (measured as condition factor) are one of the important factors determining fecundity. We highlighted also the relevance of choosing the appropriate sampling period to conduct maturity studies and ensure precise estimates of fecundity of this species.

Regularized minimum I-divergence methods for the inverse blackbody radiation problem

NASA Astrophysics Data System (ADS)

Choi, Kerkil; Lanterman, Aaron D.; Shin, Jaemin

2006-08-01

This paper proposes iterative methods for estimating the area temperature distribution of a blackbody from its total radiated power spectrum measurements. This is called the inverse blackbody radiation problem. This problem is inherently ill-posed due to the characteristics of the kernel in the underlying integral equation given by Planck's law. The functions involved in the problem are all non-negative. Csiszár's I-divergence is an information-theoretic discrepancy measure between two non-negative functions. We derive iterative methods for minimizing Csiszár's I-divergence between the measured power spectrum and the power spectrum arising from the estimate according to the integral equation. Due to the ill-posedness of the problem, unconstrained algorithms often produce poor estimates, especially when the measurements are corrupted by noise. To alleviate this difficulty, we apply regularization methods to our algorithms. Penalties based on Shannon's entropy, the L1-norm and Good's roughness are chosen to suppress the undesirable artefacts. When a penalty is applied, the pertinent optimization that needs to be performed at each iteration is no longer trivial. In particular, Good's roughness causes couplings between estimate components. To handle this issue, we adapt Green's one-step-late method. This choice is based on the important fact that our minimum I-divergence algorithms can be interpreted as asymptotic forms of certain expectation-maximization algorithms. The effectiveness of our methods is illustrated via various numerical experiments.

Noninvasive prediction of left ventricular end-diastolic pressure in patients with coronary artery disease and preserved ejection fraction.

PubMed

Abd-El-Aziz, Tarek A

2012-01-01

The aim of this study was to compare 3 different available methods for estimating left ventricular end-diastolic pressure (LVEDP) noninvasively in patients with coronary artery disease and preserved left ventricular ejection fraction (EF). We used 3 equations for noninvasive estimation of LVEDP: The equation of Mulvagh et al., LVEDP(1) = 46 - 0.22 (IVRT) - 0.10 (AFF) - 0.03 (DT) - (2 ÷ E/A) + 0.05 MAR; the equation of Stork et al., LVEDP(2) = 1.06 + 15.15 × Ai/Ei; and the equation of Abd-El-Aziz, LVEDP(3) = [0.54 (MABP) × (1 - EF)] - 2.23. ( A, A-wave velocity; AFF, atrial filling fraction; Ai, time velocity integral of A wave; DT, deceleration time; E, E-wave velocity; Ei, time velocity integral of E wave; IVRT, isovolumic relaxation time; MABP, mean arterial blood pressure; MAR, time from termination of mitral flow to the electrocardiographic R wave; Ti, time velocity integral of total wave.) LVEDP measured by catheterization was correlated with LVEDP(1) (r = 0.52, P < 0.001), LVEDP(2) (r = 0.31, P < 0.05), and LVEDP(3) (r = 0.81, P < 0.001). The equation described by Abd-El-Aziz, LVEDP = [0.54 MABP × (1 - EF)] - 2.23, appears to be the most accurate, reliable, and easily applied method for estimating LVEDP noninvasively in patients with preserved left ventricular ejection fraction and an LVEDP < 20 mm Hg. Copyright © 2012 Canadian Cardiovascular Society. Published by Elsevier Inc. All rights reserved.

Using groundwater levels to estimate recharge

USGS Publications Warehouse

Healy, R.W.; Cook, P.G.

2002-01-01

Accurate estimation of groundwater recharge is extremely important for proper management of groundwater systems. Many different approaches exist for estimating recharge. This paper presents a review of methods that are based on groundwater-level data. The water-table fluctuation method may be the most widely used technique for estimating recharge; it requires knowledge of specific yield and changes in water levels over time. Advantages of this approach include its simplicity and an insensitivity to the mechanism by which water moves through the unsaturated zone. Uncertainty in estimates generated by this method relate to the limited accuracy with which specific yield can be determined and to the extent to which assumptions inherent in the method are valid. Other methods that use water levels (mostly based on the Darcy equation) are also described. The theory underlying the methods is explained. Examples from the literature are used to illustrate applications of the different methods.

Convergence results for pseudospectral approximations of hyperbolic systems by a penalty type boundary treatment

NASA Technical Reports Server (NTRS)

Funaro, Daniele; Gottlieb, David

1989-01-01

A new method of imposing boundary conditions in the pseudospectral approximation of hyperbolic systems of equations is proposed. It is suggested to collocate the equations, not only at the inner grid points, but also at the boundary points and use the boundary conditions as penalty terms. In the pseudo-spectral Legrendre method with the new boundary treatment, a stability analysis for the case of a constant coefficient hyperbolic system is presented and error estimates are derived.

Indispensable finite time corrections for Fokker-Planck equations from time series data.

PubMed

Ragwitz, M; Kantz, H

2001-12-17

The reconstruction of Fokker-Planck equations from observed time series data suffers strongly from finite sampling rates. We show that previously published results are degraded considerably by such effects. We present correction terms which yield a robust estimation of the diffusion terms, together with a novel method for one-dimensional problems. We apply these methods to time series data of local surface wind velocities, where the dependence of the diffusion constant on the state variable shows a different behavior than previously suggested.

Estimation of total body water from bioelectrical impedance spectroscopy in oncology outpatients receiving radiotherapy and agreement with three prediction equations.

PubMed

Isenring, E; Colombo, M; Cross, G; Kellett, E; Swaney, L

2009-02-01

Bioelectrical impedance spectroscopy (BIS) may be more accurate in determining total body water (TBW) than bioelectrical impedance analysis (BIA). The present study compared the agreement between three TBW prediction equations developed using BIA and BIS-derived TBW in oncology outpatients. A cross-sectional, observational study was conducted in 37 outpatients receiving radiotherapy (27 males/10 females, aged 68.3 +/- 10.2 years). TBW was estimated by BIS (TBW(BIS)) and three BIA TBW prediction equations (TBW(ca-u): underweight cancer patients; TBW(ca-n): normal-weight cancer patients; and TBW(rad): patients receiving radiotherapy). Bland-Altman analyses determined agreement between methods. BIS-derived TBW using new resistivity constants was calculated. The mean +/- SD of TBW estimated by BIS was 39.8 +/- 8.3 L, which was significantly different from the prediction equations; TBW(rad) 35.1 +/- 7.9 L, TBW(ca-u) 33.1 +/- 7.5 L and TBW(ca-n) 32.3 +/- 7.3 L, (P < 0.001). Using new resistivity constants, TBW was 36.2 +/- 8.1 L but this still differed from the equations (P < 0.001). Bias between TBW(BIS) and that predicted by the equations was in the range 4.7-7.4 L or 1.1-3.9 L using new resistivity constants. TBW estimated by BIS cannot be directly compared with oncology-specific BIA equations, suggesting that BIS cannot be used at the group level in outpatients receiving radiotherapy. There was a reduced bias with BIS using new resistivity constants; however, further research should determine any advantage of BIS over BIA in this population.

A stochastic hybrid systems based framework for modeling dependent failure processes

PubMed Central

Fan, Mengfei; Zeng, Zhiguo; Zio, Enrico; Kang, Rui; Chen, Ying

2017-01-01

In this paper, we develop a framework to model and analyze systems that are subject to dependent, competing degradation processes and random shocks. The degradation processes are described by stochastic differential equations, whereas transitions between the system discrete states are triggered by random shocks. The modeling is, then, based on Stochastic Hybrid Systems (SHS), whose state space is comprised of a continuous state determined by stochastic differential equations and a discrete state driven by stochastic transitions and reset maps. A set of differential equations are derived to characterize the conditional moments of the state variables. System reliability and its lower bounds are estimated from these conditional moments, using the First Order Second Moment (FOSM) method and Markov inequality, respectively. The developed framework is applied to model three dependent failure processes from literature and a comparison is made to Monte Carlo simulations. The results demonstrate that the developed framework is able to yield an accurate estimation of reliability with less computational costs compared to traditional Monte Carlo-based methods. PMID:28231313

A stochastic hybrid systems based framework for modeling dependent failure processes.

PubMed

Fan, Mengfei; Zeng, Zhiguo; Zio, Enrico; Kang, Rui; Chen, Ying

2017-01-01

In this paper, we develop a framework to model and analyze systems that are subject to dependent, competing degradation processes and random shocks. The degradation processes are described by stochastic differential equations, whereas transitions between the system discrete states are triggered by random shocks. The modeling is, then, based on Stochastic Hybrid Systems (SHS), whose state space is comprised of a continuous state determined by stochastic differential equations and a discrete state driven by stochastic transitions and reset maps. A set of differential equations are derived to characterize the conditional moments of the state variables. System reliability and its lower bounds are estimated from these conditional moments, using the First Order Second Moment (FOSM) method and Markov inequality, respectively. The developed framework is applied to model three dependent failure processes from literature and a comparison is made to Monte Carlo simulations. The results demonstrate that the developed framework is able to yield an accurate estimation of reliability with less computational costs compared to traditional Monte Carlo-based methods.

Predicted versus measured resting energy expenditure in patients requiring home parenteral nutrition.

PubMed

Ławiński, Michał; Singer, Pierre; Gradowski, Łukasz; Gradowska, Aleksandra; Bzikowska, Agnieszka; Majewska, Krystyna

2015-01-01

Guidelines from the European Society for Clinical Nutrition and Metabolism (ESPEN) recommend between 20 and 35 kcal/kg daily for patients requiring home parenteral nutrition (PN). Other guidelines use predictive equations. However, these equations have not been validated. Indirect calorimetry is recommended as the gold standard for determining resting energy expenditure (REE). The aim of this study was to compare the frequently used equations with measured REE. Seventy-six hospitalized patients suffering from intestinal failure (ages 21-85 y) were enrolled between January 2012 and May 2014. They were eligible for implementation of home parenteral nutrition (HPN) due to short bowel syndrome (54%), intestinal fistulae (24%), cancer obstruction (16%), and radiation-induced intestinal injury (6%). REE measurements were compared with predictive equations by Harris and Benedict (HB), Owen, Ireton-Jones, and Mifflin, as well as recommendations from ESPEN. In all, 152 calorimetry measurements (two per patient) were performed in 76 patients, after total PN administrations. An average result of REE measurement by indirect calorimetry was 1181 ± 322 kcal/d. Variability in momentary energy expenditure (MEE) from one measurement to the other was 8% ± 7%. Bland-Altman analysis showed a mean bias of -192 ± 300 kcal/d between MEE and estimated energy expenditure using the HB equation, which means that the equation increased the score on average by 192 ± 300 kcal/d. Limits of agreement (LoA) between the two methods was -780 to +396 kcal/d. Estimation energy expenditure using the Ireton-Jones equation gave a mean bias of -359 ± 335 kcal/d. LoA between the two methods was -1015 to +297 kcal/d. For Owen equation, Bland-Altman analysis showed a mean bias of -208 ± 313 kcal/d and the LoA between the two methods was -822 to +406 kcal/d. Using the Mifflin equation, estimation energy expenditure gave a mean bias of -172 ± 312 kcal/d and the LoA between the two methods was -784 to +439 kcal/d. Using the ESPEN range (20-35 kcal/kg daily) analysis showed mean bias of -13 ± 326 kcal/d and the LoA was -652 to +626 kcal/d for 20 kcal/kg daily and mean bias of -909 ± 436 kcal/d with the LoA between the two methods -1764 to -54 kcal/d for 35 kcal/kg daily. If REE cannot be measured by indirect calorimetry in patients qualified for HPN, the Ireton-Jones equation and the 20 kcal/kg/d ESPEN recommendation seem to be the most appropriate ones as it provides results that constitute the best approximation of calorimetric examination results. Copyright © 2015 Elsevier Inc. All rights reserved.

A New Global Regression Analysis Method for the Prediction of Wind Tunnel Model Weight Corrections

NASA Technical Reports Server (NTRS)

Ulbrich, Norbert Manfred; Bridge, Thomas M.; Amaya, Max A.

2014-01-01

A new global regression analysis method is discussed that predicts wind tunnel model weight corrections for strain-gage balance loads during a wind tunnel test. The method determines corrections by combining "wind-on" model attitude measurements with least squares estimates of the model weight and center of gravity coordinates that are obtained from "wind-off" data points. The method treats the least squares fit of the model weight separate from the fit of the center of gravity coordinates. Therefore, it performs two fits of "wind- off" data points and uses the least squares estimator of the model weight as an input for the fit of the center of gravity coordinates. Explicit equations for the least squares estimators of the weight and center of gravity coordinates are derived that simplify the implementation of the method in the data system software of a wind tunnel. In addition, recommendations for sets of "wind-off" data points are made that take typical model support system constraints into account. Explicit equations of the confidence intervals on the model weight and center of gravity coordinates and two different error analyses of the model weight prediction are also discussed in the appendices of the paper.

Height intercept for estimating site index in young ponderosa pine plantations and natural stands

Treesearch

William W. Oliver

1972-01-01

Site index is difficult to estimate with any reliability in ponderosa pine (Pinus ponderosa Laws.) stands below 20 yeas old. A method of estimating site index based on 4-year height intercepts (total length of the first four internodes above breast height) is described. Equations based on two sets of published site-index curves were developed. They...

Estimating Available Fuel Weight Consumed by Prescribed Fires in the South

Treesearch

Walter A. Hough

1978-01-01

A method is proposed for estimating the weight of fuel burned (available fuel) by prescribed fires in southern pine stands. Weights of available fuel in litter alone and in litter plus understory materials can be estimated. Prediction equations were developed by regression analysis of data from a variety of locations and stand conditions. They are most reliable for...

Mixed-Poisson Point Process with Partially-Observed Covariates: Ecological Momentary Assessment of Smoking.

PubMed

Neustifter, Benjamin; Rathbun, Stephen L; Shiffman, Saul

2012-01-01

Ecological Momentary Assessment is an emerging method of data collection in behavioral research that may be used to capture the times of repeated behavioral events on electronic devices, and information on subjects' psychological states through the electronic administration of questionnaires at times selected from a probability-based design as well as the event times. A method for fitting a mixed Poisson point process model is proposed for the impact of partially-observed, time-varying covariates on the timing of repeated behavioral events. A random frailty is included in the point-process intensity to describe variation among subjects in baseline rates of event occurrence. Covariate coefficients are estimated using estimating equations constructed by replacing the integrated intensity in the Poisson score equations with a design-unbiased estimator. An estimator is also proposed for the variance of the random frailties. Our estimators are robust in the sense that no model assumptions are made regarding the distribution of the time-varying covariates or the distribution of the random effects. However, subject effects are estimated under gamma frailties using an approximate hierarchical likelihood. The proposed approach is illustrated using smoking data.

Converting wood volume to biomass for pinyon and juniper. Forest Service research note

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

Chojnacky, D.C.; Moisen, G.G.

1993-03-01

A technique was developed to convert pinyon-juniper volume equation predictions to weights. The method uses specific gravity and biomass conversion equations to obtain foliage weight and total wood weight of all stems, branches, and bark. Specific gravity data are given for several Arizona pinyon-juniper species. Biomass conversion equations are constructed from pinyon-juniper data collected in Nevada. Results provide an interim means of estimating pinyon-juniper aboveground biomass from available volume inventory data.

Study on monostable and bistable reaction-diffusion equations by iteration of travelling wave maps

NASA Astrophysics Data System (ADS)

Yi, Taishan; Chen, Yuming

2017-12-01

In this paper, based on the iterative properties of travelling wave maps, we develop a new method to obtain spreading speeds and asymptotic propagation for monostable and bistable reaction-diffusion equations. Precisely, for Dirichlet problems of monostable reaction-diffusion equations on the half line, by making links between travelling wave maps and integral operators associated with the Dirichlet diffusion kernel (the latter is NOT invariant under translation), we obtain some iteration properties of the Dirichlet diffusion and some a priori estimates on nontrivial solutions of Dirichlet problems under travelling wave transformation. We then provide the asymptotic behavior of nontrivial solutions in the space-time region for Dirichlet problems. These enable us to develop a unified method to obtain results on heterogeneous steady states, travelling waves, spreading speeds, and asymptotic spreading behavior for Dirichlet problem of monostable reaction-diffusion equations on R+ as well as of monostable/bistable reaction-diffusion equations on R.

Median and Low-Flow Characteristics for Streams under Natural and Diverted Conditions, Northeast Maui, Hawaii

USGS Publications Warehouse

Gingerich, Stephen B.

2005-01-01

Flow-duration statistics under natural (undiverted) and diverted flow conditions were estimated for gaged and ungaged sites on 21 streams in northeast Maui, Hawaii. The estimates were made using the optimal combination of continuous-record gaging-station data, low-flow measurements, and values determined from regression equations developed as part of this study. Estimated 50- and 95-percent flow duration statistics for streams are presented and the analyses done to develop and evaluate the methods used in estimating the statistics are described. Estimated streamflow statistics are presented for sites where various amounts of streamflow data are available as well as for locations where no data are available. Daily mean flows were used to determine flow-duration statistics for continuous-record stream-gaging stations in the study area following U.S. Geological Survey established standard methods. Duration discharges of 50- and 95-percent were determined from total flow and base flow for each continuous-record station. The index-station method was used to adjust all of the streamflow records to a common, long-term period. The gaging station on West Wailuaiki Stream (16518000) was chosen as the index station because of its record length (1914-2003) and favorable geographic location. Adjustments based on the index-station method resulted in decreases to the 50-percent duration total flow, 50-percent duration base flow, 95-percent duration total flow, and 95-percent duration base flow computed on the basis of short-term records that averaged 7, 3, 4, and 1 percent, respectively. For the drainage basin of each continuous-record gaged site and selected ungaged sites, morphometric, geologic, soil, and rainfall characteristics were quantified using Geographic Information System techniques. Regression equations relating the non-diverted streamflow statistics to basin characteristics of the gaged basins were developed using ordinary-least-squares regression analyses. Rainfall rate, maximum basin elevation, and the elongation ratio of the basin were the basin characteristics used in the final regression equations for 50-percent duration total flow and base flow. Rainfall rate and maximum basin elevation were used in the final regression equations for the 95-percent duration total flow and base flow. The relative errors between observed and estimated flows ranged from 10 to 20 percent for the 50-percent duration total flow and base flow, and from 29 to 56 percent for the 95-percent duration total flow and base flow. The regression equations developed for this study were used to determine the 50-percent duration total flow, 50-percent duration base flow, 95-percent duration total flow, and 95-percent duration base flow at selected ungaged diverted and undiverted sites. Estimated streamflow, prediction intervals, and standard errors were determined for 48 ungaged sites in the study area and for three gaged sites west of the study area. Relative errors were determined for sites where measured values of 95-percent duration discharge of total flow were available. East of Keanae Valley, the 95-percent duration discharge equation generally underestimated flow, and within and west of Keanae Valley, the equation generally overestimated flow. Reduction in 50- and 95-percent flow-duration values in stream reaches affected by diversions throughout the study area average 58 to 60 percent.

An analytical method for the inverse Cauchy problem of Lame equation in a rectangle

NASA Astrophysics Data System (ADS)

Grigor’ev, Yu

2018-04-01

In this paper, we present an analytical computational method for the inverse Cauchy problem of Lame equation in the elasticity theory. A rectangular domain is frequently used in engineering structures and we only consider the analytical solution in a two-dimensional rectangle, wherein a missing boundary condition is recovered from the full measurement of stresses and displacements on an accessible boundary. The essence of the method consists in solving three independent Cauchy problems for the Laplace and Poisson equations. For each of them, the Fourier series is used to formulate a first-kind Fredholm integral equation for the unknown function of data. Then, we use a Lavrentiev regularization method, and the termwise separable property of kernel function allows us to obtain a closed-form regularized solution. As a result, for the displacement components, we obtain solutions in the form of a sum of series with three regularization parameters. The uniform convergence and error estimation of the regularized solutions are proved.

40 CFR 63.1414 - Test methods and emission estimation equations.

Code of Federal Regulations, 2010 CFR

2010-07-01

... (D) Design analysis based on accepted chemical engineering principles, measurable process parameters.... Engineering assessment may be used to estimate organic HAP emissions from a batch emission episode only under... (d)(5) of this section; through engineering assessment, as defined in paragraph (d)(6)(ii) of this...

Estimates of nitric oxide production for lifting spacecraft reentry

NASA Technical Reports Server (NTRS)

Park, C.

1971-01-01

The amount of nitric oxide which may be produced by heating of air during an atmospheric reentry of a lifting spacecraft is estimated by three different methods. Two assume nitrogen fixation by the process of sudden freezing, and the third is a computer calculation using chemical rate equations.

40 CFR 63.1414 - Test methods and emission estimation equations.

Code of Federal Regulations, 2012 CFR

2012-07-01

... (D) Design analysis based on accepted chemical engineering principles, measurable process parameters.... Engineering assessment may be used to estimate organic HAP emissions from a batch emission episode only under... (d)(5) of this section; through engineering assessment, as defined in paragraph (d)(6)(ii) of this...

40 CFR 63.1414 - Test methods and emission estimation equations.

Code of Federal Regulations, 2011 CFR

2011-07-01

... (D) Design analysis based on accepted chemical engineering principles, measurable process parameters.... Engineering assessment may be used to estimate organic HAP emissions from a batch emission episode only under... (d)(5) of this section; through engineering assessment, as defined in paragraph (d)(6)(ii) of this...

40 CFR 63.1414 - Test methods and emission estimation equations.

Code of Federal Regulations, 2014 CFR

2014-07-01

... (D) Design analysis based on accepted chemical engineering principles, measurable process parameters... paragraph (d)(5) of this section. Engineering assessment may be used to estimate organic HAP emissions from... defined in paragraph (d)(5) of this section; through engineering assessment, as defined in paragraph (d)(6...

40 CFR 63.1414 - Test methods and emission estimation equations.

Code of Federal Regulations, 2013 CFR

2013-07-01

... (D) Design analysis based on accepted chemical engineering principles, measurable process parameters... paragraph (d)(5) of this section. Engineering assessment may be used to estimate organic HAP emissions from... defined in paragraph (d)(5) of this section; through engineering assessment, as defined in paragraph (d)(6...

Comparisons of estimates of annual exceedance-probability discharges for small drainage basins in Iowa, based on data through water year 2013.

DOT National Transportation Integrated Search

2015-01-01

Traditionally, the Iowa Department of Transportation : has used the Iowa Runoff Chart and single-variable regional-regression equations (RREs) from a U.S. Geological Survey : report (published in 1987) as the primary methods to estimate : annual exce...

Methods for estimating annual exceedance-probability discharges and largest recorded floods for unregulated streams in rural Missouri.

DOT National Transportation Integrated Search

2014-01-01

Regression analysis techniques were used to develop a : set of equations for rural ungaged stream sites for estimating : discharges with 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent : annual exceedance probabilities, which are equivalent to : ann...

Comparisons of estimates of annual exceedance-probability discharges for small drainage basins in Iowa, based on data through water year 2013 : [summary].

DOT National Transportation Integrated Search

2015-01-01

Traditionally, the Iowa DOT has used the Iowa Runoff Chart and single-variable regional regression equations (RREs) from a USGS report : (published in 1987) as the primary methods to estimate annual exceedance-probability discharge : (AEPD) for small...

Variance Estimation Using Replication Methods in Structural Equation Modeling with Complex Sample Data

ERIC Educational Resources Information Center

Stapleton, Laura M.

2008-01-01

This article discusses replication sampling variance estimation techniques that are often applied in analyses using data from complex sampling designs: jackknife repeated replication, balanced repeated replication, and bootstrapping. These techniques are used with traditional analyses such as regression, but are currently not used with structural…

Numerical simulation code for self-gravitating Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Madarassy, Enikő J. M.; Toth, Viktor T.

2013-04-01

We completed the development of simulation code that is designed to study the behavior of a conjectured dark matter galactic halo that is in the form of a Bose-Einstein Condensate (BEC). The BEC is described by the Gross-Pitaevskii equation, which can be solved numerically using the Crank-Nicholson method. The gravitational potential, in turn, is described by Poisson’s equation, that can be solved using the relaxation method. Our code combines these two methods to study the time evolution of a self-gravitating BEC. The inefficiency of the relaxation method is balanced by the fact that in subsequent time iterations, previously computed values of the gravitational field serve as very good initial estimates. The code is robust (as evidenced by its stability on coarse grids) and efficient enough to simulate the evolution of a system over the course of 109 years using a finer (100×100×100) spatial grid, in less than a day of processor time on a contemporary desktop computer. Catalogue identifier: AEOR_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOR_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.: 5248 No. of bytes in distributed program, including test data, etc.: 715402 Distribution format: tar.gz Programming language: C++ or FORTRAN. Computer: PCs or workstations. Operating system: Linux or Windows. Classification: 1.5. Nature of problem: Simulation of a self-gravitating Bose-Einstein condensate by simultaneous solution of the Gross-Pitaevskii and Poisson equations in three dimensions. Solution method: The Gross-Pitaevskii equation is solved numerically using the Crank-Nicholson method; Poisson’s equation is solved using the relaxation method. The time evolution of the system is governed by the Gross-Pitaevskii equation; the solution of Poisson’s equation at each time step is used as an initial estimate for the next time step, which dramatically increases the efficiency of the relaxation method. Running time: Depends on the chosen size of the problem. On a typical personal computer, a 100×100×100 grid can be solved with a time span of 10 Gyr in approx. a day of running time.

Development and validation of anthropometric equations to estimate appendicular muscle mass in elderly women.

PubMed

Pereira, Piettra Moura Galvão; da Silva, Giselma Alcântara; Santos, Gilberto Moreira; Petroski, Edio Luiz; Geraldes, Amandio Aristides Rihan

2013-07-02

This study aimed to examine the cross validity of two anthropometric equations commonly used and propose simple anthropometric equations to estimate appendicular muscle mass (AMM) in elderly women. Among 234 physically active and functionally independent elderly women, 101 (60 to 89 years) were selected through simple drawing to compose the study sample. The paired t test and the Pearson correlation coefficient were used to perform cross-validation and concordance was verified by intraclass correction coefficient (ICC) and by the Bland and Altman technique. To propose predictive models, multiple linear regression analysis, anthropometric measures of body mass (BM), height, girth, skinfolds, body mass index (BMI) were used, and muscle perimeters were included in the analysis as independent variables. Dual-Energy X-ray Absorptiometry (AMMDXA) was used as criterion measurement. The sample power calculations were carried out by Post Hoc Compute Achieved Power. Sample power values from 0.88 to 0.91 were observed. When compared, the two equations tested differed significantly from the AMMDXA (p <0.001 and p = 0.001). Ten population / specific anthropometric equations were developed to estimate AMM, among them, three equations achieved all validation criteria used: AMM (E2) = 4.150 +0.251 [bodymass (BM)] - 0.411 [bodymass index (BMI)] + 0.011 [Right forearm perimeter (PANTd) 2]; AMM (E3) = 4.087 + 0.255 (BM) - 0.371 (BMI) + 0.011 (PANTd) 2 - 0.035 [thigh skinfold (DCCO)]; MMA (E6) = 2.855 + 0.298 (BM) + 0.019 (Age) - 0,082 [hip circumference (PQUAD)] + 0.400 (PANTd) - 0.332 (BMI). The equations estimated the criterion method (p = 0.056 p = 0.158), and explained from 0.69% to 0.74% of variations observed in AMMDXA with low standard errors of the estimate (1.36 to 1.55 kg) and high concordance (ICC between 0,90 and 0.91 and concordance limits from -2,93 to 2,33 kg). The equations tested were not valid for use in physically active and functionally independent elderly women. The simple anthropometric equations developed in this study showed good practical applicability and high validity to estimate AMM in elderly women.

Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation. II

NASA Astrophysics Data System (ADS)

Kazeykina, Anna; Muñoz, Claudio

2018-04-01

We continue our study on the Cauchy problem for the two-dimensional Novikov-Veselov (NV) equation, integrable via the inverse scattering transform for the two dimensional Schrödinger operator at a fixed energy parameter. This work is concerned with the more involved case of a positive energy parameter. For the solution of the linearized equation we derive smoothing and Strichartz estimates by combining new estimates for two different frequency regimes, extending our previous results for the negative energy case [18]. The low frequency regime, which our previous result was not able to treat, is studied in detail. At non-low frequencies we also derive improved smoothing estimates with gain of almost one derivative. Then we combine the linear estimates with a Fourier decomposition method and Xs,b spaces to obtain local well-posedness of NV at positive energy in Hs, s > 1/2. Our result implies, in particular, that at least for s > 1/2, NV does not change its behavior from semilinear to quasilinear as energy changes sign, in contrast to the closely related Kadomtsev-Petviashvili equations. As a complement to our LWP results, we also provide some new explicit solutions of NV at zero energy, generalizations of the lumps solutions, which exhibit new and nonstandard long time behavior. In particular, these solutions blow up in infinite time in L2.

A comparative study of finite element and finite difference methods for Cauchy-Riemann type equations

NASA Technical Reports Server (NTRS)

Fix, G. J.; Rose, M. E.

1983-01-01

A least squares formulation of the system divu = rho, curlu = zeta is surveyed from the viewpoint of both finite element and finite difference methods. Closely related arguments are shown to establish convergence estimates.

Cockcroft-Gault revisited: New de-liver-ance on recommendations for use in cirrhosis.

PubMed

Scappaticci, Gianni B; Regal, Randolph E

2017-01-28

The Cockcroft-Gault (CG) equation has become perhaps the most popular practical approach for estimating renal function among health care professionals. Despite its widespread use, clinicians often overlook not only the limitations of the original serum creatinine (SCr) based equation, but also may not appreciate the validity of the many variations used to compensate for these limitations. For cirrhotic patients in particular, the underlying pathophysiology of the disease contributes to a falsely low SCr, thereby overestimating renal function with use of the CG equation in this population. We reviewed the original CG trial from 1976 along with data surrounding clinician specific alterations to the CG equation that followed through time. These alterations included different formulas for body weight in obese patients and the "rounding up" approach in patients with low SCr. Additionally, we described the pathophysiology and hemodynamic changes that occur in cirrhosis; and reviewed several studies that attempted to estimate renal function in this population. The evidence we reviewed regarding the most accurate manipulation of the original CG equation to estimate creatinine clearance (CrCl) was inconclusive. Unfortunately, the homogeneity of the patient population in the original CG trial limited its external validity. Elimination of body weight in the CG equation actually produced the estimate closest to the measure CrCl. Furthermore, "rounding up" of SCr values often underestimated CrCl. This approach could lead to suboptimal dosing of drug therapies in patients with low SCr. In cirrhotic patients, utilization of SCr based methods overestimated true renal function by about 50% in the literature we reviewed.

Performance of the UK Prospective Diabetes Study Risk Engine and the Framingham Risk Equations in Estimating Cardiovascular Disease in the EPIC- Norfolk Cohort

PubMed Central

Simmons, Rebecca K.; Coleman, Ruth L.; Price, Hermione C.; Holman, Rury R.; Khaw, Kay-Tee; Wareham, Nicholas J.; Griffin, Simon J.

2009-01-01

OBJECTIVE The purpose of this study was to examine the performance of the UK Prospective Diabetes Study (UKPDS) Risk Engine (version 3) and the Framingham risk equations (2008) in estimating cardiovascular disease (CVD) incidence in three populations: 1) individuals with known diabetes; 2) individuals with nondiabetic hyperglycemia, defined as A1C ≥6.0%; and 3) individuals with normoglycemia defined as A1C <6.0%. RESEARCH DESIGN AND METHODS This was a population-based prospective cohort (European Prospective Investigation of Cancer-Norfolk). Participants aged 40–79 years recruited from U.K. general practices attended a health examination (1993–1998) and were followed for CVD events/death until April 2007. CVD risk estimates were calculated for 10,137 individuals. RESULTS Over 10.1 years, there were 69 CVD events in the diabetes group (25.4%), 160 in the hyperglycemia group (17.7%), and 732 in the normoglycemia group (8.2%). Estimated CVD 10-year risk in the diabetes group was 33 and 37% using the UKPDS and Framingham equations, respectively. In the hyperglycemia group, estimated CVD risks were 31 and 22%, respectively, and for the normoglycemia group risks were 20 and 14%, respectively. There were no significant differences in the ability of the risk equations to discriminate between individuals at different risk of CVD events in each subgroup; both equations overestimated CVD risk. The Framingham equations performed better in the hyperglycemia and normoglycemia groups as they did not overestimate risk as much as the UKPDS Risk Engine, and they classified more participants correctly. CONCLUSIONS Both the UKPDS Risk Engine and Framingham risk equations were moderately effective at ranking individuals and are therefore suitable for resource prioritization. However, both overestimated true risk, which is important when one is using scores to communicate prognostic information to individuals. PMID:19114615

Validation of cystatin C-based equations for evaluating residual renal function in patients on continuous ambulatory peritoneal dialysis.

PubMed

Zhong, Hui; Zhang, Wei; Qin, Min; Gou, ZhongPing; Feng, Ping

2017-06-01

Residual renal function needs to be assessed frequently in patients on continuous ambulatory peritoneal dialysis (CAPD). A commonly used method is to measure creatinine (Cr) and urea clearance in urine collected over 24 h, but collection can be cumbersome and difficult to manage. A faster, simpler alternative is to measure levels of cystatin C (CysC) in serum, but the accuracy and reliability of this method is controversial. Our study aims to validate published CysC-based equations for estimating residual renal function in patients on CAPD. Residual renal function was measured by calculating average clearance of urea and Cr in 24-h urine as well as by applying CysC- or Cr-based equations published by Hoek and Yang. We then compared the performance of the equations against the 24-h urine results. In our sample of 255 patients ages 47.9 ± 15.6 years, the serum CysC level was 6.43 ± 1.13 mg/L. Serum CysC level was not significantly associated with age, gender, height, weight, body mass index, hemoglobin, intact parathyroid hormone, normalized protein catabolic rate or the presence of diabetes. In contrast, serum CysC levels did correlate with peritoneal clearance of CysC and with levels of prealbumin and high-sensitivity C-reactive protein. Residual renal function was 2.56 ± 2.07 mL/min/1.73 m 2 based on 24-h urine sampling, compared with estimates (mL/min/1.73 m 2 ) of 2.98 ± 0.66 for Hoek's equation, 2.03 ± 0.97 for Yang's CysC-based equation and 2.70 ± 1.30 for Yang's Cr-based equation. Accuracies within 30%/50% of measured residual renal function for the three equations were 29.02/48.24, 34.90/56.86 and 31.37/54.90. The three equations for estimating residual renal function showed similar limits of agreement and differed significantly from the measured value. Published CysC-based equations do not appear to be particularly reliable for patients on CAPD. Further development and validation of CysC-based equations should take into account peritoneal clearance of CysC and other relevant factors. © The Author 2016. Published by Oxford University Press on behalf of ERA-EDTA. All rights reserved.

Regularized Semiparametric Estimation for Ordinary Differential Equations

PubMed Central

Li, Yun; Zhu, Ji; Wang, Naisyin

2015-01-01

Ordinary differential equations (ODEs) are widely used in modeling dynamic systems and have ample applications in the fields of physics, engineering, economics and biological sciences. The ODE parameters often possess physiological meanings and can help scientists gain better understanding of the system. One key interest is thus to well estimate these parameters. Ideally, constant parameters are preferred due to their easy interpretation. In reality, however, constant parameters can be too restrictive such that even after incorporating error terms, there could still be unknown sources of disturbance that lead to poor agreement between observed data and the estimated ODE system. In this paper, we address this issue and accommodate short-term interferences by allowing parameters to vary with time. We propose a new regularized estimation procedure on the time-varying parameters of an ODE system so that these parameters could change with time during transitions but remain constants within stable stages. We found, through simulation studies, that the proposed method performs well and tends to have less variation in comparison to the non-regularized approach. On the theoretical front, we derive finite-sample estimation error bounds for the proposed method. Applications of the proposed method to modeling the hare-lynx relationship and the measles incidence dynamic in Ontario, Canada lead to satisfactory and meaningful results. PMID:26392639

Operational Retrievals of Evapotranspiration: Are we there yet?

NASA Astrophysics Data System (ADS)

Neale, C. M. U.; Anderson, M. C.; Hain, C.; Schull, M.; Isidro, C., Sr.; Goncalves, I. Z.

2017-12-01

Remote sensing based retrievals of evapotranspiration (ET) have progressed significantly over the last two decades with the improvement of methods and algorithms and the availability of multiple satellite sensors with shortwave and thermal infrared bands on polar orbiting platforms. The modeling approaches include simpler vegetation index (VI) based methods such as the reflectance-based crop coefficient approach coupled with surface reference evapotranspiration estimates to derive actual evapotranspiration of crops or, direct inputs to the Penman-Monteith equation through VI relationships with certain input variables. Methods that are more complex include one-layer or two-layer energy balance approaches that make use of both shortwave and longwave spectral band information to estimate different inputs to the energy balance equation. These models mostly differ in the estimation of sensible heat fluxes. For continental and global scale applications, other satellite-based products such as solar radiation, vegetation leaf area and cover are used as inputs, along with gridded re-analysis weather information. This presentation will review the state-of-the-art in satellite-based evapotranspiration estimation, giving examples of existing efforts to obtain operational ET retrievals over continental and global scales and discussing difficulties and challenges.

Bayesian source term estimation of atmospheric releases in urban areas using LES approach.

PubMed

Xue, Fei; Kikumoto, Hideki; Li, Xiaofeng; Ooka, Ryozo

2018-05-05

The estimation of source information from limited measurements of a sensor network is a challenging inverse problem, which can be viewed as an assimilation process of the observed concentration data and the predicted concentration data. When dealing with releases in built-up areas, the predicted data are generally obtained by the Reynolds-averaged Navier-Stokes (RANS) equations, which yields building-resolving results; however, RANS-based models are outperformed by large-eddy simulation (LES) in the predictions of both airflow and dispersion. Therefore, it is important to explore the possibility of improving the estimation of the source parameters by using the LES approach. In this paper, a novel source term estimation method is proposed based on LES approach using Bayesian inference. The source-receptor relationship is obtained by solving the adjoint equations constructed using the time-averaged flow field simulated by the LES approach based on the gradient diffusion hypothesis. A wind tunnel experiment with a constant point source downwind of a single building model is used to evaluate the performance of the proposed method, which is compared with that of the existing method using a RANS model. The results show that the proposed method reduces the errors of source location and releasing strength by 77% and 28%, respectively. Copyright © 2018 Elsevier B.V. All rights reserved.

Update to core reporting practices in structural equation modeling.

PubMed

Schreiber, James B

This paper is a technical update to "Core Reporting Practices in Structural Equation Modeling." 1 As such, the content covered in this paper includes, sample size, missing data, specification and identification of models, estimation method choices, fit and residual concerns, nested, alternative, and equivalent models, and unique issues within the SEM family of techniques. Copyright © 2016 Elsevier Inc. All rights reserved.

Agreement between VO[subscript 2peak] Predicted from PACER and One-Mile Run Time-Equated Laps

ERIC Educational Resources Information Center

Saint-Maurice, Pedro F.; Anderson, Katelin; Bai, Yang; Welk, Gregory J.

2016-01-01

Purpose: This study examined the agreement between estimated peak oxygen consumption (VO[subscript 2peak]) obtained from the Progressive Aerobic Cardiovascular Endurance Run (PACER) fitness test and equated PACER laps derived from One-Mile Run time (MR). Methods: A sample of 680 participants (324 boys and 356 girls) in Grades 7 through 12…

Comparison of Various Equations for Estimating GFR in Malawi: How to Determine Renal Function in Resource Limited Settings?

PubMed Central

Phiri, Sam; Rothenbacher, Dietrich; Neuhann, Florian

2015-01-01

Background Chronic kidney disease (CKD) is a probably underrated public health problem in Sub-Saharan-Africa, in particular in combination with HIV-infection. Knowledge about the CKD prevalence is scarce and in the available literature different methods to classify CKD are used impeding comparison and general prevalence estimates. Methods This study assessed different serum-creatinine based equations for glomerular filtration rates (eGFR) and compared them to a cystatin C based equation. The study was conducted in Lilongwe, Malawi enrolling a population of 363 adults of which 32% were HIV-positive. Results Comparison of formulae based on Bland-Altman-plots and accuracy revealed best performance for the CKD-EPI equation without the correction factor for black Americans. Analyzing the differences between HIV-positive and –negative individuals CKD-EPI systematically overestimated eGFR in comparison to cystatin C and therefore lead to underestimation of CKD in HIV-positives. Conclusions Our findings underline the importance for standardization of eGFR calculation in a Sub-Saharan African setting, to further investigate the differences with regard to HIV status and to develop potential correction factors as established for age and sex. PMID:26083345

Utility of Equations to Estimate Peak Oxygen Uptake and Work Rate From a 6-Minute Walk Test in Patients With COPD in a Clinical Setting.

PubMed

Kirkham, Amy A; Pauhl, Katherine E; Elliott, Robyn M; Scott, Jen A; Doria, Silvana C; Davidson, Hanan K; Neil-Sztramko, Sarah E; Campbell, Kristin L; Camp, Pat G

2015-01-01

To determine the utility of equations that use the 6-minute walk test (6MWT) results to estimate peak oxygen uptake ((Equation is included in full-text article.)o2) and peak work rate with chronic obstructive pulmonary disease (COPD) patients in a clinical setting. This study included a systematic review to identify published equations estimating peak (Equation is included in full-text article.)o2 and peak work rate in watts in COPD patients and a retrospective chart review of data from a hospital-based pulmonary rehabilitation program. The following variables were abstracted from the records of 42 consecutively enrolled COPD patients: measured peak (Equation is included in full-text article.)o2 and peak work rate achieved during a cycle ergometer cardiopulmonary exercise test, 6MWT distance, age, sex, weight, height, forced expiratory volume in 1 second, forced vital capacity, and lung diffusion capacity. Estimated peak (Equation is included in full-text article.)o2 and peak work rate were estimated from 6MWT distance using published equations. The error associated with using estimated peak (Equation is included in full-text article.)o2 or peak work to prescribe aerobic exercise intensities of 60% and 80% was calculated. Eleven equations from 6 studies were identified. Agreement between estimated and measured values was poor to moderate (intraclass correlation coefficients = 0.11-0.63). The error associated with using estimated peak (Equation is included in full-text article.)o2 or peak work rate to prescribe exercise intensities of 60% and 80% of measured values ranged from mean differences of 12 to 35 and 16 to 47 percentage points, respectively. There is poor to moderate agreement between measured peak (Equation is included in full-text article.)o2 and peak work rate and estimations from equations that use 6MWT distance, and the use of the estimated values for prescription of aerobic exercise intensity would result in large error. Equations estimating peak (Equation is included in full-text article.)o2 and peak work rate are of low utility for prescribing exercise intensity in pulmonary rehabilitation programs.

Adjoint Fokker-Planck equation and runaway electron dynamics

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

Liu, Chang; Brennan, Dylan P.; Bhattacharjee, Amitava

2016-01-15

The adjoint Fokker-Planck equation method is applied to study the runaway probability function and the expected slowing-down time for highly relativistic runaway electrons, including the loss of energy due to synchrotron radiation. In direct correspondence to Monte Carlo simulation methods, the runaway probability function has a smooth transition across the runaway separatrix, which can be attributed to effect of the pitch angle scattering term in the kinetic equation. However, for the same numerical accuracy, the adjoint method is more efficient than the Monte Carlo method. The expected slowing-down time gives a novel method to estimate the runaway current decay timemore » in experiments. A new result from this work is that the decay rate of high energy electrons is very slow when E is close to the critical electric field. This effect contributes further to a hysteresis previously found in the runaway electron population.« less

Methods of generating synthetic acoustic logs from resistivity logs for gas-hydrate-bearing sediments

USGS Publications Warehouse

Lee, Myung W.

1999-01-01

Methods of predicting acoustic logs from resistivity logs for hydrate-bearing sediments are presented. Modified time average equations derived from the weighted equation provide a means of relating the velocity of the sediment to the resistivity of the sediment. These methods can be used to transform resistivity logs into acoustic logs with or without using the gas hydrate concentration in the pore space. All the parameters except the unconsolidation constants, necessary for the prediction of acoustic log from resistivity log, can be estimated from a cross plot of resistivity versus porosity values. Unconsolidation constants in equations may be assumed without rendering significant errors in the prediction. These methods were applied to the acoustic and resistivity logs acquired at the Mallik 2L-38 gas hydrate research well drilled at the Mackenzie Delta, northern Canada. The results indicate that the proposed method is simple and accurate.

A stopping criterion for the iterative solution of partial differential equations

NASA Astrophysics Data System (ADS)

Rao, Kaustubh; Malan, Paul; Perot, J. Blair

2018-01-01

A stopping criterion for iterative solution methods is presented that accurately estimates the solution error using low computational overhead. The proposed criterion uses information from prior solution changes to estimate the error. When the solution changes are noisy or stagnating it reverts to a less accurate but more robust, low-cost singular value estimate to approximate the error given the residual. This estimator can also be applied to iterative linear matrix solvers such as Krylov subspace or multigrid methods. Examples of the stopping criterion's ability to accurately estimate the non-linear and linear solution error are provided for a number of different test cases in incompressible fluid dynamics.

Regression method for estimating long-term mean annual ground-water recharge rates from base flow in Pennsylvania

USGS Publications Warehouse

Risser, Dennis W.; Thompson, Ronald E.; Stuckey, Marla H.

2008-01-01

A method was developed for making estimates of long-term, mean annual ground-water recharge from streamflow data at 80 streamflow-gaging stations in Pennsylvania. The method relates mean annual base-flow yield derived from the streamflow data (as a proxy for recharge) to the climatic, geologic, hydrologic, and physiographic characteristics of the basins (basin characteristics) by use of a regression equation. Base-flow yield is the base flow of a stream divided by the drainage area of the basin, expressed in inches of water basinwide. Mean annual base-flow yield was computed for the period of available streamflow record at continuous streamflow-gaging stations by use of the computer program PART, which separates base flow from direct runoff on the streamflow hydrograph. Base flow provides a reasonable estimate of recharge for basins where streamflow is mostly unaffected by upstream regulation, diversion, or mining. Twenty-eight basin characteristics were included in the exploratory regression analysis as possible predictors of base-flow yield. Basin characteristics found to be statistically significant predictors of mean annual base-flow yield during 1971-2000 at the 95-percent confidence level were (1) mean annual precipitation, (2) average maximum daily temperature, (3) percentage of sand in the soil, (4) percentage of carbonate bedrock in the basin, and (5) stream channel slope. The equation for predicting recharge was developed using ordinary least-squares regression. The standard error of prediction for the equation on log-transformed data was 9.7 percent, and the coefficient of determination was 0.80. The equation can be used to predict long-term, mean annual recharge rates for ungaged basins, providing that the explanatory basin characteristics can be determined and that the underlying assumption is accepted that base-flow yield derived from PART is a reasonable estimate of ground-water recharge rates. For example, application of the equation for 370 hydrologic units in Pennsylvania predicted a range of ground-water recharge from about 6.0 to 22 inches per year. A map of the predicted recharge illustrates the general magnitude and variability of recharge throughout Pennsylvania.

A New Formulation of the Filter-Error Method for Aerodynamic Parameter Estimation in Turbulence

NASA Technical Reports Server (NTRS)

Grauer, Jared A.; Morelli, Eugene A.

2015-01-01

A new formulation of the filter-error method for estimating aerodynamic parameters in nonlinear aircraft dynamic models during turbulence was developed and demonstrated. The approach uses an estimate of the measurement noise covariance to identify the model parameters, their uncertainties, and the process noise covariance, in a relaxation method analogous to the output-error method. Prior information on the model parameters and uncertainties can be supplied, and a post-estimation correction to the uncertainty was included to account for colored residuals not considered in the theory. No tuning parameters, needing adjustment by the analyst, are used in the estimation. The method was demonstrated in simulation using the NASA Generic Transport Model, then applied to the subscale T-2 jet-engine transport aircraft flight. Modeling results in different levels of turbulence were compared with results from time-domain output error and frequency- domain equation error methods to demonstrate the effectiveness of the approach.