Forecasting Air Force Logistics Command Second Destination Transportation: An Application of Multiple Regression Analysis and Neural Networks

DTIC Science & Technology

1990-09-01

without the help from the DSXR staff. William Lyons, Charles Ramsey , and Martin Meeks went above and beyond to help complete this research. Special...develop a valid forecasting model that is significantly more accurate than the one presently used by DSXR and suggested the development and testing of a...method, Strom tested DSXR’s iterative linear regression forecasting technique by examining P1 in the simple regression equation to determine whether

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

USGS Publications Warehouse

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

2000-01-01

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

Reversed inverse regression for the univariate linear calibration and its statistical properties derived using a new methodology

NASA Astrophysics Data System (ADS)

Kang, Pilsang; Koo, Changhoi; Roh, Hokyu

2017-11-01

Since simple linear regression theory was established at the beginning of the 1900s, it has been used in a variety of fields. Unfortunately, it cannot be used directly for calibration. In practical calibrations, the observed measurements (the inputs) are subject to errors, and hence they vary, thus violating the assumption that the inputs are fixed. Therefore, in the case of calibration, the regression line fitted using the method of least squares is not consistent with the statistical properties of simple linear regression as already established based on this assumption. To resolve this problem, "classical regression" and "inverse regression" have been proposed. However, they do not completely resolve the problem. As a fundamental solution, we introduce "reversed inverse regression" along with a new methodology for deriving its statistical properties. In this study, the statistical properties of this regression are derived using the "error propagation rule" and the "method of simultaneous error equations" and are compared with those of the existing regression approaches. The accuracy of the statistical properties thus derived is investigated in a simulation study. We conclude that the newly proposed regression and methodology constitute the complete regression approach for univariate linear calibrations.

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.

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.

[Relation between Body Height and Combined Length of Manubrium and Mesosternum of Sternum Measured by CT-VRT in Southwest Han Population].

PubMed

Luo, Ying-zhen; Tu, Meng; Fan, Fei; Zheng, Jie-qian; Yang, Ming; Li, Tao; Zhang, Kui; Deng, Zhen-hua

2015-06-01

To establish the linear regression equation between body height and combined length of manubrium and mesostenum of sternum measured by CT volume rendering technique (CT-VRT) in southwest Han population. One hundred and sixty subjects, including 80 males and 80 females were selected from southwest Han population for routine CT-VRT (reconstruction thickness 1 mm) examination. The lengths of both manubrium and mesosternum were recorded, and the combined length of manubrium and mesosternum was equal to the algebraic sum of them. The sex-specific linear regression equations between the combined length of manubrium and mesosternum and the real body height of each subject were deduced. The sex-specific simple linear regression equations between the combined length of manubrium and mesostenum (x3) and body height (y) were established (male: y = 135.000+2.118 x3 and female: y = 120.790+2.808 x3). Both equations showed statistical significance (P < 0.05) with a 100% predictive accuracy. CT-VRT is an effective method for measurement of the index of sternum. The combined length of manubrium and mesosternum from CT-VRT can be used for body height estimation in southwest Han population.

Correlating the Subjects of Books Taken Out of and Books Used Within an Open-Stack Library

ERIC Educational Resources Information Center

McGrath, William E.

1971-01-01

Out-of-library circulation totals were found to be reliable indicators of in-library use. For predicting in-library use (and thus total use) two methods are cited: simple ratio of out to in, and the regression equation. (4 references) (Author/NH)

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

USGS Publications Warehouse

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

2002-01-01

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

Quantification of pleural effusion on CT by simple measurement.

PubMed

Hazlinger, Martin; Ctvrtlik, Filip; Langova, Katerina; Herman, Miroslav

2014-01-01

To find the simplest method for quantifying pleural effusion volume from CT scans. Seventy pleural effusions found on chest CT examination in 50 consecutive adult patients with the presence of free pleural effusion were included. The volume of pleural effusion was calculated from a three-dimensional reconstruction of CT scans. Planar measurements were made on CT scans and their two-dimensional reconstructions in the sagittal plane and at three levels on transversal scans. Individual planar measurements were statistically compared with the detected volume of pleural effusion. Regression equations, averaged absolute difference between observed and predicted values and determination coefficients were found for all measurements and their combinations. A tabular expression of the best single planar measurement was created. The most accurate correlation between the volume and a single planar measurement was found in the dimension measured perpendicular to the parietal pleura on transversal scan with the greatest depth of effusion. Conversion of this measurement to the appropriate volume is possible by regression equation: Volume = 0.365 × b(3) - 4.529 × b(2) + 159.723 × b - 88.377. We devised a simple method of conversion of a single planar measurement on CT scan to the volume of pleural effusion. The tabular expression of our equation can be easily and effectively used in routine practice.

Schooling, Literacy and Individual Earnings. International Adult Literacy Survey.

ERIC Educational Resources Information Center

Osberg, Lars

This paper uses direct measures of literacy skill levels provided by the International Adult Literacy Survey to estimate the return to literacy skills. Using a very simple human capital earnings equation and standard ordinary least squares regression, it tested estimates of the return to literacy skills for their robustness to alternative scalings…

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.

Linear models for calculating digestibile energy for sheep diets.

PubMed

Fonnesbeck, P V; Christiansen, M L; Harris, L E

1981-05-01

Equations for estimating the digestible energy (DE) content of sheep diets were generated from the chemical contents and a factorial description of diets fed to lambs in digestion trials. The diet factors were two forages (alfalfa and grass hay), harvested at three stages of maturity (late vegetative, early bloom and full bloom), fed in two ingredient combinations (all hay or a 50:50 hay and corn grain mixture) and prepared by two forage texture processes (coarsely chopped or finely chopped and pelleted). The 2 x 3 x 2 x 2 factorial arrangement produced 24 diet treatments. These were replicated twice, for a total of 48 lamb digestion trials. In model 1 regression equations, DE was calculated directly from chemical composition of the diet. In model 2, regression equations predicted the percentage of digested nutrient from the chemical contents of the diet and then DE of the diet was calculated as the sum of the gross energy of the digested organic components. Expanded forms of model 1 and model 2 were also developed that included diet factors as qualitative indicator variables to adjust the regression constant and regression coefficients for the diet description. The expanded forms of the equations accounted for significantly more variation in DE than did the simple models and more accurately estimated DE of the diet. Information provided by the diet description proved as useful as chemical analyses for the prediction of digestibility of nutrients. The statistics indicate that, with model 1, neutral detergent fiber and plant cell wall analyses provided as much information for the estimation of DE as did model 2 with the combined information from crude protein, available carbohydrate, total lipid, cellulose and hemicellulose. Regression equations are presented for estimating DE with the most currently analyzed organic components, including linear and curvilinear variables and diet factors that significantly reduce the standard error of the estimate. To estimate De of a diet, the user utilizes the equation that uses the chemical analysis information and diet description most effectively.

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.

Incorporating Learning Motivation and Self-Concept in Mathematical Communicative Ability

ERIC Educational Resources Information Center

Rajagukguk, Waminton

2016-01-01

This research is trying to determine of the mathematical concepts, instead by integrating the learning motivation (X[subscript 1]) and self-concept (X[subscript 2]) can contribute to the mathematical communicative ability (Y). The test instruments showed the following results: (1) simple regressive equation Y on X[subscript 1] was Y = 32.891 +…

Hybrid Rocket Performance Prediction with Coupling Method of CFD and Thermal Conduction Calculation

NASA Astrophysics Data System (ADS)

Funami, Yuki; Shimada, Toru

The final purpose of this study is to develop a design tool for hybrid rocket engines. This tool is a computer code which will be used in order to investigate rocket performance characteristics and unsteady phenomena lasting through the burning time, such as fuel regression or combustion oscillation. When phenomena inside a combustion chamber, namely boundary layer combustion, are described, it is difficult to use rigorous models for this target. It is because calculation cost may be too expensive. Therefore simple models are required for this calculation. In this study, quasi-one-dimensional compressible Euler equations for flowfields inside a chamber and the equation for thermal conduction inside a solid fuel are numerically solved. The energy balance equation at the solid fuel surface is solved to estimate fuel regression rate. Heat feedback model is Karabeyoglu's model dependent on total mass flux. Combustion model is global single step reaction model for 4 chemical species or chemical equilibrium model for 9 chemical species. As a first step, steady-state solutions are reported.

Nonlinear least-squares data fitting in Excel spreadsheets.

PubMed

Kemmer, Gerdi; Keller, Sandro

2010-02-01

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

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.

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

USGS Publications Warehouse

Wiley, Jeffrey B.; Atkins, John T.

2010-01-01

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

A Simultaneous Equation Demand Model for Block Rates

NASA Astrophysics Data System (ADS)

Agthe, Donald E.; Billings, R. Bruce; Dobra, John L.; Raffiee, Kambiz

1986-01-01

This paper examines the problem of simultaneous-equations bias in estimation of the water demand function under an increasing block rate structure. The Hausman specification test is used to detect the presence of simultaneous-equations bias arising from correlation of the price measures with the regression error term in the results of a previously published study of water demand in Tucson, Arizona. An alternative simultaneous equation model is proposed for estimating the elasticity of demand in the presence of block rate pricing structures and availability of service charges. This model is used to reestimate the price and rate premium elasticities of demand in Tucson, Arizona for both the usual long-run static model and for a simple short-run demand model. The results from these simultaneous equation models are consistent with a priori expectations and are unbiased.

Quantifying prosthetic gait deviation using simple outcome measures

PubMed Central

Kark, Lauren; Odell, Ross; McIntosh, Andrew S; Simmons, Anne

2016-01-01

AIM: To develop a subset of simple outcome measures to quantify prosthetic gait deviation without needing three-dimensional gait analysis (3DGA). METHODS: Eight unilateral, transfemoral amputees and 12 unilateral, transtibial amputees were recruited. Twenty-eight able-bodied controls were recruited. All participants underwent 3DGA, the timed-up-and-go test and the six-minute walk test (6MWT). The lower-limb amputees also completed the Prosthesis Evaluation Questionnaire. Results from 3DGA were summarised using the gait deviation index (GDI), which was subsequently regressed, using stepwise regression, against the other measures. RESULTS: Step-length (SL), self-selected walking speed (SSWS) and the distance walked during the 6MWT (6MWD) were significantly correlated with GDI. The 6MWD was the strongest, single predictor of the GDI, followed by SL and SSWS. The predictive ability of the regression equations were improved following inclusion of self-report data related to mobility and prosthetic utility. CONCLUSION: This study offers a practicable alternative to quantifying kinematic deviation without the need to conduct complete 3DGA. PMID:27335814

Prediction equation for calculating fat mass in young Indian adults.

PubMed

Sandhu, Jaspal Singh; Gupta, Giniya; Shenoy, Shweta

2010-06-01

Accurate measurement or prediction of fat mass is useful in physiology, nutrition and clinical medicine. Most predictive equations currently used to assess percentage of body fat or fat mass, using simple anthropometric measurements were derived from people in western societies and they may not be appropriate for individuals with other genotypic and phenotypic characteristics. We developed equations to predict fat mass from anthropometric measurements in young Indian adults. Fat mass was measured in 60 females and 58 males, aged 20 to 29 yrs by using hydrostatic weighing and by simultaneous measurement of residual lung volume. Anthropometric measure included weight (kg), height (m) and 4 skinfold thickness [STs (mm)]. Sex specific linear regression model was developed with fat mass as the dependent variable and all anthropometric measures as independent variables. The prediction equation obtained for fat mass (kg) for males was 8.46+0.32 (weight) - 15.16 (height) + 9.54 (log of sum of 4 STs) (R2= 0. 53, SEE=3.42 kg) and - 20.22 + 0.33 (weight) + 3.44 (height) + 7.66 (log of sum of 4 STs) (R2=0.72, SEE=3.01kg) for females. A new prediction equation for the measurement of fat mass was derived and internally validated in young Indian adults using simple anthropometric measurements.

A general power equation for predicting bed load transport rates in gravel bed rivers

Treesearch

Jeffrey J. Barry; John M. Buffington; John G. King

2004-01-01

A variety of formulae has been developed to predict bed load transport in gravel bed rivers, ranging from simple regressions to complex multiparameter formulations. The ability to test these formulae across numerous field sites has, until recently, been hampered by a paucity of bed load transport data for gravel bed rivers. We use 2104 bed load transport observations...

Dating tree mortality using log decay in the White Mountains of New Hampshire

Treesearch

Andrew J. Fast; Mark J. Ducey; Jeffrey H. Gove; William B. Leak

2008-01-01

Coarse woody material (CWM) is an important component of forest ecosystems. To meet specific CWM management objectives, it is important to understand rates of decay. We present results from a silvicultural trial at the Bartlett Experimental Forest, in which time of death is known for a large sample of trees. Either a simple table or regression equations that use...

Predictive Temperature Equations for Three Sites at the Grand Canyon

NASA Astrophysics Data System (ADS)

McLaughlin, Katrina Marie Neitzel

Climate data collected at a number of automated weather stations were used to create a series of predictive equations spanning from December 2009 to May 2010 in order to better predict the temperatures along hiking trails within the Grand Canyon. The central focus of this project is how atmospheric variables interact and can be combined to predict the weather in the Grand Canyon at the Indian Gardens, Phantom Ranch, and Bright Angel sites. Through the use of statistical analysis software and data regression, predictive equations were determined. The predictive equations are simple or multivariable best fits that reflect the curvilinear nature of the data. With data analysis software curves resulting from the predictive equations were plotted along with the observed data. Each equation's reduced chi2 was determined to aid the visual examination of the predictive equations' ability to reproduce the observed data. From this information an equation or pair of equations was determined to be the best of the predictive equations. Although a best predictive equation for each month and season was determined for each site, future work may refine equations to result in a more accurate predictive equation.

Effects of alloy composition on cyclic flame hot-corrosion attack of cast nickel-base superalloys at 900 deg C

NASA Technical Reports Server (NTRS)

Deadmore, D. L.

1984-01-01

The effects of Cr, Al, Ti, Mo, Ta, Nb, and W content on the hot corrosion of nickel base alloys were investigated. The alloys were tested in a Mach 0.3 flame with 0.5 ppmw sodium at a temperature of 900 C. One nondestructive and three destructive tests were conducted. The best corrosion resistance was achieved when the Cr content was 12 wt %. However, some lower-Cr-content alloys ( 10 wt%) exhibited reasonable resistance provided that the Al content alloys ( 10 wt %) exhibited reasonable resistance provided that the Al content was 2.5 wt % and the Ti content was Aa wt %. The effect of W, Ta, Mo, and Nb contents on the hot-corrosion resistance varied depending on the Al and Ti contents. Several commercial alloy compositions were also tested and the corrosion attack was measured. Predicted attack was calculated for these alloys from derived regression equations and was in reasonable agreement with that experimentally measured. The regression equations were derived from measurements made on alloys in a one-quarter replicate of a 2(7) statistical design alloy composition experiment. These regression equations represent a simple linear model and are only a very preliminary analysis of the data needed to provide insights into the experimental method.

Prediction of hearing outcomes by multiple regression analysis in patients with idiopathic sudden sensorineural hearing loss.

PubMed

Suzuki, Hideaki; Tabata, Takahisa; Koizumi, Hiroki; Hohchi, Nobusuke; Takeuchi, Shoko; Kitamura, Takuro; Fujino, Yoshihisa; Ohbuchi, Toyoaki

2014-12-01

This study aimed to create a multiple regression model for predicting hearing outcomes of idiopathic sudden sensorineural hearing loss (ISSNHL). The participants were 205 consecutive patients (205 ears) with ISSNHL (hearing level ≥ 40 dB, interval between onset and treatment ≤ 30 days). They received systemic steroid administration combined with intratympanic steroid injection. Data were examined by simple and multiple regression analyses. Three hearing indices (percentage hearing improvement, hearing gain, and posttreatment hearing level [HLpost]) and 7 prognostic factors (age, days from onset to treatment, initial hearing level, initial hearing level at low frequencies, initial hearing level at high frequencies, presence of vertigo, and contralateral hearing level) were included in the multiple regression analysis as dependent and explanatory variables, respectively. In the simple regression analysis, the percentage hearing improvement, hearing gain, and HLpost showed significant correlation with 2, 5, and 6 of the 7 prognostic factors, respectively. The multiple correlation coefficients were 0.396, 0.503, and 0.714 for the percentage hearing improvement, hearing gain, and HLpost, respectively. Predicted values of HLpost calculated by the multiple regression equation were reliable with 70% probability with a 40-dB-width prediction interval. Prediction of HLpost by the multiple regression model may be useful to estimate the hearing prognosis of ISSNHL. © The Author(s) 2014.

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.

Flood characteristics of urban watersheds in the United States

USGS Publications Warehouse

Sauer, Vernon B.; Thomas, W.O.; Stricker, V.A.; Wilson, K.V.

1983-01-01

A nationwide study of flood magnitude and frequency in urban areas was made for the purpose of reviewing available literature, compiling an urban flood data base, and developing methods of estimating urban floodflow characteristics in ungaged areas. The literature review contains synopses of 128 recent publications related to urban floodflow. A data base of 269 gaged basins in 56 cities and 31 States, including Hawaii, contains a wide variety of topographic and climatic characteristics, land-use variables, indices of urbanization, and flood-frequency estimates. Three sets of regression equations were developed to estimate flood discharges for ungaged sites for recurrence intervals of 2, 5, 10, 25, 50, 100, and 500 years. Two sets of regression equations are based on seven independent parameters and the third is based on three independent parameters. The only difference in the two sets of seven-parameter equations is the use of basin lag time in one and lake and reservoir storage in the other. Of primary importance in these equations is an independent estimate of the equivalent rural discharge for the ungaged basin. The equations adjust the equivalent rural discharge to an urban condition. The primary adjustment factor, or index of urbanization, is the basin development factor, a measure of the extent of development of the drainage system in the basin. This measure includes evaluations of storm drains (sewers), channel improvements, and curb-and-gutter streets. The basin development factor is statistically very significant and offers a simple and effective way of accounting for drainage development and runoff response in urban areas. Percentage of impervious area is also included in the seven-parameter equations as an additional measure of urbanization and apparently accounts for increased runoff volumes. This factor is not highly significant for large floods, which supports the generally held concept that imperviousness is not a dominant factor when soils become more saturated during large storms. Other parameters in the seven-parameter equations include drainage area size, channel slope, rainfall intensity, lake and reservoir storage, and basin lag time. These factors are all statistically significant and provide logical indices of basin conditions. The three-parameter equations include only the three most significant parameters: rural discharge, basin-development factor, and drainage area size. All three sets of regression equations provide unbiased estimates of urban flood frequency. The seven-parameter regression equations without basin lag time have average standard errors of regression varying from ? 37 percent for the 5-year flood to ? 44 percent for the 100-year flood and ? 49 percent for the 500-year flood. The other two sets of regression equations have similar accuracy. Several tests for bias, sensitivity, and hydrologic consistency are included which support the conclusion that the equations are useful throughout the United States. All estimating equations were developed from data collected on drainage basins where temporary in-channel storage, due to highway embankments, was not significant. Consequently, estimates made with these equations do not account for the reducing effect of this temporary detention storage.

Meteorological adjustment of yearly mean values for air pollutant concentration comparison

NASA Technical Reports Server (NTRS)

Sidik, S. M.; Neustadter, H. E.

1976-01-01

Using multiple linear regression analysis, models which estimate mean concentrations of Total Suspended Particulate (TSP), sulfur dioxide, and nitrogen dioxide as a function of several meteorologic variables, two rough economic indicators, and a simple trend in time are studied. Meteorologic data were obtained and do not include inversion heights. The goodness of fit of the estimated models is partially reflected by the squared coefficient of multiple correlation which indicates that, at the various sampling stations, the models accounted for about 23 to 47 percent of the total variance of the observed TSP concentrations. If the resulting model equations are used in place of simple overall means of the observed concentrations, there is about a 20 percent improvement in either: (1) predicting mean concentrations for specified meteorological conditions; or (2) adjusting successive yearly averages to allow for comparisons devoid of meteorological effects. An application to source identification is presented using regression coefficients of wind velocity predictor variables.

Estimation of sex and stature using anthropometry of the upper extremity in an Australian population.

PubMed

Howley, Donna; Howley, Peter; Oxenham, Marc F

2018-06-01

Stature and a further 8 anthropometric dimensions were recorded from the arms and hands of a sample of 96 staff and students from the Australian National University and The University of Newcastle, Australia. These dimensions were used to create simple and multiple logistic regression models for sex estimation and simple and multiple linear regression equations for stature estimation of a contemporary Australian population. Overall sex classification accuracies using the models created were comparable to similar studies. The stature estimation models achieved standard errors of estimates (SEE) which were comparable to and in many cases lower than those achieved in similar research. Generic, non sex-specific models achieved similar SEEs and R 2 values to the sex-specific models indicating stature may be accurately estimated when sex is unknown. Copyright © 2018 Elsevier B.V. All rights reserved.

New methodology for modeling annual-aircraft emissions at airports

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

Woodmansey, B.G.; Patterson, J.G.

An as-accurate-as-possible estimation of total-aircraft emissions are an essential component of any environmental-impact assessment done for proposed expansions at major airports. To determine the amount of emissions generated by aircraft using present models it is necessary to know the emission characteristics of all engines that are on all planes using the airport. However, the published data base does not cover all engine types and, therefore, a new methodology is needed to assist in estimating annual emissions from aircraft at airports. Linear regression equations relating quantity of emissions to aircraft weight using a known-fleet mix are developed in this paper. Total-annualmore » emissions for CO, NO[sub x], NMHC, SO[sub x], CO[sub 2], and N[sub 2]O are tabulated for Toronto's international airport for 1990. The regression equations are statistically significant for all emissions except for NMHC from large jets and NO[sub x] and NMHC for piston-engine aircraft. This regression model is a relatively simple, fast, and inexpensive method of obtaining an annual-emission inventory for an airport.« less

Common y-intercept and single compound regressions of gas-particle partitioning data vs 1/T

NASA Astrophysics Data System (ADS)

Pankow, James F.

Confidence intervals are placed around the log Kp vs 1/ T correlation equations obtained using simple linear regressions (SLR) with the gas-particle partitioning data set of Yamasaki et al. [(1982) Env. Sci. Technol.16, 189-194]. The compounds and groups of compounds studied include the polycylic aromatic hydrocarbons phenanthrene + anthracene, me-phenanthrene + me-anthracene, fluoranthene, pyrene, benzo[ a]fluorene + benzo[ b]fluorene, chrysene + benz[ a]anthracene + triphenylene, benzo[ b]fluoranthene + benzo[ k]fluoranthene, and benzo[ a]pyrene + benzo[ e]pyrene (note: me = methyl). For any given compound, at equilibrium, the partition coefficient Kp equals ( F/ TSP)/ A where F is the particulate-matter associated concentration (ng m -3), A is the gas-phase concentration (ng m -3), and TSP is the concentration of particulate matter (μg m -3). At temperatures more than 10°C from the mean sampling temperature of 17°C, the confidence intervals are quite wide. Since theory predicts that similar compounds sorbing on the same particulate matter should possess very similar y-intercepts, the data set was also fitted using a special common y-intercept regression (CYIR). For most of the compounds, the CYIR equations fell inside of the SLR 95% confidence intervals. The CYIR y-intercept value is -18.48, and is reasonably close to the type of value that can be predicted for PAH compounds. The set of CYIR regression equations is probably more reliable than the set of SLR equations. For example, the CYIR-derived desorption enthalpies are much more highly correlated with vaporization enthalpies than are the SLR-derived desorption enthalpies. It is recommended that the CYIR approach be considered whenever analysing temperature-dependent gas-particle partitioning data.

Statistical analysis of water-level, springflow, and streamflow data for the Edwards Aquifer in south-central Texas

USGS Publications Warehouse

Puente, Celso

1976-01-01

Water-level, springflow, and streamflow data were used to develop simple and multiple linear-regression equations for use in estimating water levels in wells and the flow of three major springs in the Edwards aquifer in the eastern San Antonio area. The equations provide daily, monthly, and annual estimates that compare very favorably with observed data. Analyses of geologic and hydrologic data indicate that the water discharged by the major springs is supplied primarily by regional underflow from the west and southwest and by local recharge in the infiltration area in northern Bexar, Comal, and Hays Counties.

Graphical Tools for Linear Structural Equation Modeling

DTIC Science & Technology

2014-06-01

others. 4Kenny and Milan (2011) write, “Identification is perhaps the most difficult concept for SEM researchers to understand. We have seen SEM...model to using typical SEM software to determine model identifia- bility. Kenny and Milan (2011) list the following drawbacks: (i) If poor starting...the well known recursive and null rules (Bollen, 1989) and the regression rule (Kenny and Milan , 2011). A Simple Criterion for Identifying Individual

Prediction Equation for Calculating Fat Mass in Young Indian Adults

PubMed Central

Sandhu, Jaspal Singh; Gupta, Giniya; Shenoy, Shweta

2010-01-01

Purpose Accurate measurement or prediction of fat mass is useful in physiology, nutrition and clinical medicine. Most predictive equations currently used to assess percentage of body fat or fat mass, using simple anthropometric measurements were derived from people in western societies and they may not be appropriate for individuals with other genotypic and phenotypic characteristics. We developed equations to predict fat mass from anthropometric measurements in young Indian adults. Methods Fat mass was measured in 60 females and 58 males, aged 20 to 29 yrs by using hydrostatic weighing and by simultaneous measurement of residual lung volume. Anthropometric measure included weight (kg), height (m) and 4 skinfold thickness [STs (mm)]. Sex specific linear regression model was developed with fat mass as the dependent variable and all anthropometric measures as independent variables. Results The prediction equation obtained for fat mass (kg) for males was 8.46+0.32 (weight) − 15.16 (height) + 9.54 (log of sum of 4 STs) (R2= 0. 53, SEE=3.42 kg) and − 20.22 + 0.33 (weight) + 3.44 (height) + 7.66 (log of sum of 4 STs) (R2=0.72, SEE=3.01kg) for females. Conclusion A new prediction equation for the measurement of fat mass was derived and internally validated in young Indian adults using simple anthropometric measurements. PMID:22375197

Simple prediction method of lumbar lordosis for planning of lumbar corrective surgery: radiological analysis in a Korean population.

PubMed

Lee, Chong Suh; Chung, Sung Soo; Park, Se Jun; Kim, Dong Min; Shin, Seong Kee

2014-01-01

This study aimed at deriving a lordosis predictive equation using the pelvic incidence and to establish a simple prediction method of lumbar lordosis for planning lumbar corrective surgery in Asians. Eighty-six asymptomatic volunteers were enrolled in the study. The maximal lumbar lordosis (MLL), lower lumbar lordosis (LLL), pelvic incidence (PI), and sacral slope (SS) were measured. The correlations between the parameters were analyzed using Pearson correlation analysis. Predictive equations of lumbar lordosis through simple regression analysis of the parameters and simple predictive values of lumbar lordosis using PI were derived. The PI strongly correlated with the SS (r = 0.78), and a strong correlation was found between the SS and LLL (r = 0.89), and between the SS and MLL (r = 0.83). Based on these correlations, the predictive equations of lumbar lordosis were found (SS = 0.80 + 0.74 PI (r = 0.78, R (2) = 0.61), LLL = 5.20 + 0.87 SS (r = 0.89, R (2) = 0.80), MLL = 17.41 + 0.96 SS (r = 0.83, R (2) = 0.68). When PI was between 30° to 35°, 40° to 50° and 55° to 60°, the equations predicted that MLL would be PI + 10°, PI + 5° and PI, and LLL would be PI - 5°, PI - 10° and PI - 15°, respectively. This simple calculation method can provide a more appropriate and simpler prediction of lumbar lordosis for Asian populations. The prediction of lumbar lordosis should be used as a reference for surgeons planning to restore the lumbar lordosis in lumbar corrective surgery.

Constructing general partial differential equations using polynomial and neural networks.

PubMed

Zjavka, Ladislav; Pedrycz, Witold

2016-01-01

Sum fraction terms can approximate multi-variable functions on the basis of discrete observations, replacing a partial differential equation definition with polynomial elementary data relation descriptions. Artificial neural networks commonly transform the weighted sum of inputs to describe overall similarity relationships of trained and new testing input patterns. Differential polynomial neural networks form a new class of neural networks, which construct and solve an unknown general partial differential equation of a function of interest with selected substitution relative terms using non-linear multi-variable composite polynomials. The layers of the network generate simple and composite relative substitution terms whose convergent series combinations can describe partial dependent derivative changes of the input variables. This regression is based on trained generalized partial derivative data relations, decomposed into a multi-layer polynomial network structure. The sigmoidal function, commonly used as a nonlinear activation of artificial neurons, may transform some polynomial items together with the parameters with the aim to improve the polynomial derivative term series ability to approximate complicated periodic functions, as simple low order polynomials are not able to fully make up for the complete cycles. The similarity analysis facilitates substitutions for differential equations or can form dimensional units from data samples to describe real-world problems. Copyright © 2015 Elsevier Ltd. All rights reserved.

Body composition of collegiate football players: bioelectrical impedance and skinfolds compared to hydrostatic weighing.

PubMed

Oppliger, R A; Nielsen, D H; Shetler, A C; Crowley, E T; Albright, J P

1992-01-01

The need for simple, valid techniques of body composition assessment among athletes is a growing concern of the physical therapist. This paper reports on several common methods applied to university football players. Body composition analysis was conducted on 28 Division IA football players using three different bioelectrical impedance analysis (BIA) systems, skinfolds (SF), and hydrostatic weighing (HYDRO). Correlations for all methods with HYDRO were high (>.88), but BIA significantly overpredicted body fatness. In contrast, three SF equations showed small differences with HYDRO and reasonable measurement error. Clinicians should exercise caution when using BIA based on the existing manufacturers' equations with athletic populations. Adjustments to BIA regression equations by including modifying or anthropometric variables could enhance the predictive accuracy of these methods with lean, athletic males. J Orthop Sports Phys Ther 1992;15(4):187-192.

Efficient Determination of Free Energy Landscapes in Multiple Dimensions from Biased Umbrella Sampling Simulations Using Linear Regression.

PubMed

Meng, Yilin; Roux, Benoît

2015-08-11

The weighted histogram analysis method (WHAM) is a standard protocol for postprocessing the information from biased umbrella sampling simulations to construct the potential of mean force with respect to a set of order parameters. By virtue of the WHAM equations, the unbiased density of state is determined by satisfying a self-consistent condition through an iterative procedure. While the method works very effectively when the number of order parameters is small, its computational cost grows rapidly in higher dimension. Here, we present a simple and efficient alternative strategy, which avoids solving the self-consistent WHAM equations iteratively. An efficient multivariate linear regression framework is utilized to link the biased probability densities of individual umbrella windows and yield an unbiased global free energy landscape in the space of order parameters. It is demonstrated with practical examples that free energy landscapes that are comparable in accuracy to WHAM can be generated at a small fraction of the cost.

Efficient Determination of Free Energy Landscapes in Multiple Dimensions from Biased Umbrella Sampling Simulations Using Linear Regression

PubMed Central

2015-01-01

The weighted histogram analysis method (WHAM) is a standard protocol for postprocessing the information from biased umbrella sampling simulations to construct the potential of mean force with respect to a set of order parameters. By virtue of the WHAM equations, the unbiased density of state is determined by satisfying a self-consistent condition through an iterative procedure. While the method works very effectively when the number of order parameters is small, its computational cost grows rapidly in higher dimension. Here, we present a simple and efficient alternative strategy, which avoids solving the self-consistent WHAM equations iteratively. An efficient multivariate linear regression framework is utilized to link the biased probability densities of individual umbrella windows and yield an unbiased global free energy landscape in the space of order parameters. It is demonstrated with practical examples that free energy landscapes that are comparable in accuracy to WHAM can be generated at a small fraction of the cost. PMID:26574437

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.

Robust mislabel logistic regression without modeling mislabel probabilities.

PubMed

Hung, Hung; Jou, Zhi-Yu; Huang, Su-Yun

2018-03-01

Logistic regression is among the most widely used statistical methods for linear discriminant analysis. In many applications, we only observe possibly mislabeled responses. Fitting a conventional logistic regression can then lead to biased estimation. One common resolution is to fit a mislabel logistic regression model, which takes into consideration of mislabeled responses. Another common method is to adopt a robust M-estimation by down-weighting suspected instances. In this work, we propose a new robust mislabel logistic regression based on γ-divergence. Our proposal possesses two advantageous features: (1) It does not need to model the mislabel probabilities. (2) The minimum γ-divergence estimation leads to a weighted estimating equation without the need to include any bias correction term, that is, it is automatically bias-corrected. These features make the proposed γ-logistic regression more robust in model fitting and more intuitive for model interpretation through a simple weighting scheme. Our method is also easy to implement, and two types of algorithms are included. Simulation studies and the Pima data application are presented to demonstrate the performance of γ-logistic regression. © 2017, The International Biometric Society.

Simple taper: Taper equations for the field forester

Treesearch

David R. Larsen

2017-01-01

"Simple taper" is set of linear equations that are based on stem taper rates; the intent is to provide taper equation functionality to field foresters. The equation parameters are two taper rates based on differences in diameter outside bark at two points on a tree. The simple taper equations are statistically equivalent to more complex equations. The linear...

[Predicting the probability of development and progression of primary open angle glaucoma by regression modeling].

PubMed

Likhvantseva, V G; Sokolov, V A; Levanova, O N; Kovelenova, I V

2018-01-01

Prediction of the clinical course of primary open-angle glaucoma (POAG) is one of the main directions in solving the problem of vision loss prevention and stabilization of the pathological process. Simple statistical methods of correlation analysis show the extent of each risk factor's impact, but do not indicate the total impact of these factors in personalized combinations. The relationships between the risk factors is subject to correlation and regression analysis. The regression equation represents the dependence of the mathematical expectation of the resulting sign on the combination of factor signs. To develop a technique for predicting the probability of development and progression of primary open-angle glaucoma based on a personalized combination of risk factors by linear multivariate regression analysis. The study included 66 patients (23 female and 43 male; 132 eyes) with newly diagnosed primary open-angle glaucoma. The control group consisted of 14 patients (8 male and 6 female). Standard ophthalmic examination was supplemented with biochemical study of lacrimal fluid. Concentration of matrix metalloproteinase MMP-2 and MMP-9 in tear fluid in both eyes was determined using 'sandwich' enzyme-linked immunosorbent assay (ELISA) method. The study resulted in the development of regression equations and step-by-step multivariate logistic models that can help calculate the risk of development and progression of POAG. Those models are based on expert evaluation of clinical and instrumental indicators of hydrodynamic disturbances (coefficient of outflow ease - C, volume of intraocular fluid secretion - F, fluctuation of intraocular pressure), as well as personalized morphometric parameters of the retina (central retinal thickness in the macular area) and concentration of MMP-2 and MMP-9 in the tear film. The newly developed regression equations are highly informative and can be a reliable tool for studying of the influence vector and assessment of pathogenic potential of the independent risk factors in specific personalized combinations.

Development of 1RM Prediction Equations for Bench Press in Moderately Trained Men.

PubMed

Macht, Jordan W; Abel, Mark G; Mullineaux, David R; Yates, James W

2016-10-01

Macht, JW, Abel, MG, Mullineaux, DR, and Yates, JW. Development of 1RM prediction equations for bench press in moderately trained men. J Strength Cond Res 30(10): 2901-2906, 2016-There are a variety of established 1 repetition maximum (1RM) prediction equations, however, very few prediction equations use anthropometric characteristics exclusively or in part, to estimate 1RM strength. Therefore, the purpose of this study was to develop an original 1RM prediction equation for bench press using anthropometric and performance characteristics in moderately trained male subjects. Sixty male subjects (21.2 ± 2.4 years) completed a 1RM bench press and were randomly assigned a load to complete as many repetitions as possible. In addition, body composition, upper-body anthropometric characteristics, and handgrip strength were assessed. Regression analysis was used to develop a performance-based 1RM prediction equation: 1RM = 1.20 repetition weight + 2.19 repetitions to fatigue - 0.56 biacromial width (cm) + 9.6 (R = 0.99, standard error of estimate [SEE] = 3.5 kg). Regression analysis to develop a nonperformance-based 1RM prediction equation yielded: 1RM (kg) = 0.997 cross-sectional area (CSA) (cm) + 0.401 chest circumference (cm) - 0.385%fat - 0.185 arm length (cm) + 36.7 (R = 0.81, SEE = 13.0 kg). The performance prediction equations developed in this study had high validity coefficients, minimal mean bias, and small limits of agreement. The anthropometric equations had moderately high validity coefficient but larger limits of agreement. The practical applications of this study indicate that the inclusion of anthropometric characteristics and performance variables produce a valid prediction equation for 1RM strength. In addition, the CSA of the arm uses a simple nonperformance method of estimating the lifter's 1RM. This information may be used to predict the starting load for a lifter performing a 1RM prediction protocol or a 1RM testing protocol.

Order Selection for General Expression of Nonlinear Autoregressive Model Based on Multivariate Stepwise Regression

NASA Astrophysics Data System (ADS)

Shi, Jinfei; Zhu, Songqing; Chen, Ruwen

2017-12-01

An order selection method based on multiple stepwise regressions is proposed for General Expression of Nonlinear Autoregressive model which converts the model order problem into the variable selection of multiple linear regression equation. The partial autocorrelation function is adopted to define the linear term in GNAR model. The result is set as the initial model, and then the nonlinear terms are introduced gradually. Statistics are chosen to study the improvements of both the new introduced and originally existed variables for the model characteristics, which are adopted to determine the model variables to retain or eliminate. So the optimal model is obtained through data fitting effect measurement or significance test. The simulation and classic time-series data experiment results show that the method proposed is simple, reliable and can be applied to practical engineering.

Quality-of-water data and statistical summary for selected coal-mined strip pits in Crawford and Cherokee counties, southeastern Kansas

USGS Publications Warehouse

Pope, Larry M.; Diaz, A.M.

1982-01-01

Quality-of-water data, collected October 21-23, 1980, and a statistical summary are presented for 42 coal-mined strip pits in Crawford and Cherokee Counties, Southeastern Kansas. The statistical summary includes minimum and maximum observed values , mean, and standard deviation. Simple linear regression equations relating specific conductance, dissolved solids, and acidity to concentrations of dissolved solids, sulfate, calcium, and magnesium, potassium, aluminum, and iron are also presented. (USGS)

Optimizing separate phase light hydrocarbon recovery from contaminated unconfined aquifers

NASA Astrophysics Data System (ADS)

Cooper, Grant S.; Peralta, Richard C.; Kaluarachchi, Jagath J.

A modeling approach is presented that optimizes separate phase recovery of light non-aqueous phase liquids (LNAPL) for a single dual-extraction well in a homogeneous, isotropic unconfined aquifer. A simulation/regression/optimization (S/R/O) model is developed to predict, analyze, and optimize the oil recovery process. The approach combines detailed simulation, nonlinear regression, and optimization. The S/R/O model utilizes nonlinear regression equations describing system response to time-varying water pumping and oil skimming. Regression equations are developed for residual oil volume and free oil volume. The S/R/O model determines optimized time-varying (stepwise) pumping rates which minimize residual oil volume and maximize free oil recovery while causing free oil volume to decrease a specified amount. This S/R/O modeling approach implicitly immobilizes the free product plume by reversing the water table gradient while achieving containment. Application to a simple representative problem illustrates the S/R/O model utility for problem analysis and remediation design. When compared with the best steady pumping strategies, the optimal stepwise pumping strategy improves free oil recovery by 11.5% and reduces the amount of residual oil left in the system due to pumping by 15%. The S/R/O model approach offers promise for enhancing the design of free phase LNAPL recovery systems and to help in making cost-effective operation and management decisions for hydrogeologists, engineers, and regulators.

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.

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

Using Regression Equations Built from Summary Data in the Psychological Assessment of the Individual Case: Extension to Multiple Regression

ERIC Educational Resources Information Center

Crawford, John R.; Garthwaite, Paul H.; Denham, Annie K.; Chelune, Gordon J.

2012-01-01

Regression equations have many useful roles in psychological assessment. Moreover, there is a large reservoir of published data that could be used to build regression equations; these equations could then be employed to test a wide variety of hypotheses concerning the functioning of individual cases. This resource is currently underused because…

An index of effluent aquatic toxicity designed by partial least squares regression, using acute and chronic tests and expert judgements.

PubMed

Vindimian, Éric; Garric, Jeanne; Flammarion, Patrick; Thybaud, Éric; Babut, Marc

1999-10-01

The evaluation of the ecotoxicity of effluents requires a battery of biological tests on several species. In order to derive a summary parameter from such a battery, a single endpoint was calculated for all the tests: the EC10, obtained by nonlinear regression, with bootstrap evaluation of the confidence intervals. Principal component analysis was used to characterize and visualize the correlation between the tests. The table of the toxicity of the effluents was then submitted to a panel of experts, who classified the effluents according to the test results. Partial least squares (PLS) regression was used to fit the average value of the experts' judgements to the toxicity data, using a simple equation. Furthermore, PLS regression on partial data sets and other considerations resulted in an optimum battery, with two chronic tests and one acute test. The index is intended to be used for the classification of effluents based on their toxicity to aquatic species. Copyright © 1999 SETAC.

An index of effluent aquatic toxicity designed by partial least squares regression, using acute and chronic tests and expert judgments

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

Vindimian, E.; Garric, J.; Flammarion, P.

1999-10-01

The evaluation of the ecotoxicity of effluents requires a battery of biological tests on several species. In order to derive a summary parameter from such a battery, a single endpoint was calculated for all the tests: the EC10, obtained by nonlinear regression, with bootstrap evaluation of the confidence intervals. Principal component analysis was used to characterize and visualize the correlation between the tests. The table of the toxicity of the effluents was then submitted to a panel of experts, who classified the effluents according to the test results. Partial least squares (PLS) regression was used to fit the average valuemore » of the experts' judgments to the toxicity data, using a simple equation. Furthermore, PLS regression on partial data sets and other considerations resulted in an optimum battery, with two chronic tests and one acute test. The index is intended to be used for the classification of effluents based on their toxicity to aquatic species.« less

Estimating basin lagtime and hydrograph-timing indexes used to characterize stormflows for runoff-quality analysis

USGS Publications Warehouse

Granato, Gregory E.

2012-01-01

A nationwide study to better define triangular-hydrograph statistics for use with runoff-quality and flood-flow studies was done by the U.S. Geological Survey (USGS) in cooperation with the Federal Highway Administration. Although the triangular hydrograph is a simple linear approximation, the cumulative distribution of stormflow with a triangular hydrograph is a curvilinear S-curve that closely approximates the cumulative distribution of stormflows from measured data. The temporal distribution of flow within a runoff event can be estimated using the basin lagtime, (which is the time from the centroid of rainfall excess to the centroid of the corresponding runoff hydrograph) and the hydrograph recession ratio (which is the ratio of the duration of the falling limb to the rising limb of the hydrograph). This report documents results of the study, methods used to estimate the variables, and electronic files that facilitate calculation of variables. Ten viable multiple-linear regression equations were developed to estimate basin lagtimes from readily determined drainage basin properties using data published in 37 stormflow studies. Regression equations using the basin lag factor (BLF, which is a variable calculated as the main-channel length, in miles, divided by the square root of the main-channel slope in feet per mile) and two variables describing development in the drainage basin were selected as the best candidates, because each equation explains about 70 percent of the variability in the data. The variables describing development are the USGS basin development factor (BDF, which is a function of the amount of channel modifications, storm sewers, and curb-and-gutter streets in a basin) and the total impervious area variable (IMPERV) in the basin. Two datasets were used to develop regression equations. The primary dataset included data from 493 sites that have values for the BLF, BDF, and IMPERV variables. This dataset was used to develop the best-fit regression equation using the BLF and BDF variables. The secondary dataset included data from 896 sites that have values for the BLF and IMPERV variables. This dataset was used to develop the best-fit regression equation using the BLF and IMPERV variables. Analysis of hydrograph recession ratios and basin characteristics for 41 sites indicated that recession ratios are random variables. Thus, recession ratios cannot be estimated quantitatively using multiple linear regression equations developed using the data available for these sites. The minimums of recession ratios for different streamgages are well characterized by a value of one. The most probable values and maximum values of recession ratios for different streamgages are, however, more variable than the minimums. The most probable values of recession ratios for the 41 streamgages analyzed ranged from 1.0 to 3.52 and had a median of 1.85. The maximum values ranged from 2.66 to 11.3 and had a median of 4.36.

Determination of stress intensity factors for interface cracks under mixed-mode loading

NASA Technical Reports Server (NTRS)

Naik, Rajiv A.; Crews, John H., Jr.

1992-01-01

A simple technique was developed using conventional finite element analysis to determine stress intensity factors, K1 and K2, for interface cracks under mixed-mode loading. This technique involves the calculation of crack tip stresses using non-singular finite elements. These stresses are then combined and used in a linear regression procedure to calculate K1 and K2. The technique was demonstrated by calculating three different bimaterial combinations. For the normal loading case, the K's were within 2.6 percent of an exact solution. The normalized K's under shear loading were shown to be related to the normalized K's under normal loading. Based on these relations, a simple equation was derived for calculating K1 and K2 for mixed-mode loading from knowledge of the K's under normal loading. The equation was verified by computing the K's for a mixed-mode case with equal and normal shear loading. The correlation between exact and finite element solutions is within 3.7 percent. This study provides a simple procedure to compute K2/K1 ratio which has been used to characterize the stress state at the crack tip for various combinations of materials and loadings. Tests conducted over a range of K2/K1 ratios could be used to fully characterize interface fracture toughness.

Comparison of Linear and Non-linear Regression Analysis to Determine Pulmonary Pressure in Hyperthyroidism.

PubMed

Scarneciu, Camelia C; Sangeorzan, Livia; Rus, Horatiu; Scarneciu, Vlad D; Varciu, Mihai S; Andreescu, Oana; Scarneciu, Ioan

2017-01-01

This study aimed at assessing the incidence of pulmonary hypertension (PH) at newly diagnosed hyperthyroid patients and at finding a simple model showing the complex functional relation between pulmonary hypertension in hyperthyroidism and the factors causing it. The 53 hyperthyroid patients (H-group) were evaluated mainly by using an echocardiographical method and compared with 35 euthyroid (E-group) and 25 healthy people (C-group). In order to identify the factors causing pulmonary hypertension the statistical method of comparing the values of arithmetical means is used. The functional relation between the two random variables (PAPs and each of the factors determining it within our research study) can be expressed by linear or non-linear function. By applying the linear regression method described by a first-degree equation the line of regression (linear model) has been determined; by applying the non-linear regression method described by a second degree equation, a parabola-type curve of regression (non-linear or polynomial model) has been determined. We made the comparison and the validation of these two models by calculating the determination coefficient (criterion 1), the comparison of residuals (criterion 2), application of AIC criterion (criterion 3) and use of F-test (criterion 4). From the H-group, 47% have pulmonary hypertension completely reversible when obtaining euthyroidism. The factors causing pulmonary hypertension were identified: previously known- level of free thyroxin, pulmonary vascular resistance, cardiac output; new factors identified in this study- pretreatment period, age, systolic blood pressure. According to the four criteria and to the clinical judgment, we consider that the polynomial model (graphically parabola- type) is better than the linear one. The better model showing the functional relation between the pulmonary hypertension in hyperthyroidism and the factors identified in this study is given by a polynomial equation of second degree where the parabola is its graphical representation.

Global fields of soil moisture and land surface evapotranspiration derived from observed precipitation and surface air temperature

NASA Technical Reports Server (NTRS)

Mintz, Y.; Walker, G. K.

1993-01-01

The global fields of normal monthly soil moisture and land surface evapotranspiration are derived with a simple water budget model that has precipitation and potential evapotranspiration as inputs. The precipitation is observed and the potential evapotranspiration is derived from the observed surface air temperature with the empirical regression equation of Thornthwaite (1954). It is shown that at locations where the net surface radiation flux has been measured, the potential evapotranspiration given by the Thornthwaite equation is in good agreement with those obtained with the radiation-based formulations of Priestley and Taylor (1972), Penman (1948), and Budyko (1956-1974), and this provides the justification for the use of the Thornthwaite equation. After deriving the global fields of soil moisture and evapotranspiration, the assumption is made that the potential evapotranspiration given by the Thornthwaite equation and by the Priestley-Taylor equation will everywhere be about the same; the inverse of the Priestley-Taylor equation is used to obtain the normal monthly global fields of net surface radiation flux minus ground heat storage. This and the derived evapotranspiration are then used in the equation for energy conservation at the surface of the earth to obtain the global fields of normal monthly sensible heat flux from the land surface to the atmosphere.

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.

Using Linear Equating to Map PROMIS(®) Global Health Items and the PROMIS-29 V2.0 Profile Measure to the Health Utilities Index Mark 3.

PubMed

Hays, Ron D; Revicki, Dennis A; Feeny, David; Fayers, Peter; Spritzer, Karen L; Cella, David

2016-10-01

Preference-based health-related quality of life (HR-QOL) scores are useful as outcome measures in clinical studies, for monitoring the health of populations, and for estimating quality-adjusted life-years. This was a secondary analysis of data collected in an internet survey as part of the Patient-Reported Outcomes Measurement Information System (PROMIS(®)) project. To estimate Health Utilities Index Mark 3 (HUI-3) preference scores, we used the ten PROMIS(®) global health items, the PROMIS-29 V2.0 single pain intensity item and seven multi-item scales (physical functioning, fatigue, pain interference, depressive symptoms, anxiety, ability to participate in social roles and activities, sleep disturbance), and the PROMIS-29 V2.0 items. Linear regression analyses were used to identify significant predictors, followed by simple linear equating to avoid regression to the mean. The regression models explained 48 % (global health items), 61 % (PROMIS-29 V2.0 scales), and 64 % (PROMIS-29 V2.0 items) of the variance in the HUI-3 preference score. Linear equated scores were similar to observed scores, although differences tended to be larger for older study participants. HUI-3 preference scores can be estimated from the PROMIS(®) global health items or PROMIS-29 V2.0. The estimated HUI-3 scores from the PROMIS(®) health measures can be used for economic applications and as a measure of overall HR-QOL in research.

Dry season mean monthly flow and harmonic mean flow regression equations for selected ungaged basins in Arkansas

USGS Publications Warehouse

Breaker, Brian K.

2015-01-01

Equations for two regions were found to be statistically significant for developing regression equations for estimating harmonic mean flows at ungaged basins; thus, equations are applicable only to streams in those respective regions in Arkansas. Regression equations for dry season mean monthly flows are applicable only to streams located throughout Arkansas. All regression equations are applicable only to unaltered streams where flows were not significantly affected by regulation, diversion, or urbanization. The median number of years used for dry season mean monthly flow calculation was 43, and the median number of years used for harmonic mean flow calculations was 34 for region 1 and 43 for region 2.

Low-flow, base-flow, and mean-flow regression equations for Pennsylvania streams

USGS Publications Warehouse

Stuckey, Marla H.

2006-01-01

Low-flow, base-flow, and mean-flow characteristics are an important part of assessing water resources in a watershed. These streamflow characteristics can be used by watershed planners and regulators to determine water availability, water-use allocations, assimilative capacities of streams, and aquatic-habitat needs. Streamflow characteristics are commonly predicted by use of regression equations when a nearby streamflow-gaging station is not available. Regression equations for predicting low-flow, base-flow, and mean-flow characteristics for Pennsylvania streams were developed from data collected at 293 continuous- and partial-record streamflow-gaging stations with flow unaffected by upstream regulation, diversion, or mining. Continuous-record stations used in the regression analysis had 9 years or more of data, and partial-record stations used had seven or more measurements collected during base-flow conditions. The state was divided into five low-flow regions and regional regression equations were developed for the 7-day, 10-year; 7-day, 2-year; 30-day, 10-year; 30-day, 2-year; and 90-day, 10-year low flows using generalized least-squares regression. Statewide regression equations were developed for the 10-year, 25-year, and 50-year base flows using generalized least-squares regression. Statewide regression equations were developed for harmonic mean and mean annual flow using weighted least-squares regression. Basin characteristics found to be significant explanatory variables at the 95-percent confidence level for one or more regression equations were drainage area, basin slope, thickness of soil, stream density, mean annual precipitation, mean elevation, and the percentage of glaciation, carbonate bedrock, forested area, and urban area within a basin. Standard errors of prediction ranged from 33 to 66 percent for the n-day, T-year low flows; 21 to 23 percent for the base flows; and 12 to 38 percent for the mean annual flow and harmonic mean, respectively. The regression equations are not valid in watersheds with upstream regulation, diversions, or mining activities. Watersheds with karst features need close examination as to the applicability of the regression-equation results.

The consequences of ignoring measurement invariance for path coefficients in structural equation models

PubMed Central

Guenole, Nigel; Brown, Anna

2014-01-01

We report a Monte Carlo study examining the effects of two strategies for handling measurement non-invariance – modeling and ignoring non-invariant items – on structural regression coefficients between latent variables measured with item response theory models for categorical indicators. These strategies were examined across four levels and three types of non-invariance – non-invariant loadings, non-invariant thresholds, and combined non-invariance on loadings and thresholds – in simple, partial, mediated and moderated regression models where the non-invariant latent variable occupied predictor, mediator, and criterion positions in the structural regression models. When non-invariance is ignored in the latent predictor, the focal group regression parameters are biased in the opposite direction to the difference in loadings and thresholds relative to the referent group (i.e., lower loadings and thresholds for the focal group lead to overestimated regression parameters). With criterion non-invariance, the focal group regression parameters are biased in the same direction as the difference in loadings and thresholds relative to the referent group. While unacceptable levels of parameter bias were confined to the focal group, bias occurred at considerably lower levels of ignored non-invariance than was previously recognized in referent and focal groups. PMID:25278911

New equations improve NIR prediction of body fat among high school wrestlers.

PubMed

Oppliger, R A; Clark, R R; Nielsen, D H

2000-09-01

Methodologic study to derive prediction equations for percent body fat (%BF). To develop valid regression equations using NIR to assess body composition among high school wrestlers. Clinicians need a portable, fast, and simple field method for assessing body composition among wrestlers. Near-infrared photospectrometry (NIR) meets these criteria, but its efficacy has been challenged. Subjects were 150 high school wrestlers from 2 Midwestern states with mean +/- SD age of 16.3 +/- 1.1 yrs, weight of 69.5 +/- 11.7 kg, and height of 174.4 +/- 7.0 cm. Relative body fatness (%BF) determined from hydrostatic weighing was the criterion measure, and NIR optical density (OD) measurements at multiple sites, plus height, weight, and body mass index (BMI) were the predictor variables. Four equations were developed with multiple R2s that varied from .530 to .693, root mean squared errors varied from 2.8% BF to 3.4% BF, and prediction errors varied from 2.9% BF to 3.1% BF. The best equation used OD measurements at the biceps, triceps, and thigh sites, BMI, and age. The root mean squared error and prediction error for all 4 equations were equal to or smaller than for a skinfold equation commonly used with wrestlers. The results substantiate the validity of NIR for predicting % BF among high school wrestlers. Cross-validation of these equations is warranted.

Regional Regression Equations to Estimate Flow-Duration Statistics at Ungaged Stream Sites in Connecticut

USGS Publications Warehouse

Ahearn, Elizabeth A.

2010-01-01

Multiple linear regression equations for determining flow-duration statistics were developed to estimate select flow exceedances ranging from 25- to 99-percent for six 'bioperiods'-Salmonid Spawning (November), Overwinter (December-February), Habitat Forming (March-April), Clupeid Spawning (May), Resident Spawning (June), and Rearing and Growth (July-October)-in Connecticut. Regression equations also were developed to estimate the 25- and 99-percent flow exceedances without reference to a bioperiod. In total, 32 equations were developed. The predictive equations were based on regression analyses relating flow statistics from streamgages to GIS-determined basin and climatic characteristics for the drainage areas of those streamgages. Thirty-nine streamgages (and an additional 6 short-term streamgages and 28 partial-record sites for the non-bioperiod 99-percent exceedance) in Connecticut and adjacent areas of neighboring States were used in the regression analysis. Weighted least squares regression analysis was used to determine the predictive equations; weights were assigned based on record length. The basin characteristics-drainage area, percentage of area with coarse-grained stratified deposits, percentage of area with wetlands, mean monthly precipitation (November), mean seasonal precipitation (December, January, and February), and mean basin elevation-are used as explanatory variables in the equations. Standard errors of estimate of the 32 equations ranged from 10.7 to 156 percent with medians of 19.2 and 55.4 percent to predict the 25- and 99-percent exceedances, respectively. Regression equations to estimate high and median flows (25- to 75-percent exceedances) are better predictors (smaller variability of the residual values around the regression line) than the equations to estimate low flows (less than 75-percent exceedance). The Habitat Forming (March-April) bioperiod had the smallest standard errors of estimate, ranging from 10.7 to 20.9 percent. In contrast, the Rearing and Growth (July-October) bioperiod had the largest standard errors, ranging from 30.9 to 156 percent. The adjusted coefficient of determination of the equations ranged from 77.5 to 99.4 percent with medians of 98.5 and 90.6 percent to predict the 25- and 99-percent exceedances, respectively. Descriptive information on the streamgages used in the regression, measured basin and climatic characteristics, and estimated flow-duration statistics are provided in this report. Flow-duration statistics and the 32 regression equations for estimating flow-duration statistics in Connecticut are stored on the U.S. Geological Survey World Wide Web application ?StreamStats? (http://water.usgs.gov/osw/streamstats/index.html). The regression equations developed in this report can be used to produce unbiased estimates of select flow exceedances statewide.

Nationwide summary of US Geological Survey regional regression equations for estimating magnitude and frequency of floods for ungaged sites, 1993

USGS Publications Warehouse

Jennings, M.E.; Thomas, W.O.; Riggs, H.C.

1994-01-01

For many years, the U.S. Geological Survey (USGS) has been involved in the development of regional regression equations for estimating flood magnitude and frequency at ungaged sites. These regression equations are used to transfer flood characteristics from gaged to ungaged sites through the use of watershed and climatic characteristics as explanatory or predictor variables. Generally these equations have been developed on a statewide or metropolitan area basis as part of cooperative study programs with specific State Departments of Transportation or specific cities. The USGS, in cooperation with the Federal Highway Administration and the Federal Emergency Management Agency, has compiled all the current (as of September 1993) statewide and metropolitan area regression equations into a micro-computer program titled the National Flood Frequency Program.This program includes regression equations for estimating flood-peak discharges and techniques for estimating a typical flood hydrograph for a given recurrence interval peak discharge for unregulated rural and urban watersheds. These techniques should be useful to engineers and hydrologists for planning and design applications. This report summarizes the statewide regression equations for rural watersheds in each State, summarizes the applicable metropolitan area or statewide regression equations for urban watersheds, describes the National Flood Frequency Program for making these computations, and provides much of the reference information on the extrapolation variables needed to run the program.

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.

Development of a Standalone Thermal Wellbore Simulator

NASA Astrophysics Data System (ADS)

Xiong, Wanqiang

With continuous developments of various different sophisticated wells in the petroleum industry, wellbore modeling and simulation have increasingly received more attention. Especially in unconventional oil and gas recovery processes, there is a growing demand for more accurate wellbore modeling. Despite notable advancements made in wellbore modeling, none of the existing wellbore simulators has been as successful as reservoir simulators such as Eclipse and CMG's and further research works on handling issues such as accurate heat loss modeling and multi-tubing wellbore modeling are really necessary. A series of mathematical equations including main governing equations, auxiliary equations, PVT equations, thermodynamic equations, drift-flux model equations, and wellbore heat loss calculation equations are collected and screened from publications. Based on these modeling equations, workflows for wellbore simulation and software development are proposed. Research works are conducted in key steps for developing a wellbore simulator: discretization, a grid system, a solution method, a linear equation solver, and computer language. A standalone thermal wellbore simulator is developed by using standard C++ language. This wellbore simulator can simulate single-phase injection and production, two-phase steam injection and two-phase oil and water production. By implementing a multi-part scheme which divides a wellbore with sophisticated configuration into several relative simple simulation running units, this simulator can handle different complex wellbores: wellbore with multistage casings, horizontal wells, multilateral wells and double tubing. In pursuance of improved accuracy of heat loss calculations to surrounding formations, a semi-numerical method is proposed and a series of FLUENT simulations have been conducted in this study. This semi-numerical method involves extending the 2D formation heat transfer simulation to include a casing wall and cement and adopting new correlations regressed by this study. Meanwhile, a correlation for handling heat transfer in double-tubing annulus is regressed. This work initiates the research on heat transfer in a double-tubing wellbore system. A series of validation and test works are performed in hot water injection, steam injection, real filed data, a horizontal well, a double-tubing well and comparison with the Ramey method. The program in this study also performs well in matching with real measured field data, simulation in horizontal wells and double-tubing wells.

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

USGS Publications Warehouse

Lombard, Pamela J.; Hodgkins, Glenn A.

2015-01-01

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

Role of anthropometric data in the prediction of 4-stranded hamstring graft size in anterior cruciate ligament reconstruction.

PubMed

Ho, Sean Wei Loong; Tan, Teong Jin Lester; Lee, Keng Thiam

2016-03-01

To evaluate whether pre-operative anthropometric data can predict the optimal diameter and length of hamstring tendon autograft for anterior cruciate ligament (ACL) reconstruction. This was a cohort study that involved 169 patients who underwent single-bundle ACL reconstruction (single surgeon) with 4-stranded MM Gracilis and MM Semi-Tendinosus autografts. Height, weight, body mass index (BMI), gender, race, age and -smoking status were recorded pre-operatively. Intra-operatively, the diameter and functional length of the 4-stranded autograft was recorded. Multiple regression analysis was used to determine the relationship between the anthropometric measurements and the length and diameter of the implanted autografts. The strongest correlation between 4-stranded hamstring autograft diameter was height and weight. This correlation was stronger in females than males. BMI had a moderate correlation with the diameter of the graft in females. Females had a significantly smaller graft both in diameter and length when compared with males. Linear regression models did not show any significant correlation between hamstring autograft length with height and weight (p>0.05). Simple regression analysis demonstrated that height and weight can be used to predict hamstring graft diameter. The following regression equation was obtained for females: Graft diameter=0.012+0.034*Height+0.026*Weight (R2=0.358, p=0.004) The following regression equation was obtained for males: Graft diameter=5.130+0.012*Height+0.007*Weight (R2=0.086, p=0.002). Pre-operative anthropometric data has a positive correlation with the diameter of 4 stranded hamstring autografts but no significant correlation with the length. This data can be utilised to predict the autograft diameter and may be useful for pre-operative planning and patient counseling for graft selection.

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.

Aspects of porosity prediction using multivariate linear regression

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

Byrnes, A.P.; Wilson, M.D.

1991-03-01

Highly accurate multiple linear regression models have been developed for sandstones of diverse compositions. Porosity reduction or enhancement processes are controlled by the fundamental variables, Pressure (P), Temperature (T), Time (t), and Composition (X), where composition includes mineralogy, size, sorting, fluid composition, etc. The multiple linear regression equation, of which all linear porosity prediction models are subsets, takes the generalized form: Porosity = C{sub 0} + C{sub 1}(P) + C{sub 2}(T) + C{sub 3}(X) + C{sub 4}(t) + C{sub 5}(PT) + C{sub 6}(PX) + C{sub 7}(Pt) + C{sub 8}(TX) + C{sub 9}(Tt) + C{sub 10}(Xt) + C{sub 11}(PTX) + C{submore » 12}(PXt) + C{sub 13}(PTt) + C{sub 14}(TXt) + C{sub 15}(PTXt). The first four primary variables are often interactive, thus requiring terms involving two or more primary variables (the form shown implies interaction and not necessarily multiplication). The final terms used may also involve simple mathematic transforms such as log X, e{sup T}, X{sup 2}, or more complex transformations such as the Time-Temperature Index (TTI). The X term in the equation above represents a suite of compositional variable and, therefore, a fully expanded equation may include a series of terms incorporating these variables. Numerous published bivariate porosity prediction models involving P (or depth) or Tt (TTI) are effective to a degree, largely because of the high degree of colinearity between p and TTI. However, all such bivariate models ignore the unique contributions of P and Tt, as well as various X terms. These simpler models become poor predictors in regions where colinear relations change, were important variables have been ignored, or where the database does not include a sufficient range or weight distribution for the critical variables.« less

Preliminary study of the association between the elimination parameters of phenytoin and phenobarbital.

PubMed

Methaneethorn, Janthima; Panomvana, Duangchit; Vachirayonstien, Thaveechai

2017-09-26

Therapeutic drug monitoring is essential for both phenytoin and phenobarbital therapy given their narrow therapeutic indexes. Nevertheless, the measurement of either phenytoin or phenobarbital concentrations might not be available in some rural hospitals. Information assisting individualized phenytoin and phenobarbital combination therapy is important. This study's objective was to determine the relationship between the maximum rate of metabolism of phenytoin (Vmax) and phenobarbital clearance (CLPB), which can serve as a guide to individualized drug therapy. Data on phenytoin and phenobarbital concentrations of 19 epileptic patients concurrently receiving both drugs were obtained from medical records. Phenytoin and phenobarbital pharmacokinetic parameters were studied at steady-state conditions. The relationship between the elimination parameters of both drugs was determined using simple linear regression. A high correlation coefficient between Vmax and CLPB was found [r=0.744; p<0.001 for Vmax (mg/kg/day) vs. CLPB (L/kg/day)]. Such a relatively strong linear relationship between the elimination parameters of both drugs indicates that Vmax might be predicted from CLPB and vice versa. Regression equations were established for estimating Vmax from CLPB, and vice versa in patients treated with combination of phenytoin and phenobarbital. These proposed equations can be of use in aiding individualized drug therapy.

Estimating Causal Effects with Ancestral Graph Markov Models

PubMed Central

Malinsky, Daniel; Spirtes, Peter

2017-01-01

We present an algorithm for estimating bounds on causal effects from observational data which combines graphical model search with simple linear regression. We assume that the underlying system can be represented by a linear structural equation model with no feedback, and we allow for the possibility of latent variables. Under assumptions standard in the causal search literature, we use conditional independence constraints to search for an equivalence class of ancestral graphs. Then, for each model in the equivalence class, we perform the appropriate regression (using causal structure information to determine which covariates to include in the regression) to estimate a set of possible causal effects. Our approach is based on the “IDA” procedure of Maathuis et al. (2009), which assumes that all relevant variables have been measured (i.e., no unmeasured confounders). We generalize their work by relaxing this assumption, which is often violated in applied contexts. We validate the performance of our algorithm on simulated data and demonstrate improved precision over IDA when latent variables are present. PMID:28217244

Eye Movements Reveal Students' Strategies in Simple Equation Solving

ERIC Educational Resources Information Center

Susac, Ana; Bubic, Andreja; Kaponja, Jurica; Planinic, Maja; Palmovic, Marijan

2014-01-01

Equation rearrangement is an important skill required for problem solving in mathematics and science. Eye movements of 40 university students were recorded while they were rearranging simple algebraic equations. The participants also reported on their strategies during equation solving in a separate questionnaire. The analysis of the behavioral…

Regression Equations for Estimating Flood Flows at Selected Recurrence Intervals for Ungaged Streams in Pennsylvania

USGS Publications Warehouse

Roland, Mark A.; Stuckey, Marla H.

2008-01-01

Regression equations were developed for estimating flood flows at selected recurrence intervals for ungaged streams in Pennsylvania with drainage areas less than 2,000 square miles. These equations were developed utilizing peak-flow data from 322 streamflow-gaging stations within Pennsylvania and surrounding states. All stations used in the development of the equations had 10 or more years of record and included active and discontinued continuous-record as well as crest-stage partial-record stations. The state was divided into four regions, and regional regression equations were developed to estimate the 2-, 5-, 10-, 50-, 100-, and 500-year recurrence-interval flood flows. The equations were developed by means of a regression analysis that utilized basin characteristics and flow data associated with the stations. Significant explanatory variables at the 95-percent confidence level for one or more regression equations included the following basin characteristics: drainage area; mean basin elevation; and the percentages of carbonate bedrock, urban area, and storage within a basin. The regression equations can be used to predict the magnitude of flood flows for specified recurrence intervals for most streams in the state; however, they are not valid for streams with drainage areas generally greater than 2,000 square miles or with substantial regulation, diversion, or mining activity within the basin. Estimates of flood-flow magnitude and frequency for streamflow-gaging stations substantially affected by upstream regulation are also presented.

A Simple and Specific Stability- Indicating RP-HPLC Method for Routine Assay of Adefovir Dipivoxil in Bulk and Tablet Dosage Form.

PubMed

Darsazan, Bahar; Shafaati, Alireza; Mortazavi, Seyed Alireza; Zarghi, Afshin

2017-01-01

A simple and reliable stability-indicating RP-HPLC method was developed and validated for analysis of adefovir dipivoxil (ADV).The chromatographic separation was performed on a C 18 column using a mixture of acetonitrile-citrate buffer (10 mM at pH 5.2) 36:64 (%v/v) as mobile phase, at a flow rate of 1.5 mL/min. Detection was carried out at 260 nm and a sharp peak was obtained for ADV at a retention time of 5.8 ± 0.01 min. No interferences were observed from its stress degradation products. The method was validated according to the international guidelines. Linear regression analysis of data for the calibration plot showed a linear relationship between peak area and concentration over the range of 0.5-16 μg/mL; the regression coefficient was 0.9999and the linear regression equation was y = 24844x-2941.3. The detection (LOD) and quantification (LOQ) limits were 0.12 and 0.35 μg/mL, respectively. The results proved the method was fast (analysis time less than 7 min), precise, reproducible, and accurate for analysis of ADV over a wide range of concentration. The proposed specific method was used for routine quantification of ADV in pharmaceutical bulk and a tablet dosage form.

Using structural equation modeling to construct calibration equations relating PM2.5 mass concentration samplers to the federal reference method sampler

NASA Astrophysics Data System (ADS)

Bilonick, Richard A.; Connell, Daniel P.; Talbott, Evelyn O.; Rager, Judith R.; Xue, Tao

2015-02-01

The objective of this study was to remove systematic bias among fine particulate matter (PM2.5) mass concentration measurements made by different types of samplers used in the Pittsburgh Aerosol Research and Inhalation Epidemiology Study (PARIES). PARIES is a retrospective epidemiology study that aims to provide a comprehensive analysis of the associations between air quality and human health effects in the Pittsburgh, Pennsylvania, region from 1999 to 2008. Calibration was needed in order to minimize the amount of systematic error in PM2.5 exposure estimation as a result of including data from 97 different PM2.5 samplers at 47 monitoring sites. Ordinary regression often has been used for calibrating air quality measurements from pairs of measurement devices; however, this is only appropriate when one of the two devices (the "independent" variable) is free from random error, which is rarely the case. A group of methods known as "errors-in-variables" (e.g., Deming regression, reduced major axis regression) has been developed to handle calibration between two devices when both are subject to random error, but these methods require information on the relative sizes of the random errors for each device, which typically cannot be obtained from the observed data. When data from more than two devices (or repeats of the same device) are available, the additional information is not used to inform the calibration. A more general approach that often has been overlooked is the use of a measurement error structural equation model (SEM) that allows the simultaneous comparison of three or more devices (or repeats). The theoretical underpinnings of all of these approaches to calibration are described, and the pros and cons of each are discussed. In particular, it is shown that both ordinary regression (when used for calibration) and Deming regression are particular examples of SEMs but with substantial deficiencies. To illustrate the use of SEMs, the 7865 daily average PM2.5 mass concentration measurements made by seven collocated samplers at an urban monitoring site in Pittsburgh, Pennsylvania, were used. These samplers, which included three federal reference method (FRM) samplers, three speciation samplers, and a tapered element oscillating microbalance (TEOM), operated at various times during the 10-year PARIES study period. Because TEOM measurements are known to depend on temperature, the constructed SEM provided calibration equations relating the TEOM to the FRM and speciation samplers as a function of ambient temperature. It was shown that TEOM imprecision and TEOM bias (relative to the FRM) both decreased as temperature increased. It also was shown that the temperature dependency for bias was non-linear and followed a sigmoidal (logistic) pattern. The speciation samplers exhibited only small bias relative to the FRM samplers, although the FRM samplers were shown to be substantially more precise than both the TEOM and the speciation samplers. Comparison of the SEM results to pairwise simple linear regression results showed that the regression results can differ substantially from the correctly-derived calibration equations, especially if the less-precise device is used as the independent variable in the regression.

Evaluation of spatial, radiometric and spectral Thematic Mapper performance for coastal studies

NASA Technical Reports Server (NTRS)

Klemas, V. (Principal Investigator)

1984-01-01

The effect different wetland plant canopies have upon observed reflectance in Thematic Mapper bands is studied. The three major vegetation canopy types (broadleaf, gramineous and leafless) produce unique spectral responses for a similar quantity of live biomass. The spectral biomass estimate of a broadleaf canopy is most similar to the harvest biomass estimate when a broadleaf canopy radiance model is used. All major wetland vegetation species can be identified through TM imagery. Simple regression models are developed equating the vegetation index and the infrared index with biomass. The spectral radiance index largely agreed with harvest biomass estimates.

Steady-state flow distribution and monthly flow duration in selected branches of St. Clair and Detroit rivers within the Great Lakes waterway

USGS Publications Warehouse

Holtschlag, D.J.; Koschik, J.A.

2001-01-01

St. Clair and Detroit Rivers are connecting channels between Lake Huron and Lake Erie in the Great Lakes waterway, and form part of the boundary between the United States and Canada. St. Clair River, the upper connecting channel, drains 222,400 square miles and has an average flow of about 182,000 cubic feet per second. Water from St. Clair River combines with local inflows and discharges into Lake St. Clair before flowing into Detroit River. In some reaches of St. Clair and Detroit Rivers, islands and dikes split the flow into two to four branches. Even when the flow in a reach is known, proportions of flows within individual branches of a reach are uncertain. Simple linear regression equations, subject to a flow continuity constraint, are developed to provide estimators of these proportions and flows. The equations are based on 533 paired measurements of flow in 13 reaches forming 31 branches. The equations provide a means for computing the expected values and uncertainties of steady-state flows on the basis of flow conditions specified at the upstream boundaries of the waterway. In 7 upstream reaches, flow is considered fixed because it can be determined on the basis of flows specified at waterway boundaries and flow continuity. In these reaches, the uncertainties of flow proportions indicated by the regression equations can be used directly to determine the uncertainties of the corresponding flows. In the remaining 6 downstream reaches, flow is considered uncertain because these reaches do not receive flow from all the branches of an upstream reach, or they receive flow from some branches of more than one upstream reach. Monte Carlo simulation analysis is used to quantify this increase in uncertainty associated with the propagation of uncertainties from upstream reaches to downstream reaches. To eliminate the need for Monte Carlo simulations for routine calculations, polynomial regression equations are developed to approximate the variation in uncertainties as a function of flow at the headwaters of St. Clair River. Finally, monthly flow-duration data on the main channels of St. Clair and Detroit Rivers are used with the equations developed in this report to estimate the steady-state flow-duration characteristics of selected branches.

Regression equations to estimate seasonal flow duration, n-day high-flow frequency, and n-day low-flow frequency at sites in North Dakota using data through water year 2009

USGS Publications Warehouse

Williams-Sether, Tara; Gross, Tara A.

2016-02-09

Seasonal mean daily flow data from 119 U.S. Geological Survey streamflow-gaging stations in North Dakota; the surrounding states of Montana, Minnesota, and South Dakota; and the Canadian provinces of Manitoba and Saskatchewan with 10 or more years of unregulated flow record were used to develop regression equations for flow duration, n-day high flow and n-day low flow using ordinary least-squares and Tobit regression techniques. Regression equations were developed for seasonal flow durations at the 10th, 25th, 50th, 75th, and 90th percent exceedances; the 1-, 7-, and 30-day seasonal mean high flows for the 10-, 25-, and 50-year recurrence intervals; and the 1-, 7-, and 30-day seasonal mean low flows for the 2-, 5-, and 10-year recurrence intervals. Basin and climatic characteristics determined to be significant explanatory variables in one or more regression equations included drainage area, percentage of basin drainage area that drains to isolated lakes and ponds, ruggedness number, stream length, basin compactness ratio, minimum basin elevation, precipitation, slope ratio, stream slope, and soil permeability. The adjusted coefficient of determination for the n-day high-flow regression equations ranged from 55.87 to 94.53 percent. The Chi2 values for the duration regression equations ranged from 13.49 to 117.94, whereas the Chi2 values for the n-day low-flow regression equations ranged from 4.20 to 49.68.

Effective Surfactants Blend Concentration Determination for O/W Emulsion Stabilization by Two Nonionic Surfactants by Simple Linear Regression.

PubMed

Hassan, A K

2015-01-01

In this work, O/W emulsion sets were prepared by using different concentrations of two nonionic surfactants. The two surfactants, tween 80(HLB=15.0) and span 80(HLB=4.3) were used in a fixed proportions equal to 0.55:0.45 respectively. HLB value of the surfactants blends were fixed at 10.185. The surfactants blend concentration is starting from 3% up to 19%. For each O/W emulsion set the conductivity was measured at room temperature (25±2°), 40, 50, 60, 70 and 80°. Applying the simple linear regression least squares method statistical analysis to the temperature-conductivity obtained data determines the effective surfactants blend concentration required for preparing the most stable O/W emulsion. These results were confirmed by applying the physical stability centrifugation testing and the phase inversion temperature range measurements. The results indicated that, the relation which represents the most stable O/W emulsion has the strongest direct linear relationship between temperature and conductivity. This relationship is linear up to 80°. This work proves that, the most stable O/W emulsion is determined via the determination of the maximum R² value by applying of the simple linear regression least squares method to the temperature-conductivity obtained data up to 80°, in addition to, the true maximum slope is represented by the equation which has the maximum R² value. Because the conditions would be changed in a more complex formulation, the method of the determination of the effective surfactants blend concentration was verified by applying it for more complex formulations of 2% O/W miconazole nitrate cream and the results indicate its reproducibility.

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

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

PubMed

Marill, Keith A

2004-01-01

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

Anticancer Agents Based on a New Class of Transition- State Analog Inhibitors for Serine and Cysteine Proteases

DTIC Science & Technology

1999-08-01

electrostatic repulsion between the het- eroatom and the ketone. Swain and Lupton31 have constructed a modified Hammett equation (eq 2) in which they...determined by nonlinear fit to the Michaelis-Menten equation for competitive inhibition using simple weighing. Competitive inhibition was confirmed... equation for competitive inhibition using simple weighing. Competitive inhibition was confirmed by Lineweaver - Burk analysis using simple

Estimating design-flood discharges for streams in Iowa using drainage-basin and channel-geometry characteristics

USGS Publications Warehouse

Eash, D.A.

1993-01-01

Procedures provided for applying the drainage-basin and channel-geometry regression equations depend on whether the design-flood discharge estimate is for a site on an ungaged stream, an ungaged site on a gaged stream, or a gaged site. When both a drainage-basin and a channel-geometry regression-equation estimate are available for a stream site, a procedure is presented for determining a weighted average of the two flood estimates. The drainage-basin regression equations are applicable to unregulated rural drainage areas less than 1,060 square miles, and the channel-geometry regression equations are applicable to unregulated rural streams in Iowa with stabilized channels.

Prediction of oxygen consumption in cardiac rehabilitation patients performing leg ergometry

NASA Astrophysics Data System (ADS)

Alvarez, John Gershwin

The purpose of this study was two-fold. First, to determine the validity of the ACSM leg ergometry equation in the prediction of steady-state oxygen consumption (VO2) in a heterogeneous population of cardiac patients. Second, to determine whether a more accurate prediction equation could be developed for use in the cardiac population. Thirty-one cardiac rehabilitation patients participated in the study of which 24 were men and 7 were women. Biometric variables (mean +/- sd) of the participants were as follows: age = 61.9 +/- 9.5 years; height = 172.6 +/- 1.6 cm; and body mass = 82.3 +/- 10.6 kg. Subjects exercised on a MonarchTM cycle ergometer at 0, 180, 360, 540 and 720 kgm ˙ min-1. The length of each stage was five minutes. Heart rate, ECG, and VO2 were continuously monitored. Blood pressure and heart rate were collected at the end of each stage. Steady state VO 2 was calculated for each stage using the average of the last two minutes. Correlation coefficients, standard error of estimate, coefficient of determination, total error, and mean bias were used to determine the accuracy of the ACSM equation (1995). The analysis found the ACSM equation to be a valid means of estimating VO2 in cardiac patients. Simple linear regression was used to develop a new equation. Regression analysis found workload to be a significant predictor of VO2. The following equation is the result: VO2 = (1.6 x kgm ˙ min-1) + 444 ml ˙ min-1. The r of the equation was .78 (p < .05) and the standard error of estimate was 211 ml ˙ min-1. Analysis of variance was used to determine significant differences between means for actual and predicted VO2 values for each equation. The analysis found the ACSM and new equation to significantly (p < .05) under predict VO2 during unloaded pedaling. Furthermore, the ACSM equation was found to significantly (p < .05) under predict VO 2 during the first loaded stage of exercise. When the accuracy of the ACSM and new equations were compared based on correlation coefficients, coefficients of determinations, SEEs, total error, and mean bias the new equation was found to have equal or better accuracy at all workloads. The final form of the new equation is: VO2 (ml ˙ min-1) = (kgm ˙ min-1 x 1.6 ml ˙ kgm-1) + (3.5 ml ˙ kg-1 ˙ min-1 x body mass in kg) + 156 ml ˙ min-1.

Universal GFR determination based on two time points during plasma iohexol disappearance.

PubMed

Ng, Derek K S; Schwartz, George J; Jacobson, Lisa P; Palella, Frank J; Margolick, Joseph B; Warady, Bradley A; Furth, Susan L; Muñoz, Alvaro

2011-08-01

An optimal measurement of glomerular filtration rate (GFR) should minimize the number of blood draws, and reduce procedural invasiveness and the burden to study personnel and cost, without sacrificing accuracy. Equations have been proposed to calculate GFR from the slow compartment separately for adults and children. To develop a universal equation, we used 1347 GFR measurements from two diverse groups consisting of 527 men in the Multicenter AIDS Cohort Study and 514 children in the Chronic Kidney Disease in Children cohort. Both studies used nearly identical two-compartment (fast and slow) protocols to measure GFR. To estimate the fast component from markers of body size and of the slow component, we used standard linear regression methods with the log-transformed fast area as the dependent variable. The fast area could be accurately estimated from body surface area by a simple parameter (6.4/body surface area) with no residual dependence on the slow area or other markers of body size. Our equation measures only the slow iohexol plasma disappearance curve with as few as two time points and was normalized to 1.73 m2 body surface area. It is of the form: GFR=slowGFR/[1+0.12(slowGFR/100)]. In a random sample utilizing a third of the patients for validation, there was excellent agreement between the calculated and measured GFR with low root mean square errors being 4.6 and 1.5 ml/min per 1.73 m2 for adults and children, respectively. Thus, our proposed simple equation, developed in a combined patient group with a broad range of GFRs, may be applied universally and is independent of the injected amount of iohexol.

A novel body circumferences-based estimation of percentage body fat.

PubMed

Lahav, Yair; Epstein, Yoram; Kedem, Ron; Schermann, Haggai

2018-03-01

Anthropometric measures of body composition are often used for rapid and cost-effective estimation of percentage body fat (%BF) in field research, serial measurements and screening. Our aim was to develop a validated estimate of %BF for the general population, based on simple body circumferences measures. The study cohort consisted of two consecutive samples of health club members, designated as 'development' (n 476, 61 % men, 39 % women) and 'validation' (n 224, 50 % men, 50 % women) groups. All subjects underwent anthropometric measurements as part of their registration to a health club. Dual-energy X-ray absorptiometry (DEXA) scan was used as the 'gold standard' estimate of %BF. Linear regressions where used to construct the predictive equation (%BFcal). Bland-Altman statistics, Lin concordance coefficients and percentage of subjects falling within 5 % of %BF estimate by DEXA were used to evaluate accuracy and precision of the equation. The variance inflation factor was used to check multicollinearity. Two distinct equations were developed for men and women: %BFcal (men)=10·1-0·239H+0·8A-0·5N; %BFcal (women)=19·2-0·239H+0·8A-0·5N (H, height; A, abdomen; N, neck, all in cm). Bland-Altman differences were randomly distributed and showed no fixed bias. Lin concordance coefficients of %BFcal were 0·89 in men and 0·86 in women. About 79·5 % of %BF predictions in both sexes were within ±5 % of the DEXA value. The Durnin-Womersley skinfolds equation was less accurate in our study group for prediction of %BF than %BFcal. We conclude that %BFcal offers the advantage of obtaining a reliable estimate of %BF from simple measurements that require no sophisticated tools and only a minimal prior training and experience.

Modification of Fox protocol for prediction of maximum oxygen uptake in male university students.

PubMed

Bandyopadhyay, Amit; Pal, Sangita

2015-01-01

Direct estimation of VO₂max involves labourious, exhaustive, hazardous, time consuming and expensive experimental protocols. Hence, application of various indirect protocols for prediction of VO₂max has become popular, subject to proper population-specific standardisation of the indirect protocol. Application of Fox (1973) protocol in male sedentary university students of Kolkata, India led to premature fatigue in their leg muscles that hindered the muscular activity leading to inability in completing the exercise. The present study was aimed at modifying and validating the Fox (1973) protocol with a convenient workload of 110 W (i.e., modified Fox test or MFT) in the said population. Ninety (90) sedentary male students were recruited by simple random sampling from the University of Calcutta, India and they were randomly assigned into study group (n=60) and confirmatory group (n=30). VO₂max was directly estimated by Scholander micro-gas analysis after incremental bicycle exercise. Predicted VO₂max (PVO₂max) was computed from MFT by using the submaximal heart rate (HR(sub). In the Study Group VO₂max (2216.63 ± 316.77 mL.min⁻¹ was significantly different (P< 0.001) from PVO₂max (3131.73 ± 234.32 mL.min⁻¹ measured by using the equation of Fox (1973). Simple and multiple regression equations have been computed for prediction of VO₂max from HR(sub) and physical parameters. Application of these norms in the confirmatory group depicted insignificant difference between VO₂max and PVO₂max with substantially small limits of agreement and lower values of SEE. The modified regression norms are therefore recommended for use in MFT for accurate assessment of VO₂max in the studied population.

Arterial blood gas reference values for sea level and an altitude of 1,400 meters.

PubMed

Crapo, R O; Jensen, R L; Hegewald, M; Tashkin, D P

1999-11-01

Blood gas measurements were collected on healthy lifetime nonsmokers at sea level (n = 96) and at an altitude of 1,400 meters (n = 243) to establish reference equations. At each study site, arterial blood samples were analyzed in duplicate on two separate blood gas analyzers and CO-oximeters. Arterial blood gas variables included Pa(O(2)), Pa(CO(2)), pH, and calculated alveolar-arterial PO(2) difference (AaPO(2)). CO-oximeter variables were Hb, COHb, MetHb, and Sa(O(2)). Subjects were 18 to 81 yr of age with 166 male and 173 female. Outlier data were excluded from multiple regression analysis, and reference equations were fitted to the data in two ways: (1) best fit using linear, squared, and cross-product terms; (2) simple equations, including only the variables that explained at least 3% of the variance. Two sets of equations were created: (1) using only the sea level data and (2) using the combined data with barometric pressure as an independent variable. Comparisons with earlier studies revealed small but significant differences; the decline in Pa(O(2)) with age at each altitude was consistent with most previous studies. At sea level, the equation that included barometric pressure predicted Pa(O(2)) slightly better than the sea level specific equation. The inclusion of barometric pressure in the equations allows better prediction of blood gas reference values at sea level and at altitudes as high as 1,400 meters.

Interpreting experimental data on egg production--applications of dynamic differential equations.

PubMed

France, J; Lopez, S; Kebreab, E; Dijkstra, J

2013-09-01

This contribution focuses on applying mathematical models based on systems of ordinary first-order differential equations to synthesize and interpret data from egg production experiments. Models based on linear systems of differential equations are contrasted with those based on nonlinear systems. Regression equations arising from analytical solutions to linear compartmental schemes are considered as candidate functions for describing egg production curves, together with aspects of parameter estimation. Extant candidate functions are reviewed, a role for growth functions such as the Gompertz equation suggested, and a function based on a simple new model outlined. Structurally, the new model comprises a single pool with an inflow and an outflow. Compartmental simulation models based on nonlinear systems of differential equations, and thus requiring numerical solution, are next discussed, and aspects of parameter estimation considered. This type of model is illustrated in relation to development and evaluation of a dynamic model of calcium and phosphorus flows in layers. The model consists of 8 state variables representing calcium and phosphorus pools in the crop, stomachs, plasma, and bone. The flow equations are described by Michaelis-Menten or mass action forms. Experiments that measure Ca and P uptake in layers fed different calcium concentrations during shell-forming days are used to evaluate the model. In addition to providing a useful management tool, such a simulation model also provides a means to evaluate feeding strategies aimed at reducing excretion of potential pollutants in poultry manure to the environment.

Modeling rainfall infiltration on hillslopes using Flux-concentration relation and time compression approximation

NASA Astrophysics Data System (ADS)

Wang, Jie; Chen, Li; Yu, Zhongbo

2018-02-01

Rainfall infiltration on hillslopes is an important issue in hydrology, which is related to many environmental problems, such as flood, soil erosion, and nutrient and contaminant transport. This study aimed to improve the quantification of infiltration on hillslopes under both steady and unsteady rainfalls. Starting from Darcy's law, an analytical integral infiltrability equation was derived for hillslope infiltration by use of the flux-concentration relation. Based on this equation, a simple scaling relation linking the infiltration times on hillslopes and horizontal planes was obtained which is applicable for both small and large times and can be used to simplify the solution procedure of hillslope infiltration. The infiltrability equation also improved the estimation of ponding time for infiltration under rainfall conditions. For infiltration after ponding, the time compression approximation (TCA) was applied together with the infiltrability equation. To improve the computational efficiency, the analytical integral infiltrability equation was approximated with a two-term power-like function by nonlinear regression. Procedures of applying this approach to both steady and unsteady rainfall conditions were proposed. To evaluate the performance of the new approach, it was compared with the Green-Ampt model for sloping surfaces by Chen and Young (2006) and Richards' equation. The proposed model outperformed the sloping Green-Ampt, and both ponding time and infiltration predictions agreed well with the solutions of Richards' equation for various soil textures, slope angles, initial water contents, and rainfall intensities for both steady and unsteady rainfalls.

Regression Simulation Model. Appendix X. Users Manual,

DTIC Science & Technology

1981-03-01

change as the prediction equations become refined. Whereas no notice will be provided when the changes are made, the programs will be modified such that...NATIONAL BUREAU Of STANDARDS 1963 A ___,_ __ _ __ _ . APPENDIX X ( R4/ EGRESSION IMULATION ’jDEL. Ape’A ’) 7 USERS MANUA submitted to The Great River...regression analysis and to establish a prediction equation (model). The prediction equation contains the partial regression coefficients (B-weights) which

Validation of a single-stage fixed-rate step test for the prediction of maximal oxygen uptake in healthy adults.

PubMed

Hansen, Dominique; Jacobs, Nele; Thijs, Herbert; Dendale, Paul; Claes, Neree

2016-09-01

Healthcare professionals with limited access to ergospirometry remain in need of valid and simple submaximal exercise tests to predict maximal oxygen uptake (VO2max ). Despite previous validation studies concerning fixed-rate step tests, accurate equations for the estimation of VO2max remain to be formulated from a large sample of healthy adults between age 18-75 years (n > 100). The aim of this study was to develop a valid equation to estimate VO2max from a fixed-rate step test in a larger sample of healthy adults. A maximal ergospirometry test, with assessment of cardiopulmonary parameters and VO2max , and a 5-min fixed-rate single-stage step test were executed in 112 healthy adults (age 18-75 years). During the step test and subsequent recovery, heart rate was monitored continuously. By linear regression analysis, an equation to predict VO2max from the step test was formulated. This equation was assessed for level of agreement by displaying Bland-Altman plots and calculation of intraclass correlations with measured VO2max . Validity further was assessed by employing a Jackknife procedure. The linear regression analysis generated the following equation to predict VO2max (l min(-1) ) from the step test: 0·054(BMI)+0·612(gender)+3·359(body height in m)+0·019(fitness index)-0·012(HRmax)-0·011(age)-3·475. This equation explained 78% of the variance in measured VO2max (F = 66·15, P<0·001). The level of agreement and intraclass correlation was high (ICC = 0·94, P<0·001) between measured and predicted VO2max . From this study, a valid fixed-rate single-stage step test equation has been developed to estimate VO2max in healthy adults. This tool could be employed by healthcare professionals with limited access to ergospirometry. © 2015 Scandinavian Society of Clinical Physiology and Nuclear Medicine. Published by John Wiley & Sons Ltd.

Spectrophotometric total reducing sugars assay based on cupric reduction.

PubMed

Başkan, Kevser Sözgen; Tütem, Esma; Akyüz, Esin; Özen, Seda; Apak, Reşat

2016-01-15

As the concentration of reducing sugars (RS) is controlled by European legislation for certain specific food and beverages, a simple and sensitive spectrophotometric method for the determination of RS in various food products is proposed. The method is based on the reduction of Cu(II) to Cu(I) with reducing sugars in alkaline medium in the presence of 2,9-dimethyl-1,10-phenanthroline (neocuproine: Nc), followed by the formation of a colored Cu(I)-Nc charge-transfer complex. All simple sugars tested had the linear regression equations with almost equal slope values. The proposed method was successfully applied to fresh apple juice, commercial fruit juices, milk, honey and onion juice. Interference effect of phenolic compounds in plant samples was eliminated by a solid phase extraction (SPE) clean-up process. The method was proven to have higher sensitivity and precision than the widely used dinitrosalicylic acid (DNS) colorimetric method. Copyright © 2015 Elsevier B.V. All rights reserved.

Introduction, comparison, and validation of Meta‐Essentials: A free and simple tool for meta‐analysis

PubMed Central

van Rhee, Henk; Hak, Tony

2017-01-01

We present a new tool for meta‐analysis, Meta‐Essentials, which is free of charge and easy to use. In this paper, we introduce the tool and compare its features to other tools for meta‐analysis. We also provide detailed information on the validation of the tool. Although free of charge and simple, Meta‐Essentials automatically calculates effect sizes from a wide range of statistics and can be used for a wide range of meta‐analysis applications, including subgroup analysis, moderator analysis, and publication bias analyses. The confidence interval of the overall effect is automatically based on the Knapp‐Hartung adjustment of the DerSimonian‐Laird estimator. However, more advanced meta‐analysis methods such as meta‐analytical structural equation modelling and meta‐regression with multiple covariates are not available. In summary, Meta‐Essentials may prove a valuable resource for meta‐analysts, including researchers, teachers, and students. PMID:28801932

New 1,6-heptadienes with pyrimidine bases attached: Syntheses and spectroscopic analyses

NASA Astrophysics Data System (ADS)

Hammud, Hassan H.; Ghannoum, Amer M.; Fares, Fares A.; Abramian, Lara K.; Bouhadir, Kamal H.

2008-06-01

A simple, high yielding synthesis leading to the functionalization of some pyrimidine bases with a 1,6-heptadienyl moiety spaced from the N - 1 position by a methylene group is described. A key step in this synthesis involves a Mitsunobu reaction by coupling 3N-benzoyluracil and 3N-benzoylthymine to 2-allyl-pent-4-en-1-ol followed by alkaline hydrolysis of the 3N-benzoyl protecting groups. This protocol should eventually lend itself to the synthesis of a host of N-alkylated nucleoside analogs. The absorption and emission properties of these pyrimidine derivatives ( 3- 6) were studied in solvents of different physical properties. Computerized analysis and multiple regression techniques were applied to calculate the regression and correlation coefficients based on the equation that relates peak position λmax to the solvent parameters that depend on the H-bonding ability, refractive index, and dielectric constant of solvents.

Correlation Equation of Fault Size, Moment Magnitude, and Height of Tsunami Case Study: Historical Tsunami Database in Sulawesi

NASA Astrophysics Data System (ADS)

Julius, Musa, Admiral; Pribadi, Sugeng; Muzli, Muzli

2018-03-01

Sulawesi, one of the biggest island in Indonesia, located on the convergence of two macro plate that is Eurasia and Pacific. NOAA and Novosibirsk Tsunami Laboratory show more than 20 tsunami data recorded in Sulawesi since 1820. Based on this data, determination of correlation between tsunami and earthquake parameter need to be done to proved all event in the past. Complete data of magnitudes, fault sizes and tsunami heights on this study sourced from NOAA and Novosibirsk Tsunami database, completed with Pacific Tsunami Warning Center (PTWC) catalog. This study aims to find correlation between moment magnitude, fault size and tsunami height by simple regression. The step of this research are data collecting, processing, and regression analysis. Result shows moment magnitude, fault size and tsunami heights strongly correlated. This analysis is enough to proved the accuracy of historical tsunami database in Sulawesi on NOAA, Novosibirsk Tsunami Laboratory and PTWC.

Regression analysis of sparse asynchronous longitudinal data.

PubMed

Cao, Hongyuan; Zeng, Donglin; Fine, Jason P

2015-09-01

We consider estimation of regression models for sparse asynchronous longitudinal observations, where time-dependent responses and covariates are observed intermittently within subjects. Unlike with synchronous data, where the response and covariates are observed at the same time point, with asynchronous data, the observation times are mismatched. Simple kernel-weighted estimating equations are proposed for generalized linear models with either time invariant or time-dependent coefficients under smoothness assumptions for the covariate processes which are similar to those for synchronous data. For models with either time invariant or time-dependent coefficients, the estimators are consistent and asymptotically normal but converge at slower rates than those achieved with synchronous data. Simulation studies evidence that the methods perform well with realistic sample sizes and may be superior to a naive application of methods for synchronous data based on an ad hoc last value carried forward approach. The practical utility of the methods is illustrated on data from a study on human immunodeficiency virus.

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.

A Common Mechanism for Resistance to Oxime Reactivation of Acetylcholinesterase Inhibited by Organophosphorus Compounds

DTIC Science & Technology

2013-01-01

application of the Hammett equation with the constants rph in the chemistry of organophosphorus compounds, Russ. Chem. Rev. 38 (1969) 795–811. [13...of oximes and OP compounds and the ability of oximes to reactivate OP- inhibited AChE. Multiple linear regression equations were analyzed using...phosphonate pairs, 21 oxime/ phosphoramidate pairs and 12 oxime/phosphate pairs. The best linear regression equation resulting from multiple regression anal

Estimating Flow-Duration and Low-Flow Frequency Statistics for Unregulated Streams in Oregon

USGS Publications Warehouse

Risley, John; Stonewall, Adam J.; Haluska, Tana

2008-01-01

Flow statistical datasets, basin-characteristic datasets, and regression equations were developed to provide decision makers with surface-water information needed for activities such as water-quality regulation, water-rights adjudication, biological habitat assessment, infrastructure design, and water-supply planning and management. The flow statistics, which included annual and monthly period of record flow durations (5th, 10th, 25th, 50th, and 95th percent exceedances) and annual and monthly 7-day, 10-year (7Q10) and 7-day, 2-year (7Q2) low flows, were computed at 466 streamflow-gaging stations at sites with unregulated flow conditions throughout Oregon and adjacent areas of neighboring States. Regression equations, created from the flow statistics and basin characteristics of the stations, can be used to estimate flow statistics at ungaged stream sites in Oregon. The study area was divided into 10 regression modeling regions based on ecological, topographic, geologic, hydrologic, and climatic criteria. In total, 910 annual and monthly regression equations were created to predict the 7 flow statistics in the 10 regions. Equations to predict the five flow-duration exceedance percentages and the two low-flow frequency statistics were created with Ordinary Least Squares and Generalized Least Squares regression, respectively. The standard errors of estimate of the equations created to predict the 5th and 95th percent exceedances had medians of 42.4 and 64.4 percent, respectively. The standard errors of prediction of the equations created to predict the 7Q2 and 7Q10 low-flow statistics had medians of 51.7 and 61.2 percent, respectively. Standard errors for regression equations for sites in western Oregon were smaller than those in eastern Oregon partly because of a greater density of available streamflow-gaging stations in western Oregon than eastern Oregon. High-flow regression equations (such as the 5th and 10th percent exceedances) also generally were more accurate than the low-flow regression equations (such as the 95th percent exceedance and 7Q10 low-flow statistic). The regression equations predict unregulated flow conditions in Oregon. Flow estimates need to be adjusted if they are used at ungaged sites that are regulated by reservoirs or affected by water-supply and agricultural withdrawals if actual flow conditions are of interest. The regression equations are installed in the USGS StreamStats Web-based tool (http://water.usgs.gov/osw/streamstats/index.html, accessed July 16, 2008). StreamStats provides users with a set of annual and monthly flow-duration and low-flow frequency estimates for ungaged sites in Oregon in addition to the basin characteristics for the sites. Prediction intervals at the 90-percent confidence level also are automatically computed.

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.

Using "Tracker" to Prove the Simple Harmonic Motion Equation

ERIC Educational Resources Information Center

Kinchin, John

2016-01-01

Simple harmonic motion (SHM) is a common topic for many students to study. Using the free, though versatile, motion tracking software; "Tracker", we can extend the students experience and show that the general equation for SHM does lead to the correct period of a simple pendulum.

A classical regression framework for mediation analysis: fitting one model to estimate mediation effects.

PubMed

Saunders, Christina T; Blume, Jeffrey D

2017-10-26

Mediation analysis explores the degree to which an exposure's effect on an outcome is diverted through a mediating variable. We describe a classical regression framework for conducting mediation analyses in which estimates of causal mediation effects and their variance are obtained from the fit of a single regression model. The vector of changes in exposure pathway coefficients, which we named the essential mediation components (EMCs), is used to estimate standard causal mediation effects. Because these effects are often simple functions of the EMCs, an analytical expression for their model-based variance follows directly. Given this formula, it is instructive to revisit the performance of routinely used variance approximations (e.g., delta method and resampling methods). Requiring the fit of only one model reduces the computation time required for complex mediation analyses and permits the use of a rich suite of regression tools that are not easily implemented on a system of three equations, as would be required in the Baron-Kenny framework. Using data from the BRAIN-ICU study, we provide examples to illustrate the advantages of this framework and compare it with the existing approaches. © The Author 2017. Published by Oxford University Press.

Regression Equations for Monthly and Annual Mean and Selected Percentile Streamflows for Ungaged Rivers in Maine

USGS Publications Warehouse

Dudley, Robert W.

2015-12-03

The largest average errors of prediction are associated with regression equations for the lowest streamflows derived for months during which the lowest streamflows of the year occur (such as the 5 and 1 monthly percentiles for August and September). The regression equations have been derived on the basis of streamflow and basin characteristics data for unregulated, rural drainage basins without substantial streamflow or drainage modifications (for example, diversions and (or) regulation by dams or reservoirs, tile drainage, irrigation, channelization, and impervious paved surfaces), therefore using the equations for regulated or urbanized basins with substantial streamflow or drainage modifications will yield results of unknown error. Input basin characteristics derived using techniques or datasets other than those documented in this report or using values outside the ranges used to develop these regression equations also will yield results of unknown error.

Solving Simple Kinetics without Integrals

ERIC Educational Resources Information Center

de la Pen~a, Lisandro Herna´ndez

2016-01-01

The solution of simple kinetic equations is analyzed without referencing any topic from differential equations or integral calculus. Guided by the physical meaning of the rate equation, a systematic procedure is used to generate an approximate solution that converges uniformly to the exact solution in the case of zero, first, and second order…

Comparative evaluation of urban storm water quality models

NASA Astrophysics Data System (ADS)

Vaze, J.; Chiew, Francis H. S.

2003-10-01

The estimation of urban storm water pollutant loads is required for the development of mitigation and management strategies to minimize impacts to receiving environments. Event pollutant loads are typically estimated using either regression equations or "process-based" water quality models. The relative merit of using regression models compared to process-based models is not clear. A modeling study is carried out here to evaluate the comparative ability of the regression equations and process-based water quality models to estimate event diffuse pollutant loads from impervious surfaces. The results indicate that, once calibrated, both the regression equations and the process-based model can estimate event pollutant loads satisfactorily. In fact, the loads estimated using the regression equation as a function of rainfall intensity and runoff rate are better than the loads estimated using the process-based model. Therefore, if only estimates of event loads are required, regression models should be used because they are simpler and require less data compared to process-based models.

Exploring simple, transparent, interpretable and predictive QSAR models for classification and quantitative prediction of rat toxicity of ionic liquids using OECD recommended guidelines.

PubMed

Das, Rudra Narayan; Roy, Kunal; Popelier, Paul L A

2015-11-01

The present study explores the chemical attributes of diverse ionic liquids responsible for their cytotoxicity in a rat leukemia cell line (IPC-81) by developing predictive classification as well as regression-based mathematical models. Simple and interpretable descriptors derived from a two-dimensional representation of the chemical structures along with quantum topological molecular similarity indices have been used for model development, employing unambiguous modeling strategies that strictly obey the guidelines of the Organization for Economic Co-operation and Development (OECD) for quantitative structure-activity relationship (QSAR) analysis. The structure-toxicity relationships that emerged from both classification and regression-based models were in accordance with the findings of some previous studies. The models suggested that the cytotoxicity of ionic liquids is dependent on the cationic surfactant action, long alkyl side chains, cationic lipophilicity as well as aromaticity, the presence of a dialkylamino substituent at the 4-position of the pyridinium nucleus and a bulky anionic moiety. The models have been transparently presented in the form of equations, thus allowing their easy transferability in accordance with the OECD guidelines. The models have also been subjected to rigorous validation tests proving their predictive potential and can hence be used for designing novel and "greener" ionic liquids. The major strength of the present study lies in the use of a diverse and large dataset, use of simple reproducible descriptors and compliance with the OECD norms. Copyright © 2015 Elsevier Ltd. All rights reserved.

Statistical summary of selected physical, chemical, and toxicity characteristics and estimates of annual constituent loads in urban stormwater, Maricopa County, Arizona

USGS Publications Warehouse

Fossum, Kenneth D.; O'Day, Christie M.; Wilson, Barbara J.; Monical, Jim E.

2001-01-01

Stormwater and streamflow in Maricopa County were monitored to (1) describe the physical, chemical, and toxicity characteristics of stormwater from areas having different land uses, (2) describe the physical, chemical, and toxicity characteristics of streamflow from areas that receive urban stormwater, and (3) estimate constituent loads in stormwater. Urban stormwater and streamflow had similar ranges in most constituent concentrations. The mean concentration of dissolved solids in urban stormwater was lower than in streamflow from the Salt River and Indian Bend Wash. Urban stormwater, however, had a greater chemical oxygen demand and higher concentrations of most nutrients. Mean seasonal loads and mean annual loads of 11 constituents and volumes of runoff were estimated for municipalities in the metropolitan Phoenix area, Arizona, by adjusting regional regression equations of loads. This adjustment procedure uses the original regional regression equation and additional explanatory variables that were not included in the original equation. The adjusted equations had standard errors that ranged from 161 to 196 percent. The large standard errors of the prediction result from the large variability of the constituent concentration data used in the regression analysis. Adjustment procedures produced unsatisfactory results for nine of the regressions?suspended solids, dissolved solids, total phosphorus, dissolved phosphorus, total recoverable cadmium, total recoverable copper, total recoverable lead, total recoverable zinc, and storm runoff. These equations had no consistent direction of bias and no other additional explanatory variables correlated with the observed loads. A stepwise-multiple regression or a three-variable regression (total storm rainfall, drainage area, and impervious area) and local data were used to develop local regression equations for these nine constituents. These equations had standard errors from 15 to 183 percent.

Linear regression analysis and its application to multivariate chromatographic calibration for the quantitative analysis of two-component mixtures.

PubMed

Dinç, Erdal; Ozdemir, Abdil

2005-01-01

Multivariate chromatographic calibration technique was developed for the quantitative analysis of binary mixtures enalapril maleate (EA) and hydrochlorothiazide (HCT) in tablets in the presence of losartan potassium (LST). The mathematical algorithm of multivariate chromatographic calibration technique is based on the use of the linear regression equations constructed using relationship between concentration and peak area at the five-wavelength set. The algorithm of this mathematical calibration model having a simple mathematical content was briefly described. This approach is a powerful mathematical tool for an optimum chromatographic multivariate calibration and elimination of fluctuations coming from instrumental and experimental conditions. This multivariate chromatographic calibration contains reduction of multivariate linear regression functions to univariate data set. The validation of model was carried out by analyzing various synthetic binary mixtures and using the standard addition technique. Developed calibration technique was applied to the analysis of the real pharmaceutical tablets containing EA and HCT. The obtained results were compared with those obtained by classical HPLC method. It was observed that the proposed multivariate chromatographic calibration gives better results than classical HPLC.

Discovering governing equations from data by sparse identification of nonlinear dynamical systems

PubMed Central

Brunton, Steven L.; Proctor, Joshua L.; Kutz, J. Nathan

2016-01-01

Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing. PMID:27035946

Discovering governing equations from data by sparse identification of nonlinear dynamical systems.

PubMed

Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan

2016-04-12

Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing.

Who Will Win?: Predicting the Presidential Election Using Linear Regression

ERIC Educational Resources Information Center

Lamb, John H.

2007-01-01

This article outlines a linear regression activity that engages learners, uses technology, and fosters cooperation. Students generated least-squares linear regression equations using TI-83 Plus[TM] graphing calculators, Microsoft[C] Excel, and paper-and-pencil calculations using derived normal equations to predict the 2004 presidential election.…

Multivariate logistic regression for predicting total culturable virus presence at the intake of a potable-water treatment plant: novel application of the atypical coliform/total coliform ratio.

PubMed

Black, L E; Brion, G M; Freitas, S J

2007-06-01

Predicting the presence of enteric viruses in surface waters is a complex modeling problem. Multiple water quality parameters that indicate the presence of human fecal material, the load of fecal material, and the amount of time fecal material has been in the environment are needed. This paper presents the results of a multiyear study of raw-water quality at the inlet of a potable-water plant that related 17 physical, chemical, and biological indices to the presence of enteric viruses as indicated by cytopathic changes in cell cultures. It was found that several simple, multivariate logistic regression models that could reliably identify observations of the presence or absence of total culturable virus could be fitted. The best models developed combined a fecal age indicator (the atypical coliform [AC]/total coliform [TC] ratio), the detectable presence of a human-associated sterol (epicoprostanol) to indicate the fecal source, and one of several fecal load indicators (the levels of Giardia species cysts, coliform bacteria, and coprostanol). The best fit to the data was found when the AC/TC ratio, the presence of epicoprostanol, and the density of fecal coliform bacteria were input into a simple, multivariate logistic regression equation, resulting in 84.5% and 78.6% accuracies for the identification of the presence and absence of total culturable virus, respectively. The AC/TC ratio was the most influential input variable in all of the models generated, but producing the best prediction required additional input related to the fecal source and the fecal load. The potential for replacing microbial indicators of fecal load with levels of coprostanol was proposed and evaluated by multivariate logistic regression modeling for the presence and absence of virus.

The development and validation of new equations for estimating body fat percentage among Chinese men and women.

PubMed

Liu, Xin; Sun, Qi; Sun, Liang; Zong, Geng; Lu, Ling; Liu, Gang; Rosner, Bernard; Ye, Xingwang; Li, Huaixing; Lin, Xu

2015-05-14

Equations based on simple anthropometric measurements to predict body fat percentage (BF%) are lacking in Chinese population with increasing prevalence of obesity and related abnormalities. We aimed to develop and validate BF% equations in two independent population-based samples of Chinese men and women. The equations were developed among 960 Chinese Hans living in Shanghai (age 46.2 (SD 5.3) years; 36.7% male) using a stepwise linear regression and were subsequently validated in 1150 Shanghai residents (58.7 (SD 6.0) years; 41.7% male; 99% Chinese Hans, 1% Chinese minorities). The associations of equation-derived BF% with changes of 6-year cardiometabolic outcomes and incident type 2 diabetes (T2D) were evaluated in a sub-cohort of 780 Chinese, compared with BF% measured by dual-energy X-ray absorptiometry (DXA; BF%-DXA). Sex-specific equations were established with age, BMI and waist circumference as independent variables. The BF% calculated using new sex-specific equations (BF%-CSS) were in reasonable agreement with BF%-DXA (mean difference: 0.08 (2 SD 6.64) %, P= 0.606 in men; 0.45 (2 SD 6.88) %, P< 0.001 in women). In multivariate-adjusted models, the BF%-CSS and BF%-DXA showed comparable associations with 6-year changes in TAG, HDL-cholesterol, diastolic blood pressure, C-reactive protein and uric acid (P for comparisons ≥ 0.05). Meanwhile, the BF%-CSS and BF%-DXA had comparable areas under the receiver operating characteristic curves for associations with incident T2D (men P= 0.327; women P= 0.159). The BF% equations might be used as surrogates for DXA to estimate BF% among adult Chinese. More studies are needed to evaluate the application of our equations in different populations.

Estimating selected low-flow frequency statistics and harmonic-mean flows for ungaged, unregulated streams in Indiana

USGS Publications Warehouse

Martin, Gary R.; Fowler, Kathleen K.; Arihood, Leslie D.

2016-09-06

Information on low-flow characteristics of streams is essential for the management of water resources. This report provides equations for estimating the 1-, 7-, and 30-day mean low flows for a recurrence interval of 10 years and the harmonic-mean flow at ungaged, unregulated stream sites in Indiana. These equations were developed using the low-flow statistics and basin characteristics for 108 continuous-record streamgages in Indiana with at least 10 years of daily mean streamflow data through the 2011 climate year (April 1 through March 31). The equations were developed in cooperation with the Indiana Department of Environmental Management.Regression techniques were used to develop the equations for estimating low-flow frequency statistics and the harmonic-mean flows on the basis of drainage-basin characteristics. A geographic information system was used to measure basin characteristics for selected streamgages. A final set of 25 basin characteristics measured at all the streamgages were evaluated to choose the best predictors of the low-flow statistics.Logistic-regression equations applicable statewide are presented for estimating the probability that selected low-flow frequency statistics equal zero. These equations use the explanatory variables total drainage area, average transmissivity of the full thickness of the unconsolidated deposits within 1,000 feet of the stream network, and latitude of the basin outlet. The percentage of the streamgage low-flow statistics correctly classified as zero or nonzero using the logistic-regression equations ranged from 86.1 to 88.9 percent.Generalized-least-squares regression equations applicable statewide for estimating nonzero low-flow frequency statistics use total drainage area, the average hydraulic conductivity of the top 70 feet of unconsolidated deposits, the slope of the basin, and the index of permeability and thickness of the Quaternary surficial sediments as explanatory variables. The average standard error of prediction of these regression equations ranges from 55.7 to 61.5 percent.Regional weighted-least-squares regression equations were developed for estimating the harmonic-mean flows by dividing the State into three low-flow regions. The Northern region uses total drainage area and the average transmissivity of the entire thickness of unconsolidated deposits as explanatory variables. The Central region uses total drainage area, the average hydraulic conductivity of the entire thickness of unconsolidated deposits, and the index of permeability and thickness of the Quaternary surficial sediments. The Southern region uses total drainage area and the percent of the basin covered by forest. The average standard error of prediction for these equations ranges from 39.3 to 66.7 percent.The regional regression equations are applicable only to stream sites with low flows unaffected by regulation and to stream sites with drainage basin characteristic values within specified limits. Caution is advised when applying the equations for basins with characteristics near the applicable limits and for basins with karst drainage features and for urbanized basins. Extrapolations near and beyond the applicable basin characteristic limits will have unknown errors that may be large. Equations are presented for use in estimating the 90-percent prediction interval of the low-flow statistics estimated by use of the regression equations at a given stream site.The regression equations are to be incorporated into the U.S. Geological Survey StreamStats Web-based application for Indiana. StreamStats allows users to select a stream site on a map and automatically measure the needed basin characteristics and compute the estimated low-flow statistics and associated prediction intervals.

Technique for estimating the 2- to 500-year flood discharges on unregulated streams in rural Missouri

USGS Publications Warehouse

Alexander, Terry W.; Wilson, Gary L.

1995-01-01

A generalized least-squares regression technique was used to relate the 2- to 500-year flood discharges from 278 selected streamflow-gaging stations to statistically significant basin characteristics. The regression relations (estimating equations) were defined for three hydrologic regions (I, II, and III) in rural Missouri. Ordinary least-squares regression analyses indicate that drainage area (Regions I, II, and III) and main-channel slope (Regions I and II) are the only basin characteristics needed for computing the 2- to 500-year design-flood discharges at gaged or ungaged stream locations. The resulting generalized least-squares regression equations provide a technique for estimating the 2-, 5-, 10-, 25-, 50-, 100-, and 500-year flood discharges on unregulated streams in rural Missouri. The regression equations for Regions I and II were developed from stream-flow-gaging stations with drainage areas ranging from 0.13 to 11,500 square miles and 0.13 to 14,000 square miles, and main-channel slopes ranging from 1.35 to 150 feet per mile and 1.20 to 279 feet per mile. The regression equations for Region III were developed from streamflow-gaging stations with drainage areas ranging from 0.48 to 1,040 square miles. Standard errors of estimate for the generalized least-squares regression equations in Regions I, II, and m ranged from 30 to 49 percent.

Estimation of peak-discharge frequency of urban streams in Jefferson County, Kentucky

USGS Publications Warehouse

Martin, Gary R.; Ruhl, Kevin J.; Moore, Brian L.; Rose, Martin F.

1997-01-01

An investigation of flood-hydrograph characteristics for streams in urban Jefferson County, Kentucky, was made to obtain hydrologic information needed for waterresources management. Equations for estimating peak-discharge frequencies for ungaged streams in the county were developed by combining (1) long-term annual peakdischarge data and rainfall-runoff data collected from 1991 to 1995 in 13 urban basins and (2) long-term annual peak-discharge data in four rural basins located in hydrologically similar areas of neighboring counties. The basins ranged in size from 1.36 to 64.0 square miles. The U.S. Geological Survey Rainfall- Runoff Model (RRM) was calibrated for each of the urban basins. The calibrated models were used with long-term, historical rainfall and pan-evaporation data to simulate 79 years of annual peak-discharge data. Peak-discharge frequencies were estimated by fitting the logarithms of the annual peak discharges to a Pearson-Type III frequency distribution. The simulated peak-discharge frequencies were adjusted for improved reliability by application of bias-correction factors derived from peakdischarge frequencies based on local, observed annual peak discharges. The three-parameter and the preferred seven-parameter nationwide urban-peak-discharge regression equations previously developed by USGS investigators provided biased (high) estimates for the urban basins studied. Generalized-least-square regression procedures were used to relate peakdischarge frequency to selected basin characteristics. Regression equations were developed to estimate peak-discharge frequency by adjusting peak-dischargefrequency estimates made by use of the threeparameter nationwide urban regression equations. The regression equations are presented in equivalent forms as functions of contributing drainage area, main-channel slope, and basin development factor, which is an index for measuring the efficiency of the basin drainage system. Estimates of peak discharges for streams in the county can be made for the 2-, 5-, 10-, 25-, 50-, and 100-year recurrence intervals by use of the regression equations. The average standard errors of prediction of the regression equations ranges from ? 34 to ? 45 percent. The regression equations are applicable to ungaged streams in the county having a specific range of basin characteristics.

Resting electrocardiogram and stress myocardial perfusion imaging in the determination of left ventricular systolic function: an assessment enhancing the performance of gated SPET.

PubMed

Moralidis, Efstratios; Spyridonidis, Tryfon; Arsos, Georgios; Skeberis, Vassilios; Anagnostopoulos, Constantinos; Gavrielidis, Stavros

2010-01-01

This study aimed to determine systolic dysfunction and estimate resting left ventricular ejection fraction (LVEF) from information collected during routine evaluation of patients with suspected or known coronary heart disease. This approach was then compared to gated single photon emission tomography (SPET). Patients having undergone stress (201)Tl myocardial perfusion imaging followed by equilibrium radionuclide angiography (ERNA) were separated into derivation (n=954) and validation (n=309) groups. Logistic regression analysis was used to develop scoring systems, containing clinical, electrocardiographic (ECG) and scintigraphic data, for the discrimination of an ERNA-LVEF<0.50. Linear regression analysis provided equations predicting ERNA-LVEF from those scores. In 373 patients LVEF was also assessed with (201)Tl gated SPET. Our results showed that an ECG-Scintigraphic scoring system was the best simple predictor of an ERNA-LVEF<0.50 in comparison to other models including ECG, clinical and scintigraphic variables in both the derivation and validation subpopulations. A simple linear equation was derived also for the assessment of resting LVEF from the ECG-Scintigraphic model. Equilibrium radionuclide angiography-LVEF had a good correlation with the ECG-Scintigraphic model LVEF (r=0.716, P=0.000), (201)Tl gated SPET LVEF (r=0.711, P=0.000) and the average LVEF from those assessments (r=0.796, P=0.000). The Bland-Altman statistic (mean+/-2SD) provided values of 0.001+/-0.176, 0.071+/-0.196 and 0.040+/-0.152, respectively. The average LVEF was a better discriminator of systolic dysfunction than gated SPET-LVEF in receiver operating characteristic (ROC) analysis and identified more patients (89%) with a

Morse Code, Scrabble, and the Alphabet

ERIC Educational Resources Information Center

Richardson, Mary; Gabrosek, John; Reischman, Diann; Curtiss, Phyliss

2004-01-01

In this paper we describe an interactive activity that illustrates simple linear regression. Students collect data and analyze it using simple linear regression techniques taught in an introductory applied statistics course. The activity is extended to illustrate checks for regression assumptions and regression diagnostics taught in an…

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.

Estimation of Ordinary Differential Equation Parameters Using Constrained Local Polynomial Regression.

PubMed

Ding, A Adam; Wu, Hulin

2014-10-01

We propose a new method to use a constrained local polynomial regression to estimate the unknown parameters in ordinary differential equation models with a goal of improving the smoothing-based two-stage pseudo-least squares estimate. The equation constraints are derived from the differential equation model and are incorporated into the local polynomial regression in order to estimate the unknown parameters in the differential equation model. We also derive the asymptotic bias and variance of the proposed estimator. Our simulation studies show that our new estimator is clearly better than the pseudo-least squares estimator in estimation accuracy with a small price of computational cost. An application example on immune cell kinetics and trafficking for influenza infection further illustrates the benefits of the proposed new method.

Estimation of Ordinary Differential Equation Parameters Using Constrained Local Polynomial Regression

PubMed Central

Ding, A. Adam; Wu, Hulin

2015-01-01

We propose a new method to use a constrained local polynomial regression to estimate the unknown parameters in ordinary differential equation models with a goal of improving the smoothing-based two-stage pseudo-least squares estimate. The equation constraints are derived from the differential equation model and are incorporated into the local polynomial regression in order to estimate the unknown parameters in the differential equation model. We also derive the asymptotic bias and variance of the proposed estimator. Our simulation studies show that our new estimator is clearly better than the pseudo-least squares estimator in estimation accuracy with a small price of computational cost. An application example on immune cell kinetics and trafficking for influenza infection further illustrates the benefits of the proposed new method. PMID:26401093

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

NASA Technical Reports Server (NTRS)

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

1976-01-01

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

Validity of a heart rate monitor during work in the laboratory and on the Space Shuttle

NASA Technical Reports Server (NTRS)

Moore, A. D. Jr; Lee, S. M.; Greenisen, M. C.; Bishop, P.

1997-01-01

Accurate heart rate measurement during work is required for many industrial hygiene and ergonomics situations. The purpose of this investigation was to determine the validity of heart rate measurements obtained by a simple, lightweight, commercially available wrist-worn heart rate monitor (HRM) during work (cycle exercise) sessions conducted in the laboratory and also during the particularly challenging work environment of space flight. Three different comparisons were made. The first compared HRM data to simultaneous electrocardiogram (ECG) recordings of varying heart rates that were generated by an ECG simulator. The second compared HRM data to ECG recordings collected during work sessions of 14 subjects in the laboratory. Finally, ECG downlink and HRM data were compared in four astronauts who performed cycle exercise during space flight. The data were analyzed using regression techniques. The results were that the HRM recorded virtually identical heart rates compared with ECG recordings for the data set generated by an ECG simulator. The regression equation for the relationship between ECG versus HRM heart rate data during work in the laboratory was: ECG HR = 0.99 x (HRM) + 0.82 (r2 = 0.99). Finally, the agreement between ECG downlink data and HRM data during space flight was also very high, with the regression equation being: Downlink ECG HR = 1.05 x (HRM) -5.71 (r2 = 0.99). The results of this study indicate that the HRM provides accurate data and may be used to reliably obtain valid data regarding heart rate responses during work.

Methods for estimating selected low-flow frequency statistics and mean annual flow for ungaged locations on streams in North Georgia

USGS Publications Warehouse

Gotvald, Anthony J.

2017-01-13

The U.S. Geological Survey, in cooperation with the Georgia Department of Natural Resources, Environmental Protection Division, developed regional regression equations for estimating selected low-flow frequency and mean annual flow statistics for ungaged streams in north Georgia that are not substantially affected by regulation, diversions, or urbanization. Selected low-flow frequency statistics and basin characteristics for 56 streamgage locations within north Georgia and 75 miles beyond the State’s borders in Alabama, Tennessee, North Carolina, and South Carolina were combined to form the final dataset used in the regional regression analysis. Because some of the streamgages in the study recorded zero flow, the final regression equations were developed using weighted left-censored regression analysis to analyze the flow data in an unbiased manner, with weights based on the number of years of record. The set of equations includes the annual minimum 1- and 7-day average streamflow with the 10-year recurrence interval (referred to as 1Q10 and 7Q10), monthly 7Q10, and mean annual flow. The final regional regression equations are functions of drainage area, mean annual precipitation, and relief ratio for the selected low-flow frequency statistics and drainage area and mean annual precipitation for mean annual flow. The average standard error of estimate was 13.7 percent for the mean annual flow regression equation and ranged from 26.1 to 91.6 percent for the selected low-flow frequency equations.The equations, which are based on data from streams with little to no flow alterations, can be used to provide estimates of the natural flows for selected ungaged stream locations in the area of Georgia north of the Fall Line. The regression equations are not to be used to estimate flows for streams that have been altered by the effects of major dams, surface-water withdrawals, groundwater withdrawals (pumping wells), diversions, or wastewater discharges. The regression equations should be used only for ungaged sites with drainage areas between 1.67 and 576 square miles, mean annual precipitation between 47.6 and 81.6 inches, and relief ratios between 0.146 and 0.607; these are the ranges of the explanatory variables used to develop the equations. An attempt was made to develop regional regression equations for the area of Georgia south of the Fall Line by using the same approach used during this study for north Georgia; however, the equations resulted with high average standard errors of estimates and poorly predicted flows below 0.5 cubic foot per second, which may be attributed to the karst topography common in that area.The final regression equations developed from this study are planned to be incorporated into the U.S. Geological Survey StreamStats program. StreamStats is a Web-based geographic information system that provides users with access to an assortment of analytical tools useful for water-resources planning and management, and for engineering design applications, such as the design of bridges. The StreamStats program provides streamflow statistics and basin characteristics for U.S. Geological Survey streamgage locations and ungaged sites of interest. StreamStats also can compute basin characteristics and provide estimates of streamflow statistics for ungaged sites when users select the location of a site along any stream in Georgia.

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)

Building Regression Models: The Importance of Graphics.

ERIC Educational Resources Information Center

Dunn, Richard

1989-01-01

Points out reasons for using graphical methods to teach simple and multiple regression analysis. Argues that a graphically oriented approach has considerable pedagogic advantages in the exposition of simple and multiple regression. Shows that graphical methods may play a central role in the process of building regression models. (Author/LS)

Minute ventilation of cyclists, car and bus passengers: an experimental study.

PubMed

Zuurbier, Moniek; Hoek, Gerard; van den Hazel, Peter; Brunekreef, Bert

2009-10-27

Differences in minute ventilation between cyclists, pedestrians and other commuters influence inhaled doses of air pollution. This study estimates minute ventilation of cyclists, car and bus passengers, as part of a study on health effects of commuters' exposure to air pollutants. Thirty-four participants performed a submaximal test on a bicycle ergometer, during which heart rate and minute ventilation were measured simultaneously at increasing cycling intensity. Individual regression equations were calculated between heart rate and the natural log of minute ventilation. Heart rates were recorded during 280 two hour trips by bicycle, bus and car and were calculated into minute ventilation levels using the individual regression coefficients. Minute ventilation during bicycle rides were on average 2.1 times higher than in the car (individual range from 1.3 to 5.3) and 2.0 times higher than in the bus (individual range from 1.3 to 5.1). The ratio of minute ventilation of cycling compared to travelling by bus or car was higher in women than in men. Substantial differences in regression equations were found between individuals. The use of individual regression equations instead of average regression equations resulted in substantially better predictions of individual minute ventilations. The comparability of the gender-specific overall regression equations linking heart rate and minute ventilation with one previous American study, supports that for studies on the group level overall equations can be used. For estimating individual doses, the use of individual regression coefficients provides more precise data. Minute ventilation levels of cyclists are on average two times higher than of bus and car passengers, consistent with the ratio found in one small previous study of young adults. The study illustrates the importance of inclusion of minute ventilation data in comparing air pollution doses between different modes of transport.

Estimation of Magnitude and Frequency of Floods for Streams on the Island of Oahu, Hawaii

USGS Publications Warehouse

Wong, Michael F.

1994-01-01

This report describes techniques for estimating the magnitude and frequency of floods for the island of Oahu. The log-Pearson Type III distribution and methodology recommended by the Interagency Committee on Water Data was used to determine the magnitude and frequency of floods at 79 gaging stations that had 11 to 72 years of record. Multiple regression analysis was used to construct regression equations to transfer the magnitude and frequency information from gaged sites to ungaged sites. Oahu was divided into three hydrologic regions to define relations between peak discharge and drainage-basin and climatic characteristics. Regression equations are provided to estimate the 2-, 5-, 10-, 25-, 50-, and 100-year peak discharges at ungaged sites. Significant basin and climatic characteristics included in the regression equations are drainage area, median annual rainfall, and the 2-year, 24-hour rainfall intensity. Drainage areas for sites used in this study ranged from 0.03 to 45.7 square miles. Standard error of prediction for the regression equations ranged from 34 to 62 percent. Peak-discharge data collected through water year 1988, geographic information system (GIS) technology, and generalized least-squares regression were used in the analyses. The use of GIS seems to be a more flexible and consistent means of defining and calculating basin and climatic characteristics than using manual methods. Standard errors of estimate for the regression equations in this report are an average of 8 percent less than those published in previous studies.

Mathematical and computational model for the analysis of micro hybrid rocket motor

NASA Astrophysics Data System (ADS)

Stoia-Djeska, Marius; Mingireanu, Florin

2012-11-01

The hybrid rockets use a two-phase propellant system. In the present work we first develop a simplified model of the coupling of the hybrid combustion process with the complete unsteady flow, starting from the combustion port and ending with the nozzle. The physical and mathematical model are adapted to the simulations of micro hybrid rocket motors. The flow model is based on the one-dimensional Euler equations with source terms. The flow equations and the fuel regression rate law are solved in a coupled manner. The platform of the numerical simulations is an implicit fourth-order Runge-Kutta second order cell-centred finite volume method. The numerical results obtained with this model show a good agreement with published experimental and numerical results. The computational model developed in this work is simple, computationally efficient and offers the advantage of taking into account a large number of functional and constructive parameters that are used by the engineers.

Development of a general equation to determine the transfer factor feed-to-meat for radiocesium on the basis of the body mass of domestic animals

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

Nalezinski, S.; Ruehm, W.; Wirth, E.

1996-05-01

Transfer factors from feed to meat (5{sub {integral}}), taken from literature for monogastric animals and ruminants have been correlated to their corresponding animal body mass (m{sub b}). Taking all data into account, a close relationship between both transfer factor and body mass becomes evident, yielding a regression function of (T{sub {integral}} = 8.0 x m{sub b}{sup {minus}0.91}) (r = -0.97). For monogastric animals (including poultry), the corresponding relationships are T{sub {integral}} = 1.9 x m{sub b}{sup {minus}0.72} (r = 0.78). The equations offer the opportunity to estimate the transfer factor for individual animals more precisely taking individual body masses intomore » account. They are of interest for animals, on which no or only poor data concerning radiocesium transfer factors are available. The determination of radiocesium transfer factors are reduced to a simple weighing process. 17 refs., 1 fig., 2 tabs.« less

The stationary sine-Gordon equation on metric graphs: Exact analytical solutions for simple topologies

NASA Astrophysics Data System (ADS)

Sabirov, K.; Rakhmanov, S.; Matrasulov, D.; Susanto, H.

2018-04-01

We consider the stationary sine-Gordon equation on metric graphs with simple topologies. Exact analytical solutions are obtained for different vertex boundary conditions. It is shown that the method can be extended for tree and other simple graph topologies. Applications of the obtained results to branched planar Josephson junctions and Josephson junctions with tricrystal boundaries are discussed.

Validation of Core Temperature Estimation Algorithm

DTIC Science & Technology

2016-01-29

plot of observed versus estimated core temperature with the line of identity (dashed) and the least squares regression line (solid) and line equation...estimated PSI with the line of identity (dashed) and the least squares regression line (solid) and line equation in the top left corner. (b) Bland...for comparison. The root mean squared error (RMSE) was also computed, as given by Equation 2.

A local equation for differential diagnosis of β-thalassemia trait and iron deficiency anemia by logistic regression analysis in Southeast Iran.

PubMed

Sargolzaie, Narjes; Miri-Moghaddam, Ebrahim

2014-01-01

The most common differential diagnosis of β-thalassemia (β-thal) trait is iron deficiency anemia. Several red blood cell equations were introduced during different studies for differential diagnosis between β-thal trait and iron deficiency anemia. Due to genetic variations in different regions, these equations cannot be useful in all population. The aim of this study was to determine a native equation with high accuracy for differential diagnosis of β-thal trait and iron deficiency anemia for the Sistan and Baluchestan population by logistic regression analysis. We selected 77 iron deficiency anemia and 100 β-thal trait cases. We used binary logistic regression analysis and determined best equations for probability prediction of β-thal trait against iron deficiency anemia in our population. We compared diagnostic values and receiver operative characteristic (ROC) curve related to this equation and another 10 published equations in discriminating β-thal trait and iron deficiency anemia. The binary logistic regression analysis determined the best equation for best probability prediction of β-thal trait against iron deficiency anemia with area under curve (AUC) 0.998. Based on ROC curves and AUC, Green & King, England & Frazer, and then Sirdah indices, respectively, had the most accuracy after our equation. We suggest that to get the best equation and cut-off in each region, one needs to evaluate specific information of each region, specifically in areas where populations are homogeneous, to provide a specific formula for differentiating between β-thal trait and iron deficiency anemia.

Methods for estimating flood frequency in Montana based on data through water year 1998

USGS Publications Warehouse

Parrett, Charles; Johnson, Dave R.

2004-01-01

Annual peak discharges having recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years (T-year floods) were determined for 660 gaged sites in Montana and in adjacent areas of Idaho, Wyoming, and Canada, based on data through water year 1998. The updated flood-frequency information was subsequently used in regression analyses, either ordinary or generalized least squares, to develop equations relating T-year floods to various basin and climatic characteristics, equations relating T-year floods to active-channel width, and equations relating T-year floods to bankfull width. The equations can be used to estimate flood frequency at ungaged sites. Montana was divided into eight regions, within which flood characteristics were considered to be reasonably homogeneous, and the three sets of regression equations were developed for each region. A measure of the overall reliability of the regression equations is the average standard error of prediction. The average standard errors of prediction for the equations based on basin and climatic characteristics ranged from 37.4 percent to 134.1 percent. Average standard errors of prediction for the equations based on active-channel width ranged from 57.2 percent to 141.3 percent. Average standard errors of prediction for the equations based on bankfull width ranged from 63.1 percent to 155.5 percent. In most regions, the equations based on basin and climatic characteristics generally had smaller average standard errors of prediction than equations based on active-channel or bankfull width. An exception was the Southeast Plains Region, where all equations based on active-channel width had smaller average standard errors of prediction than equations based on basin and climatic characteristics or bankfull width. Methods for weighting estimates derived from the basin- and climatic-characteristic equations and the channel-width equations also were developed. The weights were based on the cross correlation of residuals from the different methods and the average standard errors of prediction. When all three methods were combined, the average standard errors of prediction ranged from 37.4 percent to 120.2 percent. Weighting of estimates reduced the standard errors of prediction for all T-year flood estimates in four regions, reduced the standard errors of prediction for some T-year flood estimates in two regions, and provided no reduction in average standard error of prediction in two regions. A computer program for solving the regression equations, weighting estimates, and determining reliability of individual estimates was developed and placed on the USGS Montana District World Wide Web page. A new regression method, termed Region of Influence regression, also was tested. Test results indicated that the Region of Influence method was not as reliable as the regional equations based on generalized least squares regression. Two additional methods for estimating flood frequency at ungaged sites located on the same streams as gaged sites also are described. The first method, based on a drainage-area-ratio adjustment, is intended for use on streams where the ungaged site of interest is located near a gaged site. The second method, based on interpolation between gaged sites, is intended for use on streams that have two or more streamflow-gaging stations.

Flood-frequency prediction methods for unregulated streams of Tennessee, 2000

USGS Publications Warehouse

Law, George S.; Tasker, Gary D.

2003-01-01

Up-to-date flood-frequency prediction methods for unregulated, ungaged rivers and streams of Tennessee have been developed. Prediction methods include the regional-regression method and the newer region-of-influence method. The prediction methods were developed using stream-gage records from unregulated streams draining basins having from 1 percent to about 30 percent total impervious area. These methods, however, should not be used in heavily developed or storm-sewered basins with impervious areas greater than 10 percent. The methods can be used to estimate 2-, 5-, 10-, 25-, 50-, 100-, and 500-year recurrence-interval floods of most unregulated rural streams in Tennessee. A computer application was developed that automates the calculation of flood frequency for unregulated, ungaged rivers and streams of Tennessee. Regional-regression equations were derived by using both single-variable and multivariable regional-regression analysis. Contributing drainage area is the explanatory variable used in the single-variable equations. Contributing drainage area, main-channel slope, and a climate factor are the explanatory variables used in the multivariable equations. Deleted-residual standard error for the single-variable equations ranged from 32 to 65 percent. Deleted-residual standard error for the multivariable equations ranged from 31 to 63 percent. These equations are included in the computer application to allow easy comparison of results produced by the different methods. The region-of-influence method calculates multivariable regression equations for each ungaged site and recurrence interval using basin characteristics from 60 similar sites selected from the study area. Explanatory variables that may be used in regression equations computed by the region-of-influence method include contributing drainage area, main-channel slope, a climate factor, and a physiographic-region factor. Deleted-residual standard error for the region-of-influence method tended to be only slightly smaller than those for the regional-regression method and ranged from 27 to 62 percent.

Techniques for estimating magnitude and frequency of peak flows for Pennsylvania streams

USGS Publications Warehouse

Stuckey, Marla H.; Reed, Lloyd A.

2000-01-01

Regression equations for estimating the magnitude and frequency of floods on ungaged streams in Pennsylvania with drainage areas less that 2,000 square miles were developed on the basis of peak-flow data collected at 313 streamflow-gaging stations. All streamflow-gaging stations used in the development of the equations had 10 or more years of record and include active and discontinued continuous-record and crest-stage partial-record streamflow-gaging stations. Regional regression equations were developed for flood flows expected every 10, 25, 50, 100, and 500 years by the use of a weighted multiple linear regression model.The State was divided into two regions. The largest region, Region A, encompasses about 78 percent of Pennsylvania. The smaller region, Region B, includes only the northwestern part of the State. Basin characteristics used in the regression equations for Region A are drainage area, percentage of forest cover, percentage of urban development, percentage of basin underlain by carbonate bedrock, and percentage of basin controlled by lakes, swamps, and reservoirs. Basin characteristics used in the regression equations for Region B are drainage area and percentage of basin controlled by lakes, swamps, and reservoirs. The coefficient of determination (R2) values for the five flood-frequency equations for Region A range from 0.93 to 0.82, and for Region B, the range is from 0.96 to 0.89.While the regression equations can be used to predict the magnitude and frequency of peak flows for most streams in the State, they should not be used for streams with drainage areas greater than 2,000 square miles or less than 1.5 square miles, for streams that drain extensively mined areas, or for stream reaches immediately below flood-control reservoirs. In addition, the equations presented for Region B should not be used if the stream drains a basin with more than 5 percent urban development.

Estimation of flood discharges at selected annual exceedance probabilities for unregulated, rural streams in Vermont, with a section on Vermont regional skew regression

USGS Publications Warehouse

Olson, Scott A.; with a section by Veilleux, Andrea G.

2014-01-01

This report provides estimates of flood discharges at selected annual exceedance probabilities (AEPs) for streamgages in and adjacent to Vermont and equations for estimating flood discharges at AEPs of 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent (recurrence intervals of 2-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-years, respectively) for ungaged, unregulated, rural streams in Vermont. The equations were developed using generalized least-squares regression. Flood-frequency and drainage-basin characteristics from 145 streamgages were used in developing the equations. The drainage-basin characteristics used as explanatory variables in the regression equations include drainage area, percentage of wetland area, and the basin-wide mean of the average annual precipitation. The average standard errors of prediction for estimating the flood discharges at the 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent AEP with these equations are 34.9, 36.0, 38.7, 42.4, 44.9, 47.3, 50.7, and 55.1 percent, respectively. Flood discharges at selected AEPs for streamgages were computed by using the Expected Moments Algorithm. To improve estimates of the flood discharges for given exceedance probabilities at streamgages in Vermont, a new generalized skew coefficient was developed. The new generalized skew for the region is a constant, 0.44. The mean square error of the generalized skew coefficient is 0.078. This report describes a technique for using results from the regression equations to adjust an AEP discharge computed from a streamgage record. This report also describes a technique for using a drainage-area adjustment to estimate flood discharge at a selected AEP for an ungaged site upstream or downstream from a streamgage. 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.

Anthropometric Survey of US Army Personnel (1988): Correlation Coefficients and Regression Equations. Part 3. Simple and Partial Correlation Tables--Female

DTIC Science & Technology

1990-05-01

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Anthropometric Variables Accurately Predict Dual Energy X-Ray Absorptiometric-Derived Body Composition and Can Be Used to Screen for Diabetes

PubMed Central

Yavari, Reza; McEntee, Erin; McEntee, Michael; Brines, Michael

2011-01-01

The current world-wide epidemic of obesity has stimulated interest in developing simple screening methods to identify individuals with undiagnosed diabetes mellitus type 2 (DM2) or metabolic syndrome (MS). Prior work utilizing body composition obtained by sophisticated technology has shown that the ratio of abdominal fat to total fat is a good predictor for DM2 or MS. The goals of this study were to determine how well simple anthropometric variables predict the fat mass distribution as determined by dual energy x-ray absorptometry (DXA), and whether these are useful to screen for DM2 or MS within a population. To accomplish this, the body composition of 341 females spanning a wide range of body mass indices and with a 23% prevalence of DM2 and MS was determined using DXA. Stepwise linear regression models incorporating age, weight, height, waistline, and hipline predicted DXA body composition (i.e., fat mass, trunk fat, fat free mass, and total mass) with good accuracy. Using body composition as independent variables, nominal logistic regression was then performed to estimate the probability of DM2. The results show good discrimination with the receiver operating characteristic (ROC) having an area under the curve (AUC) of 0.78. The anthropometrically-derived body composition equations derived from the full DXA study group were then applied to a group of 1153 female patients selected from a general endocrinology practice. Similar to the smaller study group, the ROC from logistical regression using body composition had an AUC of 0.81 for the detection of DM2. These results are superior to screening based on questionnaires and compare favorably with published data derived from invasive testing, e.g., hemoglobin A1c. This anthropometric approach offers promise for the development of simple, inexpensive, non-invasive screening to identify individuals with metabolic dysfunction within large populations. PMID:21915276

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

The National Flood Frequency Program, version 3 : a computer program for estimating magnitude and frequency of floods for ungaged sites

USGS Publications Warehouse

Ries, Kernell G.; Crouse, Michele Y.

2002-01-01

For many years, the U.S. Geological Survey (USGS) has been developing regional regression equations for estimating flood magnitude and frequency at ungaged sites. These regression equations are used to transfer flood characteristics from gaged to ungaged sites through the use of watershed and climatic characteristics as explanatory or predictor variables. Generally, these equations have been developed on a Statewide or metropolitan-area basis as part of cooperative study programs with specific State Departments of Transportation. In 1994, the USGS released a computer program titled the National Flood Frequency Program (NFF), which compiled all the USGS available regression equations for estimating the magnitude and frequency of floods in the United States and Puerto Rico. NFF was developed in cooperation with the Federal Highway Administration and the Federal Emergency Management Agency. Since the initial release of NFF, the USGS has produced new equations for many areas of the Nation. A new version of NFF has been developed that incorporates these new equations and provides additional functionality and ease of use. NFF version 3 provides regression-equation estimates of flood-peak discharges for unregulated rural and urban watersheds, flood-frequency plots, and plots of typical flood hydrographs for selected recurrence intervals. The Program also provides weighting techniques to improve estimates of flood-peak discharges for gaging stations and ungaged sites. The information provided by NFF should be useful to engineers and hydrologists for planning and design applications. This report describes the flood-regionalization techniques used in NFF and provides guidance on the applicability and limitations of the techniques. The NFF software and the documentation for the regression equations included in NFF are available at http://water.usgs.gov/software/nff.html.

Introducing a Simple Equation to Express Oxidation States as an Alternative to Using Rules Associated with Words Alone

ERIC Educational Resources Information Center

Minkiewicz, Piotr; Darewicz, Malgorzata; Iwaniak, Anna

2018-01-01

A simple equation to calculate the oxidation states (oxidation numbers) of individual atoms in molecules and ions may be introduced instead of rules associated with words alone. The equation includes two of three categories of bonds, classified as proposed by Goodstein: number of bonds with more electronegative atoms and number of bonds with less…

Analog Computer Solution of the Electrodiffusion Equation for a Simple Membrane

ERIC Educational Resources Information Center

Onega, Ronald J.

1972-01-01

An analog solution was obtained for the Nenst-Planck and Poisson equations which describe the ion concentration across a simple membrane held at a potential difference. The electric field variation within the membrane was also determined. (Author/TS)

Model Estimation Using Ridge Regression with the Variance Normalization Criterion. Interim Report No. 2. The Education and Inequality in Canada Project.

ERIC Educational Resources Information Center

Lee, Wan-Fung; Bulcock, Jeffrey Wilson

The purposes of this study are: (1) to demonstrate the superiority of simple ridge regression over ordinary least squares regression through theoretical argument and empirical example; (2) to modify ridge regression through use of the variance normalization criterion; and (3) to demonstrate the superiority of simple ridge regression based on the…

Adding In-Plane Flexibility to the Equations of Motion of a Single Rotor Helicopter

NASA Technical Reports Server (NTRS)

Curtiss, H. C., Jr.

2000-01-01

This report describes a way to add the effects of main rotor blade flexibility in the in- plane or lead-lag direction to a large set of non-linear equations of motion for a single rotor helicopter with rigid blades(l). Differences between the frequency of the regressing lag mode predicted by the equations of (1) and that measured in flight (2) for a UH-60 helicopter indicate that some element is missing from the analytical model of (1) which assumes rigid blades. A previous study (3) noted a similar discrepancy for the CH-53 helicopter. Using a relatively simple analytical model in (3), compared to (1), it was shown that a mechanical lag damper increases significantly the coupling between the rigid lag mode and the first flexible mode. This increased coupling due to a powerful lag damper produces an increase in the lowest lag frequency when viewed in a frame rotating with the blade. Flight test measurements normally indicate the frequency of this mode in a non-rotating or fixed frame. This report presents the additions necessary to the full equations of motion, to include main rotor blade lag flexibility. Since these additions are made to a very complex nonlinear dynamic model, in order to provide physical insight, a discussion of the results obtained from a simplified set of equations of motion is included. The reduced model illustrates the physics involved in the coupling and should indicate trends in the full model.

An Approximate Solution to the Equation of Motion for Large-Angle Oscillations of the Simple Pendulum with Initial Velocity

ERIC Educational Resources Information Center

Johannessen, Kim

2010-01-01

An analytic approximation of the solution to the differential equation describing the oscillations of a simple pendulum at large angles and with initial velocity is discussed. In the derivation, a sinusoidal approximation has been applied, and an analytic formula for the large-angle period of the simple pendulum is obtained, which also includes…

Regression equations for estimating flood flows for the 2-, 10-, 25-, 50-, 100-, and 500-Year recurrence intervals in Connecticut

USGS Publications Warehouse

Ahearn, Elizabeth A.

2004-01-01

Multiple linear-regression equations were developed to estimate the magnitudes of floods in Connecticut for recurrence intervals ranging from 2 to 500 years. The equations can be used for nonurban, unregulated stream sites in Connecticut with drainage areas ranging from about 2 to 715 square miles. Flood-frequency data and hydrologic characteristics from 70 streamflow-gaging stations and the upstream drainage basins were used to develop the equations. The hydrologic characteristics?drainage area, mean basin elevation, and 24-hour rainfall?are used in the equations to estimate the magnitude of floods. Average standard errors of prediction for the equations are 31.8, 32.7, 34.4, 35.9, 37.6 and 45.0 percent for the 2-, 10-, 25-, 50-, 100-, and 500-year recurrence intervals, respectively. Simplified equations using only one hydrologic characteristic?drainage area?also were developed. The regression analysis is based on generalized least-squares regression techniques. Observed flows (log-Pearson Type III analysis of the annual maximum flows) from five streamflow-gaging stations in urban basins in Connecticut were compared to flows estimated from national three-parameter and seven-parameter urban regression equations. The comparison shows that the three- and seven- parameter equations used in conjunction with the new statewide equations generally provide reasonable estimates of flood flows for urban sites in Connecticut, although a national urban flood-frequency study indicated that the three-parameter equations significantly underestimated flood flows in many regions of the country. Verification of the accuracy of the three-parameter or seven-parameter national regression equations using new data from Connecticut stations was beyond the scope of this study. A technique for calculating flood flows at streamflow-gaging stations using a weighted average also is described. Two estimates of flood flows?one estimate based on the log-Pearson Type III analyses of the annual maximum flows at the gaging station, and the other estimate from the regression equation?are weighted together based on the years of record at the gaging station and the equivalent years of record value determined from the regression. Weighted averages of flood flows for the 2-, 10-, 25-, 50-, 100-, and 500-year recurrence intervals are tabulated for the 70 streamflow-gaging stations used in the regression analysis. Generally, weighted averages give the most accurate estimate of flood flows at gaging stations. An evaluation of the Connecticut's streamflow-gaging network was performed to determine whether the spatial coverage and range of geographic and hydrologic conditions are adequately represented for transferring flood characteristics from gaged to ungaged sites. Fifty-one of 54 stations in the current (2004) network support one or more flood needs of federal, state, and local agencies. Twenty-five of 54 stations in the current network are considered high-priority stations by the U.S. Geological Survey because of their contribution to the longterm understanding of floods, and their application for regionalflood analysis. Enhancements to the network to improve overall effectiveness for regionalization can be made by increasing the spatial coverage of gaging stations, establishing stations in regions of the state that are not well-represented, and adding stations in basins with drainage area sizes not represented. Additionally, the usefulness of the network for characterizing floods can be maintained and improved by continuing operation at the current stations because flood flows can be more accurately estimated at stations with continuous, long-term record.

Introduction, comparison, and validation of Meta-Essentials: A free and simple tool for meta-analysis.

PubMed

Suurmond, Robert; van Rhee, Henk; Hak, Tony

2017-12-01

We present a new tool for meta-analysis, Meta-Essentials, which is free of charge and easy to use. In this paper, we introduce the tool and compare its features to other tools for meta-analysis. We also provide detailed information on the validation of the tool. Although free of charge and simple, Meta-Essentials automatically calculates effect sizes from a wide range of statistics and can be used for a wide range of meta-analysis applications, including subgroup analysis, moderator analysis, and publication bias analyses. The confidence interval of the overall effect is automatically based on the Knapp-Hartung adjustment of the DerSimonian-Laird estimator. However, more advanced meta-analysis methods such as meta-analytical structural equation modelling and meta-regression with multiple covariates are not available. In summary, Meta-Essentials may prove a valuable resource for meta-analysts, including researchers, teachers, and students. © 2017 The Authors. Research Synthesis Methods published by John Wiley & Sons Ltd.

Age Estimation of Infants Through Metric Analysis of Developing Anterior Deciduous Teeth.

PubMed

Viciano, Joan; De Luca, Stefano; Irurita, Javier; Alemán, Inmaculada

2018-01-01

This study provides regression equations for estimation of age of infants from the dimensions of their developing deciduous teeth. The sample comprises 97 individuals of known sex and age (62 boys, 35 girls), aged between 2 days and 1,081 days. The age-estimation equations were obtained for the sexes combined, as well as for each sex separately, thus including "sex" as an independent variable. The values of the correlations and determination coefficients obtained for each regression equation indicate good fits for most of the equations obtained. The "sex" factor was statistically significant when included as an independent variable in seven of the regression equations. However, the "sex" factor provided an advantage for age estimation in only three of the equations, compared to those that did not include "sex" as a factor. These data suggest that the ages of infants can be accurately estimated from measurements of their developing deciduous teeth. © 2017 American Academy of Forensic Sciences.

Regression analysis of sparse asynchronous longitudinal data

PubMed Central

Cao, Hongyuan; Zeng, Donglin; Fine, Jason P.

2015-01-01

Summary We consider estimation of regression models for sparse asynchronous longitudinal observations, where time-dependent responses and covariates are observed intermittently within subjects. Unlike with synchronous data, where the response and covariates are observed at the same time point, with asynchronous data, the observation times are mismatched. Simple kernel-weighted estimating equations are proposed for generalized linear models with either time invariant or time-dependent coefficients under smoothness assumptions for the covariate processes which are similar to those for synchronous data. For models with either time invariant or time-dependent coefficients, the estimators are consistent and asymptotically normal but converge at slower rates than those achieved with synchronous data. Simulation studies evidence that the methods perform well with realistic sample sizes and may be superior to a naive application of methods for synchronous data based on an ad hoc last value carried forward approach. The practical utility of the methods is illustrated on data from a study on human immunodeficiency virus. PMID:26568699

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.

Correlation and simple linear regression.

PubMed

Eberly, Lynn E

2007-01-01

This chapter highlights important steps in using correlation and simple linear regression to address scientific questions about the association of two continuous variables with each other. These steps include estimation and inference, assessing model fit, the connection between regression and ANOVA, and study design. Examples in microbiology are used throughout. This chapter provides a framework that is helpful in understanding more complex statistical techniques, such as multiple linear regression, linear mixed effects models, logistic regression, and proportional hazards regression.

Techniques for estimating peak-streamflow frequency for unregulated streams and streams regulated by small floodwater retarding structures in Oklahoma

USGS Publications Warehouse

Tortorelli, Robert L.

1997-01-01

Statewide regression equations for Oklahoma were determined for estimating peak discharge and flood frequency for selected recurrence intervals from 2 to 500 years for ungaged sites on natural unregulated streams. The most significant independent variables required to estimate peak-streamflow frequency for natural unregulated streams in Oklahoma are contributing drainage area, main-channel slope, and mean-annual precipitation. The regression equations are applicable for watersheds with drainage areas less than 2,510 square miles that are not affected by regulation from manmade works. Limitations on the use of the regression relations and the reliability of regression estimates for natural unregulated streams are discussed. Log-Pearson Type III analysis information, basin and climatic characteristics, and the peak-stream-flow frequency estimates for 251 gaging stations in Oklahoma and adjacent states are listed. Techniques are presented to make a peak-streamflow frequency estimate for gaged sites on natural unregulated streams and to use this result to estimate a nearby ungaged site on the same stream. For ungaged sites on urban streams, an adjustment of the statewide regression equations for natural unregulated streams can be used to estimate peak-streamflow frequency. For ungaged sites on 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 frequency. The statewide regression equations are adjusted by substituting the drainage area below the floodwater retarding structures, or drainage area that represents the percentage of the unregulated basin, in the contributing drainage area parameter to obtain peak-streamflow frequency estimates.

Estimation of fat-free mass in Asian neonates using bioelectrical impedance analysis

PubMed Central

Tint, Mya-Thway; Ward, Leigh C; Soh, Shu E; Aris, Izzuddin M; Chinnadurai, Amutha; Saw, Seang Mei; Gluckman, Peter D; Godfrey, Keith M; Chong, Yap-Seng; Kramer, Michael S; Yap, Fabian; Lingwood, Barbara; Lee, Yung Seng

2016-01-01

The aims of this study were to develop and validate a prediction equation of fat-free mass (FFM) based on bioelectrical impedance analysis (BIA) and anthropometry using air displacement plethysmography (ADP) as a reference in Asian neonates and to test the applicability of the prediction equations in independent Western cohort. A total of 173 neonates at birth and 140 at week-2 of age were included. Multiple linear regression analysis was performed to develop the prediction equations in a two-third randomly selected subset and validated on the remaining one-third subset at each time point and in an independent Queensland cohort. FFM measured by ADP was the dependent variable and anthropometric measures, sex and impedance quotient (L2/R50) were independent variables in the model. Accuracy of prediction equations were assessed using intra-class correlation and Bland-Altman analyses. L2/R50 was the significant predictor of FFM at week-2 but not at birth. Compared to the model using weight, sex and length, including L2/R50 slightly improved the prediction with a bias of 0.01kg with 2SD limits of agreement (LOA) (0.18, −0.20). Prediction explained 88.9% of variation but not beyond that of anthropometry. Applying these equations to Queensland cohort provided similar performance at the appropriate age. However, when the Queensland equations were applied to our cohort, the bias increased slightly but with similar LOA. BIA appears to have limited use in predicting FFM in the first few weeks of life compared to simple anthropometry in Asian populations. There is a need for population and age appropriate FFM prediction equations. PMID:26856420

Estimation of height and body mass index from demi-span in elderly individuals.

PubMed

Weinbrenner, Tanja; Vioque, Jesús; Barber, Xavier; Asensio, Laura

2006-01-01

Obtaining accurate height and, consequently, body mass index (BMI) measurements in elderly subjects can be difficult due to changes in posture and loss of height during ageing. Measurements of other body segments can be used as an alternative to estimate standing height, but population- and age-specific equations are necessary. Our objectives were to validate existing equations, to develop new simple equations to predict height in an elderly Spanish population and to assess the accuracy of the BMI calculated by estimated height from the new equations. We measured height and demi-span in a representative sample of 592 individuals, 271 men and 321 women, 65 years and older (mean +/- SD, 73.8 +/- 6.3 years). We suggested equations to predict height from demi-span by multiple regression analyses and performed an agreement analysis between measured and estimated indices. Height estimated from demi-span correlated significantly (p < 0.001) with measured height (men: r = 0.708, women: r = 0.625). The best prediction equations were as follows: men, height (in cm) = 77.821 + (1.132 x demi-span in cm) + (-0.215 x 5-year age category); women: height (in cm) = 88.854 + (0.899 x demi-span in cm) + (-0.692 x 5-year age category). No significant differences between the mean values of estimated and measured heights were found for men (-0.03 +/- 4.6 cm) or women (-0.02 +/- 4.1 cm). The BMI derived from measured height did not differ significantly from the BMI derived from estimated height either. Predicted height values from equations based on demi-span and age may be acceptable surrogates to derive accurate nutritional indices such as the BMI, particularly in elderly populations, where height may be difficult to measure accurately.

Estimation of fat-free mass in Asian neonates using bioelectrical impedance analysis.

PubMed

Tint, Mya-Thway; Ward, Leigh C; Soh, Shu E; Aris, Izzuddin M; Chinnadurai, Amutha; Saw, Seang Mei; Gluckman, Peter D; Godfrey, Keith M; Chong, Yap-Seng; Kramer, Michael S; Yap, Fabian; Lingwood, Barbara; Lee, Yung Seng

2016-03-28

The aims of this study were to develop and validate a prediction equation of fat-free mass (FFM) based on bioelectrical impedance analysis (BIA) and anthropometry using air-displacement plethysmography (ADP) as a reference in Asian neonates and to test the applicability of the prediction equations in an independent Western cohort. A total of 173 neonates at birth and 140 at two weeks of age were included. Multiple linear regression analysis was performed to develop the prediction equations in a two-third randomly selected subset and validated on the remaining one-third subset at each time point and in an independent Queensland cohort. FFM measured by ADP was the dependent variable, and anthropometric measures, sex and impedance quotient (L2/R50) were independent variables in the model. Accuracy of prediction equations was assessed using intra-class correlation and Bland-Altman analyses. L2/R50 was the significant predictor of FFM at week two but not at birth. Compared with the model using weight, sex and length, including L2/R50 slightly improved the prediction with a bias of 0·01 kg with 2 sd limits of agreement (LOA) (0·18, -0·20). Prediction explained 88·9 % of variation but not beyond that of anthropometry. Applying these equations to the Queensland cohort provided similar performance at the appropriate age. However, when the Queensland equations were applied to our cohort, the bias increased slightly but with similar LOA. BIA appears to have limited use in predicting FFM in the first few weeks of life compared with simple anthropometry in Asian populations. There is a need for population- and age-appropriate FFM prediction equations.

Novel Approach for Solving the Equation of Motion of a Simple Harmonic Oscillator. Classroom Notes

ERIC Educational Resources Information Center

Gauthier, N.

2004-01-01

An elementary method, based on the use of complex variables, is proposed for solving the equation of motion of a simple harmonic oscillator. The method is first applied to the equation of motion for an undamped oscillator and it is then extended to the more important case of a damped oscillator. It is finally shown that the method can readily be…

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…

Data-driven discovery of partial differential equations.

PubMed

Rudy, Samuel H; Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan

2017-04-01

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg-de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable.

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.

Systolic time interval v heart rate regression equations using atropine: reproducibility studies.

PubMed Central

Kelman, A W; Sumner, D J; Whiting, B

1981-01-01

1. Systolic time intervals (STI) were recorded in six normal male subjects over a period of 3 weeks. On one day per week, each subject received incremental doses of atropine intravenously to increase heart rate, allowing the determination of individual STI v HR regression equations. On the other days STI were recorded with the subjects resting, in the supine position. 2. There were highly significant regression relationships between heart rate and both LVET and QS2, but not between heart rate and PEP. 3. The regression relationships showed little intra-subject variability, but a large degree of inter-subject variability: they proved adequate to correct the STI for the daily fluctuations in heart rate. 4. Administration of small doses of atropine intravenously provides a satisfactory and convenient method of deriving individual STI v HR regression equations which can be applied over a period of weeks. PMID:7248136

Systolic time interval v heart rate regression equations using atropine: reproducibility studies.

PubMed

Kelman, A W; Sumner, D J; Whiting, B

1981-07-01

1. Systolic time intervals (STI) were recorded in six normal male subjects over a period of 3 weeks. On one day per week, each subject received incremental doses of atropine intravenously to increase heart rate, allowing the determination of individual STI v HR regression equations. On the other days STI were recorded with the subjects resting, in the supine position. 2. There were highly significant regression relationships between heart rate and both LVET and QS2, but not between heart rate and PEP. 3. The regression relationships showed little intra-subject variability, but a large degree of inter-subject variability: they proved adequate to correct the STI for the daily fluctuations in heart rate. 4. Administration of small doses of atropine intravenously provides a satisfactory and convenient method of deriving individual STI v HR regression equations which can be applied over a period of weeks.

A simple bias correction in linear regression for quantitative trait association under two-tail extreme selection.

PubMed

Kwan, Johnny S H; Kung, Annie W C; Sham, Pak C

2011-09-01

Selective genotyping can increase power in quantitative trait association. One example of selective genotyping is two-tail extreme selection, but simple linear regression analysis gives a biased genetic effect estimate. Here, we present a simple correction for the bias.

Simple vector bundles on a nodal Weierstrass cubic and quasi-trigonometric solutions of the classical Yang-Baxter equation

NASA Astrophysics Data System (ADS)

Burban, Igor; Galinat, Lennart; Stolin, Alexander

2017-11-01

In this paper we study the combinatorics of quasi-trigonometric solutions of the classical Yang-Baxter equation, arising from simple vector bundles on a nodal Weierstraß cubic. Dedicated to the memory of Petr Petrovich Kulish.

Practical Session: Simple Linear Regression

NASA Astrophysics Data System (ADS)

Clausel, M.; Grégoire, G.

2014-12-01

Two exercises are proposed to illustrate the simple linear regression. The first one is based on the famous Galton's data set on heredity. We use the lm R command and get coefficients estimates, standard error of the error, R2, residuals …In the second example, devoted to data related to the vapor tension of mercury, we fit a simple linear regression, predict values, and anticipate on multiple linear regression. This pratical session is an excerpt from practical exercises proposed by A. Dalalyan at EPNC (see Exercises 1 and 2 of http://certis.enpc.fr/~dalalyan/Download/TP_ENPC_4.pdf).

Weather adjustment using seemingly unrelated regression

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

Noll, T.A.

1995-05-01

Seemingly unrelated regression (SUR) is a system estimation technique that accounts for time-contemporaneous correlation between individual equations within a system of equations. SUR is suited to weather adjustment estimations when the estimation is: (1) composed of a system of equations and (2) the system of equations represents either different weather stations, different sales sectors or a combination of different weather stations and different sales sectors. SUR utilizes the cross-equation error values to develop more accurate estimates of the system coefficients than are obtained using ordinary least-squares (OLS) estimation. SUR estimates can be generated using a variety of statistical software packagesmore » including MicroTSP and SAS.« less

Perturbed dark and singular optical solitons in polarization preserving fibers by modified simple equation method

NASA Astrophysics Data System (ADS)

Yaşar, Emrullah; Yıldırım, Yakup; Zhou, Qin; Moshokoa, Seithuti P.; Ullah, Malik Zaka; Triki, Houria; Biswas, Anjan; Belic, Milivoj

2017-11-01

This paper obtains optical soliton solution to perturbed nonlinear Schrödinger's equation by modified simple equation method. There are four types of nonlinear fibers studied in this paper. They are Anti-cubic law, Quadratic-cubic law, Cubic-quintic-septic law and Triple-power law. Dark and singular soliton solutions are derived. Additional solutions such as singular periodic solutions also fall out of the integration scheme.

Reference equations for the six-minute walk distance in the healthy Chinese population aged 18–59 years

PubMed Central

Zou, He; Zhu, Xiuruo; Zhang, Jia; Wang, Yi; Wu, Xiaozhen; Liu, Fang; Xie, Xiaofeng

2017-01-01

Background The six-minute walk test (6MWT) is a safe, simple, inexpensive tool for evaluating the functional exercise capacity of patients with chronic respiratory disease. However, there is a lack of standard reference equations for the six-minute walk distance (6MWD) in the healthy Chinese population aged 18–59 years. Aims The purposes of the present study were as follows: 1) to measure the anthropometric data and walking distance of a sample of healthy Chinese Han people aged 18–59 years; 2) to construct reference equations for the 6MWD; 3) to compare the measured 6MWD with previously published equations. Method The anthropometric data, demographic information, lung function, and walking distance of Chinese adults aged 18–59 years were prospectively measured using a standardized protocol. We obtained verbal consent from all the subjects before the test, and the study design was approved by the ethics committee of Wenzhou People's Hospital. The 6MWT was performed twice, and the longer distance was used for further analysis. Results A total of 643 subjects (319 females and 324 males) completed the 6MWT, and average walking distance was 601.6±55.51 m. The walking distance was compared between females and males (578±49.85 m vs. 623±52.53 m; p < 0.0001) and between physically active subjects and sedentary subjects (609.3±56.17 m vs. 592±53.23 m; p < 0.0001). Pearson’s correlation indicated that the 6MWD was significantly correlated with various demographic and the 6MWT variables, such as age, height, weight, body mass index (BMI), heart rate after the test and the difference in the heart rate before and after the test. Stepwise multiple regression analysis showed that age and height were independent predictors associated with the 6MWD. The reference equations from white, Canadian and Chilean populations tended to overestimate the walking distance in our subjects, while Brazilian and Arabian equations tended to underestimate the walking distance. There was no significant difference in the walking distance between Korean reference equations and the results of the current study. Conclusion In summary, age and height were the most significant predictors of the 6MWD, and regression equations could explain approximately 34% and 28% of the distance variance in the female and male groups, respectively. PMID:28910353

Abdominal girth and vertebral column length aid in predicting intrathecal hyperbaric bupivacaine dose for elective cesarean section

PubMed Central

Wei, Chang-Na; Zhou, Qing-He; Wang, Li-Zhong

2017-01-01

Abstract Currently, there is no consensus on how to determine the optimal dose of intrathecal bupivacaine for an individual undergoing an elective cesarean section. In this study, we developed a regression equation between intrathecal 0.5% hyperbaric bupivacaine volume and abdominal girth and vertebral column length, to determine a suitable block level (T5) for elective cesarean section patients. In phase I, we analyzed 374 parturients undergoing an elective cesarean section that received a suitable dose of intrathecal 0.5% hyperbaric bupivacaine after a combined spinal-epidural (CSE) was performed at the L3/4 interspace. Parturients with T5 blockade to pinprick were selected for establishing the regression equation between 0.5% hyperbaric bupivacaine volume and vertebral column length and abdominal girth. Six parturient and neonatal variables, intrathecal 0.5% hyperbaric bupivacaine volume, and spinal anesthesia spread were recorded. Bivariate line correlation analyses, multiple line regression analyses, and 2-tailed t tests or chi-square test were performed, as appropriate. In phase II, another 200 parturients with CSE for elective cesarean section were enrolled to verify the accuracy of the regression equation. In phase I, a total of 143 parturients were selected to establish the following regression equation: YT5 = 0.074X1 − 0.022X2 − 0.017 (YT5 = 0.5% hyperbaric bupivacaine volume for T5 block level; X1 = vertebral column length; and X2 = abdominal girth). In phase II, a total of 189 participants were enrolled in the study to verify the accuracy of the regression equation, and 155 parturients with T5 blockade were deemed eligible, which accounted for 82.01% of all participants. This study evaluated parturients with T5 blockade to pinprick after a CSE for elective cesarean section to establish a regression equation between parturient vertebral column length and abdominal girth and 0.5% hyperbaric intrathecal bupivacaine volume. This equation can accurately predict the suitable intrathecal hyperbaric bupivacaine dose for elective cesarean section. PMID:28834913

Abdominal girth and vertebral column length aid in predicting intrathecal hyperbaric bupivacaine dose for elective cesarean section.

PubMed

Wei, Chang-Na; Zhou, Qing-He; Wang, Li-Zhong

2017-08-01

Currently, there is no consensus on how to determine the optimal dose of intrathecal bupivacaine for an individual undergoing an elective cesarean section. In this study, we developed a regression equation between intrathecal 0.5% hyperbaric bupivacaine volume and abdominal girth and vertebral column length, to determine a suitable block level (T5) for elective cesarean section patients.In phase I, we analyzed 374 parturients undergoing an elective cesarean section that received a suitable dose of intrathecal 0.5% hyperbaric bupivacaine after a combined spinal-epidural (CSE) was performed at the L3/4 interspace. Parturients with T5 blockade to pinprick were selected for establishing the regression equation between 0.5% hyperbaric bupivacaine volume and vertebral column length and abdominal girth. Six parturient and neonatal variables, intrathecal 0.5% hyperbaric bupivacaine volume, and spinal anesthesia spread were recorded. Bivariate line correlation analyses, multiple line regression analyses, and 2-tailed t tests or chi-square test were performed, as appropriate. In phase II, another 200 parturients with CSE for elective cesarean section were enrolled to verify the accuracy of the regression equation.In phase I, a total of 143 parturients were selected to establish the following regression equation: YT5 = 0.074X1 - 0.022X2 - 0.017 (YT5 = 0.5% hyperbaric bupivacaine volume for T5 block level; X1 = vertebral column length; and X2 = abdominal girth). In phase II, a total of 189 participants were enrolled in the study to verify the accuracy of the regression equation, and 155 parturients with T5 blockade were deemed eligible, which accounted for 82.01% of all participants.This study evaluated parturients with T5 blockade to pinprick after a CSE for elective cesarean section to establish a regression equation between parturient vertebral column length and abdominal girth and 0.5% hyperbaric intrathecal bupivacaine volume. This equation can accurately predict the suitable intrathecal hyperbaric bupivacaine dose for elective cesarean section.

Validity and reliability of dental age estimation of teeth root translucency based on digital luminance determination.

PubMed

Ramsthaler, Frank; Kettner, Mattias; Verhoff, Marcel A

2014-01-01

In forensic anthropological casework, estimating age-at-death is key to profiling unknown skeletal remains. The aim of this study was to examine the reliability of a new, simple, fast, and inexpensive digital odontological method for age-at-death estimation. The method is based on the original Lamendin method, which is a widely used technique in the repertoire of odontological aging methods in forensic anthropology. We examined 129 single root teeth employing a digital camera and imaging software for the measurement of the luminance of the teeth's translucent root zone. Variability in luminance detection was evaluated using statistical technical error of measurement analysis. The method revealed stable values largely unrelated to observer experience, whereas requisite formulas proved to be camera-specific and should therefore be generated for an individual recording setting based on samples of known chronological age. Multiple regression analysis showed a highly significant influence of the coefficients of the variables "arithmetic mean" and "standard deviation" of luminance for the regression formula. For the use of this primer multivariate equation for age-at-death estimation in casework, a standard error of the estimate of 6.51 years was calculated. Step-by-step reduction of the number of embedded variables to linear regression analysis employing the best contributor "arithmetic mean" of luminance yielded a regression equation with a standard error of 6.72 years (p < 0.001). The results of this study not only support the premise of root translucency as an age-related phenomenon, but also demonstrate that translucency reflects a number of other influencing factors in addition to age. This new digital measuring technique of the zone of dental root luminance can broaden the array of methods available for estimating chronological age, and furthermore facilitate measurement and age classification due to its low dependence on observer experience.

Wind tunnel test of Teledyne Geotech model 1564B cup anemometer

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

Parker, M.J.; Addis, R.P.

1991-04-04

The Department of Energy (DOE) Environment, Safety and Health Compliance Assessment (Tiger Team) of the Savannah River Site (SRS) questioned the method by which wind speed sensors (cup anemometers) are calibrated by the Environmental Technology Section (ETS). The Tiger Team member was concerned that calibration data was generated by running the wind tunnel to only 26 miles per hour (mph) when speeds exceeding 50 mph are readily obtainable. A wind tunnel experiment was conducted and confirmed the validity of the practice. Wind speeds common to SRS (6 mph) were predicted more accurately by 0--25 mph regression equations than 0--50 mphmore » regression equations. Higher wind speeds were slightly overpredicted by the 0--25 mph regression equations when compared to 0--50 mph regression equations. However, the greater benefit of more accurate lower wind speed predictions accuracy outweight the benefit of slightly better high (extreme) wind speed predictions. Therefore, it is concluded that 0--25 mph regression equations should continue to be utilized by ETS at SRS. During the Department of Energy Tiger Team audit, concerns were raised about the calibration of SRS cup anemometers. Wind speed is measured by ETS with Teledyne Geotech model 1564B cup anemometers, which are calibrated in the ETS wind tunnel. Linear regression lines are fitted to data points of tunnel speed versus anemometer output voltages up to 25 mph. The regression coefficients are then implemented into the data acquisition computer software when an instrument is installed in the field. The concern raised was that since the wind tunnel at SRS is able to generate a maximum wind speed higher than 25 mph, errors may be introduced in not using the full range of the wind tunnel.« less

Wind tunnel test of Teledyne Geotech model 1564B cup anemometer

NASA Astrophysics Data System (ADS)

Parker, M. J.; Addis, R. P.

1991-04-01

The Department of Energy (DOE) Environment, Safety, and Health Compliance Assessment (Tiger Team) of the Savannah River Site (SRS) questioned the method by which wind speed sensors (cup anemometers) are calibrated by the Environmental Technology Section (ETS). The Tiger Team member was concerned that calibration data was generated by running the wind tunnel to only 26 miles per hour (mph) when speeds exceeding 50 mph are readily obtainable. A wind tunnel experiment was conducted and confirmed the validity of the practice. Wind speeds common to SRS (6 mph) were predicted more accurately by 0-25 mph regression equations than 0-50 mph regression equations. Higher wind speeds were slightly overpredicted by the 0-25 mph regression equations when compared to 0-50 mph regression equations. However, the greater benefit of more accurate lower wind speed predictions accuracy outweigh the benefit of slightly better high (extreme) wind speed predictions. Therefore, it is concluded that 0-25 mph regression equations should continue to be utilized by ETS at SRS. During the Department of Energy Tiger Team audit, concerns were raised about the calibration of SRS cup anemometers. Wind speed is measured by ETS with Teledyne Geotech model 1564B cup anemometers, which are calibrated in the ETS wind tunnel. Linear regression lines are fitted to data points of tunnel speed versus anemometer output voltages up to 25 mph. The regression coefficients are then implemented into the data acquisition computer software when an instrument is installed in the field. The concern raised was that since the wind tunnel at SRS is able to generate a maximum wind speed higher than 25 mph, errors may be introduced in not using the full range of the wind tunnel.

Evaluation of the magnitude and frequency of floods in urban watersheds in Phoenix and Tucson, Arizona

USGS Publications Warehouse

Kennedy, Jeffrey R.; Paretti, Nicholas V.

2014-01-01

Flooding in urban areas routinely causes severe damage to property and often results in loss of life. To investigate the effect of urbanization on the magnitude and frequency of flood peaks, a flood frequency analysis was carried out using data from urbanized streamgaging stations in Phoenix and Tucson, Arizona. Flood peaks at each station were predicted using the log-Pearson Type III distribution, fitted using the expected moments algorithm and the multiple Grubbs-Beck low outlier test. The station estimates were then compared to flood peaks estimated by rural-regression equations for Arizona, and to flood peaks adjusted for urbanization using a previously developed procedure for adjusting U.S. Geological Survey rural regression peak discharges in an urban setting. Only smaller, more common flood peaks at the 50-, 20-, 10-, and 4-percent annual exceedance probabilities (AEPs) demonstrate any increase in magnitude as a result of urbanization; the 1-, 0.5-, and 0.2-percent AEP flood estimates are predicted without bias by the rural-regression equations. Percent imperviousness was determined not to account for the difference in estimated flood peaks between stations, either when adjusting the rural-regression equations or when deriving urban-regression equations to predict flood peaks directly from basin characteristics. Comparison with urban adjustment equations indicates that flood peaks are systematically overestimated if the rural-regression-estimated flood peaks are adjusted upward to account for urbanization. At nearly every streamgaging station in the analysis, adjusted rural-regression estimates were greater than the estimates derived using station data. One likely reason for the lack of increase in flood peaks with urbanization is the presence of significant stormwater retention and detention structures within the watershed used in the study.

Commentary: Are Three Waves of Data Sufficient for Assessing Mediation?

ERIC Educational Resources Information Center

Reichardt, Charles S.

2011-01-01

Maxwell, Cole, and Mitchell (2011) demonstrated that simple structural equation models, when used with cross-sectional data, generally produce biased estimates of meditated effects. I extend those results by showing how simple structural equation models can produce biased estimates of meditated effects when used even with longitudinal data. Even…

A simple recipe for setting up the flux equations of cyclic and linear reaction schemes of ion transport with a high number of states: The arrow scheme.

PubMed

Hansen, Ulf-Peter; Rauh, Oliver; Schroeder, Indra

2016-01-01

The calculation of flux equations or current-voltage relationships in reaction kinetic models with a high number of states can be very cumbersome. Here, a recipe based on an arrow scheme is presented, which yields a straightforward access to the minimum form of the flux equations and the occupation probability of the involved states in cyclic and linear reaction schemes. This is extremely simple for cyclic schemes without branches. If branches are involved, the effort of setting up the equations is a little bit higher. However, also here a straightforward recipe making use of so-called reserve factors is provided for implementing the branches into the cyclic scheme, thus enabling also a simple treatment of such cases.

A simple recipe for setting up the flux equations of cyclic and linear reaction schemes of ion transport with a high number of states: The arrow scheme

PubMed Central

Hansen, Ulf-Peter; Rauh, Oliver; Schroeder, Indra

2016-01-01

abstract The calculation of flux equations or current-voltage relationships in reaction kinetic models with a high number of states can be very cumbersome. Here, a recipe based on an arrow scheme is presented, which yields a straightforward access to the minimum form of the flux equations and the occupation probability of the involved states in cyclic and linear reaction schemes. This is extremely simple for cyclic schemes without branches. If branches are involved, the effort of setting up the equations is a little bit higher. However, also here a straightforward recipe making use of so-called reserve factors is provided for implementing the branches into the cyclic scheme, thus enabling also a simple treatment of such cases. PMID:26646356

Corrigendum: New Form of Kane's Equations of Motion for Constrained Systems

NASA Technical Reports Server (NTRS)

Roithmayr, Carlos M.; Bajodah, Abdulrahman H.; Hodges, Dewey H.; Chen, Ye-Hwa

2007-01-01

A correction to the previously published article "New Form of Kane's Equations of Motion for Constrained Systems" is presented. Misuse of the transformation matrix between time rates of change of the generalized coordinates and generalized speeds (sometimes called motion variables) resulted in a false conclusion concerning the symmetry of the generalized inertia matrix. The generalized inertia matrix (sometimes referred to as the mass matrix) is in fact symmetric and usually positive definite when one forms nonminimal Kane's equations for holonomic or simple nonholonomic systems, systems subject to nonlinear nonholonomic constraints, and holonomic or simple nonholonomic systems subject to impulsive constraints according to Refs. 1, 2, and 3, respectively. The mass matrix is of course symmetric when one forms minimal equations for holonomic or simple nonholonomic systems using Kane s method as set forth in Ref. 4.

Monitoring heavy metal Cr in soil based on hyperspectral data using regression analysis

NASA Astrophysics Data System (ADS)

Zhang, Ningyu; Xu, Fuyun; Zhuang, Shidong; He, Changwei

2016-10-01

Heavy metal pollution in soils is one of the most critical problems in the global ecology and environment safety nowadays. Hyperspectral remote sensing and its application is capable of high speed, low cost, less risk and less damage, and provides a good method for detecting heavy metals in soil. This paper proposed a new idea of applying regression analysis of stepwise multiple regression between the spectral data and monitoring the amount of heavy metal Cr by sample points in soil for environmental protection. In the measurement, a FieldSpec HandHeld spectroradiometer is used to collect reflectance spectra of sample points over the wavelength range of 325-1075 nm. Then the spectral data measured by the spectroradiometer is preprocessed to reduced the influence of the external factors, and the preprocessed methods include first-order differential equation, second-order differential equation and continuum removal method. The algorithms of stepwise multiple regression are established accordingly, and the accuracy of each equation is tested. The results showed that the accuracy of first-order differential equation works best, which makes it feasible to predict the content of heavy metal Cr by using stepwise multiple regression.

Mean annual runoff and peak flow estimates based on channel geometry of streams in northeastern and western Montana

USGS Publications Warehouse

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

1983-01-01

Equations for estimating mean annual runoff and peak discharge from measurements of channel geometry were developed for western and northeastern Montana. The study area was divided into two regions for the mean annual runoff analysis, and separate multiple-regression equations were developed for each region. The active-channel width was determined to be the most important independent variable in each region. The standard error of estimate for the estimating equation using active-channel width was 61 percent in the Northeast Region and 38 percent in the West region. The study area was divided into six regions for the peak discharge analysis, and multiple regression equations relating channel geometry and basin characteristics to peak discharges having recurrence intervals of 2, 5, 10, 25, 50 and 100 years were developed for each region. The standard errors of estimate for the regression equations using only channel width as an independent variable ranged from 35 to 105 percent. The standard errors improved in four regions as basin characteristics were added to the estimating equations. (USGS)

The application of dimensional analysis to the problem of solar wind-magnetosphere energy coupling

NASA Technical Reports Server (NTRS)

Bargatze, L. F.; Mcpherron, R. L.; Baker, D. N.; Hones, E. W., Jr.

1984-01-01

The constraints imposed by dimensional analysis are used to find how the solar wind-magnetosphere energy transfer rate depends upon interplanetary parameters. The analyses assume that only magnetohydrodynamic processes are important in controlling the rate of energy transfer. The study utilizes ISEE-3 solar wind observations, the AE index, and UT from three 10-day intervals during the International Magnetospheric Study. Simple linear regression and histogram techniques are used to find the value of the magnetohydrodynamic coupling exponent, alpha, which is consistent with observations of magnetospheric response. Once alpha is estimated, the form of the solar wind energy transfer rate is obtained by substitution into an equation of the interplanetary variables whose exponents depend upon alpha.

Estimation of premorbid general fluid intelligence using traditional Chinese reading performance in Taiwanese samples.

PubMed

Chen, Ying-Jen; Ho, Meng-Yang; Chen, Kwan-Ju; Hsu, Chia-Fen; Ryu, Shan-Jin

2009-08-01

The aims of the present study were to (i) investigate if traditional Chinese word reading ability can be used for estimating premorbid general intelligence; and (ii) to provide multiple regression equations for estimating premorbid performance on Raven's Standard Progressive Matrices (RSPM), using age, years of education and Chinese Graded Word Reading Test (CGWRT) scores as predictor variables. Four hundred and twenty-six healthy volunteers (201 male, 225 female), aged 16-93 years (mean +/- SD, 41.92 +/- 18.19 years) undertook the tests individually under supervised conditions. Seventy percent of subjects were randomly allocated to the derivation group (n = 296), and the rest to the validation group (n = 130). RSPM score was positively correlated with CGWRT score and years of education. RSPM and CGWRT scores and years of education were also inversely correlated with age, but the declining trend for RSPM performance against age was steeper than that for CGWRT performance. Separate multiple regression equations were derived for estimating RSPM scores using different combinations of age, years of education, and CGWRT score for both groups. The multiple regression coefficient of each equation ranged from 0.71 to 0.80 with the standard error of estimate between 7 and 8 RSPM points. When fitting the data of one group to the equations derived from its counterpart group, the cross-validation multiple regression coefficients ranged from 0.71 to 0.79. There were no significant differences in the 'predicted-obtained' RSPM discrepancies between any equations. The regression equations derived in the present study may provide a basis for estimating premorbid RSPM performance.

Estimating air drying times of lumber with multiple regression

Treesearch

William T. Simpson

2004-01-01

In this study, the applicability of a multiple regression equation for estimating air drying times of red oak, sugar maple, and ponderosa pine lumber was evaluated. The equation allows prediction of estimated air drying times from historic weather records of temperature and relative humidity at any desired location.

National scale biomass estimators for United States tree species

Treesearch

Jennifer C. Jenkins; David C. Chojnacky; Linda S. Heath; Richard A. Birdsey

2003-01-01

Estimates of national-scale forest carbon (C) stocks and fluxes are typically based on allometric regression equations developed using dimensional analysis techniques. However, the literature is inconsistent and incomplete with respect to large-scale forest C estimation. We compiled all available diameter-based allometric regression equations for estimating total...

Data-driven discovery of partial differential equations

PubMed Central

Rudy, Samuel H.; Brunton, Steven L.; Proctor, Joshua L.; Kutz, J. Nathan

2017-01-01

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg–de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable. PMID:28508044

Development of an algorithm to predict serum vitamin D levels using a simple questionnaire based on sunlight exposure.

PubMed

Vignali, Edda; Macchia, Enrico; Cetani, Filomena; Reggiardo, Giorgio; Cianferotti, Luisella; Saponaro, Federica; Marcocci, Claudio

2017-01-01

Sun exposure is the main determinant of vitamin D production. The aim of this study was to develop an algorithm to assess individual vitamin D status, independently of serum 25(OHD) measurement, using a simple questionnaire, mostly relying upon sunlight exposure, which might help select subjects requiring serum 25(OHD) measurement. Six hundred and twenty adult subjects living in a mountain village in Southern Italy, located at 954 m above the sea level and at a latitude of 40°50'11″76N, were asked to fill the questionnaire in two different periods of the year: August 2010 and March 2011. Seven predictors were considered: month of investigation, age, sex, BMI, average daily sunlight exposure, beach holidays in the past 12 months, and frequency of going outdoors. The statistical model assumes four classes of serum 25(OHD) concentrations: ≤10, 10-19.9, 20-29.9, and ≥30 ng/ml. The algorithm was developed using a two-step procedure. In Step 1, the linear regression equation was defined in 385 randomly selected subjects. In Step 2, the predictive ability of the regression model was tested in the remaining 235 subjects. Seasonality, daily sunlight exposure and beach holidays in the past 12 months accounted for 27.9, 13.5, and 6.4 % of the explained variance in predicting vitamin D status, respectively. The algorithm performed extremely well: 212 of 235 (90.2 %) subjects were assigned to the correct vitamin D status. In conclusion, our pilot study demonstrates that an algorithm to estimate the vitamin D status can be developed using a simple questionnaire based on sunlight exposure.

Comparison of methods for the prediction of human clearance from hepatocyte intrinsic clearance for a set of reference compounds and an external evaluation set.

PubMed

Yamagata, Tetsuo; Zanelli, Ugo; Gallemann, Dieter; Perrin, Dominique; Dolgos, Hugues; Petersson, Carl

2017-09-01

1. We compared direct scaling, regression model equation and the so-called "Poulin et al." methods to scale clearance (CL) from in vitro intrinsic clearance (CL int ) measured in human hepatocytes using two sets of compounds. One reference set comprised of 20 compounds with known elimination pathways and one external evaluation set based on 17 compounds development in Merck (MS). 2. A 90% prospective confidence interval was calculated using the reference set. This interval was found relevant for the regression equation method. The three outliers identified were justified on the basis of their elimination mechanism. 3. The direct scaling method showed a systematic underestimation of clearance in both the reference and evaluation sets. The "Poulin et al." and the regression equation methods showed no obvious bias in either the reference or evaluation sets. 4. The regression model equation was slightly superior to the "Poulin et al." method in the reference set and showed a better absolute average fold error (AAFE) of value 1.3 compared to 1.6. A larger difference was observed in the evaluation set were the regression method and "Poulin et al." resulted in an AAFE of 1.7 and 2.6, respectively (removing the three compounds with known issues mentioned above). A similar pattern was observed for the correlation coefficient. Based on these data we suggest the regression equation method combined with a prospective confidence interval as the first choice for the extrapolation of human in vivo hepatic metabolic clearance from in vitro systems.

Simplified Two-Time Step Method for Calculating Combustion Rates and Nitrogen Oxide Emissions for Hydrogen/Air and Hydorgen/Oxygen

NASA Technical Reports Server (NTRS)

Molnar, Melissa; Marek, C. John

2005-01-01

A simplified single rate expression for hydrogen combustion and nitrogen oxide production was developed. Detailed kinetics are predicted for the chemical kinetic times using the complete chemical mechanism over the entire operating space. These times are then correlated to the reactor conditions using an exponential fit. Simple first order reaction expressions are then used to find the conversion in the reactor. The method uses a two-time step kinetic scheme. The first time averaged step is used at the initial times with smaller water concentrations. This gives the average chemical kinetic time as a function of initial overall fuel air ratio, temperature, and pressure. The second instantaneous step is used at higher water concentrations (> 1 x 10(exp -20) moles/cc) in the mixture which gives the chemical kinetic time as a function of the instantaneous fuel and water mole concentrations, pressure and temperature (T4). The simple correlations are then compared to the turbulent mixing times to determine the limiting properties of the reaction. The NASA Glenn GLSENS kinetics code calculates the reaction rates and rate constants for each species in a kinetic scheme for finite kinetic rates. These reaction rates are used to calculate the necessary chemical kinetic times. This time is regressed over the complete initial conditions using the Excel regression routine. Chemical kinetic time equations for H2 and NOx are obtained for H2/air fuel and for the H2/O2. A similar correlation is also developed using data from NASA s Chemical Equilibrium Applications (CEA) code to determine the equilibrium temperature (T4) as a function of overall fuel/air ratio, pressure and initial temperature (T3). High values of the regression coefficient R2 are obtained.

Summary of Simplified Two Time Step Method for Calculating Combustion Rates and Nitrogen Oxide Emissions for Hydrogen/Air and Hydrogen/Oxygen

NASA Technical Reports Server (NTRS)

Marek, C. John; Molnar, Melissa

2005-01-01

A simplified single rate expression for hydrogen combustion and nitrogen oxide production was developed. Detailed kinetics are predicted for the chemical kinetic times using the complete chemical mechanism over the entire operating space. These times are then correlated to the reactor conditions using an exponential fit. Simple first order reaction expressions are then used to find the conversion in the reactor. The method uses a two time step kinetic scheme. The first time averaged step is used at the initial times with smaller water concentrations. This gives the average chemical kinetic time as a function of initial overall fuel air ratio, temperature, and pressure. The second instantaneous step is used at higher water concentrations (greater than l x 10(exp -20)) moles per cc) in the mixture which gives the chemical kinetic time as a function of the instantaneous fuel and water mole concentrations, pressure and temperature (T(sub 4)). The simple correlations are then compared to the turbulent mixing times to determine the limiting properties of the reaction. The NASA Glenn GLSENS kinetics code calculates the reaction rates and rate constants for each species in a kinetic scheme for finite kinetic rates. These reaction rates are used to calculate the necessary chemical kinetic times. This time is regressed over the complete initial conditions using the Excel regression routine. Chemical kinetic time equations for H2 and NOx are obtained for H2/Air fuel and for H2/O2. A similar correlation is also developed using data from NASA's Chemical Equilibrium Applications (CEA) code to determine the equilibrium temperature (T(sub 4)) as a function of overall fuel/air ratio, pressure and initial temperature (T(sub 3)). High values of the regression coefficient R squared are obtained.

Comparison of methods for the analysis of relatively simple mediation models.

PubMed

Rijnhart, Judith J M; Twisk, Jos W R; Chinapaw, Mai J M; de Boer, Michiel R; Heymans, Martijn W

2017-09-01

Statistical mediation analysis is an often used method in trials, to unravel the pathways underlying the effect of an intervention on a particular outcome variable. Throughout the years, several methods have been proposed, such as ordinary least square (OLS) regression, structural equation modeling (SEM), and the potential outcomes framework. Most applied researchers do not know that these methods are mathematically equivalent when applied to mediation models with a continuous mediator and outcome variable. Therefore, the aim of this paper was to demonstrate the similarities between OLS regression, SEM, and the potential outcomes framework in three mediation models: 1) a crude model, 2) a confounder-adjusted model, and 3) a model with an interaction term for exposure-mediator interaction. Secondary data analysis of a randomized controlled trial that included 546 schoolchildren. In our data example, the mediator and outcome variable were both continuous. We compared the estimates of the total, direct and indirect effects, proportion mediated, and 95% confidence intervals (CIs) for the indirect effect across OLS regression, SEM, and the potential outcomes framework. OLS regression, SEM, and the potential outcomes framework yielded the same effect estimates in the crude mediation model, the confounder-adjusted mediation model, and the mediation model with an interaction term for exposure-mediator interaction. Since OLS regression, SEM, and the potential outcomes framework yield the same results in three mediation models with a continuous mediator and outcome variable, researchers can continue using the method that is most convenient to them.

Paleoflood investigations to improve peak-streamflow regional-regression equations for natural streamflow in eastern Colorado, 2015

USGS Publications Warehouse

Kohn, Michael S.; Stevens, Michael R.; Harden, Tessa M.; Godaire, Jeanne E.; Klinger, Ralph E.; Mommandi, Amanullah

2016-09-09

The U.S. Geological Survey (USGS), in cooperation with the Colorado Department of Transportation, developed regional-regression equations for estimating the 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, 0.2-percent annual exceedance-probability discharge (AEPD) for natural streamflow in eastern Colorado. A total of 188 streamgages, consisting of 6,536 years of record and a mean of approximately 35 years of record per streamgage, were used to develop the peak-streamflow regional-regression equations. The estimated AEPDs for each streamgage were computed using the USGS software program PeakFQ. The AEPDs were determined using systematic data through water year 2013. Based on previous studies conducted in Colorado and neighboring States and on the availability of data, 72 characteristics (57 basin and 15 climatic characteristics) were evaluated as candidate explanatory variables in the regression analysis. Paleoflood and non-exceedance bound ages were established based on reconnaissance-level methods. Multiple lines of evidence were used at each streamgage to arrive at a conclusion (age estimate) to add a higher degree of certainty to reconnaissance-level estimates. Paleoflood or nonexceedance bound evidence was documented at 41 streamgages, and 3 streamgages had previously collected paleoflood data.To determine the peak discharge of a paleoflood or non-exceedanc bound, two different hydraulic models were used.The mean standard error of prediction (SEP) for all 8 AEPDs was reduced approximately 25 percent compared to the previous flood-frequency study. For paleoflood data to be effective in reducing the SEP in eastern Colorado, a larger ratio than 44 of 188 (23 percent) streamgages would need paleoflood data and that paleoflood data would need to increase the record length by more than 25 years for the 1-percent AEPD. The greatest reduction in SEP for the peak-streamflow regional-regression equations was observed when additional new basin characteristics were included in the peak-streamflow regional-regression equations and when eastern Colorado was divided into two separate hydrologic regions. To make further reductions in the uncertainties of the peak-streamflow regional-regression equations in the Foothills and Plains hydrologic regions, additional streamgages or crest-stage gages are needed to collect peak-streamflow data on natural streams in eastern Colorado.Generalized-Least Squares regression was used to compute the final peak-streamflow regional-regression equations for peak-streamflow. Dividing eastern Colorado into two new individual regions at –104° longitude resulted in peak-streamflow regional-regression equations with the smallest SEP. The new hydrologic region located between –104° longitude and the Kansas-Nebraska State line will be designated the Plains hydrologic region and the hydrologic region comprising the rest of eastern Colorado located west of the –104° longitude and east of the Rocky Mountains and below 7,500 feet in the South Platte River Basin and below 9,000 feet in the Arkansas River Basin will be designated the Foothills hydrologic region.

A Modified Double Multiple Nonlinear Regression Constitutive Equation for Modeling and Prediction of High Temperature Flow Behavior of BFe10-1-2 Alloy

NASA Astrophysics Data System (ADS)

Cai, Jun; Wang, Kuaishe; Shi, Jiamin; Wang, Wen; Liu, Yingying

2018-01-01

Constitutive analysis for hot working of BFe10-1-2 alloy was carried out by using experimental stress-strain data from isothermal hot compression tests, in a wide range of temperature of 1,023 1,273 K, and strain rate range of 0.001 10 s-1. A constitutive equation based on modified double multiple nonlinear regression was proposed considering the independent effects of strain, strain rate, temperature and their interrelation. The predicted flow stress data calculated from the developed equation was compared with the experimental data. Correlation coefficient (R), average absolute relative error (AARE) and relative errors were introduced to verify the validity of the developed constitutive equation. Subsequently, a comparative study was made on the capability of strain-compensated Arrhenius-type constitutive model. The results showed that the developed constitutive equation based on modified double multiple nonlinear regression could predict flow stress of BFe10-1-2 alloy with good correlation and generalization.

Teaching the Concept of Breakdown Point in Simple Linear Regression.

ERIC Educational Resources Information Center

Chan, Wai-Sum

2001-01-01

Most introductory textbooks on simple linear regression analysis mention the fact that extreme data points have a great influence on ordinary least-squares regression estimation; however, not many textbooks provide a rigorous mathematical explanation of this phenomenon. Suggests a way to fill this gap by teaching students the concept of breakdown…

Universal shocks in the Wishart random-matrix ensemble.

PubMed

Blaizot, Jean-Paul; Nowak, Maciej A; Warchoł, Piotr

2013-05-01

We show that the derivative of the logarithm of the average characteristic polynomial of a diffusing Wishart matrix obeys an exact partial differential equation valid for an arbitrary value of N, the size of the matrix. In the large N limit, this equation generalizes the simple inviscid Burgers equation that has been obtained earlier for Hermitian or unitary matrices. The solution, through the method of characteristics, presents singularities that we relate to the precursors of shock formation in the Burgers equation. The finite N effects appear as a viscosity term in the Burgers equation. Using a scaling analysis of the complete equation for the characteristic polynomial, in the vicinity of the shocks, we recover in a simple way the universal Bessel oscillations (so-called hard-edge singularities) familiar in random-matrix theory.

A new formulation for anisotropic radiative transfer problems. I - Solution with a variational technique

NASA Technical Reports Server (NTRS)

Cheyney, H., III; Arking, A.

1976-01-01

The equations of radiative transfer in anisotropically scattering media are reformulated as linear operator equations in a single independent variable. The resulting equations are suitable for solution by a variety of standard mathematical techniques. The operators appearing in the resulting equations are in general nonsymmetric; however, it is shown that every bounded linear operator equation can be embedded in a symmetric linear operator equation and a variational solution can be obtained in a straightforward way. For purposes of demonstration, a Rayleigh-Ritz variational method is applied to three problems involving simple phase functions. It is to be noted that the variational technique demonstrated is of general applicability and permits simple solutions for a wide range of otherwise difficult mathematical problems in physics.

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.

Creatinine Clearance and Estimated Glomerular Filtration Rate--When are they Interchangeable.

PubMed

Simetić, Lucija; Zibar, Lada; Drmić, Sandra; Begić, Ivana; Serić, Vatroslav

2015-09-01

Study goal was to examine which of glomerular rate equations is most suitable for prediction of creatinine clearance (CrCl). Using a retrospective review of data from 500 hospital patients we calculated glomerular filtration rate according to Cockcroft-Gault equation (C-G), Modification of Diet in Renal Disease Study equation (MDRD) and Chronic Kidney Disease Epidemiology Collaboration equation (CKD-EPI). We determined if results of these equations were compatible with CrCl, and does stage of kidney disease, body-mass index (BMI), diabetes or old age have an impact on their ability to predict creatinine clearance. All of the equations showed high correlations with CrCl, regardless of diabetes, overweight or old age. There was no significant difference (p<0.05) between diagnostic accuracy when comparing ROC plots for MDRD and CKD-EPIat CrCl cut offs of 60 ml/min/1.73 m2 and 90 ml/min/1.73 m2 when analyzing data for all patients, older patients (>65 years) and diabetics. The percentage of overweight patients (BMI > or = 25) in patients with normal CrCl and decreased GFR was 64.81% for C-G, 92.04% for MDRD and 91.36% for CKD-EPI. Large number of overweight patients with normal CrCl and decreased GFR would indicate that CrCl overestimates GFR in overweight patients. The simple correction in CrCl for obese subjects is purposed. Passing-Bablok regression showed agreement between CrCl and MDRD and CrCl and CKD-EPI only in cases of severely decreased GFR (G4 and G5 stage of chronic kidney disease). Only in these stages of chronic kidney disease can CrCl and MDRD or CrCl and CKD-EPI be used simultaneously.

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

Simple, Flexible, Trigonometric Taper Equations

Treesearch

Charles E. Thomas; Bernard R. Parresol

1991-01-01

There have been numerous approaches to modeling stem form in recent decades. The majority have concentrated on the simpler coniferous bole form and have become increasingly complex mathematical expressions. Use of trigonometric equations provides a simple expression of taper that is flexible enough to fit both coniferous and hard-wood bole forms. As an illustration, we...

Blending and nudging in fluid dynamics: some simple observations

NASA Astrophysics Data System (ADS)

Germano, M.

2017-10-01

Blending and nudging methods have been recently applied in fluid dynamics, particularly regarding the assimilation of experimental data into the computations. In the paper we formally derive the differential equation associated to blending and compare it to the standard nudging equation. Some simple considerations related to these techniques and their mutual relations are exposed.

A regression technique for evaluation and quantification for water quality parameters from remote sensing data

NASA Technical Reports Server (NTRS)

Whitlock, C. H.; Kuo, C. Y.

1979-01-01

The objective of this paper is to define optical physics and/or environmental conditions under which the linear multiple-regression should be applicable. An investigation of the signal-response equations is conducted and the concept is tested by application to actual remote sensing data from a laboratory experiment performed under controlled conditions. Investigation of the signal-response equations shows that the exact solution for a number of optical physics conditions is of the same form as a linearized multiple-regression equation, even if nonlinear contributions from surface reflections, atmospheric constituents, or other water pollutants are included. Limitations on achieving this type of solution are defined.

Visualising ‘work done’ with a simple flying wheel toy

NASA Astrophysics Data System (ADS)

Amir, Nazir

2018-07-01

A way to scaffold students’ understanding of abstract physics concepts is through fun activities that help in visualisation. This article highlights a simple flying wheel toy can be used as a demonstration kit in presenting the equation ‘Work Done  =  Force  ×  Distance’. The kit has helped the author’s students visualise the equation, getting them to appreciate how components of the equation are related to one another, which otherwise may have been abstract for them.

Simple Derivation of the Lindblad Equation

ERIC Educational Resources Information Center

Pearle, Philip

2012-01-01

The Lindblad equation is an evolution equation for the density matrix in quantum theory. It is the general linear, Markovian, form which ensures that the density matrix is Hermitian, trace 1, positive and completely positive. Some elementary examples of the Lindblad equation are given. The derivation of the Lindblad equation presented here is…

Northeastern forest survey revised cubic-foot volume equations

Treesearch

Charles T. Scott

1981-01-01

Cubic-foot volume equations are presented for the 17 species groups used in the forest survey of the 14 northeastern states. The previous cubic- foot volume equations were simple linear in form; the revised cubic-foot volume equations are nonlinear.

A Simple, Analytical Model of Collisionless Magnetic Reconnection in a Pair Plasma

NASA Technical Reports Server (NTRS)

Hesse, Michael; Zenitani, Seiji; Kuznetova, Masha; Klimas, Alex

2011-01-01

A set of conservation equations is utilized to derive balance equations in the reconnection diffusion region of a symmetric pair plasma. The reconnection electric field is assumed to have the function to maintain the current density in the diffusion region, and to impart thermal energy to the plasma by means of quasi-viscous dissipation. Using these assumptions it is possible to derive a simple set of equations for diffusion region parameters in dependence on inflow conditions and on plasma compressibility. These equations are solved by means of a simple, iterative, procedure. The solutions show expected features such as dominance of enthalpy flux in the reconnection outflow, as well as combination of adiabatic and quasi-viscous heating. Furthermore, the model predicts a maximum reconnection electric field of E(sup *)=0.4, normalized to the parameters at the inflow edge of the diffusion region.

A simple, analytical model of collisionless magnetic reconnection in a pair plasma

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

Hesse, Michael; Zenitani, Seiji; Kuznetsova, Masha

2009-10-15

A set of conservation equations is utilized to derive balance equations in the reconnection diffusion region of a symmetric pair plasma. The reconnection electric field is assumed to have the function to maintain the current density in the diffusion region and to impart thermal energy to the plasma by means of quasiviscous dissipation. Using these assumptions it is possible to derive a simple set of equations for diffusion region parameters in dependence on inflow conditions and on plasma compressibility. These equations are solved by means of a simple, iterative procedure. The solutions show expected features such as dominance of enthalpymore » flux in the reconnection outflow, as well as combination of adiabatic and quasiviscous heating. Furthermore, the model predicts a maximum reconnection electric field of E{sup *}=0.4, normalized to the parameters at the inflow edge of the diffusion region.« less

A Comparison of Regional and SiteSpecific Volume Estimation Equations

Treesearch

Joe P. McClure; Jana Anderson; Hans T. Schreuder

1987-01-01

Regression equations for volume by region and site class were examined for lobiolly pine. The regressions for the Coastal Plain and Piedmont regions had significantly different slopes. The results shared important practical differences in percentage of confidence intervals containing the true total volume and in percentage of estimates within a specific proportion of...

Testing Mediation Using Multiple Regression and Structural Equation Modeling Analyses in Secondary Data

ERIC Educational Resources Information Center

Li, Spencer D.

2011-01-01

Mediation analysis in child and adolescent development research is possible using large secondary data sets. This article provides an overview of two statistical methods commonly used to test mediated effects in secondary analysis: multiple regression and structural equation modeling (SEM). Two empirical studies are presented to illustrate the…

Equation of state and Helmholtz free energy for the atomic system of the repulsive Lennard-Jones particles.

PubMed

Mirzaeinia, Ali; Feyzi, Farzaneh; Hashemianzadeh, Seyed Majid

2017-12-07

Simple and accurate expressions are presented for the equation of state (EOS) and absolute Helmholtz free energy of a system composed of simple atomic particles interacting through the repulsive Lennard-Jones potential model in the fluid and solid phases. The introduced EOS has 17 and 22 coefficients for fluid and solid phases, respectively, which are regressed to the Monte Carlo (MC) simulation data over the reduced temperature range of 0.6≤T * ≤6.0 and the packing fraction range of 0.1 ≤ η ≤ 0.72. The average absolute relative percent deviation in fitting the EOS parameters to the MC data is 0.06 and 0.14 for the fluid and solid phases, respectively. The thermodynamic integration method is used to calculate the free energy using the MC simulation results. The Helmholtz free energy of the ideal gas is employed as the reference state for the fluid phase. For the solid phase, the values of the free energy at the reduced density equivalent to the close-packed of a hard sphere are used as the reference state. To check the validity of the predicted values of the Helmholtz free energy, the Widom particle insertion method and the Einstein crystal technique of Frenkel and Ladd are employed. The results obtained from the MC simulation approaches are well agreed to the EOS results, which show that the proposed model can reliably be utilized in the framework of thermodynamic theories.

Equation of state and Helmholtz free energy for the atomic system of the repulsive Lennard-Jones particles

NASA Astrophysics Data System (ADS)

Mirzaeinia, Ali; Feyzi, Farzaneh; Hashemianzadeh, Seyed Majid

2017-12-01

Simple and accurate expressions are presented for the equation of state (EOS) and absolute Helmholtz free energy of a system composed of simple atomic particles interacting through the repulsive Lennard-Jones potential model in the fluid and solid phases. The introduced EOS has 17 and 22 coefficients for fluid and solid phases, respectively, which are regressed to the Monte Carlo (MC) simulation data over the reduced temperature range of 0.6 ≤T*≤6.0 and the packing fraction range of 0.1 ≤ η ≤ 0.72. The average absolute relative percent deviation in fitting the EOS parameters to the MC data is 0.06 and 0.14 for the fluid and solid phases, respectively. The thermodynamic integration method is used to calculate the free energy using the MC simulation results. The Helmholtz free energy of the ideal gas is employed as the reference state for the fluid phase. For the solid phase, the values of the free energy at the reduced density equivalent to the close-packed of a hard sphere are used as the reference state. To check the validity of the predicted values of the Helmholtz free energy, the Widom particle insertion method and the Einstein crystal technique of Frenkel and Ladd are employed. The results obtained from the MC simulation approaches are well agreed to the EOS results, which show that the proposed model can reliably be utilized in the framework of thermodynamic theories.

Simple waves in a two-component Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Ivanov, S. K.; Kamchatnov, A. M.

2018-04-01

We study the dynamics of so-called simple waves in a two-component Bose-Einstein condensate. The evolution of the condensate is described by Gross-Pitaevskii equations which can be reduced for these simple wave solutions to a system of ordinary differential equations which coincide with those derived by Ovsyannikov for the two-layer fluid dynamics. We solve the Ovsyannikov system for two typical situations of large and small difference between interspecies and intraspecies nonlinear interaction constants. Our analytic results are confirmed by numerical simulations.

Using Simple Linear Regression to Assess the Success of the Montreal Protocol in Reducing Atmospheric Chlorofluorocarbons

ERIC Educational Resources Information Center

Nelson, Dean

2009-01-01

Following the Guidelines for Assessment and Instruction in Statistics Education (GAISE) recommendation to use real data, an example is presented in which simple linear regression is used to evaluate the effect of the Montreal Protocol on atmospheric concentration of chlorofluorocarbons. This simple set of data, obtained from a public archive, can…

Is complex allometry in field metabolic rates of mammals a statistical artifact?

PubMed

Packard, Gary C

2017-01-01

Recent reports indicate that field metabolic rates (FMRs) of mammals conform to a pattern of complex allometry in which the exponent in a simple, two-parameter power equation increases steadily as a dependent function of body mass. The reports were based, however, on indirect analyses performed on logarithmic transformations of the original data. I re-examined values for FMR and body mass for 114 species of mammal by the conventional approach to allometric analysis (to illustrate why the approach is unreliable) and by linear and nonlinear regression on untransformed variables (to illustrate the power and versatility of newer analytical methods). The best of the regression models fitted directly to untransformed observations is a three-parameter power equation with multiplicative, lognormal, heteroscedastic error and an allometric exponent of 0.82. The mean function is a good fit to data in graphical display. The significant intercept in the model may simply have gone undetected in prior analyses because conventional allometry assumes implicitly that the intercept is zero; or the intercept may be a spurious finding resulting from bias introduced by the haphazard sampling that underlies "exploratory" analyses like the one reported here. The aforementioned issues can be resolved only by gathering new data specifically intended to address the question of scaling of FMR with body mass in mammals. However, there is no support for the concept of complex allometry in the relationship between FMR and body size in mammals. Copyright © 2016 Elsevier Inc. All rights reserved.

Fokker-Planck equation for the non-Markovian Brownian motion in the presence of a magnetic field

NASA Astrophysics Data System (ADS)

Das, Joydip; Mondal, Shrabani; Bag, Bidhan Chandra

2017-10-01

In the present study, we have proposed the Fokker-Planck equation in a simple way for a Langevin equation of motion having ordinary derivative (OD), the Gaussian random force and a generalized frictional memory kernel. The equation may be associated with or without conservative force field from harmonic potential. We extend this method for a charged Brownian particle in the presence of a magnetic field. Thus, the present method is applicable for a Langevin equation of motion with OD, the Gaussian colored thermal noise and any kind of linear force field that may be conservative or not. It is also simple to apply this method for the colored Gaussian noise that is not related to the damping strength.

Fokker-Planck equation for the non-Markovian Brownian motion in the presence of a magnetic field.

PubMed

Das, Joydip; Mondal, Shrabani; Bag, Bidhan Chandra

2017-10-28

In the present study, we have proposed the Fokker-Planck equation in a simple way for a Langevin equation of motion having ordinary derivative (OD), the Gaussian random force and a generalized frictional memory kernel. The equation may be associated with or without conservative force field from harmonic potential. We extend this method for a charged Brownian particle in the presence of a magnetic field. Thus, the present method is applicable for a Langevin equation of motion with OD, the Gaussian colored thermal noise and any kind of linear force field that may be conservative or not. It is also simple to apply this method for the colored Gaussian noise that is not related to the damping strength.

Thermal requirements of Dermanyssus gallinae (De Geer, 1778) (Acari: Dermanyssidae).

PubMed

Tucci, Edna Clara; do Prado, Angelo P; de Araújo, Raquel Pires

2008-01-01

The thermal requirements for development of Dermanyssus gallinae were studied under laboratory conditions at 15, 20, 25, 30 and 35 degrees C, a 12h photoperiod and 60-85% RH. The thermal requirements for D. gallinae were as follows. Preoviposition: base temperature 3.4 degrees C, thermal constant (k) 562.85 degree-hours, determination coefficient (R(2)) 0.59, regression equation: Y= -0.006035 + 0.001777x. Egg: base temperature 10.60 degrees C, thermal constant (k) 689.65 degree-hours, determination coefficient (R(2)) 0.94, regression equation: Y= -0.015367 + 0.001450x. Larva: base temperature 9.82 degrees C, thermal constant (k) 464.91 degree-hours, determination coefficient (R(2)) 0.87, regression equation: Y= -0.021123 + 0.002151x. Protonymph: base temperature 10.17 degrees C, thermal constant (k) 504.49 degree-hours, determination coefficient (R(2)) 0.90, regression equation: Y= -0.020152 + 0.001982x. Deutonymph: base temperature 11.80 degrees C, thermal constant (k) 501.11 degree-hours, determination coefficient (R(2)) 0.99, regression equation: Y= -0.023555 + 0.001996x. The results obtained showed that 15 to 42 generations of Dermanyssus gallinae may occur during the year in the State of São Paulo, as estimated based on isotherm charts. Dermanyssus gallinae may develop continually in the State of São Paulo, with a population decrease in the winter. There were differences between the developmental stages of D. gallinae in relation to thermal requirements.

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.

Selected Streamflow Statistics and Regression Equations for Predicting Statistics at Stream Locations in Monroe County, Pennsylvania

USGS Publications Warehouse

Thompson, Ronald E.; Hoffman, Scott A.

2006-01-01

A suite of 28 streamflow statistics, ranging from extreme low to high flows, was computed for 17 continuous-record streamflow-gaging stations and predicted for 20 partial-record stations in Monroe County and contiguous counties in north-eastern Pennsylvania. The predicted statistics for the partial-record stations were based on regression analyses relating inter-mittent flow measurements made at the partial-record stations indexed to concurrent daily mean flows at continuous-record stations during base-flow conditions. The same statistics also were predicted for 134 ungaged stream locations in Monroe County on the basis of regression analyses relating the statistics to GIS-determined basin characteristics for the continuous-record station drainage areas. The prediction methodology for developing the regression equations used to estimate statistics was developed for estimating low-flow frequencies. This study and a companion study found that the methodology also has application potential for predicting intermediate- and high-flow statistics. The statistics included mean monthly flows, mean annual flow, 7-day low flows for three recurrence intervals, nine flow durations, mean annual base flow, and annual mean base flows for two recurrence intervals. Low standard errors of prediction and high coefficients of determination (R2) indicated good results in using the regression equations to predict the statistics. Regression equations for the larger flow statistics tended to have lower standard errors of prediction and higher coefficients of determination (R2) than equations for the smaller flow statistics. The report discusses the methodologies used in determining the statistics and the limitations of the statistics and the equations used to predict the statistics. Caution is indicated in using the predicted statistics for small drainage area situations. Study results constitute input needed by water-resource managers in Monroe County for planning purposes and evaluation of water-resources availability.

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)

An Anharmonic Solution to the Equation of Motion for the Simple Pendulum

ERIC Educational Resources Information Center

Johannessen, Kim

2011-01-01

An anharmonic solution to the differential equation describing the oscillations of a simple pendulum at large angles is discussed. The solution is expressed in terms of functions not involving the Jacobi elliptic functions. In the derivation, a sinusoidal expression, including a linear and a Fourier sine series in the argument, has been applied.…

Predicting the cover-up of dead branches using a simple single regressor equation

Treesearch

Christopher M. Oswalt; Wayne K. Clatterbuck; E.C. Burkhardt

2007-01-01

Information on the effects of branch diameter on branch occlusion is necessary for building models capable of forecasting the effect of management decisions on tree or log grade. We investigated the relationship between branch size and subsequent branch occlusion through diameter growth with special attention toward the development of a simple single regressor equation...

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.

Continuous water-quality monitoring and regression analysis to estimate constituent concentrations and loads in the Red River of the North at Fargo and Grand Forks, North Dakota, 2003-12

USGS Publications Warehouse

Galloway, Joel M.

2014-01-01

The Red River of the North (hereafter referred to as “Red River”) Basin is an important hydrologic region where water is a valuable resource for the region’s economy. Continuous water-quality monitors have been operated by the U.S. Geological Survey, in cooperation with the North Dakota Department of Health, Minnesota Pollution Control Agency, City of Fargo, City of Moorhead, City of Grand Forks, and City of East Grand Forks at the Red River at Fargo, North Dakota, from 2003 through 2012 and at Grand Forks, N.Dak., from 2007 through 2012. The purpose of the monitoring was to provide a better understanding of the water-quality dynamics of the Red River and provide a way to track changes in water quality. Regression equations were developed that can be used to estimate concentrations and loads for dissolved solids, sulfate, chloride, nitrate plus nitrite, total phosphorus, and suspended sediment using explanatory variables such as streamflow, specific conductance, and turbidity. Specific conductance was determined to be a significant explanatory variable for estimating dissolved solids concentrations at the Red River at Fargo and Grand Forks. The regression equations provided good relations between dissolved solid concentrations and specific conductance for the Red River at Fargo and at Grand Forks, with adjusted coefficients of determination of 0.99 and 0.98, respectively. Specific conductance, log-transformed streamflow, and a seasonal component were statistically significant explanatory variables for estimating sulfate in the Red River at Fargo and Grand Forks. Regression equations provided good relations between sulfate concentrations and the explanatory variables, with adjusted coefficients of determination of 0.94 and 0.89, respectively. For the Red River at Fargo and Grand Forks, specific conductance, streamflow, and a seasonal component were statistically significant explanatory variables for estimating chloride. For the Red River at Grand Forks, a time component also was a statistically significant explanatory variable for estimating chloride. The regression equations for chloride at the Red River at Fargo provided a fair relation between chloride concentrations and the explanatory variables, with an adjusted coefficient of determination of 0.66 and the equation for the Red River at Grand Forks provided a relatively good relation between chloride concentrations and the explanatory variables, with an adjusted coefficient of determination of 0.77. Turbidity and streamflow were statistically significant explanatory variables for estimating nitrate plus nitrite concentrations at the Red River at Fargo and turbidity was the only statistically significant explanatory variable for estimating nitrate plus nitrite concentrations at Grand Forks. The regression equation for the Red River at Fargo provided a relatively poor relation between nitrate plus nitrite concentrations, turbidity, and streamflow, with an adjusted coefficient of determination of 0.46. The regression equation for the Red River at Grand Forks provided a fair relation between nitrate plus nitrite concentrations and turbidity, with an adjusted coefficient of determination of 0.73. Some of the variability that was not explained by the equations might be attributed to different sources contributing nitrates to the stream at different times. Turbidity, streamflow, and a seasonal component were statistically significant explanatory variables for estimating total phosphorus at the Red River at Fargo and Grand Forks. The regression equation for the Red River at Fargo provided a relatively fair relation between total phosphorus concentrations, turbidity, streamflow, and season, with an adjusted coefficient of determination of 0.74. The regression equation for the Red River at Grand Forks provided a good relation between total phosphorus concentrations, turbidity, streamflow, and season, with an adjusted coefficient of determination of 0.87. For the Red River at Fargo, turbidity and streamflow were statistically significant explanatory variables for estimating suspended-sediment concentrations. For the Red River at Grand Forks, turbidity was the only statistically significant explanatory variable for estimating suspended-sediment concentration. The regression equation at the Red River at Fargo provided a good relation between suspended-sediment concentration, turbidity, and streamflow, with an adjusted coefficient of determination of 0.95. The regression equation for the Red River at Grand Forks provided a good relation between suspended-sediment concentration and turbidity, with an adjusted coefficient of determination of 0.96.

A stream-gaging network analysis for the 7-day, 10-year annual low flow in New Hampshire streams

USGS Publications Warehouse

Flynn, Robert H.

2003-01-01

The 7-day, 10-year (7Q10) low-flow-frequency statistic is a widely used measure of surface-water availability in New Hampshire. Regression equations and basin-characteristic digital data sets were developed to help water-resource managers determine surface-water resources during periods of low flow in New Hampshire streams. These regression equations and data sets were developed to estimate streamflow statistics for the annual and seasonal low-flow-frequency, and period-of-record and seasonal period-of-record flow durations. generalized-least-squares (GLS) regression methods were used to develop the annual 7Q10 low-flow-frequency regression equation from 60 continuous-record stream-gaging stations in New Hampshire and in neighboring States. In the regression equation, the dependent variables were the annual 7Q10 flows at the 60 stream-gaging stations. The independent (or predictor) variables were objectively selected characteristics of the drainage basins that contribute flow to those stations. In contrast to ordinary-least-squares (OLS) regression analysis, GLS-developed estimating equations account for differences in length of record and spatial correlations among the flow-frequency statistics at the various stations.A total of 93 measurable drainage-basin characteristics were candidate independent variables. On the basis of several statistical parameters that were used to evaluate which combination of basin characteristics contribute the most to the predictive power of the equations, three drainage-basin characteristics were determined to be statistically significant predictors of the annual 7Q10: (1) total drainage area, (2) mean summer stream-gaging station precipitation from 1961 to 90, and (3) average mean annual basinwide temperature from 1961 to 1990.To evaluate the effectiveness of the stream-gaging network in providing regional streamflow data for the annual 7Q10, the computer program GLSNET (generalized-least-squares NETwork) was used to analyze the network by application of GLS regression between streamflow and the climatic and basin characteristics of the drainage basin upstream from each stream-gaging station. Improvement to the predictive ability of the regression equations developed for the network analyses is measured by the reduction in the average sampling-error variance, and can be achieved by collecting additional streamflow data at existing stations. The predictive ability of the regression equations is enhanced even further with the addition of new stations to the network. Continued data collection at unregulated stream-gaging stations with less than 14 years of record resulted in the greatest cost-weighted reduction to the average sampling-error variance of the annual 7Q10 regional regression equation. The addition of new stations in basins with underrepresented values for the independent variables of the total drainage area, average mean annual basinwide temperature, or mean summer stream-gaging station precipitation in the annual 7Q10 regression equation yielded a much greater cost-weighted reduction to the average sampling-error variance than when more data were collected at existing unregulated stations. To maximize the regional information obtained from the stream-gaging network for the annual 7Q10, ranking of the streamflow data can be used to determine whether an active station should be continued or if a new or discontinued station should be activated for streamflow data collection. Thus, this network analysis can help determine the costs and benefits of continuing the operation of a particular station or activating a new station at another location to predict the 7Q10 at ungaged stream reaches. The decision to discontinue an existing station or activate a new station, however, must also consider its contribution to other water-resource analyses such as flood management, water quality, or trends in land use or climatic change.

Use of Thematic Mapper for water quality assessment

NASA Technical Reports Server (NTRS)

Horn, E. M.; Morrissey, L. A.

1984-01-01

The evaluation of simulated TM data obtained on an ER-2 aircraft at twenty-five predesignated sample sites for mapping water quality factors such as conductivity, pH, suspended solids, turbidity, temperature, and depth, is discussed. Using a multiple regression for the seven TM bands, an equation is developed for the suspended solids. TM bands 1, 2, 3, 4, and 6 are used with logarithm conductivity in a multiple regression. The assessment of regression equations for a high coefficient of determination (R-squared) and statistical significance is considered. Confidence intervals about the mean regression point are calculated in order to assess the robustness of the regressions used for mapping conductivity, turbidity, and suspended solids, and by regressing random subsamples of sites and comparing the resultant range of R-squared, cross validation is conducted.

Development of Multiple Regression Equations To Predict Fourth Graders' Achievement in Reading and Selected Content Areas.

ERIC Educational Resources Information Center

Hafner, Lawrence E.

A study developed a multiple regression prediction equation for each of six selected achievement variables in a popular standardized test of achievement. Subjects, 42 fourth-grade pupils randomly selected across several classes in a large elementary school in a north Florida city, were administered several standardized tests to determine predictor…

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.

The Krylov accelerated SIMPLE(R) method for flow problems in industrial furnaces

NASA Astrophysics Data System (ADS)

Vuik, C.; Saghir, A.; Boerstoel, G. P.

2000-08-01

Numerical modeling of the melting and combustion process is an important tool in gaining understanding of the physical and chemical phenomena that occur in a gas- or oil-fired glass-melting furnace. The incompressible Navier-Stokes equations are used to model the gas flow in the furnace. The discrete Navier-Stokes equations are solved by the SIMPLE(R) pressure-correction method. In these applications, many SIMPLE(R) iterations are necessary to obtain an accurate solution. In this paper, Krylov accelerated versions are proposed: GCR-SIMPLE(R). The properties of these methods are investigated for a simple two-dimensional flow. Thereafter, the efficiencies of the methods are compared for three-dimensional flows in industrial glass-melting furnaces. Copyright

Comparison of rigorous and simple vibrational models for the CO2 gasdynamic laser

NASA Technical Reports Server (NTRS)

Monson, D. J.

1977-01-01

The accuracy of a simple vibrational model for computing the gain in a CO2 gasdynamic laser is assessed by comparing results computed from it with results computed from a rigorous vibrational model. The simple model is that of Anderson et al. (1971), in which the vibrational kinetics are modeled by grouping the nonequilibrium vibrational degrees of freedom into two modes, to each of which there corresponds an equation describing vibrational relaxation. The two models agree fairly well in the computed gain at low temperatures, but the simple model predicts too high a gain at the higher temperatures of current interest. The sources of error contributing to the overestimation given by the simple model are determined by examining the simplified relaxation equations.

[Determination of Bloodstain Age by UV Visible Integrating Sphere Reflection Spectrum].

PubMed

Yan, L Q; Gao, Y

2016-10-01

To establish a method for rapid identification of bloodstain age. Under laboratory conditions （20 ℃, 25 ℃ and 30 ℃）, an integrating sphere ISR-240A was used as a reflection accessory on an UV-2450 UV-vis spectrophotometer, and a standard white board of BaSO₄ was used as reference, the reflection spectrums of bloodstain from human ears' venous blood were measured at regular intervals. The reflection radios R ₅₄₁ and R ₅₇₇ at a specific wavelength were collected and the value of R ₅₄₁/ R ₅₇₇ was calculated. The linear fitting and regression analysis were done by SPSS 17.0. The results of regression analysis showed that R ² of the ratios of bloodstain age to UV visible reflectivity in specific wavelengths were larger than 0.8 within 8 hours and under certain circumstances. The regression equation was established. The bloodstain age had significant correlation with the value of R ₅₄₁/ R ₅₇₇. The method of inspection is simple, rapid and nondestructive with a good reliability, and can be used to identify the bloodstain age within 8 hours elapsed-time standards under laboratory conditions. Copyright© by the Editorial Department of Journal of Forensic Medicine

Testing of a simplified LED based vis/NIR system for rapid ripeness evaluation of white grape (Vitis vinifera L.) for Franciacorta wine.

PubMed

Giovenzana, Valentina; Civelli, Raffaele; Beghi, Roberto; Oberti, Roberto; Guidetti, Riccardo

2015-11-01

The aim of this work was to test a simplified optical prototype for a rapid estimation of the ripening parameters of white grape for Franciacorta wine directly in field. Spectral acquisition based on reflectance at four wavelengths (630, 690, 750 and 850 nm) was proposed. The integration of a simple processing algorithm in the microcontroller software would allow to visualize real time values of spectral reflectance. Non-destructive analyses were carried out on 95 grape bunches for a total of 475 berries. Samplings were performed weekly during the last ripening stages. Optical measurements were carried out both using the simplified system and a portable commercial vis/NIR spectrophotometer, as reference instrument for performance comparison. Chemometric analyses were performed in order to extract the maximum useful information from optical data. Principal component analysis (PCA) was performed for a preliminary evaluation of the data. Correlations between the optical data matrix and ripening parameters (total soluble solids content, SSC; titratable acidity, TA) were carried out using partial least square (PLS) regression for spectra and using multiple linear regression (MLR) for data from the simplified device. Classification analysis were also performed with the aim of discriminate ripe and unripe samples. PCA, MLR and classification analyses show the effectiveness of the simplified system in separating samples among different sampling dates and in discriminating ripe from unripe samples. Finally, simple equations for SSC and TA prediction were calculated. Copyright © 2015 Elsevier B.V. All rights reserved.

Effect of walking velocity on ground reaction force variables in the hind limb of clinically normal horses.

PubMed

Khumsap, S; Clayton, H M; Lanovaz, J L

2001-06-01

To measure the effect of subject velocity on hind limb ground reaction force variables at the walk and to use the data to predict the force variables at different walking velocities in horses. 5 clinically normal horses. Kinematic and force data were collected simultaneously. Each horse was led over a force plate at a range of walking velocities. Stance duration and force data were recorded for the right hind limb. To avoid the effect of horse size on the outcome variables, the 8 force variables were standardized to body mass and height at the shoulders. Velocity was standardized to height at the shoulders and expressed as velocity in dimensionless units (VDU). Stance duration was also expressed in dimensionless units (SDU). Simple regression analysis was performed, using stance duration and force variables as dependent variables and VDU as the independent variable. Fifty-six trials were recorded with velocities ranging from 0.24 to 0.45 VDU (0.90 to 1.72 m/s). Simple regression models between measured variables and VDU were significant (R2 > 0.69) for SDU, first peak of vertical force, dip between the 2 vertical force peaks, vertical impulse, and timing of second peak of vertical force. Subject velocity affects vertical force components only. In the future, differences between the forces measured in lame horses and the expected forces calculated for the same velocity will be studied to determine whether the equations can be used as diagnostic criteria.

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.

Computational methods and traveling wave solutions for the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave dynamical equation via two methods and its applications

NASA Astrophysics Data System (ADS)

Ali, Asghar; Seadawy, Aly R.; Lu, Dianchen

2018-05-01

The aim of this article is to construct some new traveling wave solutions and investigate localized structures for fourth-order nonlinear Ablowitz-Kaup-Newell-Segur (AKNS) water wave dynamical equation. The simple equation method (SEM) and the modified simple equation method (MSEM) are applied in this paper to construct the analytical traveling wave solutions of AKNS equation. The different waves solutions are derived by assigning special values to the parameters. The obtained results have their importance in the field of physics and other areas of applied sciences. All the solutions are also graphically represented. The constructed results are often helpful for studying several new localized structures and the waves interaction in the high-dimensional models.

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.

A Simple Equation to Predict a Subscore's Value

ERIC Educational Resources Information Center

Feinberg, Richard A.; Wainer, Howard

2014-01-01

Subscores are often used to indicate test-takers' relative strengths and weaknesses and so help focus remediation. But a subscore is not worth reporting if it is too unreliable to believe or if it contains no information that is not already contained in the total score. It is possible, through the use of a simple linear equation provided in…

Computational prediction of the pKas of small peptides through Conceptual DFT descriptors

NASA Astrophysics Data System (ADS)

Frau, Juan; Hernández-Haro, Noemí; Glossman-Mitnik, Daniel

2017-03-01

The experimental pKa of a group of simple amines have been plotted against several Conceptual DFT descriptors calculated by means of different density functionals, basis sets and solvation schemes. It was found that the best fits are those that relate the pKa of the amines with the global hardness η through the MN12SX density functional in connection with the Def2TZVP basis set and the SMD solvation model, using water as a solvent. The parameterized equation resulting from the linear regression analysis has then been used for the prediction of the pKa of small peptides of interest in the study of diabetes and Alzheimer disease. The accuracy of the results is relatively good, with a MAD of 0.36 units of pKa.

How Darcy's equation is linked to the linear reservoir at catchment scale

NASA Astrophysics Data System (ADS)

Savenije, Hubert H. G.

2017-04-01

In groundwater hydrology two simple linear equations exist that describe the relation between groundwater flow and the gradient that drives it: Darcy's equation and the linear reservoir. Both equations are empirical at heart: Darcy's equation at the laboratory scale and the linear reservoir at the watershed scale. Although at first sight they show similarity, without having detailed knowledge of the structure of the underlying aquifers it is not trivial to upscale Darcy's equation to the watershed scale. In this paper, a relatively simple connection is provided between the two, based on the assumption that the groundwater system is organized by an efficient drainage network, a mostly invisible pattern that has evolved over geological time scales. This drainage network provides equally distributed resistance to flow along the streamlines that connect the active groundwater body to the stream, much like a leaf is organized to provide all stomata access to moisture at equal resistance.

A Simple Global View of Fuel Burnup

NASA Astrophysics Data System (ADS)

Sekimoto, Hiroshi

2017-01-01

Reactor physics and fuel burnup are discussed in order to obtain a simple global view of the effects of nuclear reactor characteristics to fuel cycle system performance. It may provide some idea of free thinking and overall vision, though it is still a small part of nuclear energy system. At the beginning of this lecture, governing equations for nuclear reactors are presented. Since the set of these equations is so big and complicated, it is simplified by imposing some extreme conditions and the nuclear equilibrium equation is derived. Some features of future nuclear equilibrium state are obtained by solving this equation. The contribution of a nucleus charged into reactor core to the system performance indexes such as criticality is worth for understanding the importance of each nuclide. It is called nuclide importance and can be evaluated by using the equations adjoint to the nuclear equilibrium equation. Examples of some importances and their application to criticalily search problem are presented.

The Pendulum and the Calculus.

ERIC Educational Resources Information Center

Sworder, Steven C.

A pair of experiments, appropriate for the lower division fourth semester calculus or differential equations course, are presented. The second order differential equation representing the equation of motion of a simple pendulum is derived. The period of oscillation for a particular pendulum can be predicted from the solution to this equation. As a…

A simple finite element method for non-divergence form elliptic equation

DOE PAGES

Mu, Lin; Ye, Xiu

2017-03-01

Here, we develop a simple finite element method for solving second order elliptic equations in non-divergence form by combining least squares concept with discontinuous approximations. This simple method has a symmetric and positive definite system and can be easily analyzed and implemented. We could have also used general meshes with polytopal element and hanging node in the method. We prove that our finite element solution approaches to the true solution when the mesh size approaches to zero. Numerical examples are tested that demonstrate the robustness and flexibility of the method.

A simple finite element method for non-divergence form elliptic equation

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

Mu, Lin; Ye, Xiu

Here, we develop a simple finite element method for solving second order elliptic equations in non-divergence form by combining least squares concept with discontinuous approximations. This simple method has a symmetric and positive definite system and can be easily analyzed and implemented. We could have also used general meshes with polytopal element and hanging node in the method. We prove that our finite element solution approaches to the true solution when the mesh size approaches to zero. Numerical examples are tested that demonstrate the robustness and flexibility of the method.

A simple finite element method for the Stokes equations

DOE PAGES

Mu, Lin; Ye, Xiu

2017-03-21

The goal of this paper is to introduce a simple finite element method to solve the Stokes equations. This method is in primal velocity-pressure formulation and is so simple such that both velocity and pressure are approximated by piecewise constant functions. Implementation issues as well as error analysis are investigated. A basis for a divergence free subspace of the velocity field is constructed so that the original saddle point problem can be reduced to a symmetric and positive definite system with much fewer unknowns. The numerical experiments indicate that the method is accurate.

A simple finite element method for the Stokes equations

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

Mu, Lin; Ye, Xiu

The goal of this paper is to introduce a simple finite element method to solve the Stokes equations. This method is in primal velocity-pressure formulation and is so simple such that both velocity and pressure are approximated by piecewise constant functions. Implementation issues as well as error analysis are investigated. A basis for a divergence free subspace of the velocity field is constructed so that the original saddle point problem can be reduced to a symmetric and positive definite system with much fewer unknowns. The numerical experiments indicate that the method is accurate.

Escherichia coli bacteria density in relation to turbidity, streamflow characteristics, and season in the Chattahoochee River near Atlanta, Georgia, October 2000 through September 2008—Description, statistical analysis, and predictive modeling

USGS Publications Warehouse

Lawrence, Stephen J.

2012-01-01

Regression analyses show that E. coli density in samples was strongly related to turbidity, streamflow characteristics, and season at both sites. The regression equation chosen for the Norcross data showed that 78 percent of the variability in E. coli density (in log base 10 units) was explained by the variability in turbidity values (in log base 10 units), streamflow event (dry-weather flow or stormflow), season (cool or warm), and an interaction term that is the cross product of streamflow event and turbidity. The regression equation chosen for the Atlanta data showed that 76 percent of the variability in E. coli density (in log base 10 units) was explained by the variability in turbidity values (in log base 10 units), water temperature, streamflow event, and an interaction term that is the cross product of streamflow event and turbidity. Residual analysis and model confirmation using new data indicated the regression equations selected at both sites predicted E. coli density within the 90 percent prediction intervals of the equations and could be used to predict E. coli density in real time at both sites.

Rational solutions of CYBE for simple compact real Lie algebras

NASA Astrophysics Data System (ADS)

Pop, Iulia; Stolin, Alexander

2007-04-01

In [A.A. Stolin, On rational solutions of Yang-Baxter equation for sl(n), Math. Scand. 69 (1991) 57-80; A.A. Stolin, On rational solutions of Yang-Baxter equation. Maximal orders in loop algebra, Comm. Math. Phys. 141 (1991) 533-548; A. Stolin, A geometrical approach to rational solutions of the classical Yang-Baxter equation. Part I, in: Walter de Gruyter & Co. (Ed.), Symposia Gaussiana, Conf. Alg., Berlin, New York, 1995, pp. 347-357] a theory of rational solutions of the classical Yang-Baxter equation for a simple complex Lie algebra g was presented. We discuss this theory for simple compact real Lie algebras g. We prove that up to gauge equivalence all rational solutions have the form X(u,v)={Ω}/{u-v}+t1∧t2+⋯+t∧t2n, where Ω denotes the quadratic Casimir element of g and {ti} are linearly independent elements in a maximal torus t of g. The quantization of these solutions is also emphasized.

A simple, direct derivation and proof of the validity of the SLLOD equations of motion for generalized homogeneous flows.

PubMed

Daivis, Peter J; Todd, B D

2006-05-21

We present a simple and direct derivation of the SLLOD equations of motion for molecular simulations of general homogeneous flows. We show that these equations of motion (1) generate the correct particle trajectories, (2) conserve the total thermal momentum without requiring the center of mass to be located at the origin, and (3) exactly generate the required energy dissipation. These equations of motion are compared with the g-SLLOD and p-SLLOD equations of motion, which are found to be deficient. Claims that the SLLOD equations of motion are incorrect for elongational flows are critically examined and found to be invalid. It is confirmed that the SLLOD equations are, in general, non-Hamiltonian. We derive a Hamiltonian from which they can be obtained in the special case of a symmetric velocity gradient tensor. In this case, it is possible to perform a canonical transformation that results in the well-known DOLLS tensor Hamiltonian.

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

USGS Publications Warehouse

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

2016-08-04

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

Fokker-Planck Equations of Stochastic Acceleration: A Study of Numerical Methods

NASA Astrophysics Data System (ADS)

Park, Brian T.; Petrosian, Vahe

1996-03-01

Stochastic wave-particle acceleration may be responsible for producing suprathermal particles in many astrophysical situations. The process can be described as a diffusion process through the Fokker-Planck equation. If the acceleration region is homogeneous and the scattering mean free path is much smaller than both the energy change mean free path and the size of the acceleration region, then the Fokker-Planck equation reduces to a simple form involving only the time and energy variables. in an earlier paper (Park & Petrosian 1995, hereafter Paper 1), we studied the analytic properties of the Fokker-Planck equation and found analytic solutions for some simple cases. In this paper, we study the numerical methods which must be used to solve more general forms of the equation. Two classes of numerical methods are finite difference methods and Monte Carlo simulations. We examine six finite difference methods, three fully implicit and three semi-implicit, and a stochastic simulation method which uses the exact correspondence between the Fokker-Planck equation and the it5 stochastic differential equation. As discussed in Paper I, Fokker-Planck equations derived under the above approximations are singular, causing problems with boundary conditions and numerical overflow and underflow. We evaluate each method using three sample equations to test its stability, accuracy, efficiency, and robustness for both time-dependent and steady state solutions. We conclude that the most robust finite difference method is the fully implicit Chang-Cooper method, with minor extensions to account for the escape and injection terms. Other methods suffer from stability and accuracy problems when dealing with some Fokker-Planck equations. The stochastic simulation method, although simple to implement, is susceptible to Poisson noise when insufficient test particles are used and is computationally very expensive compared to the finite difference method.

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

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.

Estimates of streamflow characteristics for selected small streams, Baker River basin, Washington

USGS Publications Warehouse

Williams, John R.

1987-01-01

Regression equations were used to estimate streamflow characteristics at eight ungaged sites on small streams in the Baker River basin in the North Cascade Mountains, Washington, that could be suitable for run-of-the-river hydropower development. The regression equations were obtained by relating known streamflow characteristics at 25 gaging stations in nearby basins to several physical and climatic variables that could be easily measured in gaged or ungaged basins. The known streamflow characteristics were mean annual flows, 1-, 3-, and 7-day low flows and high flows, mean monthly flows, and flow duration. Drainage area and mean annual precipitation were not the most significant variables in all the regression equations. Variance in the low flows and the summer mean monthly flows was reduced by including an index of glacierized area within the basin as a third variable. Standard errors of estimate of the regression equations ranged from 25 to 88%, and the largest errors were associated with the low flow characteristics. Discharge measurements made at the eight sites near midmonth each month during 1981 were used to estimate monthly mean flows at the sites for that period. These measurements also were correlated with concurrent daily mean flows from eight operating gaging stations. The correlations provided estimates of mean monthly flows that compared reasonably well with those estimated by the regression analyses. (Author 's abstract)

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.

An approach to derive some simple empirical equations to calibrate nuclear and acoustic well logging tools.

PubMed

Mohammad Al Alfy, Ibrahim

2018-01-01

A set of three pads was constructed from primary materials (sand, gravel and cement) to calibrate the gamma-gamma density tool. A simple equation was devised to convert the qualitative cps values to quantitative g/cc values. The neutron-neutron porosity tool measures the qualitative cps porosity values. A direct equation was derived to calculate the porosity percentage from the cps porosity values. Cement-bond log illustrates the cement quantities, which surround well pipes. This log needs a difficult process due to the existence of various parameters, such as: drilling well diameter as well as internal diameter, thickness and type of well pipes. An equation was invented to calculate the cement percentage at standard conditions. This equation can be modified according to varying conditions. Copyright © 2017 Elsevier Ltd. All rights reserved.

Expressions of the fundamental equation of gradient elution and a numerical solution of these equations under any gradient profile.

PubMed

Nikitas, P; Pappa-Louisi, A

2005-09-01

The original work carried out by Freiling and Drake in gradient liquid chromatography is rewritten in the current language of reversed-phase liquid chromatography. This allows for the rigorous derivation of the fundamental equation for gradient elution and the development of two alternative expressions of this equation, one of which is free from the constraint that the holdup time must be constant. In addition, the above derivation results in a very simple numerical solution of the various equations of gradient elution under any gradient profile. The theory was tested using eight catechol-related solutes in mobile phases modified with methanol, acetonitrile, or 2-propanol. It was found to be a satisfactory prediction of solute gradient retention behavior even if we used a simple linear description for the isocratic elution of these solutes.

Catmull-Rom Curve Fitting and Interpolation Equations

ERIC Educational Resources Information Center

Jerome, Lawrence

2010-01-01

Computer graphics and animation experts have been using the Catmull-Rom smooth curve interpolation equations since 1974, but the vector and matrix equations can be derived and simplified using basic algebra, resulting in a simple set of linear equations with constant coefficients. A variety of uses of Catmull-Rom interpolation are demonstrated,…

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.

Estimating peak-flow frequency statistics for selected gaged and ungaged sites in naturally flowing streams and rivers in Idaho

USGS Publications Warehouse

Wood, Molly S.; Fosness, Ryan L.; Skinner, Kenneth D.; Veilleux, Andrea G.

2016-06-27

The U.S. Geological Survey, in cooperation with the Idaho Transportation Department, updated regional regression equations to estimate peak-flow statistics at ungaged sites on Idaho streams using recent streamflow (flow) data and new statistical techniques. Peak-flow statistics with 80-, 67-, 50-, 43-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities (1.25-, 1.50-, 2.00-, 2.33-, 5.00-, 10.0-, 25.0-, 50.0-, 100-, 200-, and 500-year recurrence intervals, respectively) were estimated for 192 streamgages in Idaho and bordering States with at least 10 years of annual peak-flow record through water year 2013. The streamgages were selected from drainage basins with little or no flow diversion or regulation. The peak-flow statistics were estimated by fitting a log-Pearson type III distribution to records of annual peak flows and applying two additional statistical methods: (1) the Expected Moments Algorithm to help describe uncertainty in annual peak flows and to better represent missing and historical record; and (2) the generalized Multiple Grubbs Beck Test to screen out potentially influential low outliers and to better fit the upper end of the peak-flow distribution. Additionally, a new regional skew was estimated for the Pacific Northwest and used to weight at-station skew at most streamgages. The streamgages were grouped into six regions (numbered 1_2, 3, 4, 5, 6_8, and 7, to maintain consistency in region numbering with a previous study), and the estimated peak-flow statistics were related to basin and climatic characteristics to develop regional regression equations using a generalized least squares procedure. Four out of 24 evaluated basin and climatic characteristics were selected for use in the final regional peak-flow regression equations.Overall, the standard error of prediction for the regional peak-flow regression equations ranged from 22 to 132 percent. Among all regions, regression model fit was best for region 4 in west-central Idaho (average standard error of prediction=46.4 percent; pseudo-R2>92 percent) and region 5 in central Idaho (average standard error of prediction=30.3 percent; pseudo-R2>95 percent). Regression model fit was poor for region 7 in southern Idaho (average standard error of prediction=103 percent; pseudo-R2<78 percent) compared to other regions because few streamgages in region 7 met the criteria for inclusion in the study, and the region’s semi-arid climate and associated variability in precipitation patterns causes substantial variability in peak flows.A drainage area ratio-adjustment method, using ratio exponents estimated using generalized least-squares regression, was presented as an alternative to the regional regression equations if peak-flow estimates are desired at an ungaged site that is close to a streamgage selected for inclusion in this study. The alternative drainage area ratio-adjustment method is appropriate for use when the drainage area ratio between the ungaged and gaged sites is between 0.5 and 1.5.The updated regional peak-flow regression equations had lower total error (standard error of prediction) than all regression equations presented in a 1982 study and in four of six regions presented in 2002 and 2003 studies in Idaho. A more extensive streamgage screening process used in the current study resulted in fewer streamgages used in the current study than in the 1982, 2002, and 2003 studies. Fewer streamgages used and the selection of different explanatory variables were likely causes of increased error in some regions compared to previous studies, but overall, regional peak‑flow regression model fit was generally improved for Idaho. The revised statistical procedures and increased streamgage screening applied in the current study most likely resulted in a more accurate representation of natural peak-flow conditions.The updated, regional peak-flow regression equations will be integrated in the U.S. Geological Survey StreamStats program to allow users to estimate basin and climatic characteristics and peak-flow statistics at ungaged locations of interest. StreamStats estimates peak-flow statistics with quantifiable certainty only when used at sites with basin and climatic characteristics within the range of input variables used to develop the regional regression equations. Both the regional regression equations and StreamStats should be used to estimate peak-flow statistics only in naturally flowing, relatively unregulated streams without substantial local influences to flow, such as large seeps, springs, or other groundwater-surface water interactions that are not widespread or characteristic of the respective region.

Equations for predicting biomass in 2- to 6-year-old Eucalyptus saligna in Hawaii

Treesearch

Craig D. Whitesell; Susan C. Miyasaka; Robert F. Strand; Thomas H. Schubert; Katharine E. McDuffie

1988-01-01

Eucalyptus saligna trees grown in short-rotation plantations on the island of Hawaii were measured, harvested, and weighed to provide data for developing regression equations using non-destructive stand measurements. Regression analysis of the data from 190 trees in the 2.0- to 3.5-year range and 96 trees in the 4- to 6-year range related stem-only...

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 (...

Regression Levels of Selected Affective Factors on Science Achievement: A Structural Equation Model with TIMSS 2011 Data

ERIC Educational Resources Information Center

Akilli, Mustafa

2015-01-01

The aim of this study is to demonstrate the science success regression levels of chosen emotional features of 8th grade students using Structural Equation Model. The study was conducted by the analysis of students' questionnaires and science success in TIMSS 2011 data using SEM. Initially, the factors that are thought to have an effect on science…

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.

Regression equations for estimating concentrations of selected water-quality constituents for selected gaging stations in the Red River of the North Basin, North Dakota, Minnesota, and South Dakota

USGS Publications Warehouse

Williams-Sether, Tara

2004-01-01

The Dakota Water Resources Act, passed by the U.S. Congress on December 15, 2000, authorized the Secretary of the Interior to conduct a comprehensive study of future water-quantity and quality needs of the Red River of the North Basin in North Dakota and possible options to meet those water needs. Previous Red River of the North Basin studies conducted by the Bureau of Reclamation used streamflow and water-quality data bases developed by the U.S. Geological Survey that included data for 1931-84. As a result of the recent congressional authorization and results of previous studies by the Bureau of Reclamation, redevelopment of the streamflow and water-quality data bases with current data through 1999 are needed in order to evaluate and predict the water-quantity and quality effects within the Red River of the North Basin. This report provides updated statistical summaries of selected water-quality constituents and streamflow and the regression relations between them.  Available data for 1931-99 were used to develop regression equations between 5 selected water-quality constituents and streamflow for 38 gaging stations in the Red River of the North Basin. The water-quality constituents that were regressed against streamflow were hardness (as CaCO3), sodium, chloride, sulfate, and dissolved solids. Statistical summaries of the selected water-quality constituents and streamflow for the gaging stations used in the regression equations development and the applications and limitations of the regression equations are presented in this report.

Numerical study of centrifugal compressor stage vaneless diffusers

NASA Astrophysics Data System (ADS)

Galerkin, Y.; Soldatova, K.; Solovieva, O.

2015-08-01

The authors analyzed CFD calculations of flow in vaneless diffusers with relative width in range from 0.014 to 0.100 at inlet flow angles in range from 100 to 450 with different inlet velocity coefficients, Reynolds numbers and surface roughness. The aim is to simulate calculated performances by simple algebraic equations. The friction coefficient that represents head losses as friction losses is proposed for simulation. The friction coefficient and loss coefficient are directly connected by simple equation. The advantage is that friction coefficient changes comparatively little in range of studied parameters. Simple equations for this coefficient are proposed by the authors. The simulation accuracy is sufficient for practical calculations. To create the complete algebraic model of the vaneless diffuser the authors plan to widen this method of modeling to diffusers with different relative length and for wider range of Reynolds numbers.

5 CFR 1315.17 - Formulas.

Code of Federal Regulations, 2010 CFR

2010-01-01

...) Daily simple interest formula. (1) To calculate daily simple interest the following formula may be used... a payment is due on April 1 and the payment is not made until April 11, a simple interest... equation calculates simple interest on any additional days beyond a monthly increment. (3) For example, if...

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.

A Unified Approach to Teaching Quadratic and Cubic Equations.

ERIC Educational Resources Information Center

Ward, A. J. B.

2003-01-01

Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)

Estimating linear temporal trends from aggregated environmental monitoring data

USGS Publications Warehouse

Erickson, Richard A.; Gray, Brian R.; Eager, Eric A.

2017-01-01

Trend estimates are often used as part of environmental monitoring programs. These trends inform managers (e.g., are desired species increasing or undesired species decreasing?). Data collected from environmental monitoring programs is often aggregated (i.e., averaged), which confounds sampling and process variation. State-space models allow sampling variation and process variations to be separated. We used simulated time-series to compare linear trend estimations from three state-space models, a simple linear regression model, and an auto-regressive model. We also compared the performance of these five models to estimate trends from a long term monitoring program. We specifically estimated trends for two species of fish and four species of aquatic vegetation from the Upper Mississippi River system. We found that the simple linear regression had the best performance of all the given models because it was best able to recover parameters and had consistent numerical convergence. Conversely, the simple linear regression did the worst job estimating populations in a given year. The state-space models did not estimate trends well, but estimated population sizes best when the models converged. We found that a simple linear regression performed better than more complex autoregression and state-space models when used to analyze aggregated environmental monitoring data.

Magnitude, frequency, and trends of floods at gaged and ungaged sites in Washington, based on data through water year 2014

USGS Publications Warehouse

Mastin, Mark C.; Konrad, Christopher P.; Veilleux, Andrea G.; Tecca, Alison E.

2016-09-20

An investigation into the magnitude and frequency of floods in Washington State computed the annual exceedance probability (AEP) statistics for 648 U.S. Geological Survey unregulated streamgages in and near the borders of Washington using the recorded annual peak flows through water year 2014. This is an updated report from a previous report published in 1998 that used annual peak flows through the water year 1996. New in this report, a regional skew coefficient was developed for the Pacific Northwest region that includes areas in Oregon, Washington, Idaho and western Montana within the Columbia River drainage basin south of the United States-Canada border, the coastal areas of Oregon and western Washington, and watersheds draining into Puget Sound, Washington. The skew coefficient is an important term in the Log Pearson Type III equation used to define the distribution of the log-transformed annual peaks. The Expected Moments Algorithm was used to fit historical and censored peak-flow data to the log Pearson Type III distribution. A Multiple Grubb-Beck test was employed to censor low outliers of annual peak flows to improve on the frequency distribution. This investigation also includes a section on observed trends in annual peak flows that showed significant trends (p-value < 0.05) in 21 of 83 long-term sites, but with small magnitude Kendall tau values suggesting a limited monotonic trend in the time series of annual peaks. Most of the sites with a significant trend in western Washington were positive and all the sites with significant trends (three sites) in eastern Washington were negative.Multivariate regression analysis with measured basin characteristics and the AEP statistics at long-term, unregulated, and un-urbanized (defined as drainage basins with less than 5 percent impervious land cover for this investigation) streamgages within Washington and some in Idaho and Oregon that are near the Washington border was used to develop equations to estimate AEP statistics at ungaged basins. Washington was divided into four regions to improve the accuracy of the regression equations; a set of equations for eight selected AEPs and for each region were constructed. Selected AEP statistics included the annual peak flows that equaled or exceeded 50, 20, 10, 4, 2, 1, 0.5 and 0.2 percent of the time equivalent to peak flows for peaks with a 2-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-year recurrence intervals, respectively. Annual precipitation and drainage area were the significant basin characteristics in the regression equations for all four regression regions in Washington and forest cover was significant for the two regression regions in eastern Washington. Average standard error of prediction for the regional regression equations ranged from 70.19 to 125.72 percent for Regression Regions 1 and 2 on the eastern side of the Cascade Mountains and from 43.22 to 58.04 percent for Regression Regions 3 and 4 on the western side of the Cascade Mountains. The pseudo coefficient of determination (where a value of 100 signifies a perfect regression model) ranged from 68.39 to 90.68 for Regression Regions 1 and 2, and 92.35 to 95.44 for Regions 3 and 4.The calculated AEP statistics for the streamgages and the regional regression equations are expected to be incorporated into StreamStats after the publication of this report. StreamStats is the interactive Web-based map tool created by the U.S. Geological Survey to allow the user to choose a streamgage and obtain published statistics or choose ungaged locations where the program automatically applies the regional regression equations and computes the estimates of the AEP statistics.

Regional regression equations for estimation of natural streamflow statistics in Colorado

USGS Publications Warehouse

Capesius, Joseph P.; Stephens, Verlin C.

2009-01-01

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

Echocardiographic estimation of left atrial pressure in beagle dogs with experimentally-induced mitral valve regurgitation.

PubMed

Ishikawa, Taisuke; Fukushima, Ryuji; Suzuki, Shuji; Miyaishi, Yuka; Nishimura, Taiki; Hira, Satoshi; Hamabe, Lina; Tanaka, Ryou

2011-08-01

Non-invasive and immediate estimation of left atrial pressure (LAP) is very useful for the management of mitral regurgitation (MR), and many reports have assessed echocardiographic estimations of LAP to date. However, it has been unclear of which examination and evaluate article possess the best accuracy for the MR severity. The present research aims to establish the echocardiographic estimation equation of LAP that is well applicable for clinical MR dogs. After the chordae tendineae rupture was experimentally induced via left atriotomy in six healthy beagle dogs (three males and three females, two years old, weighing between 9.8 to 12.8 kg), a radio telemetry transmitter catheter was inserted, which allows the continuous recordings of LAP without the use of sedation. Approximately 5 weeks after the surgery, echocardiographic examination, indirect blood pressure measurement, measurement of plasma atrial natriuretic peptide (ANP) and LAP measurement by way of the radio telemetry system was performed simultaneously. Subsequently, simple linear regression equations between LAP and each variable were obtained, and the equations were evaluated whether to be applicable for clinical MR dogs. As a result, the ratio of early diastolic mitral flow to early diastolic lateral mitral annulus velocity (E/Ea) had the strongest correlation as maximum LAP=7.03*(E/Ea)-54.86 (r=0.74), and as mean LAP=4.94*(E/Ea)-40.37 (r=0.70) among the all variables. Therefore, these two equations associated with E/Ea should bring more precise and instant estimations of maximum and mean LAP in clinical MR dogs.

Development of regression equations to revise estimates of historical streamflows for the St. Croix River at Stillwater, Minnesota (water years 1910-2011), and Prescott, Wisconsin (water years 1910-2007)

USGS Publications Warehouse

Ziegeweid, Jeffrey R.; Magdalene, Suzanne

2015-01-01

The new regression equations were used to calculate revised estimates of historical streamflows for Stillwater and Prescott starting in 1910 and ending when index-velocity streamgages were installed. Monthly, annual, 30-year, and period of record statistics were examined between previous and revised estimates of historical streamflows. The abilities of the new regression equations to estimate historical streamflows were evaluated by using percent differences to compare new estimates of historical daily streamflows to discrete streamflow measurements made at Stillwater and Prescott before the installation of index-velocity streamgages. Although less variability was observed between estimated and measured streamflows at Stillwater compared to Prescott, the percent difference data indicated that the new estimates closely approximated measured streamflows at both locations.

The Hartman-Grobman theorem for semilinear hyperbolic evolution equations

NASA Astrophysics Data System (ADS)

Hein, Marie-Luise; Prüss, Jan

2016-10-01

The famous Hartman-Grobman theorem for ordinary differential equations is extended to abstract semilinear hyperbolic evolution equations in Banach spaces by means of simple direct proof. It is also shown that the linearising map is Hölder continuous. Several applications to abstract and specific damped wave equations are given, to demonstrate the strength of our results.

Cable logging production rate equations for thinning young-growth Douglas-fir

Treesearch

Chris B. LeDoux; Lawson W. Starnes

1986-01-01

A cable logging thinning simulation model and field study data from cable thinning production studies have been assembled and converted into a set of simple equations. These equations can be used to estimate the hourly production rates of various cable thinning machines operating in the mountainous terrain of western Oregon and western Washington. The equations include...

Use of the forced-oscillation technique to estimate spirometry values.

PubMed

Yamamoto, Shoichiro; Miyoshi, Seigo; Katayama, Hitoshi; Okazaki, Mikio; Shigematsu, Hisayuki; Sano, Yoshifumi; Matsubara, Minoru; Hamaguchi, Naohiko; Okura, Takafumi; Higaki, Jitsuo

2017-01-01

Spirometry is sometimes difficult to perform in elderly patients and in those with severe respiratory distress. The forced-oscillation technique (FOT) is a simple and noninvasive method of measuring respiratory impedance. The aim of this study was to determine if FOT data reflect spirometric indices. Patients underwent both FOT and spirometry procedures prior to inclusion in development (n=1,089) and validation (n=552) studies. Multivariate linear regression analysis was performed to identify FOT parameters predictive of vital capacity (VC), forced VC (FVC), and forced expiratory volume in 1 second (FEV 1 ). A regression equation was used to calculate estimated VC, FVC, and FEV 1 . We then determined whether the estimated data reflected spirometric indices. Agreement between actual and estimated spirometry data was assessed by Bland-Altman analysis. Significant correlations were observed between actual and estimated VC, FVC, and FEV 1 values (all r >0.8 and P <0.001). These results were deemed robust by a separate validation study (all r >0.8 and P <0.001). Bias between the actual data and estimated data for VC, FVC, and FEV 1 in the development study was 0.007 L (95% limits of agreement [LOA] 0.907 and -0.893 L), -0.064 L (95% LOA 0.843 and -0.971 L), and -0.039 L (95% LOA 0.735 and -0.814 L), respectively. On the other hand, bias between the actual data and estimated data for VC, FVC, and FEV 1 in the validation study was -0.201 L (95% LOA 0.62 and -1.022 L), -0.262 L (95% LOA 0.582 and -1.106 L), and -0.174 L (95% LOA 0.576 and -0.923 L), respectively, suggesting that the estimated data in the validation study did not have high accuracy. Further studies are needed to generate more accurate regression equations for spirometric indices based on FOT measurements.

Adjustment of ionized calcium concentration for serum pH is not a valid marker of calcium homeostasis: implications for identifying individuals at risk of calcium metabolic disorders.

PubMed

Lam, Virginie; Dhaliwal, Satvinder S; Mamo, John C

2013-05-01

Ionized calcium (iCa) is the biologically active form of this micronutrient. Serum determination of iCa is measured via ion-electrode potentiometry (IEP) and reporting iCa relative to pH 7.4 is normally utilized to avoid the potential confounding effects of ex vivo changes to serum pH. Adjustment of iCa for pH has not been adequately justified. In this study, utilizing carefully standardized protocols for blood collection, the preparation of serum and controlling time of collection-to-analysis, we determined serum iCa and pH utilizing an IEP-analyser hosted at an accredited diagnostic laboratory. Regression analysis of unadjusted-iCa (iCa(raw)) concentration versus pH was described by linear regression and accounted for 37% of serum iCa(raw) variability. iCa(raw) was then expressed at pH 7.4 by either adjusting iCa(raw) based on the linear regression equation describing the association of iCa with serum pH (iCa(regr)) or using IEP coded published normative equations (iCa(pub)). iCa(regr) was comparable to iCa(raw), indicating that blood collection and processing methodologies were sound. However, iCa(pub) yielded values that were significantly lower than iCa(raw). iCa(pub) did not identify 15% subjects who had greater than desirable serum concentration of iCa based on iCa(raw). Sixty percent of subjects with low levels of iCa(raw) were also not detected by iCa(pub). Determination of the kappa value measure of agreement for iCa(raw) versus iCa(pub) showed relatively poor concordance (κ = 0.42). With simple protocols that avoid sampling artefacts, expressing iCa(raw) is likely to be a more valid and physiologically relevant marker of calcium homeostasis than is iCa(pub).

Exact Analysis of Squared Cross-Validity Coefficient in Predictive Regression Models

ERIC Educational Resources Information Center

Shieh, Gwowen

2009-01-01

In regression analysis, the notion of population validity is of theoretical interest for describing the usefulness of the underlying regression model, whereas the presumably more important concept of population cross-validity represents the predictive effectiveness for the regression equation in future research. It appears that the inference…

Symmetries and Special Solutions of Reductions of the Lattice Potential KdV Equation

NASA Astrophysics Data System (ADS)

Ormerod, Christopher M.

2014-01-01

We identify a periodic reduction of the non-autonomous lattice potential Korteweg-de Vries equation with the additive discrete Painlevé equation with E_6^{(1)} symmetry. We present a description of a set of symmetries of the reduced equations and their relations to the symmetries of the discrete Painlevé equation. Finally, we exploit the simple symmetric form of the reduced equations to find rational and hypergeometric solutions of this discrete Painlevé equation.

Predicting tropical cyclone intensity using satellite measured equivalent blackbody temperatures of cloud tops. [regression analysis

NASA Technical Reports Server (NTRS)

Gentry, R. C.; Rodgers, E.; Steranka, J.; Shenk, W. E.

1978-01-01

A regression technique was developed to forecast 24 hour changes of the maximum winds for weak (maximum winds less than or equal to 65 Kt) and strong (maximum winds greater than 65 Kt) tropical cyclones by utilizing satellite measured equivalent blackbody temperatures around the storm alone and together with the changes in maximum winds during the preceding 24 hours and the current maximum winds. Independent testing of these regression equations shows that the mean errors made by the equations are lower than the errors in forecasts made by the peristence techniques.

A general relaxation theory of simple liquids

NASA Technical Reports Server (NTRS)

Merilo, M.; Morgan, E. J.

1973-01-01

A relatively simple relaxation theory to account for the behavior of liquids under dynamic conditions was proposed. The general dynamical equations are similar in form to the phenomenological relaxation equations used in theories of viscoelasticity, however, they differ in that all the coefficients of the present equations are expressed in terms of thermodynamic and molecular quantities. The theory is based on the concept that flow in a liquid distorts both the radial and the velocity distribution functions, and that relaxation equations describing the return of these functions to their isotropic distributions, characterizing a stationary liquid, can be written. The theory was applied to the problems of steady and oscillatory shear flows and to the propagation of longitudinal waves. In all cases classical results are predicted for strain rates, and an expression for the viscosity of a liquid, simular to the Macedo-Litovitz equation, is obtained.

Quantized Algebra I Texts

NASA Astrophysics Data System (ADS)

DeBuvitz, William

2014-03-01

I am a volunteer reader at the Princeton unit of "Learning Ally" (formerly "Recording for the Blind & Dyslexic") and I recently discovered that high school students are introduced to the concept of quantization well before they take chemistry and physics. For the past few months I have been reading onto computer files a popular Algebra I textbook, and I was surprised and dismayed by how it treated simultaneous equations and quadratic equations. The coefficients are always simple integers in examples and exercises, even when they are related to physics. This is probably a good idea when these topics are first presented to the students. It makes it easy to solve simultaneous equations by the method of elimination of a variable. And it makes it easy to solve some quadratic equations by factoring. The textbook also discusses the method of substitution for linear equations and the use of the quadratic formula, but only with simple integers.

Methods for estimating the magnitude and frequency of floods for urban and small, rural streams in Georgia, South Carolina, and North Carolina, 2011

USGS Publications Warehouse

Feaster, Toby D.; Gotvald, Anthony J.; Weaver, J. Curtis

2014-01-01

Reliable estimates of the magnitude and frequency of floods are essential for the design of transportation and water-conveyance structures, flood-insurance studies, and flood-plain management. Such estimates are particularly important in densely populated urban areas. In order to increase the number of streamflow-gaging stations (streamgages) available for analysis, expand the geographical coverage that would allow for application of regional regression equations across State boundaries, and build on a previous flood-frequency investigation of rural U.S Geological Survey streamgages in the Southeast United States, a multistate approach was used to update methods for determining the magnitude and frequency of floods in urban and small, rural streams that are not substantially affected by regulation or tidal fluctuations in Georgia, South Carolina, and North Carolina. The at-site flood-frequency analysis of annual peak-flow data for urban and small, rural streams (through September 30, 2011) included 116 urban streamgages and 32 small, rural streamgages, defined in this report as basins draining less than 1 square mile. The regional regression analysis included annual peak-flow data from an additional 338 rural streamgages previously included in U.S. Geological Survey flood-frequency reports and 2 additional rural streamgages in North Carolina that were not included in the previous Southeast rural flood-frequency investigation for a total of 488 streamgages included in the urban and small, rural regression analysis. The at-site flood-frequency analyses for the urban and small, rural streamgages included the expected moments algorithm, which is a modification of the Bulletin 17B log-Pearson type III method for fitting the statistical distribution to the logarithms of the annual peak flows. Where applicable, the flood-frequency analysis also included low-outlier and historic information. Additionally, the application of a generalized Grubbs-Becks test allowed for the detection of multiple potentially influential low outliers. Streamgage basin characteristics were determined using geographical information system techniques. Initial ordinary least squares regression simulations reduced the number of basin characteristics on the basis of such factors as statistical significance, coefficient of determination, Mallow’s Cp statistic, and ease of measurement of the explanatory variable. Application of generalized least squares regression techniques produced final predictive (regression) equations for estimating the 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probability flows for urban and small, rural ungaged basins for three hydrologic regions (HR1, Piedmont–Ridge and Valley; HR3, Sand Hills; and HR4, Coastal Plain), which previously had been defined from exploratory regression analysis in the Southeast rural flood-frequency investigation. Because of the limited availability of urban streamgages in the Coastal Plain of Georgia, South Carolina, and North Carolina, additional urban streamgages in Florida and New Jersey were used in the regression analysis for this region. Including the urban streamgages in New Jersey allowed for the expansion of the applicability of the predictive equations in the Coastal Plain from 3.5 to 53.5 square miles. Average standard error of prediction for the predictive equations, which is a measure of the average accuracy of the regression equations when predicting flood estimates for ungaged sites, range from 25.0 percent for the 10-percent annual exceedance probability regression equation for the Piedmont–Ridge and Valley region to 73.3 percent for the 0.2-percent annual exceedance probability regression equation for the Sand Hills region.

Correcting the initialization of models with fractional derivatives via history-dependent conditions

NASA Astrophysics Data System (ADS)

Du, Maolin; Wang, Zaihua

2016-04-01

Fractional differential equations are more and more used in modeling memory (history-dependent, non-local, or hereditary) phenomena. Conventional initial values of fractional differential equations are defined at a point, while recent works define initial conditions over histories. We prove that the conventional initialization of fractional differential equations with a Riemann-Liouville derivative is wrong with a simple counter-example. The initial values were assumed to be arbitrarily given for a typical fractional differential equation, but we find one of these values can only be zero. We show that fractional differential equations are of infinite dimensions, and the initial conditions, initial histories, are defined as functions over intervals. We obtain the equivalent integral equation for Caputo case. With a simple fractional model of materials, we illustrate that the recovery behavior is correct with the initial creep history, but is wrong with initial values at the starting point of the recovery. We demonstrate the application of initial history by solving a forced fractional Lorenz system numerically.

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.

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.

Temperature-viscosity models reassessed.

PubMed

Peleg, Micha

2017-05-04

The temperature effect on viscosity of liquid and semi-liquid foods has been traditionally described by the Arrhenius equation, a few other mathematical models, and more recently by the WLF and VTF (or VFT) equations. The essence of the Arrhenius equation is that the viscosity is proportional to the absolute temperature's reciprocal and governed by a single parameter, namely, the energy of activation. However, if the absolute temperature in K in the Arrhenius equation is replaced by T + b where both T and the adjustable b are in °C, the result is a two-parameter model, which has superior fit to experimental viscosity-temperature data. This modified version of the Arrhenius equation is also mathematically equal to the WLF and VTF equations, which are known to be equal to each other. Thus, despite their dissimilar appearances all three equations are essentially the same model, and when used to fit experimental temperature-viscosity data render exactly the same very high regression coefficient. It is shown that three new hybrid two-parameter mathematical models, whose formulation bears little resemblance to any of the conventional models, can also have excellent fit with r 2 ∼ 1. This is demonstrated by comparing the various models' regression coefficients to published viscosity-temperature relationships of 40% sucrose solution, soybean oil, and 70°Bx pear juice concentrate at different temperature ranges. Also compared are reconstructed temperature-viscosity curves using parameters calculated directly from 2 or 3 data points and fitted curves obtained by nonlinear regression using a larger number of experimental viscosity measurements.

Binary dislocation junction formation and strength in hexagonal close-packed crystals

DOE PAGES

Wu, Chi -Chin; Aubry, Sylvie; Arsenlis, Athanasios; ...

2015-12-17

This work examines binary dislocation interactions, junction formation and junction strengths in hexagonal close-packed ( hcp ) crystals. Through a line-tension model and dislocation dynamics (DD) simulations, the interaction and dissociation of different sets of binary junctions are investigated involving one dislocation on the (011¯0) prismatic plane and a second dislocation on one of the following planes: (0001) basal, (11¯00) prismatic, (11¯01) primary pyramidal, or (2¯112) secondary pyramidal. Varying pairs of Burgers vectors are chosen from among the common types the basal type < a > 1/3 < 112¯0 >, prismatic type < c > <0001>, and pyramidal type 1/3 < 112¯3¯ >. For binary interaction due to dislocation intersection, both the analytical results and DD-simulations indicate a relationship between symmetry of interaction maps and the relative magnitude of the Burgers vectors that constitute the junction. Using analytical formulae, a simple regressive model is also developed to represent the junction yield surface. The equation is treated as a degenerated super elliptical equation to quantify the aspect ratio and tilting angle. Lastly, the results provide analytical insights on binary dislocation interactions that may occur in general hcp metals.« less

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…

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

USGS Publications Warehouse

Southard, Rodney E.

2010-01-01

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

Hawaii StreamStats; a web application for defining drainage-basin characteristics and estimating peak-streamflow statistics

USGS Publications Warehouse

Rosa, Sarah N.; Oki, Delwyn S.

2010-01-01

Reliable estimates of the magnitude and frequency of floods are necessary for the safe and efficient design of roads, bridges, water-conveyance structures, and flood-control projects and for the management of flood plains and flood-prone areas. StreamStats provides a simple, fast, and reproducible method to define drainage-basin characteristics and estimate the frequency and magnitude of peak discharges in Hawaii?s streams using recently developed regional regression equations. StreamStats allows the user to estimate the magnitude of floods for streams where data from stream-gaging stations do not exist. Existing estimates of the magnitude and frequency of peak discharges in Hawaii can be improved with continued operation of existing stream-gaging stations and installation of additional gaging stations for areas where limited stream-gaging data are available.

The 3-year disease management effect: understanding the positive return on investment.

PubMed

Nyman, John A; Jeffery, Molly Moore; Abraham, Jean M; Jutkowitz, Eric; Dowd, Bryan E

2013-11-01

Conventional wisdom suggests that health promotion programs yield a positive return on investment (ROI) in year 3. In the case of the University of Minnesota's program, a positive ROI was achieved in the third year, but it was due entirely to the effectiveness of the disease management (DM) program. The objective of this study is to investigate why. Differences-in-differences regression equations were estimated to determine the effect of DM participation on spending (overall and service specific), hospitalizations, and avoidable hospitalizations. Disease management participation reduced expenditures overall, and especially in the third year for employees, and reduced hospitalizations and avoidable hospitalizations. The positive ROI at Minnesota was due to increased effectiveness of DM in the third year (mostly due to fewer hospitalizations) but also to the simple durability of the average DM effect.

Quantitative analysis of matrine in liquid crystalline nanoparticles by HPLC.

PubMed

Peng, Xinsheng; Li, Baohong; Hu, Min; Ling, Yahao; Tian, Yuan; Zhou, Yanxing; Zhou, Yanfang

2014-01-01

A reversed-phase high-performance liquid chromatographic method has been developed to quantitatively determine matrine in liquid crystal nanoparticles. The chromatographic method is carried out using an isocratic system. The mobile phase was composed of methanol-PBS(pH6.8)-triethylamine (50 : 50 : 0.1%) with a flow rate of 1 mL/min with SPD-20A UV/vis detector and the detection wavelength was at 220 nm. The linearity of matrine is in the range of 1.6 to 200.0  μ g/mL. The regression equation is y = 10706x - 2959 (R (2) = 1.0). The average recovery is 101.7%; RSD = 2.22%  (n = 9). This method provides a simple and accurate strategy to determine matrine in liquid crystalline nanoparticle.

Remote sensing of biomass and annual net aerial primary productivity of a salt marsh

NASA Technical Reports Server (NTRS)

Hardisky, M. A.; Klemas, V.; Daiber, F. C.; Roman, C. T.

1984-01-01

Net aerial primary productivity is the rate of storage of organic matter in above-ground plant issues exceeding the respiratory use by the plants during the period of measurement. It is pointed out that this plant tissue represents the fixed carbon available for transfer to and consumption by the heterotrophic organisms in a salt marsh or the estuary. One method of estimating annual net aerial primary productivity (NAPP) required multiple harvesting of the marsh vegetation. A rapid nondestructive remote sensing technique for estimating biomass and NAPP would, therefore, be a significant asset. The present investigation was designed to employ simple regression models, equating spectral radiance indices with Spartina alterniflora biomass to nondestructively estimate salt marsh biomass. The results of the study showed that the considered approach can be successfully used to estimate salt marsh biomass.

Remote Sensing of Coastal Wetlands Biomass Using Thematic Mapper Wavebands. [Lewes, Delaware

NASA Technical Reports Server (NTRS)

Hardisky, M. A.; Klemas, V.

1985-01-01

Spectral data, simulating thematic mapper bands 3, 4 and 5 were gathered in salt and brackish marshes using a hand-held radiometer. Simple regression models were developed equating spectral radiance indicies with total live biomass for S. alterniflora in a salt marsh and for a variety of plant species in a brackish marsh. Models were then tested and compared to harvest estimates of biomass. In the salt marsh, biomass estimates from spectral data were similar to harvest biomass estimates during most of the growing season. Estimates of annual net aerial primary productivity calculated from spectral data were within 21% of production estimated from harvest data. During August, biomass estimates from spectral data in the brackish marsh were similar to biomass estimated by harvesting techniques but not always comparable at other times in the growing season.

Direct localization of poles of a meromorphic function from measurements on an incomplete boundary

NASA Astrophysics Data System (ADS)

Nara, Takaaki; Ando, Shigeru

2010-01-01

This paper proposes an algebraic method to reconstruct the positions of multiple poles in a meromorphic function field from measurements on an arbitrary simple arc in it. A novel issue is the exactness of the algorithm depending on whether the arc is open or closed, and whether it encloses or does not enclose the poles. We first obtain a differential equation that can equivalently determine the meromorphic function field. From it, we derive linear equations that relate the elementary symmetric polynomials of the pole positions to weighted integrals of the field along the simple arc and end-point terms of the arc when it is an open one. Eliminating the end-point terms based on an appropriate choice of weighting functions and a combination of the linear equations, we obtain a simple system of linear equations for solving the elementary symmetric polynomials. We also show that our algorithm can be applied to a 2D electric impedance tomography problem. The effects of the proximity of the poles, the number of measurements and noise on the localization accuracy are numerically examined.

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

PubMed

Gurka, Matthew J; Kuperminc, Michelle N; Busby, Marjorie G; Bennis, Jacey A; Grossberg, Richard I; Houlihan, Christine M; Stevenson, Richard D; Henderson, Richard C

2010-02-01

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). 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. 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. 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.

Cost evaluation of clinical laboratory in Taiwan's National Health System by using activity-based costing.

PubMed

Su, Bin-Guang; Chen, Shao-Fen; Yeh, Shu-Hsing; Shih, Po-Wen; Lin, Ching-Chiang

2016-11-01

To cope with the government's policies to reduce medical costs, Taiwan's healthcare service providers are striving to survive by pursuing profit maximization through cost control. This article aimed to present the results of cost evaluation using activity-based costing performed in the laboratory in order to throw light on the differences between costs and the payment system of National Health Insurance (NHI). This study analyzed the data of costs and income of the clinical laboratory. Direct costs belong to their respective sections of the department. The department's shared costs, including public expenses and administrative assigned costs, were allocated to the department's respective sections. A simple regression equation was created to predict profit and loss, and evaluate the department's break-even point, fixed cost, and contribution margin ratio. In clinical chemistry and seroimmunology sections, the cost per test was lower than the NHI payment and their major laboratory tests had revenues with the profitability ratio of 8.7%, while the other sections had a higher cost per test than the NHI payment and their major tests were in deficit. The study found a simple linear regression model as follows: "Balance=-84,995+0.543×income (R2=0.544)". In order to avoid deficit, laboratories are suggested to increase test volumes, enhance laboratory test specialization, and become marginal scale. A hospital could integrate with regional medical institutions through alliances or OEM methods to increase volumes to reach marginal scale and reduce laboratory costs, enhancing the level and quality of laboratory medicine.

Simple radiative transfer model for relationships between canopy biomass and reflectance

NASA Technical Reports Server (NTRS)

Park, J. K.; Deering, D. W.

1982-01-01

A modified Kubelka-Munk model has been utilized to derive useful equations for the analysis of apparent canopy reflectance. Based on the solution to the model simple working equations were formulated by employing reflectance characteristic parameters. The relationships derived show the asymptotic nature of reflectance data that is typically observed in remote sensing studies of plant biomass. They also establish the range of expected apparent canopy reflectance values for specific plant canopy types. The usefulness of the simplified equations was demonstrated by the exceptionally close fit of the theoretical curves to two separately acquired data sets for alfalfa and shortgrass prairie canopies.

A simple equation to estimate body fat percentage in children with overweightness or obesity: a retrospective study.

PubMed

Cortés-Castell, Ernesto; Juste, Mercedes; Palazón-Bru, Antonio; Monge, Laura; Sánchez-Ferrer, Francisco; Rizo-Baeza, María Mercedes

2017-01-01

Dual-energy X-ray absorptiometry (DXA) provides separate measurements of fat mass, fat-free mass and bone mass, and is a quick, accurate, and safe technique, yet one that is not readily available in routine clinical practice. Consequently, we aimed to develop statistical formulas to predict fat mass (%) and fat mass index (FMI) with simple parameters (age, sex, weight and height). We conducted a retrospective observational cross-sectional study in 416 overweight or obese patients aged 4-18 years that involved assessing adiposity by DXA (fat mass percentage and FMI), body mass index (BMI), sex and age. We randomly divided the sample into two parts (construction and validation). In the construction sample, we developed formulas to predict fat mass and FMI using linear multiple regression models. The formulas were validated in the other sample, calculating the intraclass correlation coefficient via bootstrapping. The fat mass percentage formula had a coefficient of determination of 0.65. This value was 0.86 for FMI. In the validation, the constructed formulas had an intraclass correlation coefficient of 0.77 for fat mass percentage and 0.92 for FMI. Our predictive formulas accurately predicted fat mass and FMI with simple parameters (BMI, sex and age) in children with overweight and obesity. The proposed methodology could be applied in other fields. Further studies are needed to externally validate these formulas.

Continuous water-quality monitoring and regression analysis to estimate constituent concentrations and loads in the Red River of the North, Fargo, North Dakota, 2003-05

USGS Publications Warehouse

Ryberg, Karen R.

2006-01-01

This report presents the results of a study by the U.S. Geological Survey, done in cooperation with the Bureau of Reclamation, U.S. Department of the Interior, to estimate water-quality constituent concentrations in the Red River of the North at Fargo, North Dakota. Regression analysis of water-quality data collected in 2003-05 was used to estimate concentrations and loads for alkalinity, dissolved solids, sulfate, chloride, total nitrite plus nitrate, total nitrogen, total phosphorus, and suspended sediment. The explanatory variables examined for regression relation were continuously monitored physical properties of water-streamflow, specific conductance, pH, water temperature, turbidity, and dissolved oxygen. For the conditions observed in 2003-05, streamflow was a significant explanatory variable for all estimated constituents except dissolved solids. pH, water temperature, and dissolved oxygen were not statistically significant explanatory variables for any of the constituents in this study. Specific conductance was a significant explanatory variable for alkalinity, dissolved solids, sulfate, and chloride. Turbidity was a significant explanatory variable for total phosphorus and suspended sediment. For the nutrients, total nitrite plus nitrate, total nitrogen, and total phosphorus, cosine and sine functions of time also were used to explain the seasonality in constituent concentrations. The regression equations were evaluated using common measures of variability, including R2, or the proportion of variability in the estimated constituent explained by the regression equation. R2 values ranged from 0.703 for total nitrogen concentration to 0.990 for dissolved-solids concentration. The regression equations also were evaluated by calculating the median relative percentage difference (RPD) between measured constituent concentration and the constituent concentration estimated by the regression equations. Median RPDs ranged from 1.1 for dissolved solids to 35.2 for total nitrite plus nitrate. Regression equations also were used to estimate daily constituent loads. Load estimates can be used by water-quality managers for comparison of current water-quality conditions to water-quality standards expressed as total maximum daily loads (TMDLs). TMDLs are a measure of the maximum amount of chemical constituents that a water body can receive and still meet established water-quality standards. The peak loads generally occurred in June and July when streamflow also peaked.

Regression model for estimating inactivation of microbial aerosols by solar radiation.

PubMed

Ben-David, Avishai; Sagripanti, Jose-Luis

2013-01-01

The inactivation of pathogenic aerosols by solar radiation is relevant to public health and biodefense. We investigated whether a relatively simple method to calculate solar diffuse and total irradiances could be developed and used in environmental photobiology estimations instead of complex atmospheric radiative transfer computer programs. The second-order regression model that we developed reproduced 13 radiation quantities calculated for equinoxes and solstices at 35(°) latitude with a computer-intensive and rather complex atmospheric radiative transfer program (MODTRAN) with a mean error <6% (2% for most radiation quantities). Extending the application of the regression model from a reference latitude and date (chosen as 35° latitude for 21 March) to different latitudes and days of the year was accomplished with variable success: usually with a mean error <15% (but as high as 150% for some combination of latitudes and days of year). This accuracy of the methodology proposed here compares favorably to photobiological experiments where the microbial survival is usually measured with an accuracy no better than ±0.5 log10 units. The approach and equations presented in this study should assist in estimating the maximum time during which microbial pathogens remain infectious after accidental or intentional aerosolization in open environments. © Published 2013. This article is a U.S. Government work and is in the public domain in the USA. Photochemistry and Photobiology © 2013 The American Society of Photobiology.

Flood characteristics of Alaskan streams

USGS Publications Warehouse

Lamke, R.D.

1979-01-01

Peak discharge data for Alaskan streams are summarized and analyzed. Multiple-regression equations relating peak discharge magnitude and frequency to climatic and physical characteristics of 260 gaged basins were determined in order to estimate average recurrence interval of floods at ungaged sites. These equations are for 1.25-, 2-, 5-, 10-, 25-, and 50-year average recurrence intervals. In this report, Alaska was divided into two regions, one having a maritime climate with fall and winter rains and floods, the other having spring and summer floods of a variety or combinations of causes. Average standard errors of the six multiple-regression equations for these two regions were 48 and 74 percent, respectively. Maximum recorded floods at more than 400 sites throughout Alaska are tabulated. Maps showing lines of equal intensity of the principal climatic variables found to be significant (mean annual precipitation and mean minimum January temperature), and location of the 260 sites used in the multiple-regression analyses are included. Little flood data have been collected in western and arctic Alaska, and the predictive equations are therefore less reliable for those areas. (Woodard-USGS)

A stochastic process approach of the drake equation parameters

NASA Astrophysics Data System (ADS)

Glade, Nicolas; Ballet, Pascal; Bastien, Olivier

2012-04-01

The number N of detectable (i.e. communicating) extraterrestrial civilizations in the Milky Way galaxy is usually calculated by using the Drake equation. This equation was established in 1961 by Frank Drake and was the first step to quantifying the Search for ExtraTerrestrial Intelligence (SETI) field. Practically, this equation is rather a simple algebraic expression and its simplistic nature leaves it open to frequent re-expression. An additional problem of the Drake equation is the time-independence of its terms, which for example excludes the effects of the physico-chemical history of the galaxy. Recently, it has been demonstrated that the main shortcoming of the Drake equation is its lack of temporal structure, i.e., it fails to take into account various evolutionary processes. In particular, the Drake equation does not provides any error estimation about the measured quantity. Here, we propose a first treatment of these evolutionary aspects by constructing a simple stochastic process that will be able to provide both a temporal structure to the Drake equation (i.e. introduce time in the Drake formula in order to obtain something like N(t)) and a first standard error measure.

Retro-regression--another important multivariate regression improvement.

PubMed

Randić, M

2001-01-01

We review the serious problem associated with instabilities of the coefficients of regression equations, referred to as the MRA (multivariate regression analysis) "nightmare of the first kind". This is manifested when in a stepwise regression a descriptor is included or excluded from a regression. The consequence is an unpredictable change of the coefficients of the descriptors that remain in the regression equation. We follow with consideration of an even more serious problem, referred to as the MRA "nightmare of the second kind", arising when optimal descriptors are selected from a large pool of descriptors. This process typically causes at different steps of the stepwise regression a replacement of several previously used descriptors by new ones. We describe a procedure that resolves these difficulties. The approach is illustrated on boiling points of nonanes which are considered (1) by using an ordered connectivity basis; (2) by using an ordering resulting from application of greedy algorithm; and (3) by using an ordering derived from an exhaustive search for optimal descriptors. A novel variant of multiple regression analysis, called retro-regression (RR), is outlined showing how it resolves the ambiguities associated with both "nightmares" of the first and the second kind of MRA.

Postoperative liver volume was accurately predicted by a medical image three dimensional visualization system in hepatectomy for liver cancer.

PubMed

Cai, Wei; Fan, Yingfang; Hu, Haoyu; Xiang, Nan; Fang, Chihua; Jia, Fucang

2017-06-01

Liver cancer is the second most common cause of cancer death worldwide. The hepatectomy is the most effective and the only potentially curative treatment for patients with resectable neoplasm. Precisely preoperative assessment of remnant liver volume is essential in preventing postoperative liver failure. The aim of our study is to report our experience of using a medical image three dimensional (3D) visualization system (MI-3DVS), which was developed by our team, in assisting hepatectomy for patients with liver cancer. Between January 2010 and June 2016, 69 patients with liver cancer underwent hepatic resection based on the MI-3DVS were enrolled in this study. All patients underwent CT scan 5 days before the surgery and within 5 days after resection. CT images were reconstructed with the MI-3DVS to assist to perform hepatectomy. Simple linear regression, intra-class correlation coefficient (ICC) and Bland-Altman analysis were used to evaluate the relationship and agreement between actual excisional liver volume (AELV) and predicted excisional liver volume (PELV). Among 69 patients in this study, 62(89.85%) of them were diagnosed with hepatocellular carcinoma by histopathologic examination, and 41(59.42%) underwent major hepatectomy. The average AELV was 330.13 cm 3 and the average PELV was 287.67 cm 3 . The simple regression equation is AELV = 1.016 × PELV+30.39(r = 0.966; p < 0.0003). PELV (ICC = 0.964) achieved an excellent agreement with AELV with statistical significance (p < 0.001). 65 of 69 dots are in the range of 95% confidence interval in Bland-Altman analyses. The MI-3DVS has advantages of simple usage and convenient hold. It is accurate in assessment of postoperative liver volume and improve safety in liver resection. Copyright © 2017 Elsevier Ltd. All rights reserved.

Linear regression techniques for use in the EC tracer method of secondary organic aerosol estimation

NASA Astrophysics Data System (ADS)

Saylor, Rick D.; Edgerton, Eric S.; Hartsell, Benjamin E.

A variety of linear regression techniques and simple slope estimators are evaluated for use in the elemental carbon (EC) tracer method of secondary organic carbon (OC) estimation. Linear regression techniques based on ordinary least squares are not suitable for situations where measurement uncertainties exist in both regressed variables. In the past, regression based on the method of Deming [1943. Statistical Adjustment of Data. Wiley, London] has been the preferred choice for EC tracer method parameter estimation. In agreement with Chu [2005. Stable estimate of primary OC/EC ratios in the EC tracer method. Atmospheric Environment 39, 1383-1392], we find that in the limited case where primary non-combustion OC (OC non-comb) is assumed to be zero, the ratio of averages (ROA) approach provides a stable and reliable estimate of the primary OC-EC ratio, (OC/EC) pri. In contrast with Chu [2005. Stable estimate of primary OC/EC ratios in the EC tracer method. Atmospheric Environment 39, 1383-1392], however, we find that the optimal use of Deming regression (and the more general York et al. [2004. Unified equations for the slope, intercept, and standard errors of the best straight line. American Journal of Physics 72, 367-375] regression) provides excellent results as well. For the more typical case where OC non-comb is allowed to obtain a non-zero value, we find that regression based on the method of York is the preferred choice for EC tracer method parameter estimation. In the York regression technique, detailed information on uncertainties in the measurement of OC and EC is used to improve the linear best fit to the given data. If only limited information is available on the relative uncertainties of OC and EC, then Deming regression should be used. On the other hand, use of ROA in the estimation of secondary OC, and thus the assumption of a zero OC non-comb value, generally leads to an overestimation of the contribution of secondary OC to total measured OC.

Modeling animal movements using stochastic differential equations

Treesearch

Haiganoush K. Preisler; Alan A. Ager; Bruce K. Johnson; John G. Kie

2004-01-01

We describe the use of bivariate stochastic differential equations (SDE) for modeling movements of 216 radiocollared female Rocky Mountain elk at the Starkey Experimental Forest and Range in northeastern Oregon. Spatially and temporally explicit vector fields were estimated using approximating difference equations and nonparametric regression techniques. Estimated...

Heuristic approach to capillary pressures averaging

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

Coca, B.P.

1980-10-01

Several methods are available to average capillary pressure curves. Among these are the J-curve and regression equations of the wetting-fluid saturation in porosity and permeability (capillary pressure held constant). While the regression equation seem completely empiric, the J-curve method seems to be theoretically sound due to its expression based on a relation between the average capillary radius and the permeability-porosity ratio. An analysis is given of each of these methods.

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.

Solving ay'' + by' + cy = 0 with a Simple Product Rule Approach

ERIC Educational Resources Information Center

Tolle, John

2011-01-01

When elementary ordinary differential equations (ODEs) of first and second order are included in the calculus curriculum, second-order linear constant coefficient ODEs are typically solved by a method more appropriate to differential equations courses. This method involves the characteristic equation and its roots, complex-valued solutions, and…

Balancing Chemical Equations: The Role of Developmental Level and Mental Capacity.

ERIC Educational Resources Information Center

Niaz, Mansoor; Lawson, Anton E.

1985-01-01

Tested two hypotheses: (1) formal reasoning is required to balance simple one-step equations; and (2) formal reasoning plus sufficient mental capacity are required to balance many-step equations. Independent variables included intellectual development, mental capacity, and degree of field dependence/independence. With 25 subjects, significance was…

Graphical Solution of Polynomial Equations

ERIC Educational Resources Information Center

Grishin, Anatole

2009-01-01

Graphing utilities, such as the ubiquitous graphing calculator, are often used in finding the approximate real roots of polynomial equations. In this paper the author offers a simple graphing technique that allows one to find all solutions of a polynomial equation (1) of arbitrary degree; (2) with real or complex coefficients; and (3) possessing…

On symmetries, conservation laws and exact solutions of the nonlinear Schrödinger-Hirota equation

NASA Astrophysics Data System (ADS)

Akbulut, Arzu; Taşcan, Filiz

2018-04-01

In this paper, conservation laws and exact solution are found for nonlinear Schrödinger-Hirota equation. Conservation theorem is used for finding conservation laws. We get modified conservation laws for given equation. Modified simple equation method is used to obtain the exact solutions of the nonlinear Schrödinger-Hirota equation. It is shown that the suggested method provides a powerful mathematical instrument for solving nonlinear equations in mathematical physics and engineering.

Biomass equations for major tree species of the Northeast

Treesearch

Louise M. Tritton; James W. Hornbeck

1982-01-01

Regression equations are used in both forestry and ecosystem studies to estimate tree biomass from field measurements of dbh (diameter at breast height) or a combination of dbh and height. Literature on biomass is reviewed, and 178 sets of publish equation for 25 species common to the Northeastern Unites States are listed. On the basis of these equations, estimates of...

Weighing Evidence "Steampunk" Style via the Meta-Analyser.

PubMed

Bowden, Jack; Jackson, Chris

2016-10-01

The funnel plot is a graphical visualization of summary data estimates from a meta-analysis, and is a useful tool for detecting departures from the standard modeling assumptions. Although perhaps not widely appreciated, a simple extension of the funnel plot can help to facilitate an intuitive interpretation of the mathematics underlying a meta-analysis at a more fundamental level, by equating it to determining the center of mass of a physical system. We used this analogy to explain the concepts of weighing evidence and of biased evidence to a young audience at the Cambridge Science Festival, without recourse to precise definitions or statistical formulas and with a little help from Sherlock Holmes! Following on from the science fair, we have developed an interactive web-application (named the Meta-Analyser) to bring these ideas to a wider audience. We envisage that our application will be a useful tool for researchers when interpreting their data. First, to facilitate a simple understanding of fixed and random effects modeling approaches; second, to assess the importance of outliers; and third, to show the impact of adjusting for small study bias. This final aim is realized by introducing a novel graphical interpretation of the well-known method of Egger regression.

Guidelines and Procedures for Computing Time-Series Suspended-Sediment Concentrations and Loads from In-Stream Turbidity-Sensor and Streamflow Data

USGS Publications Warehouse

Rasmussen, Patrick P.; Gray, John R.; Glysson, G. Douglas; Ziegler, Andrew C.

2009-01-01

In-stream continuous turbidity and streamflow data, calibrated with measured suspended-sediment concentration data, can be used to compute a time series of suspended-sediment concentration and load at a stream site. Development of a simple linear (ordinary least squares) regression model for computing suspended-sediment concentrations from instantaneous turbidity data is the first step in the computation process. If the model standard percentage error (MSPE) of the simple linear regression model meets a minimum criterion, this model should be used to compute a time series of suspended-sediment concentrations. Otherwise, a multiple linear regression model using paired instantaneous turbidity and streamflow data is developed and compared to the simple regression model. If the inclusion of the streamflow variable proves to be statistically significant and the uncertainty associated with the multiple regression model results in an improvement over that for the simple linear model, the turbidity-streamflow multiple linear regression model should be used to compute a suspended-sediment concentration time series. The computed concentration time series is subsequently used with its paired streamflow time series to compute suspended-sediment loads by standard U.S. Geological Survey techniques. Once an acceptable regression model is developed, it can be used to compute suspended-sediment concentration beyond the period of record used in model development with proper ongoing collection and analysis of calibration samples. Regression models to compute suspended-sediment concentrations are generally site specific and should never be considered static, but they represent a set period in a continually dynamic system in which additional data will help verify any change in sediment load, type, and source.

Analysis of the streamflow-gaging station network in Ohio for effectiveness in providing regional streamflow information

USGS Publications Warehouse

Straub, D.E.

1998-01-01

The streamflow-gaging station network in Ohio was evaluated for its effectiveness in providing regional streamflow information. The analysis involved application of the principles of generalized least squares regression between streamflow and climatic and basin characteristics. Regression equations were developed for three flow characteristics: (1) the instantaneous peak flow with a 100-year recurrence interval (P100), (2) the mean annual flow (Qa), and (3) the 7-day, 10-year low flow (7Q10). All active and discontinued gaging stations with 5 or more years of unregulated-streamflow data with respect to each flow characteristic were used to develop the regression equations. The gaging-station network was evaluated for the current (1996) condition of the network and estimated conditions of various network strategies if an additional 5 and 20 years of streamflow data were collected. Any active or discontinued gaging station with (1) less than 5 years of unregulated-streamflow record, (2) previously defined basin and climatic characteristics, and (3) the potential for collection of more unregulated-streamflow record were included in the network strategies involving the additional 5 and 20 years of data. The network analysis involved use of the regression equations, in combination with location, period of record, and cost of operation, to determine the contribution of the data for each gaging station to regional streamflow information. The contribution of each gaging station was based on a cost-weighted reduction of the mean square error (average sampling-error variance) associated with each regional estimating equation. All gaging stations included in the network analysis were then ranked according to their contribution to the regional information for each flow characteristic. The predictive ability of the regression equations developed from the gaging station network could be improved for all three flow characteristics with the collection of additional streamflow data. The addition of new gaging stations to the network would result in an even greater improvement of the accuracy of the regional regression equations. Typically, continued data collection at stations with unregulated streamflow for all flow conditions that had less than 11 years of record with drainage areas smaller than 200 square miles contributed the largest cost-weighted reduction to the average sampling-error variance of the regional estimating equations. The results of the network analyses can be used to prioritize the continued operation of active gaging stations or the reactivation of discontinued gaging stations if the objective is to maximize the regional information content in the streamflow-gaging station network.

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

Kim, J.; Moon, T.J.; Howell, J.R.

This paper presents an analysis of the heat transfer occurring during an in-situ curing process for which infrared energy is provided on the surface of polymer composite during winding. The material system is Hercules prepreg AS4/3501-6. Thermoset composites have an exothermic chemical reaction during the curing process. An Eulerian thermochemical model is developed for the heat transfer analysis of helical winding. The model incorporates heat generation due to the chemical reaction. Several assumptions are made leading to a two-dimensional, thermochemical model. For simplicity, 360{degree} heating around the mandrel is considered. In order to generate the appropriate process windows, the developedmore » heat transfer model is combined with a simple winding time model. The process windows allow for a proper selection of process variables such as infrared energy input and winding velocity to give a desired end-product state. Steady-state temperatures are found for each combination of the process variables. A regression analysis is carried out to relate the process variables to the resulting steady-state temperatures. Using regression equations, process windows for a wide range of cylinder diameters are found. A general procedure to find process windows for Hercules AS4/3501-6 prepreg tape is coded in a FORTRAN program.« less

Fundamental equations of a mixture of gas and small spherical solid particles from simple kinetic theory.

NASA Technical Reports Server (NTRS)

Pai, S. I.

1973-01-01

The fundamental equations of a mixture of a gas and pseudofluid of small spherical solid particles are derived from the Boltzmann equation of two-fluid theory. The distribution function of the gas molecules is defined in the same manner as in the ordinary kinetic theory of gases, but the distribution function for the solid particles is different from that of the gas molecules, because it is necessary to take into account the different size and physical properties of solid particles. In the proposed simple kinetic theory, two additional parameters are introduced: one is the radius of the spheres and the other is the instantaneous temperature of the solid particles in the distribution of the solid particles. The Boltzmann equation for each species of the mixture is formally written, and the transfer equations of these Boltzmann equations are derived and compared to the well-known fundamental equations of the mixture of a gas and small solid particles from continuum theory. The equations obtained reveal some insight into various terms in the fundamental equations. For instance, the partial pressure of the pseudofluid of solid particles is not negligible if the volume fraction of solid particles is not negligible as in the case of lunar ash flow.

Consistent Yokoya-Chen Approximation to Beamstrahlung(LCC-0010)

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

Peskin, M

2004-04-22

I reconsider the Yokoya-Chen approximate evolution equation for beamstrahlung and modify it slightly to generate simple, consistent analytical approximations for the electron and photon energy spectra. I compare these approximations to previous ones, and to simulation data.I reconsider the Yokoya-Chen approximate evolution equation for beamstrahlung and modify it slightly to generate simple, consistent analytical approximations for the electron and photon energy spectra. I compare these approximations to previous ones, and to simulation data.

A simple method to design non-collision relative orbits for close spacecraft formation flying

NASA Astrophysics Data System (ADS)

Jiang, Wei; Li, JunFeng; Jiang, FangHua; Bernelli-Zazzera, Franco

2018-05-01

A set of linearized relative motion equations of spacecraft flying on unperturbed elliptical orbits are specialized for particular cases, where the leader orbit is circular or equatorial. Based on these extended equations, we are able to analyze the relative motion regulation between a pair of spacecraft flying on arbitrary unperturbed orbits with the same semi-major axis in close formation. Given the initial orbital elements of the leader, this paper presents a simple way to design initial relative orbital elements of close spacecraft with the same semi-major axis, thus preventing collision under non-perturbed conditions. Considering the mean influence of J 2 perturbation, namely secular J 2 perturbation, we derive the mean derivatives of orbital element differences, and then expand them to first order. Thus the first order expansion of orbital element differences can be added to the relative motion equations for further analysis. For a pair of spacecraft that will never collide under non-perturbed situations, we present a simple method to determine whether a collision will occur when J 2 perturbation is considered. Examples are given to prove the validity of the extended relative motion equations and to illustrate how the methods presented can be used. The simple method for designing initial relative orbital elements proposed here could be helpful to the preliminary design of the relative orbital elements between spacecraft in a close formation, when collision avoidance is necessary.

Allometric Biomass Equations for 98 Species of Herbs, Shrubs, and Small Trees

Treesearch

W. Brad Smith; Gary J. Brand

1983-01-01

Biomass regression coefficients from the literature for the allometric equation form are presented for 98 species of shrubs and herbs in the northern U.S. and Canada. The equation and coeffients provide estimates of grams of biomass (oven-dry weight) for foliage, woody stem and total biomass.

Methods for Adjusting U.S. Geological Survey Rural Regression Peak Discharges in an Urban Setting

USGS Publications Warehouse

Moglen, Glenn E.; Shivers, Dorianne E.

2006-01-01

A study was conducted of 78 U.S. Geological Survey gaged streams that have been subjected to varying degrees of urbanization over the last three decades. Flood-frequency analysis coupled with nonlinear regression techniques were used to generate a set of equations for converting peak discharge estimates determined from rural regression equations to a set of peak discharge estimates that represent known urbanization. Specifically, urban regression equations for the 2-, 5-, 10-, 25-, 50-, 100-, and 500-year return periods were calibrated as a function of the corresponding rural peak discharge and the percentage of impervious area in a watershed. The results of this study indicate that two sets of equations, one set based on imperviousness and one set based on population density, performed well. Both sets of equations are dependent on rural peak discharges, a measure of development (average percentage of imperviousness or average population density), and a measure of homogeneity of development within a watershed. Average imperviousness was readily determined by using geographic information system methods and commonly available land-cover data. Similarly, average population density was easily determined from census data. Thus, a key advantage to the equations developed in this study is that they do not require field measurements of watershed characteristics as did the U.S. Geological Survey urban equations developed in an earlier investigation. During this study, the U.S. Geological Survey PeakFQ program was used as an integral tool in the calibration of all equations. The scarcity of historical land-use data, however, made exclusive use of flow records necessary for the 30-year period from 1970 to 2000. Such relatively short-duration streamflow time series required a nonstandard treatment of the historical data function of the PeakFQ program in comparison to published guidelines. Thus, the approach used during this investigation does not fully comply with the guidelines set forth in U.S. Geological Survey Bulletin 17B, and modifications may be needed before it can be applied in practice.

Effectiveness of the New Hampshire stream-gaging network in providing regional streamflow information

USGS Publications Warehouse

Olson, Scott A.

2003-01-01

The stream-gaging network in New Hampshire was analyzed for its effectiveness in providing regional information on peak-flood flow, mean-flow, and low-flow frequency. The data available for analysis were from stream-gaging stations in New Hampshire and selected stations in adjacent States. The principles of generalized-least-squares regression analysis were applied to develop regional regression equations that relate streamflow-frequency characteristics to watershed characteristics. Regression equations were developed for (1) the instantaneous peak flow with a 100-year recurrence interval, (2) the mean-annual flow, and (3) the 7-day, 10-year low flow. Active and discontinued stream-gaging stations with 10 or more years of flow data were used to develop the regression equations. Each stream-gaging station in the network was evaluated and ranked on the basis of how much the data from that station contributed to the cost-weighted sampling-error component of the regression equation. The potential effect of data from proposed and new stream-gaging stations on the sampling error also was evaluated. The stream-gaging network was evaluated for conditions in water year 2000 and for estimated conditions under various network strategies if an additional 5 years and 20 years of streamflow data were collected. The effectiveness of the stream-gaging network in providing regional streamflow information could be improved for all three flow characteristics with the collection of additional flow data, both temporally and spatially. With additional years of data collection, the greatest reduction in the average sampling error of the regional regression equations was found for the peak- and low-flow characteristics. In general, additional data collection at stream-gaging stations with unregulated flow, relatively short-term record (less than 20 years), and drainage areas smaller than 45 square miles contributed the largest cost-weighted reduction to the average sampling error of the regional estimating equations. The results of the network analyses can be used to prioritize the continued operation of active stations, the reactivation of discontinued stations, or the activation of new stations to maximize the regional information content provided by the stream-gaging network. Final decisions regarding altering the New Hampshire stream-gaging network would require the consideration of the many uses of the streamflow data serving local, State, and Federal interests.

Thermodynamics of high temperature, Mie-Gruneisen solids

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

Lemons, Don S.; Lund, Carl M.

1999-12-01

We construct a set of equations of state for condensed matter at temperatures well above the Debye temperature. These equations incorporate the Mie-Gruneisen equation of state and generic properties of high temperature solids. They are simple enough to provide an alternative to the ideal gas and the van der Waals equations of state for illustrating thermodynamic concepts. (c) 1999 American Association of Physics Teachers.

Coincidence degree and periodic solutions of neutral equations

NASA Technical Reports Server (NTRS)

Hale, J. K.; Mawhin, J.

1973-01-01

The problem of existence of periodic solutions for some nonautonomous neutral functional differential equations is examined. It is an application of a basic theorem on the Fredholm alternative for periodic solutions of some linear neutral equations and of a generalized Leray-Schauder theory. Although proofs are simple, the results are nontrivial extensions to the neutral case of existence theorems for periodic solutions of functional differential equations.

Assessment of power output in jump tests for applicants to a sports sciences degree.

PubMed

Lara, A J; Abián, J; Alegre, L M; Jiménez, L; Aguado, X

2006-09-01

Our study aimed: 1) to describe the jump performance in a population of male applicants to a Faculty of Sports Sciences, 2) to apply different power equations from the literature to assess their accuracy, and 3) to develop a new regression equation from this population. The push off phases of the counter-movement jumps (CMJ) on a force platform of 161 applicants (age: 19+/-2.9 years; weight: 70.4+/-8.3 kg) to a Spanish Faculty of Sports Sciences were recorded and subsequently analyzed. Their hands had to be placed on the hips and the knee angle during the counter movement was not controlled. Each subject had 2 trials to reach a minimum of 29 cm of jump height, and when 2 jumps were performed the best trial was analyzed. Multiple regression analysis was performed to develop a new regression equation. Mean jump height was 34.6+/-4.3 cm, peak vertical force 1 663.9+/-291.1 N and peak power 3524.4+/-562 W. All the equations underestimated power, from 74% (Lewis) to 8% (Sayers). However, there were high and significant correlations between peak power measured on the force platform, and those assessed by the equations. The results of the present study support the development of power equations for specific populations, to achieve more accurate assessments. The power equation from this study [Power = (62.5 x jump height (cm)) + (50.3 x body mass (kg)) 2184.7] can be used accurately in populations of male physical education students.

Deletion Diagnostics for Alternating Logistic Regressions

PubMed Central

Preisser, John S.; By, Kunthel; Perin, Jamie; Qaqish, Bahjat F.

2013-01-01

Deletion diagnostics are introduced for the regression analysis of clustered binary outcomes estimated with alternating logistic regressions, an implementation of generalized estimating equations (GEE) that estimates regression coefficients in a marginal mean model and in a model for the intracluster association given by the log odds ratio. The diagnostics are developed within an estimating equations framework that recasts the estimating functions for association parameters based upon conditional residuals into equivalent functions based upon marginal residuals. Extensions of earlier work on GEE diagnostics follow directly, including computational formulae for one-step deletion diagnostics that measure the influence of a cluster of observations on the estimated regression parameters and on the overall marginal mean or association model fit. The diagnostic formulae are evaluated with simulations studies and with an application concerning an assessment of factors associated with health maintenance visits in primary care medical practices. The application and the simulations demonstrate that the proposed cluster-deletion diagnostics for alternating logistic regressions are good approximations of their exact fully iterated counterparts. PMID:22777960

Isolating the Effects of Training Using Simple Regression Analysis: An Example of the Procedure.

ERIC Educational Resources Information Center

Waugh, C. Keith

This paper provides a case example of simple regression analysis, a forecasting procedure used to isolate the effects of training from an identified extraneous variable. This case example focuses on results of a three-day sales training program to improve bank loan officers' knowledge, skill-level, and attitude regarding solicitation and sale of…

Determination of cellulose I crystallinity by FT-Raman spectroscopy

Treesearch

Umesh P. Agarwal; Richard S. Reiner; Sally A. Ralph

2009-01-01

Two new methods based on FT-Raman spectroscopy, one simple, based on band intensity ratio, and the other, using a partial least-squares (PLS) regression model, are proposed to determine cellulose I crystallinity. In the simple method, crystallinity in semicrystalline cellulose I samples was determined based on univariate regression that was first developed using the...

Generation of a new cystatin C-based estimating equation for glomerular filtration rate by use of 7 assays standardized to the international calibrator.

PubMed

Grubb, Anders; Horio, Masaru; Hansson, Lars-Olof; Björk, Jonas; Nyman, Ulf; Flodin, Mats; Larsson, Anders; Bökenkamp, Arend; Yasuda, Yoshinari; Blufpand, Hester; Lindström, Veronica; Zegers, Ingrid; Althaus, Harald; Blirup-Jensen, Søren; Itoh, Yoshi; Sjöström, Per; Nordin, Gunnar; Christensson, Anders; Klima, Horst; Sunde, Kathrin; Hjort-Christensen, Per; Armbruster, David; Ferrero, Carlo

2014-07-01

Many different cystatin C-based equations exist for estimating glomerular filtration rate. Major reasons for this are the previous lack of an international cystatin C calibrator and the nonequivalence of results from different cystatin C assays. Use of the recently introduced certified reference material, ERM-DA471/IFCC, and further work to achieve high agreement and equivalence of 7 commercially available cystatin C assays allowed a substantial decrease of the CV of the assays, as defined by their performance in an external quality assessment for clinical laboratory investigations. By use of 2 of these assays and a population of 4690 subjects, with large subpopulations of children and Asian and Caucasian adults, with their GFR determined by either renal or plasma inulin clearance or plasma iohexol clearance, we attempted to produce a virtually assay-independent simple cystatin C-based equation for estimation of GFR. We developed a simple cystatin C-based equation for estimation of GFR comprising only 2 variables, cystatin C concentration and age. No terms for race and sex are required for optimal diagnostic performance. The equation, [Formula: see text] is also biologically oriented, with 1 term for the theoretical renal clearance of small molecules and 1 constant for extrarenal clearance of cystatin C. A virtually assay-independent simple cystatin C-based and biologically oriented equation for estimation of GFR, without terms for sex and race, was produced. © 2014 The American Association for Clinical Chemistry.

Relationship between body composition and postural control in prepubertal overweight/obese children: A cross-sectional study.

PubMed

Villarrasa-Sapiña, Israel; Álvarez-Pitti, Julio; Cabeza-Ruiz, Ruth; Redón, Pau; Lurbe, Empar; García-Massó, Xavier

2018-02-01

Excess body weight during childhood causes reduced motor functionality and problems in postural control, a negative influence which has been reported in the literature. Nevertheless, no information regarding the effect of body composition on the postural control of overweight and obese children is available. The objective of this study was therefore to establish these relationships. A cross-sectional design was used to establish relationships between body composition and postural control variables obtained in bipedal eyes-open and eyes-closed conditions in twenty-two children. Centre of pressure signals were analysed in the temporal and frequency domains. Pearson correlations were applied to establish relationships between variables. Principal component analysis was applied to the body composition variables to avoid potential multicollinearity in the regression models. These principal components were used to perform a multiple linear regression analysis, from which regression models were obtained to predict postural control. Height and leg mass were the body composition variables that showed the highest correlation with postural control. Multiple regression models were also obtained and several of these models showed a higher correlation coefficient in predicting postural control than simple correlations. These models revealed that leg and trunk mass were good predictors of postural control. More equations were found in the eyes-open than eyes-closed condition. Body weight and height are negatively correlated with postural control. However, leg and trunk mass are better postural control predictors than arm or body mass. Finally, body composition variables are more useful in predicting postural control when the eyes are open. Copyright © 2017 Elsevier Ltd. All rights reserved.

Water quality parameter measurement using spectral signatures

NASA Technical Reports Server (NTRS)

White, P. E.

1973-01-01

Regression analysis is applied to the problem of measuring water quality parameters from remote sensing spectral signature data. The equations necessary to perform regression analysis are presented and methods of testing the strength and reliability of a regression are described. An efficient algorithm for selecting an optimal subset of the independent variables available for a regression is also presented.

Is adult gait less susceptible than paediatric gait to hip joint centre regression equation error?

PubMed

Kiernan, D; Hosking, J; O'Brien, T

2016-03-01

Hip joint centre (HJC) regression equation error during paediatric gait has recently been shown to have clinical significance. In relation to adult gait, it has been inferred that comparable errors with children in absolute HJC position may in fact result in less significant kinematic and kinetic error. This study investigated the clinical agreement of three commonly used regression equation sets (Bell et al., Davis et al. and Orthotrak) for adult subjects against the equations of Harrington et al. The relationship between HJC position error and subject size was also investigated for the Davis et al. set. Full 3-dimensional gait analysis was performed on 12 healthy adult subjects with data for each set compared to Harrington et al. The Gait Profile Score, Gait Variable Score and GDI-kinetic were used to assess clinical significance while differences in HJC position between the Davis and Harrington sets were compared to leg length and subject height using regression analysis. A number of statistically significant differences were present in absolute HJC position. However, all sets fell below the clinically significant thresholds (GPS <1.6°, GDI-Kinetic <3.6 points). Linear regression revealed a statistically significant relationship for both increasing leg length and increasing subject height with decreasing error in anterior/posterior and superior/inferior directions. Results confirm a negligible clinical error for adult subjects suggesting that any of the examined sets could be used interchangeably. Decreasing error with both increasing leg length and increasing subject height suggests that the Davis set should be used cautiously on smaller subjects. Copyright © 2016 Elsevier B.V. All rights reserved.

Growth and inactivation of Salmonella at low refrigerated storage temperatures and thermal inactivation on raw chicken meat and laboratory media: mixed effect meta-analysis.

PubMed

Smadi, Hanan; Sargeant, Jan M; Shannon, Harry S; Raina, Parminder

2012-12-01

Growth and inactivation regression equations were developed to describe the effects of temperature on Salmonella concentration on chicken meat for refrigerated temperatures (⩽10°C) and for thermal treatment temperatures (55-70°C). The main objectives were: (i) to compare Salmonella growth/inactivation in chicken meat versus laboratory media; (ii) to create regression equations to estimate Salmonella growth in chicken meat that can be used in quantitative risk assessment (QRA) modeling; and (iii) to create regression equations to estimate D-values needed to inactivate Salmonella in chicken meat. A systematic approach was used to identify the articles, critically appraise them, and pool outcomes across studies. Growth represented in density (Log10CFU/g) and D-values (min) as a function of temperature were modeled using hierarchical mixed effects regression models. The current meta-analysis analysis found a significant difference (P⩽0.05) between the two matrices - chicken meat and laboratory media - for both growth at refrigerated temperatures and inactivation by thermal treatment. Growth and inactivation were significantly influenced by temperature after controlling for other variables; however, no consistent pattern in growth was found. Validation of growth and inactivation equations against data not used in their development is needed. Copyright © 2012 Ministry of Health, Saudi Arabia. Published by Elsevier Ltd. All rights reserved.

Sample size determination for logistic regression on a logit-normal distribution.

PubMed

Kim, Seongho; Heath, Elisabeth; Heilbrun, Lance

2017-06-01

Although the sample size for simple logistic regression can be readily determined using currently available methods, the sample size calculation for multiple logistic regression requires some additional information, such as the coefficient of determination ([Formula: see text]) of a covariate of interest with other covariates, which is often unavailable in practice. The response variable of logistic regression follows a logit-normal distribution which can be generated from a logistic transformation of a normal distribution. Using this property of logistic regression, we propose new methods of determining the sample size for simple and multiple logistic regressions using a normal transformation of outcome measures. Simulation studies and a motivating example show several advantages of the proposed methods over the existing methods: (i) no need for [Formula: see text] for multiple logistic regression, (ii) available interim or group-sequential designs, and (iii) much smaller required sample size.

The discovery of indicator variables for QSAR using inductive logic programming

NASA Astrophysics Data System (ADS)

King, Ross D.; Srinivasan, Ashwin

1997-11-01

A central problem in forming accurate regression equations in QSAR studies isthe selection of appropriate descriptors for the compounds under study. Wedescribe a novel procedure for using inductive logic programming (ILP) todiscover new indicator variables (attributes) for QSAR problems, and show thatthese improve the accuracy of the derived regression equations. ILP techniqueshave previously been shown to work well on drug design problems where thereis a large structural component or where clear comprehensible rules arerequired. However, ILP techniques have had the disadvantage of only being ableto make qualitative predictions (e.g. active, inactive) and not to predictreal numbers (regression). We unify ILP and linear regression techniques togive a QSAR method that has the strength of ILP at describing stericstructure, with the familiarity and power of linear regression. We evaluatedthe utility of this new QSAR technique by examining the prediction ofbiological activity with and without the addition of new structural indicatorvariables formed by ILP. In three out of five datasets examined the additionof ILP variables produced statistically better results (P < 0.01) over theoriginal description. The new ILP variables did not increase the overallcomplexity of the derived QSAR equations and added insight into possiblemechanisms of action. We conclude that ILP can aid in the process of drugdesign.

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

Accuracy analysis of automodel solutions for Lévy flight-based transport: from resonance radiative transfer to a simple general model

NASA Astrophysics Data System (ADS)

Kukushkin, A. B.; Sdvizhenskii, P. A.

2017-12-01

The results of accuracy analysis of automodel solutions for Lévy flight-based transport on a uniform background are presented. These approximate solutions have been obtained for Green’s function of the following equations: the non-stationary Biberman-Holstein equation for three-dimensional (3D) radiative transfer in plasma and gases, for various (Doppler, Lorentz, Voigt and Holtsmark) spectral line shapes, and the 1D transport equation with a simple longtailed step-length probability distribution function with various power-law exponents. The results suggest the possibility of substantial extension of the developed method of automodel solution to other fields far beyond physics.

Linear analysis of auto-organization in Hebbian neural networks.

PubMed

Carlos Letelier, J; Mpodozis, J

1995-01-01

The self-organization of neurotopies where neural connections follow Hebbian dynamics is framed in terms of linear operator theory. A general and exact equation describing the time evolution of the overall synaptic strength connecting two neural laminae is derived. This linear matricial equation, which is similar to the equations used to describe oscillating systems in physics, is modified by the introduction of non-linear terms, in order to capture self-organizing (or auto-organizing) processes. The behavior of a simple and small system, that contains a non-linearity that mimics a metabolic constraint, is analyzed by computer simulations. The emergence of a simple "order" (or degree of organization) in this low-dimensionality model system is discussed.

Stature estimation from body segment lengths in young adults--application to people with physical disabilities.

PubMed

Canda, Alicia

2009-03-01

Knowledge of stature is necessary for evaluating nutritional status and for correcting certain functional parameters. Measuring stature is difficult or impossible in bedridden or wheelchair-bound persons and may also be diminished by disorders of the spinal column or extremities. The purpose of this work is to develop estimation equations for young adult athletes for their subsequent application to disabled persons. The main sample comprised 445 male and 401 female sportspersons. Cross validation was also performed on 100 males and 101 females. All were Caucasian, the males being over 21 and the females over 18, and all practiced some kind of sport. The following variables were included: stature, sitting height, arm span, and lengths of upper arm, forearm, hand, thigh, lower leg, and foot. Simple and multiple regression analyses were performed using stature as a dependent variable and the others as predictive variables. The best equation for males (R(2)=0.978; RMSE=1.41 cm; PE=1.54 cm) was stature: 1.346+1.023 * lower leg+0.957 * sitting height+0.530 * thigh+0.493 * upper arm+0.228 * forearm. For females (R(2)=0.959; RMSE=1.57 cm; PE=1.25 cm) it was stature: 1.772+0.159 * arm span+0.957 * sitting height+0.424 * thigh+0.966 * lower leg. Alternative equations were developed for when a particular variable cannot be included for reasons of mobility, technical difficulty, or segment loss.

Regression Analysis by Example. 5th Edition

ERIC Educational Resources Information Center

Chatterjee, Samprit; Hadi, Ali S.

2012-01-01

Regression analysis is a conceptually simple method for investigating relationships among variables. Carrying out a successful application of regression analysis, however, requires a balance of theoretical results, empirical rules, and subjective judgment. "Regression Analysis by Example, Fifth Edition" has been expanded and thoroughly…

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.

General Nature of Multicollinearity in Multiple Regression Analysis.

ERIC Educational Resources Information Center

Liu, Richard

1981-01-01

Discusses multiple regression, a very popular statistical technique in the field of education. One of the basic assumptions in regression analysis requires that independent variables in the equation should not be highly correlated. The problem of multicollinearity and some of the solutions to it are discussed. (Author)

Path-Following Solutions Of Nonlinear Equations

NASA Technical Reports Server (NTRS)

Barger, Raymond L.; Walters, Robert W.

1989-01-01

Report describes some path-following techniques for solution of nonlinear equations and compares with other methods. Use of multipurpose techniques applicable at more than one stage of path-following computation results in system relatively simple to understand, program, and use. Comparison of techniques with method of parametric differentiation (MPD) reveals definite advantages for path-following methods. Emphasis in investigation on multiuse techniques being applied at more than one stage of path-following computation. Incorporation of multipurpose techniques results in concise computer code relatively simple to use.

Receptor binding kinetics equations: Derivation using the Laplace transform method.

PubMed

Hoare, Sam R J

Measuring unlabeled ligand receptor binding kinetics is valuable in optimizing and understanding drug action. Unfortunately, deriving equations for estimating kinetic parameters is challenging because it involves calculus; integration can be a frustrating barrier to the pharmacologist seeking to measure simple rate parameters. Here, a well-known tool for simplifying the derivation, the Laplace transform, is applied to models of receptor-ligand interaction. The method transforms differential equations to a form in which simple algebra can be applied to solve for the variable of interest, for example the concentration of ligand-bound receptor. The goal is to provide instruction using familiar examples, to enable investigators familiar with handling equilibrium binding equations to derive kinetic equations for receptor-ligand interaction. First, the Laplace transform is used to derive the equations for association and dissociation of labeled ligand binding. Next, its use for unlabeled ligand kinetic equations is exemplified by a full derivation of the kinetics of competitive binding equation. Finally, new unlabeled ligand equations are derived using the Laplace transform. These equations incorporate a pre-incubation step with unlabeled or labeled ligand. Four equations for measuring unlabeled ligand kinetics were compared and the two new equations verified by comparison with numerical solution. Importantly, the equations have not been verified with experimental data because no such experiments are evident in the literature. Equations were formatted for use in the curve-fitting program GraphPad Prism 6.0 and fitted to simulated data. This description of the Laplace transform method will enable pharmacologists to derive kinetic equations for their model or experimental paradigm under study. Application of the transform will expand the set of equations available for the pharmacologist to measure unlabeled ligand binding kinetics, and for other time-dependent pharmacological activities. Copyright © 2017 Elsevier Inc. All rights reserved.

Decreasing Multicollinearity: A Method for Models with Multiplicative Functions.

ERIC Educational Resources Information Center

Smith, Kent W.; Sasaki, M. S.

1979-01-01

A method is proposed for overcoming the problem of multicollinearity in multiple regression equations where multiplicative independent terms are entered. The method is not a ridge regression solution. (JKS)

Explicit bounds for the positive root of classes of polynomials with applications

NASA Astrophysics Data System (ADS)

Herzberger, Jürgen

2003-03-01

We consider a certain type of polynomial equations for which there exists--according to Descartes' rule of signs--only one simple positive root. These equations are occurring in Numerical Analysis when calculating or estimating the R-order or Q-order of convergence of certain iterative processes with an error-recursion of special form. On the other hand, these polynomial equations are very common as defining equations for the effective rate of return for certain cashflows like bonds or annuities in finance. The effective rate of interest i* for those cashflows is i*=q*-1, where q* is the unique positive root of such polynomial. We construct bounds for i* for a special problem concerning an ordinary simple annuity which is obtained by changing the conditions of such an annuity with given data applying the German rule (Preisangabeverordnung or short PAngV). Moreover, we consider a number of results for such polynomial roots in Numerical Analysis showing that by a simple variable transformation we can derive several formulas out of earlier results by applying this transformation. The same is possible in finance in order to generalize results to more complicated cashflows.

Simple, explicitly time-dependent, and regular solutions of the linearized vacuum Einstein equations in Bondi-Sachs coordinates

NASA Astrophysics Data System (ADS)

Mädler, Thomas

2013-05-01

Perturbations of the linearized vacuum Einstein equations in the Bondi-Sachs formulation of general relativity can be derived from a single master function with spin weight two, which is related to the Weyl scalar Ψ0, and which is determined by a simple wave equation. By utilizing a standard spin representation of tensors on a sphere and two different approaches to solve the master equation, we are able to determine two simple and explicitly time-dependent solutions. Both solutions, of which one is asymptotically flat, comply with the regularity conditions at the vertex of the null cone. For the asymptotically flat solution we calculate the corresponding linearized perturbations, describing all multipoles of spin-2 waves that propagate on a Minkowskian background spacetime. We also analyze the asymptotic behavior of this solution at null infinity using a Penrose compactification and calculate the Weyl scalar Ψ4. Because of its simplicity, the asymptotically flat solution presented here is ideally suited for test bed calculations in the Bondi-Sachs formulation of numerical relativity. It may be considered as a sibling of the Bergmann-Sachs or Teukolsky-Rinne solutions, on spacelike hypersurfaces, for a metric adapted to null hypersurfaces.

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

USGS Publications Warehouse

Koltun, G.F.; Roberts, J.W.

1990-01-01

Multiple-regression equations are presented for estimating flood-peak discharges having recurrence intervals of 2, 5, 10, 25, 50, and 100 years at ungaged sites on rural, unregulated streams in Ohio. The average standard errors of prediction for the equations range from 33.4% to 41.4%. Peak discharge estimates determined by log-Pearson Type III analysis using data collected through the 1987 water year are reported for 275 streamflow-gaging stations. Ordinary least-squares multiple-regression techniques were used to divide the State into three regions and to identify a set of basin characteristics that help explain station-to- station variation in the log-Pearson estimates. Contributing drainage area, main-channel slope, and storage area were identified as suitable explanatory variables. Generalized least-square procedures, which include historical flow data and account for differences in the variance of flows at different gaging stations, spatial correlation among gaging station records, and variable lengths of station record were used to estimate the regression parameters. Weighted peak-discharge estimates computed as a function of the log-Pearson Type III and regression estimates are reported for each station. A method is provided to adjust regression estimates for ungaged sites by use of weighted and regression estimates for a gaged site located on the same stream. Limitations and shortcomings cited in an earlier report on the magnitude and frequency of floods in Ohio are addressed in this study. Geographic bias is no longer evident for the Maumee River basin of northwestern Ohio. No bias is found to be associated with the forested-area characteristic for the range used in the regression analysis (0.0 to 99.0%), nor is this characteristic significant in explaining peak discharges. Surface-mined area likewise is not significant in explaining peak discharges, and the regression equations are not biased when applied to basins having approximately 30% or less surface-mined area. Analyses of residuals indicate that the equations tend to overestimate flood-peak discharges for basins having approximately 30% or more surface-mined area. (USGS)

Graphical Calculation of Estimated Energy Expenditure in Burn Patients.

PubMed

Egro, Francesco M; Manders, Ernest C; Manders, Ernest K

2018-03-01

Historically, estimated energy expenditure (EEE) has been related to the percent of body surface area burned. Subsequent evaluations of these estimates have indicated that the earlier formulas may overestimate the amount of caloric support necessary for burn-injured patients. Ireton-Jones et al derived 2 equations for determining the EEE required to support burn patients, 1 for ventilator-dependent patients and 1 for spontaneously breathing patients. Evidence has proved their reliability, but they remain challenging to apply in a clinical setting given the difficult and cumbersome mathematics involved. This study aims to introduce a graphical calculation of EEE in burn patients that can be easily used in the clinical setting. The multivariant linear regression analysis from Ireton-Jones et al yielded equations that were rearranged into the form of a simple linear equation of the type y = mx + b. By choosing an energy expenditure and the age of the subject, the weight was calculated. The endpoints were then calculated, and a graph was mapped by means of Adobe FrameMaker. A graphical representation of Ireton-Jones et al's equations was obtained by plotting the weight (kg) on the y axis, the age (years) on the x axis, and a series of parallel lines representing the EEE in burn patients. The EEE has been displayed graphically on a grid to allow rapid determination of the EEE needed for a given patient of a designated weight and age. Two graphs were plotted: 1 for ventilator-dependent patients and 1 for spontaneously breathing patients. Correction factors for sex, the presence of additional trauma, and obesity are indicated on the graphical calculators. We propose a graphical tool to calculate caloric requirements in a fast, easy, and portable manner.

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.

Simple Harmonics Motion experiment based on LabVIEW interface for Arduino

NASA Astrophysics Data System (ADS)

Tong-on, Anusorn; Saphet, Parinya; Thepnurat, Meechai

2017-09-01

In this work, we developed an affordable modern innovative physics lab apparatus. The ultrasonic sensor is used to measure the position of a mass attached on a spring as a function of time. The data acquisition system and control device were developed based on LabVIEW interface for Arduino UNO R3. The experiment was designed to explain wave propagation which is modeled by simple harmonic motion. The simple harmonic system (mass and spring) was observed and the motion can be realized using curve fitting to the wave equation in Mathematica. We found that the spring constants provided by Hooke’s law and the wave equation fit are 9.9402 and 9.1706 N/m, respectively.

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-...

Comprehensive database of diameter-based biomass regressions for North American tree species

Treesearch

Jennifer C. Jenkins; David C. Chojnacky; Linda S. Heath; Richard A. Birdsey

2004-01-01

A database consisting of 2,640 equations compiled from the literature for predicting the biomass of trees and tree components from diameter measurements of species found in North America. Bibliographic information, geographic locations, diameter limits, diameter and biomass units, equation forms, statistical errors, and coefficients are provided for each equation,...

Biomass equations for shrub species of Tamualipan thornscrub of North-Eastern Mexico

Treesearch

J. Navar; E. Mendez; A. Najera; J. Graciano; V. Dale; B. Parresol

2004-01-01

Nine additive allometric equations for computing above-ground, standing biomass were developed for the plant community and for each of 18 single species typical of the Tamaulipan thornscrub of north-eastern Mexico. Equations developed using additive procedures in seemingly unrelated linear regression provided statistical efficiency in total biomass estimates at the...

Design and Development of a Model to Simulate 0-G Treadmill Running Using the European Space Agency's Subject Loading System

NASA Technical Reports Server (NTRS)

Caldwell, E. C.; Cowley, M. S.; Scott-Pandorf, M. M.

2010-01-01

Develop a model that simulates a human running in 0 G using the European Space Agency s (ESA) Subject Loading System (SLS). The model provides ground reaction forces (GRF) based on speed and pull-down forces (PDF). DESIGN The theoretical basis for the Running Model was based on a simple spring-mass model. The dynamic properties of the spring-mass model express theoretical vertical GRF (GRFv) and shear GRF in the posterior-anterior direction (GRFsh) during running gait. ADAMs VIEW software was used to build the model, which has a pelvis, thigh segment, shank segment, and a spring foot (see Figure 1).the model s movement simulates the joint kinematics of a human running at Earth gravity with the aim of generating GRF data. DEVELOPMENT & VERIFICATION ESA provided parabolic flight data of subjects running while using the SLS, for further characterization of the model s GRF. Peak GRF data were fit to a linear regression line dependent on PDF and speed. Interpolation and extrapolation of the regression equation provided a theoretical data matrix, which is used to drive the model s motion equations. Verification of the model was conducted by running the model at 4 different speeds, with each speed accounting for 3 different PDF. The model s GRF data fell within a 1-standard-deviation boundary derived from the empirical ESA data. CONCLUSION The Running Model aids in conducting various simulations (potential scenarios include a fatigued runner or a powerful runner generating high loads at a fast cadence) to determine limitations for the T2 vibration isolation system (VIS) aboard the International Space Station. This model can predict how running with the ESA SLS affects the T2 VIS and may be used for other exercise analyses in the future.

Factors affecting fat content in mottled ducks on the Upper Texas Gulf Coast

USGS Publications Warehouse

Kearns, Brian; Haukos, David A.; Walther, Patrick; Conway, Warren C.

2014-01-01

Body condition, or an individual's ability to address metabolic needs, is an important measure of organism health. For waterfowl, body condition, usually some measure of fat, provides a useful proxy for assessing energy budgets during different life history periods and potentially is a measure of response to ecosystem changes. The mottled duck (Anas fulvigula) is relatively poorly studied in respect to these dynamics and presents a unique case because its non-migratory life-history strategy releases it from metabolic costs experienced by many related migratory waterfowl species. Additionally, as a species in decline and of conservation concern in many parts of its range, traditional methods of fat content estimation that involve destructive sampling are less viable. The goal of this study was to produce an equation for estimating fat content in mottled ducks using birds (n = 24) donated at hunter-check stations or collected by law enforcement efforts on the Texas Chenier Plain National Wildlife Refuge Complex from 2005 - 2007. Morphometric measurements were taken, and ether extraction and fat removal was used to estimate percent body fat content and abdominal fat mass, respectively. A hierarchical simple linear regression modeling approach was used to determine external morphometrics that best predicted abdominal fat content. A ratio model based on body mass and a length metric (keel and wing chord length possessed equal model support) provided the best relationship with abdominal fat in sampled individuals. We then applied the regression equation to historical check station data to examine fluctuations in fat content over time; fat content or condition varied relatively little with the exception of years characterized by major disturbances. The mottled duck condition model created here can be used to better monitor population status and health without destructively sampling individuals.

High-throughput determination of octanol/water partition coefficients using a shake-flask method and novel two-phase solvent system.

PubMed

Morikawa, Go; Suzuka, Chihiro; Shoji, Atsushi; Shibusawa, Yoichi; Yanagida, Akio

2016-01-05

A high-throughput method for determining the octanol/water partition coefficient (P(o/w)) of a large variety of compounds exhibiting a wide range in hydrophobicity was established. The method combines a simple shake-flask method with a novel two-phase solvent system comprising an acetonitrile-phosphate buffer (0.1 M, pH 7.4)-1-octanol (25:25:4, v/v/v; AN system). The AN system partition coefficients (K(AN)) of 51 standard compounds for which log P(o/w) (at pH 7.4; log D) values had been reported were determined by single two-phase partitioning in test tubes, followed by measurement of the solute concentration in both phases using an automatic flow injection-ultraviolet detection system. The log K(AN) values were closely related to reported log D values, and the relationship could be expressed by the following linear regression equation: log D=2.8630 log K(AN) -0.1497(n=51). The relationship reveals that log D values (+8 to -8) for a large variety of highly hydrophobic and/or hydrophilic compounds can be estimated indirectly from the narrow range of log K(AN) values (+3 to -3) determined using the present method. Furthermore, log K(AN) values for highly polar compounds for which no log D values have been reported, such as amino acids, peptides, proteins, nucleosides, and nucleotides, can be estimated using the present method. The wide-ranging log D values (+5.9 to -7.5) of these molecules were estimated for the first time from their log K(AN) values and the above regression equation. Copyright © 2015 Elsevier B.V. All rights reserved.

Equations of prediction for abdominal fat in brown egg-laying hens fed different diets.

PubMed

Souza, C; Jaimes, J J B; Gewehr, C E

2017-06-01

The objective was to use noninvasive measurements to formulate equations for predicting the abdominal fat weight of laying hens in a noninvasive manner. Hens were fed with different diets; the external body measurements of birds were used as regressors. We used 288 Hy-Line Brown laying hens, distributed in a completely randomized design in a factorial arrangement, submitted for 16 wk to 2 metabolizable energy levels (2,550 and 2,800 kcal/kg) and 3 levels of crude protein in the diet (150, 160, and 170 g/kg), totaling 6 treatments, with 48 hens each. Sixteen hens per treatment of 92 wk age were utilized to evaluate body weight, bird length, tarsus and sternum, greater and lesser diameter of the tarsus, and abdominal fat weight, after slaughter. The equations were obtained by using measures evaluated with regressors through simple and multiple linear regression with the stepwise method of indirect elimination (backward), with P < 0.10 for all variables remaining in the model. The weight of abdominal fat as predicted by the equations and observed values for each bird were subjected to Pearson's correlation analysis. The equations generated by energy levels showed coefficients of determination of 0.50 and 0.74 for 2,800 and 2,550 kcal/kg of metabolizable energy, respectively, with correlation coefficients of 0.71 and 0.84, with a highly significant correlation between the calculated and observed values of abdominal fat. For protein levels of 150, 160, and 170 g/kg in the diet, it was possible to obtain coefficients of determination of 0.75, 0.57, and 0.61, with correlation coefficients of 0.86, 0.75, and 0.78, respectively. Regarding the general equation for predicting abdominal fat weight, the coefficient of determination was 0.62; the correlation coefficient was 0.79. The equations for predicting abdominal fat weight in laying hens, based on external measurements of the birds, showed positive coefficients of determination and correlation coefficients, thus allowing researchers to determine abdominal fat weight in vivo. © 2016 Poultry Science Association Inc.

Pauling bond strength, bond length and electron density distribution

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

Gibbs, Gerald V.; Ross, Nancy L.; Cox, David F.

2014-01-18

A power law regression equation, = 1.46(/r)-0.19, connecting the average experimental bond lengths, , with the average accumulation of the electron density at the bond critical point, , between bonded metal M and oxygen atoms, determined at ambient conditions for oxide crystals, where r is the row number of the M atom, is similar to the regression equation R(M-O) = 1.39(ρ(rc)/r)-0.21 determined for three perovskite crystals for pressures as high as 80 GPa. The two equations are also comparable with those, = 1.43( /r)-0.21, determined for a large number of oxide crystals at ambient conditions and = 1.39(/r)-0.22, determined formore » geometry optimized hydroxyacid molecules, that connect the bond lengths to the average Pauling electrostatic bond strength, , for the M-O bonded interactions. On the basis of the correspondence between the two sets of equations connecting ρ(rc) and the Pauling bond strength s with bond length, it appears that Pauling’s simple definition of bond strength closely mimics the accumulation of the electron density between bonded pairs of atoms. The similarity of the expressions for the crystals and molecules is compelling evidence that the M-O bonded interactions for the crystals and molecules 2 containing the same bonded interactions are comparable. Similar expressions, connecting bond lengths and bond strength, have also been found to hold for fluoride, nitride and sulfide molecules and crystals. The Brown-Shannon bond valence, σ, power law expression σ = [R1/(R(M-O)]N that has found wide use in crystal chemistry, is shown to be connected to a more universal expression determined for oxides and the perovskites, = r[(1.41)/]4.76, demonstrating that the bond valence for a bonded interaction is likewise closely connected to the accumulation of the electron density between the bonded atoms. Unlike the Brown-Shannon expression, it is universal in that it holds for the M-O bonded interactions for a relatively wide range of M atoms of the periodic table. The power law equation determined for the oxide crystals at ambient conditions is similar to the power law expression = r[1.46/]5.26 determined for the perovskites at pressures as high as 80 GPa, indicating that the intrinsic connection between R(M-O) and ρ(rc) that holds at ambient conditions also holds, to a first approximation, at high pressures.« less

Gauge-invariant flow equation

NASA Astrophysics Data System (ADS)

Wetterich, C.

2018-06-01

We propose a closed gauge-invariant functional flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations. Deriving this equation from a functional integral we employ the freedom in the precise choice of the macroscopic field and the effective average action in order to realize a closed and simple form of the flow equation.

Steric effects in the dynamics of electrolytes at large applied voltages. II. Modified Poisson-Nernst-Planck equations.

PubMed

Kilic, Mustafa Sabri; Bazant, Martin Z; Ajdari, Armand

2007-02-01

In situations involving large potentials or surface charges, the Poisson-Boltzman (PB) equation has shortcomings because it neglects ion-ion interactions and steric effects. This has been widely recognized by the electrochemistry community, leading to the development of various alternative models resulting in different sets "modified PB equations," which have had at least qualitative success in predicting equilibrium ion distributions. On the other hand, the literature is scarce in terms of descriptions of concentration dynamics in these regimes. Here, adapting strategies developed to modify the PB equation, we propose a simple modification of the widely used Poisson-Nernst-Planck (PNP) equations for ionic transport, which at least qualitatively accounts for steric effects. We analyze numerical solutions of these modified PNP equations on the model problem of the charging of a simple electrolyte cell, and compare the outcome to that of the standard PNP equations. Finally, we repeat the asymptotic analysis of Bazant, Thornton, and Ajdari [Phys. Rev. E 70, 021506 (2004)] for this new system of equations to further document the interest and limits of validity of the simpler equivalent electrical circuit models introduced in Part I [Kilic, Bazant, and Ajdari, Phys. Rev. E 75, 021502 (2007)] for such problems.

Partner symmetries and non-invariant solutions of four-dimensional heavenly equations

NASA Astrophysics Data System (ADS)

Malykh, A. A.; Nutku, Y.; Sheftel, M. B.

2004-07-01

We extend our method of partner symmetries to the hyperbolic complex Monge-Ampère equation and the second heavenly equation of Plebañski. We show the existence of partner symmetries and derive the relations between them. For certain simple choices of partner symmetries the resulting differential constraints together with the original heavenly equations are transformed to systems of linear equations by an appropriate Legendre transformation. The solutions of these linear equations are generically non-invariant. As a consequence we obtain explicitly new classes of heavenly metrics without Killing vectors.

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

Cellulose I crystallinity determination using FT-Raman spectroscopy : univariate and multivariate methods

Treesearch

Umesh P. Agarwal; Richard S. Reiner; Sally A. Ralph

2010-01-01

Two new methods based on FT–Raman spectroscopy, one simple, based on band intensity ratio, and the other using a partial least squares (PLS) regression model, are proposed to determine cellulose I crystallinity. In the simple method, crystallinity in cellulose I samples was determined based on univariate regression that was first developed using the Raman band...

Advantages of the net benefit regression framework for economic evaluations of interventions in the workplace: a case study of the cost-effectiveness of a collaborative mental health care program for people receiving short-term disability benefits for psychiatric disorders.

PubMed

Hoch, Jeffrey S; Dewa, Carolyn S

2014-04-01

Economic evaluations commonly accompany trials of new treatments or interventions; however, regression methods and their corresponding advantages for the analysis of cost-effectiveness data are not well known. To illustrate regression-based economic evaluation, we present a case study investigating the cost-effectiveness of a collaborative mental health care program for people receiving short-term disability benefits for psychiatric disorders. We implement net benefit regression to illustrate its strengths and limitations. Net benefit regression offers a simple option for cost-effectiveness analyses of person-level data. By placing economic evaluation in a regression framework, regression-based techniques can facilitate the analysis and provide simple solutions to commonly encountered challenges. Economic evaluations of person-level data (eg, from a clinical trial) should use net benefit regression to facilitate analysis and enhance results.

The serial use of child neurocognitive tests: development versus practice effects.

PubMed

Slade, Peter D; Townes, Brenda D; Rosenbaum, Gail; Martins, Isabel P; Luis, Henrique; Bernardo, Mario; Martin, Michael D; Derouen, Timothy A

2008-12-01

When serial neurocognitive assessments are performed, 2 main factors are of importance: test-retest reliability and practice effects. With children, however, there is a third, developmental factor, which occurs as a result of maturation. Child tests recognize this factor through the provision of age-corrected scaled scores. Thus, a ready-made method for estimating the relative contribution of developmental versus practice effects is the comparison of raw (developmental and practice) and scaled (practice only) scores. Data from a pool of 507 Portuguese children enrolled in a study of dental amalgams (T. A. DeRouen, B. G. Leroux, et al., 2002; T. A. DeRouen, M. D. Martin, et al., 2006) showed that practice effects over a 5-year period varied on 8 neurocognitive tests. Simple regression equations are provided for calculating individual retest scores from initial test scores. (c) 2008 APA, all rights reserved.

Northeastern Florida Bay estuarine creek data, water years 1996-2000

USGS Publications Warehouse

Hittle, Clinton D.; Zucker, Mark A.

2004-01-01

From October 1995 to September 2000 (water years 1996-2000), continuous 15-minute stage, water velocity, salinity, and water temperature data were collected at seven estuarine creeks that flow into northeastern Florida Bay. These creeks include West Highway Creek, Stillwater Creek, Trout Creek, Mud Creek, Taylor River, Upstream Taylor River, and McCormick Creek. Discharge was computed at 15-minute intervals using mean water velocity and the cross-sectional area of the channel. Fifteen-minute unit values are presented for comparison of the quantity, quality, timing, and distribution of flows through the creeks. Revised discharge estimation formulas are presented for three noninstrumented sites (East Highway Creek, Oregon Creek and Stillwater Creek) that utilize an improved West Highway discharge rating. Stillwater Creek and Upstream Taylor River were originally noninstrumented sites; both were fully instrumented in 1999. Discharge rating equations are presented for these sites and were developed using a simple linear regression.

Recovery of zinc and manganese from alkaline and zinc-carbon spent batteries

NASA Astrophysics Data System (ADS)

De Michelis, I.; Ferella, F.; Karakaya, E.; Beolchini, F.; Vegliò, F.

This paper concerns the recovery of zinc and manganese from alkaline and zinc-carbon spent batteries. The metals were dissolved by a reductive-acid leaching with sulphuric acid in the presence of oxalic acid as reductant. Leaching tests were realised according to a full factorial design, then simple regression equations for Mn, Zn and Fe extraction were determined from the experimental data as a function of pulp density, sulphuric acid concentration, temperature and oxalic acid concentration. The main effects and interactions were investigated by the analysis of variance (ANOVA). This analysis evidenced the best operating conditions of the reductive acid leaching: 70% of manganese and 100% of zinc were extracted after 5 h, at 80 °C with 20% of pulp density, 1.8 M sulphuric acid concentration and 59.4 g L -1 of oxalic acid. Both manganese and zinc extraction yields higher than 96% were obtained by using two sequential leaching steps.

Spectrophotometric determination of 1-(3-dimethylaminopropyl)-3-ethylcarbodiimide hydrochloride by flow injection analysis.

PubMed

Seno, Kunihiko; Matumura, Kazuki; Oshima, Mitsuko; Motomizu, Shoji

2008-04-01

1-(3-dimethylaminopropyl)-3-ethylcarbodiimide hydrochloride (EDC.HCl) is a very useful agent to form amide bonds (peptide bonds) in an aqueous medium. A simple and fast detection system was developed using the reaction with pyridine and ethylenediamine in acidic aqueous solution and spectrophotometric flow injection analysis. The absorbances were measured at 400 nm and the reaction was accelerated at 40 degrees C. The calibration graph showed good linearity from 0 to 10% of EDC.HCl solutions: the regression equation was y=3.15x10(4)x (y, peak area; x, % concentration of EDC.HCl). The RSD was under 1.0%. Sample throughput was 15 h(-1). This method was applied to monitoring the EDC.HCl concentration that remained after the anhydration of phthalic acid in water, esterification of acetic acid in methanol or dehydration condensation of malonic acid and ethylenediamine in water.

Parsimonious nonstationary flood frequency analysis

NASA Astrophysics Data System (ADS)

Serago, Jake M.; Vogel, Richard M.

2018-02-01

There is now widespread awareness of the impact of anthropogenic influences on extreme floods (and droughts) and thus an increasing need for methods to account for such influences when estimating a frequency distribution. We introduce a parsimonious approach to nonstationary flood frequency analysis (NFFA) based on a bivariate regression equation which describes the relationship between annual maximum floods, x, and an exogenous variable which may explain the nonstationary behavior of x. The conditional mean, variance and skewness of both x and y = ln (x) are derived, and combined with numerous common probability distributions including the lognormal, generalized extreme value and log Pearson type III models, resulting in a very simple and general approach to NFFA. Our approach offers several advantages over existing approaches including: parsimony, ease of use, graphical display, prediction intervals, and opportunities for uncertainty analysis. We introduce nonstationary probability plots and document how such plots can be used to assess the improved goodness of fit associated with a NFFA.

Octanol-air partition coefficients of polybrominated biphenyls.

PubMed

Hongxia, Zhao; Jingwen, Chen; Xie, Quan; Baocheng, Qu; Xinmiao, Liang

2009-03-01

The octanol-air partition coefficients (K(OA)) for PBB15, PBB26, PBB31, PBB49, PBB103 and PBB153 were determined as a function of temperature using a gas chromatographic retention time technique with 1,1,1-trichloro-2,2-bis (4-chlorophenyl) ethane (p,p'-DDT) as a reference substance. The internal energies of phase change from octanol to air (Delta(OA)U) were calculated for the six compounds and were in the range from 74 to 116 kJ mol(-1). Simple regression equations of log K(OA) versus relative retention times (RRTs) on gas chromatography (GC), and log K(OA) versus molecular connectivity indexes (MCI) were obtained, for which the correlation coefficients (r(2)) were greater than 0.985 at 283.15K and 298.15K. Thus the K(OA) values of the remaining PBBs can be predicted by using their RRTs and MCI according to these relationships.

The Bach equations in spin-coefficient form

NASA Astrophysics Data System (ADS)

Forbes, Hamish

2018-06-01

Conformal gravity theories are defined by field equations that determine only the conformal structure of the spacetime manifold. The Bach equations represent an early example of such a theory, we present them here in component form in terms of spin- and boost-weighted spin-coefficients using the compacted spin-coefficient formalism. These equations can be used as an efficient alternative to the standard tensor form. As a simple application we solve the Bach equations for pp-wave and static spherically symmetric spacetimes.

A fully distributed implementation of mean annual streamflow regional regression equations

USGS Publications Warehouse

Verdin, K.L.; Worstell, B.

2008-01-01

Estimates of mean annual streamflow are needed for a variety of hydrologic assessments. Away from gage locations, regional regression equations that are a function of upstream area, precipitation, and temperature are commonly used. Geographic information systems technology has facilitated their use for projects, but traditional approaches using the polygon overlay operator have been too inefficient for national scale applications. As an alternative, the Elevation Derivatives for National Applications (EDNA) database was used as a framework for a fully distributed implementation of mean annual streamflow regional regression equations. The raster “flow accumulation” operator was used to efficiently achieve spatially continuous parameterization of the equations for every 30 m grid cell of the conterminous United States (U.S.). Results were confirmed by comparing with measured flows at stations of the Hydro-Climatic Data Network, and their applications value demonstrated in the development of a national geospatial hydropower assessment. Interactive tools at the EDNA website make possible the fast and efficient query of mean annual streamflow for any location in the conterminous U.S., providing a valuable complement to other national initiatives (StreamStats and the National Hydrography Dataset Plus).

Regional regression equations for the estimation of selected monthly low-flow duration and frequency statistics at ungaged sites on streams in New Jersey

USGS Publications Warehouse

Watson, Kara M.; McHugh, Amy R.

2014-01-01

Regional regression equations were developed for estimating monthly flow-duration and monthly low-flow frequency statistics for ungaged streams in Coastal Plain and non-coastal regions of New Jersey for baseline and current land- and water-use conditions. The equations were developed to estimate 87 different streamflow statistics, which include the monthly 99-, 90-, 85-, 75-, 50-, and 25-percentile flow-durations of the minimum 1-day daily flow; the August–September 99-, 90-, and 75-percentile minimum 1-day daily flow; and the monthly 7-day, 10-year (M7D10Y) low-flow frequency. These 87 streamflow statistics were computed for 41 continuous-record streamflow-gaging stations (streamgages) with 20 or more years of record and 167 low-flow partial-record stations in New Jersey with 10 or more streamflow measurements. The regression analyses used to develop equations to estimate selected streamflow statistics were performed by testing the relation between flow-duration statistics and low-flow frequency statistics for 32 basin characteristics (physical characteristics, land use, surficial geology, and climate) at the 41 streamgages and 167 low-flow partial-record stations. The regression analyses determined drainage area, soil permeability, average April precipitation, average June precipitation, and percent storage (water bodies and wetlands) were the significant explanatory variables for estimating the selected flow-duration and low-flow frequency statistics. Streamflow estimates were computed for two land- and water-use conditions in New Jersey—land- and water-use during the baseline period of record (defined as the years a streamgage had little to no change in development and water use) and current land- and water-use conditions (1989–2008)—for each selected station using data collected through water year 2008. The baseline period of record is representative of a period when the basin was unaffected by change in development. The current period is representative of the increased development of the last 20 years (1989–2008). The two different land- and water-use conditions were used as surrogates for development to determine whether there have been changes in low-flow statistics as a result of changes in development over time. The State was divided into two low-flow regression regions, the Coastal Plain and the non-coastal region, in order to improve the accuracy of the regression equations. The left-censored parametric survival regression method was used for the analyses to account for streamgages and partial-record stations that had zero flow values for some of the statistics. The average standard error of estimate for the 348 regression equations ranged from 16 to 340 percent. These regression equations and basin characteristics are presented in the U.S. Geological Survey (USGS) StreamStats Web-based geographic information system application. This tool allows users to click on an ungaged site on a stream in New Jersey and get the estimated flow-duration and low-flow frequency statistics. Additionally, the user can click on a streamgage or partial-record station and get the “at-site” streamflow statistics. The low-flow characteristics of a stream ultimately affect the use of the stream by humans. Specific information on the low-flow characteristics of streams is essential to water managers who deal with problems related to municipal and industrial water supply, fish and wildlife conservation, and dilution of wastewater.

Acceleration and Velocity Sensing from Measured Strain

NASA Technical Reports Server (NTRS)

Pak, Chan-Gi; Truax, Roger

2015-01-01

A simple approach for computing acceleration and velocity of a structure from the strain is proposed in this study. First, deflection and slope of the structure are computed from the strain using a two-step theory. Frequencies of the structure are computed from the time histories of strain using a parameter estimation technique together with an autoregressive moving average model. From deflection, slope, and frequencies of the structure, acceleration and velocity of the structure can be obtained using the proposed approach. Simple harmonic motion is assumed for the acceleration computations, and the central difference equation with a linear autoregressive model is used for the computations of velocity. A cantilevered rectangular wing model is used to validate the simple approach. Quality of the computed deflection, acceleration, and velocity values are independent of the number of fibers. The central difference equation with a linear autoregressive model proposed in this study follows the target response with reasonable accuracy. Therefore, the handicap of the backward difference equation, phase shift, is successfully overcome.

Maine StreamStats: a water-resources web application

USGS Publications Warehouse

Lombard, Pamela J.

2015-01-01

Reports referenced in this fact sheet present the regression equations used to estimate the flow statistics, describe the errors associated with the estimates, and describe the methods used to develop the equations and to measure the basin characteristics used in the equations. Limitations of the methods are also described in the reports; for example, all of the equations are appropriate only for ungaged, unregulated, rural streams in Maine.

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.

Preliminary bioelectrical impedance analysis (BIA) equation for body composition assessment in young females from Colombia

NASA Astrophysics Data System (ADS)

Caicedo-Eraso, J. C.; González-Correa, C. H.; González-Correa, C. A.

2013-04-01

A previous study showed that reported BIA equations for body composition are not suitable for Colombian population. The purpose of this study was to develop and validate a preliminary BIA equation for body composition assessment in young females from Colombia, using hydrodensitometry as reference method. A sample of 30 young females was evaluated. Inclusion and exclusion criteria were defined to minimize the variability of BIA. Height, weight, BIA, residual lung volume (RV) and underwater weight (UWW) were measured. A preliminary BIA equation was developed (r2 = 0.72, SEE = 2.48 kg) by stepwise multiple regression with fat-free mass (FFM) as dependent variable and weight, height and impedance measurements as independent variables. The quality of regression was evaluated and a cross-validation against 50% of sample confirmed that results obtained with the preliminary BIA equation is interchangeable with results obtained with hydrodensitometry (r2 = 0.84, SEE = 2.62 kg). The preliminary BIA equation can be used for body composition assessment in young females from Colombia until a definitive equation is developed. The next step will be increasing the sample, including a second reference method, as deuterium oxide dilution (D2O), and using multi-frequency BIA (MF-BIA). It would also be desirable to develop equations for males and other ethnic groups in Colombia.

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.

Connecting Related Rates and Differential Equations

ERIC Educational Resources Information Center

Brandt, Keith

2012-01-01

This article points out a simple connection between related rates and differential equations. The connection can be used for in-class examples or homework exercises, and it is accessible to students who are familiar with separation of variables.

On an example of a system of differential equations that are integrated in Abelian functions

NASA Astrophysics Data System (ADS)

Malykh, M. D.; Sevastianov, L. A.

2017-12-01

The short review of the theory of Abelian functions and its applications in mechanics and analytical theory of differential equations is given. We think that Abelian functions are the natural generalization of commonly used functions because if the general solution of the 2nd order differential equation depends algebraically on the constants of integration, then integrating this equation does not lead out of the realm of commonly used functions complemented by the Abelian functions (Painlevé theorem). We present a relatively simple example of a dynamical system that is integrated in Abelian integrals by “pairing” two copies of a hyperelliptic curve. Unfortunately, initially simple formulas unfold into very long ones. Apparently the theory of Abelian functions hasn’t been finished in the last century because without computer algebra systems it was impossible to complete the calculations to the end. All calculations presented in our report are performed in Sage.

Methods for estimating annual exceedance-probability discharges for streams in Iowa, based on data through water year 2010

USGS Publications Warehouse

Eash, David A.; Barnes, Kimberlee K.; Veilleux, Andrea G.

2013-01-01

A statewide study was performed to develop regional regression equations for estimating selected annual exceedance-probability statistics for ungaged stream sites in Iowa. The study area comprises streamgages located within Iowa and 50 miles beyond the State’s borders. Annual exceedance-probability estimates were computed for 518 streamgages by using the expected moments algorithm to fit a Pearson Type III distribution to the logarithms of annual peak discharges for each streamgage using annual peak-discharge data through 2010. The estimation of the selected statistics included a Bayesian weighted least-squares/generalized least-squares regression analysis to update regional skew coefficients for the 518 streamgages. Low-outlier and historic information were incorporated into the annual exceedance-probability analyses, and a generalized Grubbs-Beck test was used to detect multiple potentially influential low flows. Also, geographic information system software was used to measure 59 selected basin characteristics for each streamgage. Regional regression analysis, using generalized least-squares regression, was used to develop a set of equations for each flood region in Iowa for estimating discharges for ungaged stream sites with 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities, which are equivalent to annual flood-frequency recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years, respectively. A total of 394 streamgages were included in the development of regional regression equations for three flood regions (regions 1, 2, and 3) that were defined for Iowa based on landform regions and soil regions. Average standard errors of prediction range from 31.8 to 45.2 percent for flood region 1, 19.4 to 46.8 percent for flood region 2, and 26.5 to 43.1 percent for flood region 3. The pseudo coefficients of determination for the generalized least-squares equations range from 90.8 to 96.2 percent for flood region 1, 91.5 to 97.9 percent for flood region 2, and 92.4 to 96.0 percent for flood region 3. The regression equations are applicable only to stream sites in Iowa with flows not significantly affected by regulation, diversion, channelization, backwater, or urbanization and with basin characteristics within the range of those used to develop the equations. 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 eight selected statistics; in addition, 90-percent prediction intervals and the measured basin characteristics for the ungaged sites also are provided by the Web-based tool. StreamStats also allows users to click on any streamgage in Iowa and estimates computed for these eight selected statistics are provided for the streamgage.

Solution of Poisson's Equation with Global, Local and Nonlocal Boundary Conditions

ERIC Educational Resources Information Center

Aliev, Nihan; Jahanshahi, Mohammad

2002-01-01

Boundary value problems (BVPs) for partial differential equations are common in mathematical physics. The differential equation is often considered in simple and symmetric regions, such as a circle, cube, cylinder, etc., with global and separable boundary conditions. In this paper and other works of the authors, a general method is used for the…

Clausius-Clapeyron Equation and Saturation Vapour Pressure: Simple Theory Reconciled with Practice

ERIC Educational Resources Information Center

Koutsoyiannis, Demetris

2012-01-01

While the Clausius-Clapeyron equation is very important as it determines the saturation vapour pressure, in practice it is replaced by empirical, typically Magnus-type, equations which are more accurate. It is shown that the reduced accuracy reflects an inconsistent assumption that the latent heat of vaporization is constant. Not only is this…

An implicit semianalytic numerical method for the solution of nonequilibrium chemistry problems

NASA Technical Reports Server (NTRS)

Graves, R. A., Jr.; Gnoffo, P. A.; Boughner, R. E.

1974-01-01

The first order differential equation form systems of equations. They are solved by a simple and relatively accurate implicit semianalytic technique which is derived from a quadrature solution of the governing equation. This method is mathematically simpler than most implicit methods and has the exponential nature of the problem embedded in the solution.

Representative equations for the thermodynamic and transport properties of fluids near the gas-liquid critical point

NASA Technical Reports Server (NTRS)

Sengers, J. V.; Basu, R. S.; Sengers, J. M. H. L.

1981-01-01

A survey is presented of representative equations for various thermophysical properties of fluids in the critical region. Representative equations for the transport properties are included. Semi-empirical modifications of the theoretically predicted asymtotic critical behavior that yield simple and practical representations of the fluid properties in the critical region are emphasized.

Probabilistic estimates of number of undiscovered deposits and their total tonnages in permissive tracts using deposit densities

USGS Publications Warehouse

Singer, Donald A.; Kouda, Ryoichi

2011-01-01

Empirical evidence indicates that processes affecting number and quantity of resources in geologic settings are very general across deposit types. Sizes of permissive tracts that geologically could contain the deposits are excellent predictors of numbers of deposits. In addition, total ore tonnage of mineral deposits of a particular type in a tract is proportional to the type’s median tonnage in a tract. Regressions using size of permissive tracts and median tonnage allow estimation of number of deposits and of total tonnage of mineralization. These powerful estimators, based on 10 different deposit types from 109 permissive worldwide control tracts, generalize across deposit types. Estimates of number of deposits and of total tonnage of mineral deposits are made by regressing permissive area, and mean (in logs) tons in deposits of the type, against number of deposits and total tonnage of deposits in the tract for the 50th percentile estimates. The regression equations (R2 = 0.91 and 0.95) can be used for all deposit types just by inserting logarithmic values of permissive area in square kilometers, and mean tons in deposits in millions of metric tons. The regression equations provide estimates at the 50th percentile, and other equations are provided for 90% confidence limits for lower estimates and 10% confidence limits for upper estimates of number of deposits and total tonnage. Equations for these percentile estimates along with expected value estimates are presented here along with comparisons with independent expert estimates. Also provided are the equations for correcting for the known well-explored deposits in a tract. These deposit-density models require internally consistent grade and tonnage models and delineations for arriving at unbiased estimates.

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.

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

Applicability of the Tanaka-Johnston and Moyers mixed dentition analyses in Northeast Han Chinese.

PubMed

Sherpa, Jangbu; Sah, Gopal; Rong, Zeng; Wu, Lipeng

2015-06-01

To assess applicability of the Tanaka-Johnston and Moyers prediction methods in a Han ethnic group from Northeast China and to develop prediction equations for this same population. Cross-sectional study. Department of Orthodontics, School of Stomatology, Jiamusi University, Heilongjiang, China. A total of 130 subjects (65 male and 65 female) aged 16-21 years from a Han ethnic group of Northeast China were recruited from dental students and patients seeking orthodontic treatment. Ethnicity was verified by questionnaire. Mesio-distal tooth width was measured using Digital Vernier calipers. Predicted values were obtained from the Tanaka-Johnston and Moyers methods in both arches were compared with the actual measured widths. Based on regression analysis, prediction equations were developed. Tanaka-Johnston equations were not precise, except for the upper arch in males. However, the Moyers 85th percentile in the upper arch and 75th percentile in the lower arch predicted the sum precisely in males. For females, the Moyers 75th percentile predicted the sum precisely for the upper arch, but none of the Moyers percentiles predicted in the lower arch. Both the Tanaka-Johnston and Moyers method may not be applied universally without question. Hence, it may be safer to develop regression equations for specific populations. Validating studies must be conducted to confirm the precision of these newly developed regression equations.

Using Time-Series Regression to Predict Academic Library Circulations.

ERIC Educational Resources Information Center

Brooks, Terrence A.

1984-01-01

Four methods were used to forecast monthly circulation totals in 15 midwestern academic libraries: dummy time-series regression, lagged time-series regression, simple average (straight-line forecasting), monthly average (naive forecasting). In tests of forecasting accuracy, dummy regression method and monthly mean method exhibited smallest average…

A logistic regression equation for estimating the probability of a stream in Vermont having intermittent flow

USGS Publications Warehouse

Olson, Scott A.; Brouillette, Michael C.

2006-01-01

A logistic regression equation was developed for estimating the probability of a stream flowing intermittently at unregulated, rural stream sites in Vermont. These determinations can be used for a wide variety of regulatory and planning efforts at the Federal, State, regional, county and town levels, including such applications as assessing fish and wildlife habitats, wetlands classifications, recreational opportunities, water-supply potential, waste-assimilation capacities, and sediment transport. The equation will be used to create a derived product for the Vermont Hydrography Dataset having the streamflow characteristic of 'intermittent' or 'perennial.' The Vermont Hydrography Dataset is Vermont's implementation of the National Hydrography Dataset and was created at a scale of 1:5,000 based on statewide digital orthophotos. The equation was developed by relating field-verified perennial or intermittent status of a stream site during normal summer low-streamflow conditions in the summer of 2005 to selected basin characteristics of naturally flowing streams in Vermont. The database used to develop the equation included 682 stream sites with drainage areas ranging from 0.05 to 5.0 square miles. When the 682 sites were observed, 126 were intermittent (had no flow at the time of the observation) and 556 were perennial (had flowing water at the time of the observation). The results of the logistic regression analysis indicate that the probability of a stream having intermittent flow in Vermont is a function of drainage area, elevation of the site, the ratio of basin relief to basin perimeter, and the areal percentage of well- and moderately well-drained soils in the basin. Using a probability cutpoint (a lower probability indicates the site has perennial flow and a higher probability indicates the site has intermittent flow) of 0.5, the logistic regression equation correctly predicted the perennial or intermittent status of 116 test sites 85 percent of the time.

Bifurcations of solitary wave solutions for (two and three)-dimensional nonlinear partial differential equation in quantum and magnetized plasma by using two different methods

NASA Astrophysics Data System (ADS)

Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen

2018-06-01

In this research, we study new two techniques that called the extended simple equation method and the novel (G‧/G) -expansion method. The extended simple equation method depend on the auxiliary equation (dϕ/dξ = α + λϕ + μϕ2) which has three ways for solving depends on the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (α = 0) this auxiliary equation reduces to Bernoulli equation and when (α ≠ 0, λ ≠ 0, μ ≠ 0) we the general solutions of this auxiliary equation while the novel (G‧/G) -expansion method depends also on similar auxiliary equation (G‧/G)‧ = μ + λ(G‧/G) + (v - 1)(G‧/G) 2 which depend also on the value of (λ2 - 4 (v - 1) μ) and the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (μ = 0) this auxiliary equation reduces to Bernoulli equation and when (λ2 ≠ 4 (v - 1) μ) we the general solutions of this auxiliary equation. This show how both of these auxiliary equation are special cases of Riccati equation. We apply these methods on two dimensional nonlinear Kadomtsev-Petviashvili Burgers equation in quantum plasma and three-dimensional nonlinear modified Zakharov-Kuznetsov equation of ion-acoustic waves in a magnetized plasma. We obtain the exact traveling wave solutions of these important models and under special condition on the parameters, we get solitary traveling wave solutions. All calculations in this study have been established and verified back with the aid of the Maple package program. The executed method is powerful, effective and straightforward for solving nonlinear partial differential equations to obtain more and new solutions.

Contribution of strategy use to performance on complex and simple span tasks.

PubMed

Bailey, Heather; Dunlosky, John; Kane, Michael J

2011-04-01

Simple and complex span tasks are widely thought to measure related but separable memory constructs. Recently, however, research has demonstrated that simple and complex span tasks may tap, in part, the same construct because both similarly predict performance on measures of fluid intelligence (Gf) when the number of items retrieved from secondary memory (SM) is equated (Unsworth & Engle, Journal of Memory and Language 54:68-80 2006). Two studies (n = 105 and n = 152) evaluated whether retrieval from SM is influenced by individual differences in the use of encoding strategies during span tasks. Results demonstrated that, after equating the number of items retrieved from SM, simple and complex span performance similarly predicted Gf performance, but rates of effective strategy use did not mediate the span-Gf relationships. Moreover, at the level of individual differences, effective strategy use was more highly related to complex span performance than to simple span performance. Thus, even though individual differences in effective strategy use influenced span performance on trials that required retrieval from SM, strategic behavior at encoding cannot account for the similarities between simple and complex span tasks.

Annual peak streamflow and ancillary data for small watersheds in central and western Texas

USGS Publications Warehouse

Harwell, Glenn R.; Asquith, William H.

2011-01-01

Estimates of annual peak-streamflow frequency are needed for flood-plain management, assessment of flood risk, and design of structures, such as roads, bridges, culverts, dams, and levees. Regional regression equations have been developed and are used extensively to estimate annual peak-streamflow frequency for ungaged sites in natural (unregulated and rural or nonurbanized) watersheds in Texas (Asquith and Slade, 1997; Asquith and Thompson, 2008; Asquith and Roussel, 2009). The most recent regional regression equations were developed by using data from 638 Texas streamflow-gaging stations throughout the State with eight or more years of data by using drainage area, channel slope, and mean annual precipitation as predictor variables (Asquith and Roussel, 2009). However, because of a lack of sufficient historical streamflow data from small, rural watersheds in certain parts of the State (central and western), substantial uncertainity exists when using the regional regression equations for the purpose of estimating annual peak-streamflow frequency.

Establishing a Mathematical Equations and Improving the Production of L-tert-Leucine by Uniform Design and Regression Analysis.

PubMed

Jiang, Wei; Xu, Chao-Zhen; Jiang, Si-Zhi; Zhang, Tang-Duo; Wang, Shi-Zhen; Fang, Bai-Shan

2017-04-01

L-tert-Leucine (L-Tle) and its derivatives are extensively used as crucial building blocks for chiral auxiliaries, pharmaceutically active ingredients, and ligands. Combining with formate dehydrogenase (FDH) for regenerating the expensive coenzyme NADH, leucine dehydrogenase (LeuDH) is continually used for synthesizing L-Tle from α-keto acid. A multilevel factorial experimental design was executed for research of this system. In this work, an efficient optimization method for improving the productivity of L-Tle was developed. And the mathematical model between different fermentation conditions and L-Tle yield was also determined in the form of the equation by using uniform design and regression analysis. The multivariate regression equation was conveniently implemented in water, with a space time yield of 505.9 g L -1  day -1 and an enantiomeric excess value of >99 %. These results demonstrated that this method might become an ideal protocol for industrial production of chiral compounds and unnatural amino acids such as chiral drug intermediates.

A new solution procedure for a nonlinear infinite beam equation of motion

NASA Astrophysics Data System (ADS)

Jang, T. S.

2016-10-01

Our goal of this paper is of a purely theoretical question, however which would be fundamental in computational partial differential equations: Can a linear solution-structure for the equation of motion for an infinite nonlinear beam be directly manipulated for constructing its nonlinear solution? Here, the equation of motion is modeled as mathematically a fourth-order nonlinear partial differential equation. To answer the question, a pseudo-parameter is firstly introduced to modify the equation of motion. And then, an integral formalism for the modified equation is found here, being taken as a linear solution-structure. It enables us to formulate a nonlinear integral equation of second kind, equivalent to the original equation of motion. The fixed point approach, applied to the integral equation, results in proposing a new iterative solution procedure for constructing the nonlinear solution of the original beam equation of motion, which consists luckily of just the simple regular numerical integration for its iterative process; i.e., it appears to be fairly simple as well as straightforward to apply. A mathematical analysis is carried out on both natures of convergence and uniqueness of the iterative procedure by proving a contractive character of a nonlinear operator. It follows conclusively,therefore, that it would be one of the useful nonlinear strategies for integrating the equation of motion for a nonlinear infinite beam, whereby the preceding question may be answered. In addition, it may be worth noticing that the pseudo-parameter introduced here has double roles; firstly, it connects the original beam equation of motion with the integral equation, second, it is related with the convergence of the iterative method proposed here.

Estimating Dbh from Stump Diameter for 15 Southern Species

Treesearch

Carl V. Bylin

1982-01-01

Regression equations for predicting dbh from tree stump diameter inside and outside bark are presented for 15 southern species. Equations were certified on idependent test subsets using the F distrubution statistic with signigicance level of .05.

The study of correlation among different scattering parameters in an aggregate dust model

NASA Astrophysics Data System (ADS)

Mazarbhuiya, A. M.; Das, H. S.

2017-09-01

We study the light scattering properties of aggregate particles in a wide range of complex refractive indices (m = n + i k, where 1.4 ≤ n ≤ 2.0, 0.001 ≤ k ≤1.0) and wavelengths (0.45 ≤ λ≤1.25 μ m) to investigate the correlation among different parameters e.g., the positive polarization maximum (P_{max}), the amplitude of the negative polarization (P_{min}), geometric albedo (A), (n,k) and λ. Numerical computations are performed by the Superposition T-matrix code with Ballistic Cluster-Cluster Aggregate (BCCA) particles of 128 monomers and Ballistic Aggregates (BA) particles of 512 monomers, where monomer's radius of aggregates is considered to be 0.1 μm. At a fixed value of k, P_{max} and n are correlated via a quadratic regression equation and this nature is observed at all wavelengths. Further, P_{max} and k are found to be related via a polynomial regression equation when n is taken to be fixed. The degree of the equation depends on the wavelength, higher the wavelength lower is the degree. We find that A and P_{max} are correlated via a cubic regression at λ= 0.45 μ m whereas this correlation is quadratic at higher wavelengths. We notice that |P_{min}| increases with the decrease of P_{max} and a strong linear correlation between them is observed when n is fixed at some value and k is changed from higher to lower value. Further, at a fix value of k, P_{min} and P_{max} can be fitted well via a quartic regression equation when n is changed from higher to lower value. We also find that P_{max} increases with λ and they are correlated via a quartic regression.

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).

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.

Estimating annual suspended-sediment loads in the northern and central Appalachian Coal region

USGS Publications Warehouse

Koltun, G.F.

1985-01-01

Multiple-regression equations were developed for estimating the annual suspended-sediment load, for a given year, from small to medium-sized basins in the northern and central parts of the Appalachian coal region. The regression analysis was performed with data for land use, basin characteristics, streamflow, rainfall, and suspended-sediment load for 15 sites in the region. Two variables, the maximum mean-daily discharge occurring within the year and the annual peak discharge, explained much of the variation in the annual suspended-sediment load. Separate equations were developed employing each of these discharge variables. Standard errors for both equations are relatively large, which suggests that future predictions will probably have a low level of precision. This level of precision, however, may be acceptable for certain purposes. It is therefore left to the user to asses whether the level of precision provided by these equations is acceptable for the intended application.

Prediction of elemental creep. [steady state and cyclic data from regression analysis

NASA Technical Reports Server (NTRS)

Davis, J. W.; Rummler, D. R.

1975-01-01

Cyclic and steady-state creep tests were performed to provide data which were used to develop predictive equations. These equations, describing creep as a function of stress, temperature, and time, were developed through the use of a least squares regression analyses computer program for both the steady-state and cyclic data sets. Comparison of the data from the two types of tests, revealed that there was no significant difference between the cyclic and steady-state creep strains for the L-605 sheet under the experimental conditions investigated (for the same total time at load). Attempts to develop a single linear equation describing the combined steady-state and cyclic creep data resulted in standard errors of estimates higher than obtained for the individual data sets. A proposed approach to predict elemental creep in metals uses the cyclic creep equation and a computer program which applies strain and time hardening theories of creep accumulation.

An alternative to the breeder's and Lande's equations.

PubMed

Houchmandzadeh, Bahram

2014-01-10

The breeder's equation is a cornerstone of quantitative genetics, widely used in evolutionary modeling. Noting the mean phenotype in parental, selected parents, and the progeny by E(Z0), E(ZW), and E(Z1), this equation relates response to selection R = E(Z1) - E(Z0) to the selection differential S = E(ZW) - E(Z0) through a simple proportionality relation R = h(2)S, where the heritability coefficient h(2) is a simple function of genotype and environment factors variance. The validity of this relation relies strongly on the normal (Gaussian) distribution of the parent genotype, which is an unobservable quantity and cannot be ascertained. In contrast, we show here that if the fitness (or selection) function is Gaussian with mean μ, an alternative, exact linear equation of the form R' = j(2)S' can be derived, regardless of the parental genotype distribution. Here R' = E(Z1) - μ and S' = E(ZW) - μ stand for the mean phenotypic lag with respect to the mean of the fitness function in the offspring and selected populations. The proportionality coefficient j(2) is a simple function of selection function and environment factors variance, but does not contain the genotype variance. To demonstrate this, we derive the exact functional relation between the mean phenotype in the selected and the offspring population and deduce all cases that lead to a linear relation between them. These results generalize naturally to the concept of G matrix and the multivariate Lande's equation Δ(z) = GP(-1)S. The linearity coefficient of the alternative equation are not changed by Gaussian selection.

ΛCDM Cosmology for Astronomers

NASA Astrophysics Data System (ADS)

Condon, J. J.; Matthews, A. M.

2018-07-01

The homogeneous, isotropic, and flat ΛCDM universe favored by observations of the cosmic microwave background can be described using only Euclidean geometry, locally correct Newtonian mechanics, and the basic postulates of special and general relativity. We present simple derivations of the most useful equations connecting astronomical observables (redshift, flux density, angular diameter, brightness, local space density, ...) with the corresponding intrinsic properties of distant sources (lookback time, distance, spectral luminosity, linear size, specific intensity, source counts, ...). We also present an analytic equation for lookback time that is accurate within 0.1% for all redshifts z. The exact equation for comoving distance is an elliptic integral that must be evaluated numerically, but we found a simple approximation with errors <0.2% for all redshifts up to z ≈ 50.

Boundary transfer matrices and boundary quantum KZ equations

NASA Astrophysics Data System (ADS)

Vlaar, Bart

2015-07-01

A simple relation between inhomogeneous transfer matrices and boundary quantum Knizhnik-Zamolodchikov (KZ) equations is exhibited for quantum integrable systems with reflecting boundary conditions, analogous to an observation by Gaudin for periodic systems. Thus, the boundary quantum KZ equations receive a new motivation. We also derive the commutativity of Sklyanin's boundary transfer matrices by merely imposing appropriate reflection equations, in particular without using the conditions of crossing symmetry and unitarity of the R-matrix.

An Evaluation of Statistical Strategies for Making Equating Function Selections. Research Report. ETS RR-08-60

ERIC Educational Resources Information Center

Moses, Tim

2008-01-01

Nine statistical strategies for selecting equating functions in an equivalent groups design were evaluated. The strategies of interest were likelihood ratio chi-square tests, regression tests, Kolmogorov-Smirnov tests, and significance tests for equated score differences. The most accurate strategies in the study were the likelihood ratio tests…

Family differences in equations for predicting biomass and leaf area in Douglas-fir (Pseudotsuga menziesii var. menziesii).

Treesearch

J.B. St. Clair

1993-01-01

Logarithmic regression equations were developed to predict component biomass and leaf area for an 18-yr-old genetic test of Douglas-fir (Pseudotsuga menziesii [Mirb.] Franco var. menziesii) based on stem diameter or cross-sectional sapwood area. Equations did not differ among open-pollinated families in slope, but intercepts...

Estimating leaf area and leaf biomass of open-grown deciduous urban trees

Treesearch

David J. Nowak

1996-01-01

Logarithmic regression equations were developed to predict leaf area and leaf biomass for open-grown deciduous urban trees based on stem diameter and crown parameters. Equations based on crown parameters produced more reliable estimates. The equations can be used to help quantify forest structure and functions, particularly in urbanizing and urban/suburban areas.

Estimation model for habitual 24-hour urinary-sodium excretion using simple questionnaires from normotensive Koreans.

PubMed

Kong, Ji-Sook; Lee, Yeon-Kyung; Kim, Mi Kyung; Choi, Mi-Kyeong; Heo, Young-Ran; Hyun, Taisun; Kim, Sun Mee; Lyu, Eun-Soon; Oh, Se-Young; Park, Hae-Ryun; Rhee, Moo-Yong; Ro, Hee-Kyong; Song, Mi Kyung

2018-01-01

This study was conducted to develop an equation for estimation of 24-h urinary-sodium excretion that can serve as an alternative to 24-h dietary recall and 24-h urine collection for normotensive Korean adults. In total, data on 640 healthy Korean adults aged 19 to 69 years from 4 regions of the country were collected as a training set. In order to externally validate the equation developed from that training set, 200 subjects were recruited independently as a validation set. Due to heterogeneity by gender, we constructed a gender-specific equation for estimation of 24-h urinary-sodium excretion by using a multivariable linear regression model and assessed the performance of the developed equation in validation set. The best model consisted of age, body weight, dietary behavior ('eating salty food', 'Kimchi consumption', 'Korean soup or stew consumption', 'soy sauce or red pepper paste consumption'), and smoking status in men, and age, body weight, dietary behavior ('salt preference', 'eating salty food', 'checking sodium content for processed foods', 'nut consumption'), and smoking status in women, respectively. When this model was tested in the external validation set, the mean bias between the measured and estimated 24-h urinary-sodium excretion from Bland-Altman plots was -1.92 (95% CI: -113, 110) mmol/d for men and -1.51 (95% CI: -90.6, 87.6) mmol/d for women. The cut-points of sodium intake calculated based on the equations were ≥4,000 mg/d for men and ≥3,500 mg/d for women, with 89.8 and 76.6% sensitivity and 29.3 and 64.2% specificity, respectively. In this study, a habitual 24-hour urinary-sodium-excretion-estimation model of normotensive Korean adults based on anthropometric and lifestyle factors was developed and showed feasibility for an asymptomatic population.

Estimation model for habitual 24-hour urinary-sodium excretion using simple questionnaires from normotensive Koreans

PubMed Central

Choi, Mi-Kyeong; Heo, Young-Ran; Hyun, Taisun; Kim, Sun Mee; Lyu, Eun-Soon; Oh, Se-Young; Park, Hae-Ryun; Rhee, Moo-Yong; Ro, Hee-Kyong; Song, Mi Kyung

2018-01-01

This study was conducted to develop an equation for estimation of 24-h urinary-sodium excretion that can serve as an alternative to 24-h dietary recall and 24-h urine collection for normotensive Korean adults. In total, data on 640 healthy Korean adults aged 19 to 69 years from 4 regions of the country were collected as a training set. In order to externally validate the equation developed from that training set, 200 subjects were recruited independently as a validation set. Due to heterogeneity by gender, we constructed a gender-specific equation for estimation of 24-h urinary-sodium excretion by using a multivariable linear regression model and assessed the performance of the developed equation in validation set. The best model consisted of age, body weight, dietary behavior (‘eating salty food’, ‘Kimchi consumption’, ‘Korean soup or stew consumption’, ‘soy sauce or red pepper paste consumption’), and smoking status in men, and age, body weight, dietary behavior (‘salt preference’, ‘eating salty food’, ‘checking sodium content for processed foods’, ‘nut consumption’), and smoking status in women, respectively. When this model was tested in the external validation set, the mean bias between the measured and estimated 24-h urinary-sodium excretion from Bland-Altman plots was -1.92 (95% CI: -113, 110) mmol/d for men and -1.51 (95% CI: -90.6, 87.6) mmol/d for women. The cut-points of sodium intake calculated based on the equations were ≥4,000 mg/d for men and ≥3,500 mg/d for women, with 89.8 and 76.6% sensitivity and 29.3 and 64.2% specificity, respectively. In this study, a habitual 24-hour urinary-sodium-excretion-estimation model of normotensive Korean adults based on anthropometric and lifestyle factors was developed and showed feasibility for an asymptomatic population. PMID:29447201

A Large Class of Exact Solutions to the One-Dimensional Schrodinger Equation

ERIC Educational Resources Information Center

Karaoglu, Bekir

2007-01-01

A remarkable property of a large class of functions is exploited to generate exact solutions to the one-dimensional Schrodinger equation. The method is simple and easy to implement. (Contains 1 table and 1 figure.)

Using Simple Quadratic Equations to Estimate Equilibrium Concentrations of an Acid

ERIC Educational Resources Information Center

Brilleslyper, Michael A.

2004-01-01

Application of quadratic equations to standard problem in chemistry like finding equilibrium concentrations of ions in an acid solution is explained. This clearly shows that pure mathematical analysis has meaningful applications in other areas as well.

Tolerance of ciliated protozoan Paramecium bursaria (Protozoa, Ciliophora) to ammonia and nitrites

NASA Astrophysics Data System (ADS)

Xu, Henglong; Song, Weibo; Lu, Lu; Alan, Warren

2005-09-01

The tolerance to ammonia and nitrites in freshwater ciliate Paramecium bursaria was measured in a conventional open system. The ciliate was exposed to different concentrations of ammonia and nitrites for 2h and 12h in order to determine the lethal concentrations. Linear regression analysis revealed that the 2h-LC50 value for ammonia was 95.94 mg/L and for nitrite 27.35 mg/L using probit scale method (with 95% confidence intervals). There was a linear correlation between the mortality probit scale and logarithmic concentration of ammonia which fit by a regression equation y=7.32 x 9.51 ( R 2=0.98; y, mortality probit scale; x, logarithmic concentration of ammonia), by which 2 h-LC50 value for ammonia was found to be 95.50 mg/L. A linear correlation between mortality probit scales and logarithmic concentration of nitrite is also followed the regression equation y=2.86 x+0.89 ( R 2=0.95; y, mortality probit scale; x, logarithmic concentration of nitrite). The regression analysis of toxicity curves showed that the linear correlation between exposed time of ammonia-N LC50 value and ammonia-N LC50 value followed the regression equation y=2 862.85 e -0.08 x ( R 2=0.95; y, duration of exposure to LC50 value; x, LC50 value), and that between exposed time of nitrite-N LC50 value and nitrite-N LC50 value followed the regression equation y=127.15 e -0.13 x ( R 2=0.91; y, exposed time of LC50 value; x, LC50 value). The results demonstrate that the tolerance to ammonia in P. bursaria is considerably higher than that of the larvae or juveniles of some metozoa, e.g. cultured prawns and oysters. In addition, ciliates, as bacterial predators, are likely to play a positive role in maintaining and improving water quality in aquatic environments with high-level ammonium, such as sewage treatment systems.

Equivalent circuit models for interpreting impedance perturbation spectroscopy data

NASA Astrophysics Data System (ADS)

Smith, R. Lowell

2004-07-01

As in-situ structural integrity monitoring disciplines mature, there is a growing need to process sensor/actuator data efficiently in real time. Although smaller, faster embedded processors will contribute to this, it is also important to develop straightforward, robust methods to reduce the overall computational burden for practical applications of interest. This paper addresses the use of equivalent circuit modeling techniques for inferring structure attributes monitored using impedance perturbation spectroscopy. In pioneering work about ten years ago significant progress was associated with the development of simple impedance models derived from the piezoelectric equations. Using mathematical modeling tools currently available from research in ultrasonics and impedance spectroscopy is expected to provide additional synergistic benefits. For purposes of structural health monitoring the objective is to use impedance spectroscopy data to infer the physical condition of structures to which small piezoelectric actuators are bonded. Features of interest include stiffness changes, mass loading, and damping or mechanical losses. Equivalent circuit models are typically simple enough to facilitate the development of practical analytical models of the actuator-structure interaction. This type of parametric structure model allows raw impedance/admittance data to be interpreted optimally using standard multiple, nonlinear regression analysis. One potential long-term outcome is the possibility of cataloging measured viscoelastic properties of the mechanical subsystems of interest as simple lists of attributes and their statistical uncertainties, whose evolution can be followed in time. Equivalent circuit models are well suited for addressing calibration and self-consistency issues such as temperature corrections, Poisson mode coupling, and distributed relaxation processes.

RAWS II: A MULTIPLE REGRESSION ANALYSIS PROGRAM,

DTIC Science & Technology

This memorandum gives instructions for the use and operation of a revised version of RAWS, a multiple regression analysis program. The program...of preprocessed data, the directed retention of variable, listing of the matrix of the normal equations and its inverse, and the bypassing of the regression analysis to provide the input variable statistics only. (Author)

Regression analysis for solving diagnosis problem of children's health

NASA Astrophysics Data System (ADS)

Cherkashina, Yu A.; Gerget, O. M.

2016-04-01

The paper includes results of scientific researches. These researches are devoted to the application of statistical techniques, namely, regression analysis, to assess the health status of children in the neonatal period based on medical data (hemostatic parameters, parameters of blood tests, the gestational age, vascular-endothelial growth factor) measured at 3-5 days of children's life. In this paper a detailed description of the studied medical data is given. A binary logistic regression procedure is discussed in the paper. Basic results of the research are presented. A classification table of predicted values and factual observed values is shown, the overall percentage of correct recognition is determined. Regression equation coefficients are calculated, the general regression equation is written based on them. Based on the results of logistic regression, ROC analysis was performed, sensitivity and specificity of the model are calculated and ROC curves are constructed. These mathematical techniques allow carrying out diagnostics of health of children providing a high quality of recognition. The results make a significant contribution to the development of evidence-based medicine and have a high practical importance in the professional activity of the author.

Combustion performance and scale effect from N2O/HTPB hybrid rocket motor simulations

NASA Astrophysics Data System (ADS)

Shan, Fanli; Hou, Lingyun; Piao, Ying

2013-04-01

HRM code for the simulation of N2O/HTPB hybrid rocket motor operation and scale effect analysis has been developed. This code can be used to calculate motor thrust and distributions of physical properties inside the combustion chamber and nozzle during the operational phase by solving the unsteady Navier-Stokes equations using a corrected compressible difference scheme and a two-step, five species combustion model. A dynamic fuel surface regression technique and a two-step calculation method together with the gas-solid coupling are applied in the calculation of fuel regression and the determination of combustion chamber wall profile as fuel regresses. Both the calculated motor thrust from start-up to shut-down mode and the combustion chamber wall profile after motor operation are in good agreements with experimental data. The fuel regression rate equation and the relation between fuel regression rate and axial distance have been derived. Analysis of results suggests improvements in combustion performance to the current hybrid rocket motor design and explains scale effects in the variation of fuel regression rate with combustion chamber diameter.

Inflammation, homocysteine and carotid intima-media thickness.

PubMed

Baptista, Alexandre P; Cacdocar, Sanjiva; Palmeiro, Hugo; Faísca, Marília; Carrasqueira, Herménio; Morgado, Elsa; Sampaio, Sandra; Cabrita, Ana; Silva, Ana Paula; Bernardo, Idalécio; Gome, Veloso; Neves, Pedro L

2008-01-01

Cardiovascular disease is the main cause of morbidity and mortality in chronic renal patients. Carotid intima-media thickness (CIMT) is one of the most accurate markers of atherosclerosis risk. In this study, the authors set out to evaluate a population of chronic renal patients to determine which factors are associated with an increase in intima-media thickness. We included 56 patients (F=22, M=34), with a mean age of 68.6 years, and an estimated glomerular filtration rate of 15.8 ml/min (calculated by the MDRD equation). Various laboratory and inflammatory parameters (hsCRP, IL-6 and TNF-alpha) were evaluated. All subjects underwent measurement of internal carotid artery intima-media thickness by high-resolution real-time B-mode ultrasonography using a 10 MHz linear transducer. Intima-media thickness was used as a dependent variable in a simple linear regression model, with the various laboratory parameters as independent variables. Only parameters showing a significant correlation with CIMT were evaluated in a multiple regression model: age (p=0.001), hemoglobin (p=00.3), logCRP (p=0.042), logIL-6 (p=0.004) and homocysteine (p=0.002). In the multiple regression model we found that age (p=0.001) and homocysteine (p=0.027) were independently correlated with CIMT. LogIL-6 did not reach statistical significance (p=0.057), probably due to the small population size. The authors conclude that age and homocysteine correlate with carotid intima-media thickness, and thus can be considered as markers/risk factors in chronic renal patients.

Code Samples Used for Complexity and Control

NASA Astrophysics Data System (ADS)

Ivancevic, Vladimir G.; Reid, Darryn J.

2015-11-01

The following sections are included: * MathematicaⓇ Code * Generic Chaotic Simulator * Vector Differential Operators * NLS Explorer * 2C++ Code * C++ Lambda Functions for Real Calculus * Accelerometer Data Processor * Simple Predictor-Corrector Integrator * Solving the BVP with the Shooting Method * Linear Hyperbolic PDE Solver * Linear Elliptic PDE Solver * Method of Lines for a Set of the NLS Equations * C# Code * Iterative Equation Solver * Simulated Annealing: A Function Minimum * Simple Nonlinear Dynamics * Nonlinear Pendulum Simulator * Lagrangian Dynamics Simulator * Complex-Valued Crowd Attractor Dynamics * Freeform Fortran Code * Lorenz Attractor Simulator * Complex Lorenz Attractor * Simple SGE Soliton * Complex Signal Presentation * Gaussian Wave Packet * Hermitian Matrices * Euclidean L2-Norm * Vector/Matrix Operations * Plain C-Code: Levenberg-Marquardt Optimizer * Free Basic Code: 2D Crowd Dynamics with 3000 Agents

Influence of social and environmental factors on dust, lead, hand lead, and blood lead levels in young children

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

Bornschein, R.L.; Succop, P.; Dietrich, K.N.

The roles of environmental and behavioral factors in determining blood lead levels were studied in a cohort of young children living in an urban environment. The subjects were observed at 3-month intervals from birth to 24 months of age. Repeated measurements were made of the children's blood lead levels, environmental levels of lead in house dust, and in the dust found on the children's hands. A qualitative rating of the residence and of the socioeconomic status of the family was obtained. Interviews and direct observation of parent and child at home were used to evaluate various aspects of caretaker-child interactions.more » Data analysis consisted of a comparison of results obtained by (a) simple correlational analysis, (b) multiple regression analysis, and (c) structural equations analysis. The results demonstrated that structural equation modeling offers a useful approach to unraveling the complex interactions present in the data set. In this preliminary analysis, the suspected relationship between the levels of lead in house dust and on hands and the blood lead level was clearly demonstrated. Furthermore, the analyses indicated an important interplay between environmental sources and social factors in the determination of hand lead and blood lead levels in very young children.« less

The modelling influence of water content to mechanical parameter of soil in analysis of slope stability

NASA Astrophysics Data System (ADS)

Gusman, M.; Nazki, A.; Putra, R. R.

2018-04-01

One of the parameters in slope stability analysis is the shear strength of the soil. Changes in soil shear strength characteristics lead to a decrease in safety factors on the slopes. This study aims to see the effect of increased moisture content on soil mechanical parameters. The case study study was conducted on the slopes of Sitinjau Lauik Kota Padang. The research method was done by laboratory analysis and simple liniear regression analysis and multiple. Based on the test soil results show that the increase in soil water content causes a decrease in cohesion values and internal shear angle. The relationship of moisture content to cohesion is described in equation Y = 55.713-0,6X with R2 = 0.842. While the relationship of water content to shear angle in soil is described in the equation Y = 38.878-0.258X with R2 = 0.915. From several simulations of soil water level improvement, calculation of safety factor (SF) of slope. The calculation results show that the increase of groundwater content is very significant affect the safety factor (SF) slope. SF slope values are in safe condition when moisture content is 50% and when it reaches maximum water content 73.74% slope safety factor value potentially for landslide.

The numerical solution of linear multi-term fractional differential equations: systems of equations

NASA Astrophysics Data System (ADS)

Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

2002-11-01

In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

An accessible four-dimensional treatment of Maxwell's equations in terms of differential forms

NASA Astrophysics Data System (ADS)

Sá, Lucas

2017-03-01

Maxwell’s equations are derived in terms of differential forms in the four-dimensional Minkowski representation, starting from the three-dimensional vector calculus differential version of these equations. Introducing all the mathematical and physical concepts needed (including the tool of differential forms), using only knowledge of elementary vector calculus and the local vector version of Maxwell’s equations, the equations are reduced to a simple and elegant set of two equations for a unified quantity, the electromagnetic field. The treatment should be accessible for students taking a first course on electromagnetism.

Exact solutions for (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation and coupled Klein-Gordon equations.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Islam, S M Rayhanul

2014-01-01

In this work, recently developed modified simple equation (MSE) method is applied to find exact traveling wave solutions of nonlinear evolution equations (NLEEs). To do so, we consider the (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony (DMBBM) equation and coupled Klein-Gordon (cKG) equations. Two classes of explicit exact solutions-hyperbolic and trigonometric solutions of the associated equations are characterized with some free parameters. Then these exact solutions correspond to solitary waves for particular values of the parameters. 02.30.Jr; 02.70.Wz; 05.45.Yv; 94.05.Fg.

On some theoretical and practical aspects of multigrid methods. [to solve finite element systems from elliptic equations

NASA Technical Reports Server (NTRS)

Nicolaides, R. A.

1979-01-01

A description and explanation of a simple multigrid algorithm for solving finite element systems is given. Numerical results for an implementation are reported for a number of elliptic equations, including cases with singular coefficients and indefinite equations. The method shows the high efficiency, essentially independent of the grid spacing, predicted by the theory.

Numerical solutions to the time-dependent Bloch equations revisited.

PubMed

Murase, Kenya; Tanki, Nobuyoshi

2011-01-01

The purpose of this study was to demonstrate a simple and fast method for solving the time-dependent Bloch equations. First, the time-dependent Bloch equations were reduced to a homogeneous linear differential equation, and then a simple equation was derived to solve it using a matrix operation. The validity of this method was investigated by comparing with the analytical solutions in the case of constant radiofrequency irradiation. There was a good agreement between them, indicating the validity of this method. As a further example, this method was applied to the time-dependent Bloch equations in the two-pool exchange model for chemical exchange saturation transfer (CEST) or amide proton transfer (APT) magnetic resonance imaging (MRI), and the Z-spectra and asymmetry spectra were calculated from their solutions. They were also calculated using the fourth/fifth-order Runge-Kutta-Fehlberg (RKF) method for comparison. There was also a good agreement between them, and this method was much faster than the RKF method. In conclusion, this method will be useful for analyzing the complex CEST or APT contrast mechanism and/or investigating the optimal conditions for CEST or APT MRI. Copyright © 2011 Elsevier Inc. All rights reserved.

Correlation and simple linear regression.

PubMed

Zou, Kelly H; Tuncali, Kemal; Silverman, Stuart G

2003-06-01

In this tutorial article, the concepts of correlation and regression are reviewed and demonstrated. The authors review and compare two correlation coefficients, the Pearson correlation coefficient and the Spearman rho, for measuring linear and nonlinear relationships between two continuous variables. In the case of measuring the linear relationship between a predictor and an outcome variable, simple linear regression analysis is conducted. These statistical concepts are illustrated by using a data set from published literature to assess a computed tomography-guided interventional technique. These statistical methods are important for exploring the relationships between variables and can be applied to many radiologic studies.

Cervical Vertebral Body's Volume as a New Parameter for Predicting the Skeletal Maturation Stages.

PubMed

Choi, Youn-Kyung; Kim, Jinmi; Yamaguchi, Tetsutaro; Maki, Koutaro; Ko, Ching-Chang; Kim, Yong-Il

2016-01-01

This study aimed to determine the correlation between the volumetric parameters derived from the images of the second, third, and fourth cervical vertebrae by using cone beam computed tomography with skeletal maturation stages and to propose a new formula for predicting skeletal maturation by using regression analysis. We obtained the estimation of skeletal maturation levels from hand-wrist radiographs and volume parameters derived from the second, third, and fourth cervical vertebrae bodies from 102 Japanese patients (54 women and 48 men, 5-18 years of age). We performed Pearson's correlation coefficient analysis and simple regression analysis. All volume parameters derived from the second, third, and fourth cervical vertebrae exhibited statistically significant correlations (P < 0.05). The simple regression model with the greatest R-square indicated the fourth-cervical-vertebra volume as an independent variable with a variance inflation factor less than ten. The explanation power was 81.76%. Volumetric parameters of cervical vertebrae using cone beam computed tomography are useful in regression models. The derived regression model has the potential for clinical application as it enables a simple and quantitative analysis to evaluate skeletal maturation level.

Cervical Vertebral Body's Volume as a New Parameter for Predicting the Skeletal Maturation Stages

PubMed Central

Choi, Youn-Kyung; Kim, Jinmi; Maki, Koutaro; Ko, Ching-Chang

2016-01-01

This study aimed to determine the correlation between the volumetric parameters derived from the images of the second, third, and fourth cervical vertebrae by using cone beam computed tomography with skeletal maturation stages and to propose a new formula for predicting skeletal maturation by using regression analysis. We obtained the estimation of skeletal maturation levels from hand-wrist radiographs and volume parameters derived from the second, third, and fourth cervical vertebrae bodies from 102 Japanese patients (54 women and 48 men, 5–18 years of age). We performed Pearson's correlation coefficient analysis and simple regression analysis. All volume parameters derived from the second, third, and fourth cervical vertebrae exhibited statistically significant correlations (P < 0.05). The simple regression model with the greatest R-square indicated the fourth-cervical-vertebra volume as an independent variable with a variance inflation factor less than ten. The explanation power was 81.76%. Volumetric parameters of cervical vertebrae using cone beam computed tomography are useful in regression models. The derived regression model has the potential for clinical application as it enables a simple and quantitative analysis to evaluate skeletal maturation level. PMID:27340668

Improving precision of glomerular filtration rate estimating model by ensemble learning.

PubMed

Liu, Xun; Li, Ningshan; Lv, Linsheng; Fu, Yongmei; Cheng, Cailian; Wang, Caixia; Ye, Yuqiu; Li, Shaomin; Lou, Tanqi

2017-11-09

Accurate assessment of kidney function is clinically important, but estimates of glomerular filtration rate (GFR) by regression are imprecise. We hypothesized that ensemble learning could improve precision. A total of 1419 participants were enrolled, with 1002 in the development dataset and 417 in the external validation dataset. GFR was independently estimated from age, sex and serum creatinine using an artificial neural network (ANN), support vector machine (SVM), regression, and ensemble learning. GFR was measured by 99mTc-DTPA renal dynamic imaging calibrated with dual plasma sample 99mTc-DTPA GFR. Mean measured GFRs were 70.0 ml/min/1.73 m 2 in the developmental and 53.4 ml/min/1.73 m 2 in the external validation cohorts. In the external validation cohort, precision was better in the ensemble model of the ANN, SVM and regression equation (IQR = 13.5 ml/min/1.73 m 2 ) than in the new regression model (IQR = 14.0 ml/min/1.73 m 2 , P < 0.001). The precision of ensemble learning was the best of the three models, but the models had similar bias and accuracy. The median difference ranged from 2.3 to 3.7 ml/min/1.73 m 2 , 30% accuracy ranged from 73.1 to 76.0%, and P was > 0.05 for all comparisons of the new regression equation and the other new models. An ensemble learning model including three variables, the average ANN, SVM, and regression equation values, was more precise than the new regression model. A more complex ensemble learning strategy may further improve GFR estimates.

Interpretation of commonly used statistical regression models.

PubMed

Kasza, Jessica; Wolfe, Rory

2014-01-01

A review of some regression models commonly used in respiratory health applications is provided in this article. Simple linear regression, multiple linear regression, logistic regression and ordinal logistic regression are considered. The focus of this article is on the interpretation of the regression coefficients of each model, which are illustrated through the application of these models to a respiratory health research study. © 2013 The Authors. Respirology © 2013 Asian Pacific Society of Respirology.

Rank-preserving regression: a more robust rank regression model against outliers.

PubMed

Chen, Tian; Kowalski, Jeanne; Chen, Rui; Wu, Pan; Zhang, Hui; Feng, Changyong; Tu, Xin M

2016-08-30

Mean-based semi-parametric regression models such as the popular generalized estimating equations are widely used to improve robustness of inference over parametric models. Unfortunately, such models are quite sensitive to outlying observations. The Wilcoxon-score-based rank regression (RR) provides more robust estimates over generalized estimating equations against outliers. However, the RR and its extensions do not sufficiently address missing data arising in longitudinal studies. In this paper, we propose a new approach to address outliers under a different framework based on the functional response models. This functional-response-model-based alternative not only addresses limitations of the RR and its extensions for longitudinal data, but, with its rank-preserving property, even provides more robust estimates than these alternatives. The proposed approach is illustrated with both real and simulated data. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Guiding-center equations for electrons in ultraintense laser fields

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

Moore, J.E.; Fisch, N.J.

1994-01-01

The guiding-center equations are derived for electrons in arbitrarily intense laser fields also subject to external fields and ponderomotive forces. Exhibiting the relativistic mass increase of the oscillating electrons, a simple frame-invariant equation is shown to govern the behavior of the electrons for sufficiently weak background fields and ponderomotive forces. The parameter regime for which such a formulation is valid is made precise, and some predictions of the equation are checked by numerical simulation.

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

Dubrovsky, V. G.; Topovsky, A. V.

New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u{sup (n)}, n= 1, Horizontal-Ellipsis , N are constructed via Zakharov and Manakov {partial_derivative}-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u{sup (n)} and calculated by {partial_derivative}-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schroedinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums ofmore » special solutions u{sup (n)}. It is shown that the sums u=u{sup (k{sub 1})}+...+u{sup (k{sub m})}, 1 Less-Than-Or-Slanted-Equal-To k{sub 1} < k{sub 2} < Horizontal-Ellipsis < k{sub m} Less-Than-Or-Slanted-Equal-To N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schroedinger equation and can serve as model potentials for electrons in planar structures of modern electronics.« less

Backscattering and absorption coefficients for electrons: Solutions of invariant embedding transport equations using a method of convergence

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

Figueroa, C.; Brizuela, H.; Heluani, S. P.

2014-05-21

The backscattering coefficient is a magnitude whose measurement is fundamental for the characterization of materials with techniques that make use of particle beams and particularly when performing microanalysis. In this work, we report the results of an analytic method to calculate the backscattering and absorption coefficients of electrons in similar conditions to those of electron probe microanalysis. Starting on a five level states ladder model in 3D, we deduced a set of integro-differential coupled equations of the coefficients with a method know as invariant embedding. By means of a procedure proposed by authors, called method of convergence, two types ofmore » approximate solutions for the set of equations, namely complete and simple solutions, can be obtained. Although the simple solutions were initially proposed as auxiliary forms to solve higher rank equations, they turned out to be also useful for the estimation of the aforementioned coefficients. In previous reports, we have presented results obtained with the complete solutions. In this paper, we present results obtained with the simple solutions of the coefficients, which exhibit a good degree of fit with the experimental data. Both the model and the calculation method presented here can be generalized to other techniques that make use of different sorts of particle beams.« less

A simple level set method for solving Stefan problems

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

Chen, S.; Merriman, B.; Osher, S.

1997-07-15

Discussed in this paper is an implicit finite difference scheme for solving a heat equation and a simple level set method for capturing the interface between solid and liquid phases which are used to solve Stefan problems.

Numerics made easy: solving the Navier-Stokes equation for arbitrary channel cross-sections using Microsoft Excel.

PubMed

Richter, Christiane; Kotz, Frederik; Giselbrecht, Stefan; Helmer, Dorothea; Rapp, Bastian E

2016-06-01

The fluid mechanics of microfluidics is distinctively simpler than the fluid mechanics of macroscopic systems. In macroscopic systems effects such as non-laminar flow, convection, gravity etc. need to be accounted for all of which can usually be neglected in microfluidic systems. Still, there exists only a very limited selection of channel cross-sections for which the Navier-Stokes equation for pressure-driven Poiseuille flow can be solved analytically. From these equations, velocity profiles as well as flow rates can be calculated. However, whenever a cross-section is not highly symmetric (rectangular, elliptical or circular) the Navier-Stokes equation can usually not be solved analytically. In all of these cases, numerical methods are required. However, in many instances it is not necessary to turn to complex numerical solver packages for deriving, e.g., the velocity profile of a more complex microfluidic channel cross-section. In this paper, a simple spreadsheet analysis tool (here: Microsoft Excel) will be used to implement a simple numerical scheme which allows solving the Navier-Stokes equation for arbitrary channel cross-sections.

Low-Dispersion Scheme for Nonlinear Acoustic Waves in Nonuniform Flow

NASA Technical Reports Server (NTRS)

Baysal, Oktay; Kaushik, Dinesh K.; Idres, Moumen

1997-01-01

The linear dispersion-relation-preserving scheme and its boundary conditions have been extended to the nonlinear Euler equations. This allowed computing, a nonuniform flowfield and a nonlinear acoustic wave propagation in such a medium, by the same scheme. By casting all the equations, boundary conditions, and the solution scheme in generalized curvilinear coordinates, the solutions were made possible for non-Cartesian domains and, for the better deployment of the grid points, nonuniform grid step sizes could be used. It has been tested for a number of simple initial-value and periodic-source problems. A simple demonstration of the difference between a linear and nonlinear propagation was conducted. The wall boundary condition, derived from the momentum equations and implemented through a pressure at a ghost point, and the radiation boundary condition, derived from the asymptotic solution to the Euler equations, have proven to be effective for the nonlinear equations and nonuniform flows. The nonreflective characteristic boundary conditions also have shown success but limited to the nonlinear waves in no mean flow, and failed for nonlinear waves in nonuniform flow.

Acoustic equations of state for simple lattice Boltzmann velocity sets.

PubMed

Viggen, Erlend Magnus

2014-07-01

The lattice Boltzmann (LB) method typically uses an isothermal equation of state. This is not sufficient to simulate a number of acoustic phenomena where the equation of state cannot be approximated as linear and constant. However, it is possible to implement variable equations of state by altering the LB equilibrium distribution. For simple velocity sets with velocity components ξ(iα)∈(-1,0,1) for all i, these equilibria necessarily cause error terms in the momentum equation. These error terms are shown to be either correctable or negligible at the cost of further weakening the compressibility. For the D1Q3 velocity set, such an equilibrium distribution is found and shown to be unique. Its sound propagation properties are found for both forced and free waves, with some generality beyond D1Q3. Finally, this equilibrium distribution is applied to a nonlinear acoustics simulation where both mechanisms of nonlinearity are simulated with good results. This represents an improvement on previous such simulations and proves that the compressibility of the method is still sufficiently strong even for nonlinear acoustics.

Phytoplankton productivity in relation to light intensity: A simple equation

USGS Publications Warehouse

Peterson, D.H.; Perry, M.J.; Bencala, K.E.; Talbot, M.C.

1987-01-01

A simple exponential equation is used to describe photosynthetic rate as a function of light intensity for a variety of unicellular algae and higher plants where photosynthesis is proportional to (1-e-??1). The parameter ?? (=Ik-1) is derived by a simultaneous curve-fitting method, where I is incident quantum-flux density. The exponential equation is tested against a wide range of data and is found to adequately describe P vs. I curves. The errors associated with photosynthetic parameters are calculated. A simplified statistical model (Poisson) of photon capture provides a biophysical basis for the equation and for its ability to fit a range of light intensities. The exponential equation provides a non-subjective simultaneous curve fitting estimate for photosynthetic efficiency (a) which is less ambiguous than subjective methods: subjective methods assume that a linear region of the P vs. I curve is readily identifiable. Photosynthetic parameters ?? and a are used widely in aquatic studies to define photosynthesis at low quantum flux. These parameters are particularly important in estuarine environments where high suspended-material concentrations and high diffuse-light extinction coefficients are commonly encountered. ?? 1987.

Crown area equations for 13 species of trees and shrubs in northern California and southwestern Oregon

Treesearch

Fabian C.C. Uzoh; Martin W. Ritchie

1996-01-01

The equations presented predict crown area for 13 species of trees and shrubs which may be found growing in competition with commercial conifers during early stages of stand development. The equations express crown area as a function of basal area and height. Parameters were estimated for each species individually using weighted nonlinear least square regression.

Calibration of volume and component biomass equations for Douglas-fir and lodgepole pine in Western Oregon forests

Treesearch

Krishna P. Poudel; Temesgen Hailemariam

2016-01-01

Using data from destructively sampled Douglas-fir and lodgepole pine trees, we evaluated the performance of regional volume and component biomass equations in terms of bias and RMSE. The volume and component biomass equations were calibrated using three different adjustment methods that used: (a) a correction factor based on ordinary least square regression through...

Prediction of the Main Engine Power of a New Container Ship at the Preliminary Design Stage

NASA Astrophysics Data System (ADS)

Cepowski, Tomasz

2017-06-01

The paper presents mathematical relationships that allow us to forecast the estimated main engine power of new container ships, based on data concerning vessels built in 2005-2015. The presented approximations allow us to estimate the engine power based on the length between perpendiculars and the number of containers the ship will carry. The approximations were developed using simple linear regression and multivariate linear regression analysis. The presented relations have practical application for estimation of container ship engine power needed in preliminary parametric design of the ship. It follows from the above that the use of multiple linear regression to predict the main engine power of a container ship brings more accurate solutions than simple linear regression.

Prediction of Water Quality Parameters Using Statistical Methods: A Case Study in a Specially Protected Area, Ankara, Turkey

NASA Astrophysics Data System (ADS)

Alp, E.; Yücel, Ö.; Özcan, Z.

2014-12-01

Turkey has been making many legal arrangements for sustainable water management during the harmonization process with the European Union. In order to make cost effective and efficient decisions, monitoring network in Turkey has been expanding. However, due to time and budget constraints, desired number of monitoring campaigns can not be carried. Hence, in this study, independent parameters that can be measured easily and quickly are used to estimate water quality parameters in Lake Mogan and Eymir using linear regression. Nonpoint sources are one of the major pollutant components in Eymir and Mogan lakes. In this paper, a correlation between easily measurable parameters, DO, temperature, electrical conductivity, pH, precipitation and dependent variables, TN, TP, COD, Chl-a, TSS, Total Coliform is investigated. Simple regression analysis is performed for each season in Eymir and Mogan lakes by using SPSS Statistical program using the water quality data collected between 2006-2012. Regression analysis demonstrated significant linear relationship between measured and simulated concentrations for TN (R2=0.86), TP (R2=0.85), TSS (R2=0.91), Chl-a (R2=0.94), COD (R2=0.99), T. Coliform (R2=0.97) which are the best results in each season for Eymir and Mogan Lakes. The overall results of this study shows that by using easily measurable parameters even in ungauged situation the water quality of lakes can be predicted. Moreover, the outputs obtained from the regression equations can be used as an input for water quality models such as phosphorus budget model which is used to calculate the required reduction in the external phosphorus load to Lake Mogan to meet the water quality standards.

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

Walton, Mark A.

Quantum mechanics in phase space (or deformation quantization) appears to fail as an autonomous quantum method when infinite potential walls are present. The stationary physical Wigner functions do not satisfy the normal eigen equations, the *-eigen equations, unless an ad hoc boundary potential is added [N.C. Dias, J.N. Prata, J. Math. Phys. 43 (2002) 4602 (quant-ph/0012140)]. Alternatively, they satisfy a different, higher-order, '*-eigen-* equation', locally, i.e. away from the walls [S. Kryukov, M.A. Walton, Ann. Phys. 317 (2005) 474 (quant-ph/0412007)]. Here we show that this substitute equation can be written in a very simple form, even in the presence ofmore » an additional, arbitrary, but regular potential. The more general applicability of the *-eigen-* equation is then demonstrated. First, using an idea from [D.B. Fairlie, C.A. Manogue, J. Phys. A 24 (1991) 3807], we extend it to a dynamical equation describing time evolution. We then show that also for general contact interactions, the *-eigen-* equation is satisfied locally. Specifically, we treat the most general possible (Robin) boundary conditions at an infinite wall, general one-dimensional point interactions, and a finite potential jump. Finally, we examine a smooth potential, that has simple but different expressions for x positive and negative. We find that the *-eigen-* equation is again satisfied locally. It seems, therefore, that the *-eigen-* equation is generally relevant to the matching of Wigner functions; it can be solved piece-wise and its solutions then matched.« less

American Mathematics from 1940 to the Day Before Yesterday

ERIC Educational Resources Information Center

Ewing, J. H.; And Others

1976-01-01

Ten recent results in pure mathematics are described, covering the continuum hypothesis, Diophantine equations, simple groups, resolution of singularities, Weil conjectures, Lie groups, Poincare conjecture, exotic spheres, differential equations, and the index theorem. Proofs are omitted, but references are provided. (DT)

Elementary Hemodynamic Principles Based on Modified Bernoulli's Equation.

ERIC Educational Resources Information Center

Badeer, Henry S.

1985-01-01

Develops and expands basic concepts of Bernoulli's equation as it applies to vascular hemodynamics. Simple models are used to illustrate gravitational potential energy, steady nonturbulent flow, pump-driven streamline flow, and other areas. Relationships to the circulatory system are also discussed. (DH)

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

ERIC Educational Resources Information Center

Bulcock, J. W.; And Others

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

Effects of land use on water quality and transport of selected constituents in streams in Mecklenburg County, North Carolina, 1994–98

USGS Publications Warehouse

Ferrell, Gloria M.

2001-01-01

Transport rates for total solids, total nitrogen, total phosphorus, biochemical oxygen demand, chromium, copper, lead, nickel, and zinc during 1994–98 were computed for six stormwater-monitoring sites in Mecklenburg County, North Carolina. These six stormwater-monitoring sites were operated by the Mecklenburg County Department of Environmental Protection, in cooperation with the City of Charlotte, and are located near the mouths of major streams. Constituent transport at the six study sites generally was dominated by nonpoint sources, except for nitrogen and phosphorus at two sites located downstream from the outfalls of major municipal wastewater-treatment plants.To relate land use to constituent transport, regression equations to predict constituent yield were developed by using water-quality data from a previous study of nine stormwater-monitoring sites on small streams in Mecklenburg County. The drainage basins of these nine stormwater sites have relatively homogeneous land-use characteristics compared to the six study sites. Mean annual construction activity, based on building permit files, was estimated for all stormwater-monitoring sites and included as an explanatory variable in the regression equations. These regression equations were used to predict constituent yield for the six study sites. Predicted yields generally were in agreement with computed yields. In addition, yields were predicted by using regression equations derived from a national urban water-quality database. Yields predicted from the regional regression equations generally were about an order of magnitude lower than computed yields.Regression analysis indicated that construction activity was a major contributor to transport of the constituents evaluated in this study except for total nitrogen and biochemical oxygen demand. Transport of total nitrogen and biochemical oxygen demand was dominated by point-source contributions. The two study basins that had the largest amounts of construction activity also had the highest total solids yields (1,300 and 1,500 tons per square mile per year). The highest total phosphorus yields (3.2 and 1.7 tons per square mile per year) attributable to nonpoint sources also occurred in these basins. Concentrations of chromium, copper, lead, nickel, and zinc were positively correlated with total solids concentrations at most of the study sites (Pearson product-moment correlation >0.50). The site having the highest median concentrations of chromium, copper, and nickel also was the site having the highest computed yield for total solids.

A study to ascertain the viability of ultrasonic nondestructive testing to determine the mechanical characteristics of wood/agricultural hardboards with soybean based adhesives

NASA Astrophysics Data System (ADS)

Colen, Charles Raymond, Jr.

There have been numerous studies with ultrasonic nondestructive testing and wood fiber composites. The problem of the study was to ascertain whether ultrasonic nondestructive testing can be used in place of destructive testing to obtain the modulus of elasticity (MOE) of the wood/agricultural material with comparable results. The uniqueness of this research is that it addressed the type of content (cornstalks and switchgrass) being used with the wood fibers and the type of adhesives (soybean-based) associated with the production of these composite materials. Two research questions were addressed in the study. The major objective was to determine if one can predict the destructive test MOE value based on the nondestructive test MOE value. The population of the study was wood/agricultural fiberboards made from wood fibers, cornstalks, and switchgrass bonded together with soybean-based, urea-formaldehyde, and phenol-formaldehyde adhesives. Correlational analysis was used to determine if there was a relationship between the two tests. Regression analysis was performed to determine a prediction equation for the destructive test MOE value. Data were collected on both procedures using ultrasonic nondestructing testing and 3-point destructive testing. The results produced a simple linear regression model for this study which was adequate in the prediction of destructive MOE values if the nondestructive MOE value is known. An approximation very close to the entire error in the model equation was explained from the destructive test MOE values for the composites. The nondestructive MOE values used to produce a linear regression model explained 83% of the variability in the destructive test MOE values. The study also showed that, for the particular destructive test values obtained with the equipment used, the model associated with the study is as good as it could be due to the variability in the results from the destructive tests. In this study, an ultrasonic signal was used to determine the MOE values on nondestructive tests. Future research studies could use the same or other hardboards to examine how the resins affect the ultrasonic signal.

Weighing Evidence “Steampunk” Style via the Meta-Analyser

PubMed Central

Bowden, Jack; Jackson, Chris

2016-01-01

ABSTRACT The funnel plot is a graphical visualization of summary data estimates from a meta-analysis, and is a useful tool for detecting departures from the standard modeling assumptions. Although perhaps not widely appreciated, a simple extension of the funnel plot can help to facilitate an intuitive interpretation of the mathematics underlying a meta-analysis at a more fundamental level, by equating it to determining the center of mass of a physical system. We used this analogy to explain the concepts of weighing evidence and of biased evidence to a young audience at the Cambridge Science Festival, without recourse to precise definitions or statistical formulas and with a little help from Sherlock Holmes! Following on from the science fair, we have developed an interactive web-application (named the Meta-Analyser) to bring these ideas to a wider audience. We envisage that our application will be a useful tool for researchers when interpreting their data. First, to facilitate a simple understanding of fixed and random effects modeling approaches; second, to assess the importance of outliers; and third, to show the impact of adjusting for small study bias. This final aim is realized by introducing a novel graphical interpretation of the well-known method of Egger regression. PMID:28003684

Estimating population trends with a linear model: Technical comments

USGS Publications Warehouse

Sauer, John R.; Link, William A.; Royle, J. Andrew

2004-01-01

Controversy has sometimes arisen over whether there is a need to accommodate the limitations of survey design in estimating population change from the count data collected in bird surveys. Analyses of surveys such as the North American Breeding Bird Survey (BBS) can be quite complex; it is natural to ask if the complexity is necessary, or whether the statisticians have run amok. Bart et al. (2003) propose a very simple analysis involving nothing more complicated than simple linear regression, and contrast their approach with model-based procedures. We review the assumptions implicit to their proposed method, and document that these assumptions are unlikely to be valid for surveys such as the BBS. One fundamental limitation of a purely design-based approach is the absence of controls for factors that influence detection of birds at survey sites. We show that failure to model observer effects in survey data leads to substantial bias in estimation of population trends from BBS data for the 20 species that Bart et al. (2003) used as the basis of their simulations. Finally, we note that the simulations presented in Bart et al. (2003) do not provide a useful evaluation of their proposed method, nor do they provide a valid comparison to the estimating- equations alternative they consider.

An Alternative to the Breeder’s and Lande’s Equations

PubMed Central

Houchmandzadeh, Bahram

2013-01-01

The breeder’s equation is a cornerstone of quantitative genetics, widely used in evolutionary modeling. Noting the mean phenotype in parental, selected parents, and the progeny by E(Z0), E(ZW), and E(Z1), this equation relates response to selection R = E(Z1) − E(Z0) to the selection differential S = E(ZW) − E(Z0) through a simple proportionality relation R = h2S, where the heritability coefficient h2 is a simple function of genotype and environment factors variance. The validity of this relation relies strongly on the normal (Gaussian) distribution of the parent genotype, which is an unobservable quantity and cannot be ascertained. In contrast, we show here that if the fitness (or selection) function is Gaussian with mean μ, an alternative, exact linear equation of the form R′ = j2S′ can be derived, regardless of the parental genotype distribution. Here R′ = E(Z1) − μ and S′ = E(ZW) − μ stand for the mean phenotypic lag with respect to the mean of the fitness function in the offspring and selected populations. The proportionality coefficient j2 is a simple function of selection function and environment factors variance, but does not contain the genotype variance. To demonstrate this, we derive the exact functional relation between the mean phenotype in the selected and the offspring population and deduce all cases that lead to a linear relation between them. These results generalize naturally to the concept of G matrix and the multivariate Lande’s equation Δz¯=GP−1S. The linearity coefficient of the alternative equation are not changed by Gaussian selection. PMID:24212080

Coordinating Procedural and Conceptual Knowledge to Make Sense of Word Equations: Understanding the Complexity of a "Simple" Completion Task at the Learner's Resolution

ERIC Educational Resources Information Center

Taber, Keith S.; Bricheno, Pat

2009-01-01

The present paper discusses the conceptual demands of an apparently straightforward task set to secondary-level students--completing chemical word equations with a single omitted term. Chemical equations are of considerable importance in chemistry, and school students are expected to learn to be able to write and interpret them. However, it is…

A Simple Method to Find out when an Ordinary Differential Equation Is Separable

ERIC Educational Resources Information Center

Cid, Jose Angel

2009-01-01

We present an alternative method to that of Scott (D. Scott, "When is an ordinary differential equation separable?", "Amer. Math. Monthly" 92 (1985), pp. 422-423) to teach the students how to discover whether a differential equation y[prime] = f(x,y) is separable or not when the nonlinearity f(x, y) is not explicitly factorized. Our approach is…

A Heuristic Fast Method to Solve the Nonlinear Schroedinger Equation in Fiber Bragg Gratings with Arbitrary Shape Input Pulse

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

Emami, F.; Hatami, M.; Keshavarz, A. R.

2009-08-13

Using a combination of Runge-Kutta and Jacobi iterative method, we could solve the nonlinear Schroedinger equation describing the pulse propagation in FBGs. By decomposing the electric field to forward and backward components in fiber Bragg grating and utilizing the Fourier series analysis technique, the boundary value problem of a set of coupled equations governing the pulse propagation in FBG changes to an initial condition coupled equations which can be solved by simple Runge-Kutta method.

Fluid dynamics of out of equilibrium boost invariant plasmas

NASA Astrophysics Data System (ADS)

Blaizot, Jean-Paul; Yan, Li

2018-05-01

By solving a simple kinetic equation, in the relaxation time approximation, and for a particular set of moments of the distribution function, we establish a set of equations which, on the one hand, capture exactly the dynamics of the kinetic equation, and, on the other hand, coincide with the hierarchy of equations of viscous hydrodynamics, to arbitrary order in the viscous corrections. This correspondence sheds light on the underlying mechanism responsible for the apparent success of hydrodynamics in regimes that are far from local equilibrium.

Transient Nonequilibrium Molecular Dynamic Simulations of Thermal Conductivity: 1. Simple Fluids

NASA Astrophysics Data System (ADS)

Hulse, R. J.; Rowley, R. L.; Wilding, W. V.

2005-01-01

Thermal conductivity has been previously obtained from molecular dynamics (MD) simulations using either equilibrium (EMD) simulations (from Green--Kubo equations) or from steady-state nonequilibrium (NEMD) simulations. In the case of NEMD, either boundary-driven steady states are simulated or constrained equations of motion are used to obtain steady-state heat transfer rates. Like their experimental counterparts, these nonequilibrium steady-state methods are time consuming and may have convection problems. Here we report a new transient method developed to provide accurate thermal conductivity predictions from MD simulations. In the proposed MD method, molecules that lie within a specified volume are instantaneously heated. The temperature decay of the system of molecules inside the heated volume is compared to the solution of the transient energy equation, and the thermal diffusivity is regressed. Since the density of the fluid is set in the simulation, only the isochoric heat capacity is needed in order to obtain the thermal conductivity. In this study the isochoric heat capacity is determined from energy fluctuations within the simulated fluid. The method is valid in the liquid, vapor, and critical regions. Simulated values for the thermal conductivity of a Lennard-Jones (LJ) fluid were obtained using this new method over a temperature range of 90 to 900 K and a density range of 1-35 kmol · m-3. These values compare favorably with experimental values for argon. The new method has a precision of ±10%. Compared to other methods, the algorithm is quick, easy to code, and applicable to small systems, making the simulations very efficient.

Prediction of work metabolism from heart rate measurements in forest work: some practical methodological issues.

PubMed

Dubé, Philippe-Antoine; Imbeau, Daniel; Dubeau, Denise; Auger, Isabelle; Leone, Mario

2015-01-01

Individual heart rate (HR) to workload relationships were determined using 93 submaximal step-tests administered to 26 healthy participants attending physical activities in a university training centre (laboratory study) and 41 experienced forest workers (field study). Predicted maximum aerobic capacity (MAC) was compared to measured MAC from a maximal treadmill test (laboratory study) to test the effect of two age-predicted maximum HR Equations (220-age and 207-0.7 × age) and two clothing insulation levels (0.4 and 0.91 clo) during the step-test. Work metabolism (WM) estimated from forest work HR was compared against concurrent work V̇O2 measurements while taking into account the HR thermal component. Results show that MAC and WM can be accurately predicted from work HR measurements and simple regression models developed in this study (1% group mean prediction bias and up to 25% expected prediction bias for a single individual). Clothing insulation had no impact on predicted MAC nor age-predicted maximum HR equations. Practitioner summary: This study sheds light on four practical methodological issues faced by practitioners regarding the use of HR methodology to assess WM in actual work environments. More specifically, the effect of wearing work clothes and the use of two different maximum HR prediction equations on the ability of a submaximal step-test to assess MAC are examined, as well as the accuracy of using an individual's step-test HR to workload relationship to predict WM from HR data collected during actual work in the presence of thermal stress.

A simple, analytic 3-dimensional downburst model based on boundary layer stagnation flow

NASA Technical Reports Server (NTRS)

Oseguera, Rosa M.; Bowles, Roland L.

1988-01-01

A simple downburst model is developed for use in batch and real-time piloted simulation studies of guidance strategies for terminal area transport aircraft operations in wind shear conditions. The model represents an axisymmetric stagnation point flow, based on velocity profiles from the Terminal Area Simulation System (TASS) model developed by Proctor and satisfies the mass continuity equation in cylindrical coordinates. Altitude dependence, including boundary layer effects near the ground, closely matches real-world measurements, as do the increase, peak, and decay of outflow and downflow with increasing distance from the downburst center. Equations for horizontal and vertical winds were derived, and found to be infinitely differentiable, with no singular points existent in the flow field. In addition, a simple relationship exists among the ratio of maximum horizontal to vertical velocities, the downdraft radius, depth of outflow, and altitude of maximum outflow. In use, a microburst can be modeled by specifying four characteristic parameters, velocity components in the x, y and z directions, and the corresponding nine partial derivatives are obtained easily from the velocity equations.

Equations for predicting biomass of six introduced tree species, island of Hawaii

Treesearch

Thomas H. Schukrt; Robert F. Strand; Thomas G. Cole; Katharine E. McDuffie

1988-01-01

Regression equations to predict total and stem-only above-ground dry biomass for six species (Acacia melanoxylon, Albizio falcataria, Eucalyptus globulus, E. grandis, E. robusta, and E. urophylla) were developed by felling and measuring 2- to 6-year-old...

Principal component regression analysis with SPSS.

PubMed

Liu, R X; Kuang, J; Gong, Q; Hou, X L

2003-06-01

The paper introduces all indices of multicollinearity diagnoses, the basic principle of principal component regression and determination of 'best' equation method. The paper uses an example to describe how to do principal component regression analysis with SPSS 10.0: including all calculating processes of the principal component regression and all operations of linear regression, factor analysis, descriptives, compute variable and bivariate correlations procedures in SPSS 10.0. The principal component regression analysis can be used to overcome disturbance of the multicollinearity. The simplified, speeded up and accurate statistical effect is reached through the principal component regression analysis with SPSS.

Branson: A Mini-App for Studying Parallel IMC, Version 1.0

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

Long, Alex

This code solves the gray thermal radiative transfer (TRT) equations in parallel using simple opacities and Cartesian meshes. Although Branson solves the TRT equations it is not designed to model radiation transport: Branson contains simple physics and does not have a multigroup treatment, nor can it use physical material data. The opacities have are simple polynomials in temperature there is a limited ability to specify complex geometries and sources. Branson was designed only to capture the computational demands of production IMC codes, especially in large parallel runs. It was also intended to foster collaboration with vendors, universities and other DOEmore » partners. Branson is similar in character to the neutron transport proxy-app Quicksilver from LLNL, which was recently open-sourced.« less

Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana

USGS Publications Warehouse

Sando, Steven K.; Morgan, Timothy J.; Dutton, DeAnn M.; McCarthy, Peter M.

2009-01-01

Charles M. Russell National Wildlife Refuge (CMR) encompasses about 1.1 million acres (including Fort Peck Reservoir on the Missouri River) in northeastern Montana. To ensure that sufficient streamflow remains in the tributary streams to maintain the riparian corridors, the U.S. Fish and Wildlife Service is negotiating water-rights issues with the Reserved Water Rights Compact Commission of Montana. The U.S. Geological Survey, in cooperation with the U.S. Fish and Wildlife Service, conducted a study to gage, for a short period, selected streams that cross CMR, and analyze data to estimate long-term streamflow characteristics for CMR. The long-term streamflow characteristics of primary interest include the monthly and annual 90-, 80-, 50-, and 20-percent exceedance streamflows and mean streamflows (Q.90, Q.80, Q.50, Q.20, and QM, respectively), and the 1.5-, 2-, and 2.33- year peak flows (PK1.5, PK2, and PK2.33, respectively). The Regional Adjustment Relationship (RAR) was investigated for estimating the monthly and annual Q.90, Q.80, Q.50, Q.20, and QM, and the PK1.5, PK2, and PK2.33 for the short-term CMR gaging stations (hereinafter referred to as CMR stations). The RAR was determined to provide acceptable results for estimating the long-term Q.90, Q.80, Q.50, Q.20, and QM on a monthly basis for the months of March through June, and also on an annual basis. For the months of September through January, the RAR regression equations did not provide acceptable results for any long-term streamflow characteristic. For the month of February, the RAR regression equations provided acceptable results for the long-term Q.50 and QM, but poor results for the long-term Q.90, Q.80, and Q.20. For the months of July and August, the RAR provided acceptable results for the long-term Q.50, Q.20, and QM, but poor results for the long-term Q.90 and Q.80. Estimation coefficients were developed for estimating the long-term streamflow characteristics for which the RAR did not provide acceptable results. The RAR also was determined to provide acceptable results for estimating the PK1.5., PK2, and PK2.33 for the three CMR stations that lacked suitable peak-flow records. Methods for estimating streamflow characteristics at ungaged sites also were derived. Regression analyses that relate individual streamflow characteristics to various basin and climatic characteristics for gaging stations were performed to develop regression equations to estimate streamflow characteristics at ungaged sites. Final equations for the annual Q.50, Q.20, and QM are reported. Acceptable equations also were developed for estimating QM for the months of February, March, April, June, and July, and Q.50, Q.20, and QM on an annual basis. However, equations for QM for the months of February, March, April, June, and July were determined to be less consistent and reliable than the use of estimation coefficients applied to the regression equation results for the annual QM. Acceptable regression equations also were developed for the PK1.5, PK2, and PK2.33.

Estimated fecal coliform bacteria concentrations using near real-time continuous water-quality and streamflow data from five stream sites in Chester County, Pennsylvania, 2007–16

USGS Publications Warehouse

Senior, Lisa A.

2017-09-15

Several streams used for recreational activities, such as fishing, swimming, and boating, in Chester County, Pennsylvania, are known to have periodic elevated concentrations of fecal coliform bacteria, a type of bacteria used to indicate the potential presence of fecally related pathogens that may pose health risks to humans exposed through water contact. The availability of near real-time continuous stream discharge, turbidity, and other water-quality data for some streams in the county presents an opportunity to use surrogates to estimate near real-time concentrations of fecal coliform (FC) bacteria and thus provide some information about associated potential health risks during recreational use of streams.The U.S. Geological Survey (USGS), in cooperation with the Chester County Health Department (CCHD) and the Chester County Water Resources Authority (CCWRA), has collected discrete stream samples for analysis of FC concentrations during March–October annually at or near five gaging stations where near real-time continuous data on stream discharge, turbidity, and water temperature have been collected since 2007 (or since 2012 at 2 of the 5 stations). In 2014, the USGS, in cooperation with the CCWRA and CCHD, began to develop regression equations to estimate FC concentrations using available near real-time continuous data. Regression equations included possible explanatory variables of stream discharge, turbidity, water temperature, and seasonal factors calculated using Julian Day with base-10 logarithmic (log) transformations of selected variables.The regression equations were developed using the data from 2007 to 2015 (101–106 discrete bacteria samples per site) for three gaging stations on Brandywine Creek (West Branch Brandywine Creek at Modena, East Branch Brandywine Creek below Downingtown, and Brandywine Creek at Chadds Ford) and from 2012 to 2015 (37–38 discrete bacteria samples per site) for one station each on French Creek near Phoenixville and White Clay Creek near Strickersville. Fecal coliform bacteria data collected by USGS in 2016 (about nine samples per site) were used to validate the equations. The best-fit regression equations included log turbidity and seasonality factors computed using Julian Day as explanatory variables to estimate log FC concentrations at all five stream sites. The adjusted coefficient of determination for the equations ranged from 0.61 to 0.76, with the strength of the regression equations likely affected in part by the limited amount and variability of FC bacteria data. During summer months, the estimated and measured FC concentrations commonly were greater than the Pennsylvania Department of Environmental Protection established standards of 200 and 400 colonies per 100 milliliters for water contact from May through September at the 5 stream sites, with concentrations typically higher at 2 sites (White Clay Creek and West Branch Brandywine Creek at Modena) than at the other 3 sites. The estimated concentrations of FC bacteria during the summer months commonly were higher than measured concentrations and therefore could be considered cautious estimates of potential human-health risk. Additional water-quality data are needed to maintain and (or) improve the ability of regression equations to estimate FC concentrations by use of surrogate data.

Alfven Simple Waves

NASA Astrophysics Data System (ADS)

Webb, G. M.; Zank, G. P.; Burrows, R.

2009-12-01

Multi-dimensional Alfvén simple waves in magnetohydrodynamics (MHD) are investigated using Boillat's formalism. For simple wave solutions, all physical variables (the gas density, pressure, fluid velocity, entropy, and magnetic field induction in the MHD case) depend on a single phase function ǎrphi which is a function of the space and time variables. The simple wave ansatz requires that the wave normal and the normal speed of the wave front depend only on the phase function ǎrphi. This leads to an implicit equation for the phase function, and a generalisation of the concept of a plane wave. We obtain examples of Alfvén simple waves, based on the right eigenvector solutions for the Alfvén mode. The Alfvén mode solutions have six integrals, namely that the entropy, density, magnetic pressure and the group velocity (the sum of the Alfvén and fluid velocity) are constant throughout the wave. The eigen-equations require that the rate of change of the magnetic induction B with ǎrphi throughout the wave is perpendicular to both the wave normal n and B. Methods to construct simple wave solutions based on specifying either a solution ansatz for n(ǎrphi) or B(ǎrphi) are developed.

Development of a traveltime prediction equation for streams in Arkansas

USGS Publications Warehouse

Funkhouser, Jaysson E.; Barks, C. Shane

2004-01-01

During 1971 and 1981 and 2001 and 2003, traveltime measurements were made at 33 sample sites on 18 streams throughout northern and western Arkansas using fluorescent dye. Most measurements were made during steady-state base-flow conditions with the exception of three measurements made during near steady-state medium-flow conditions (for the study described in this report, medium-flow is approximately 100-150 percent of the mean monthly streamflow during the month the dye trace was conducted). These traveltime data were compared to the U.S. Geological Survey?s national traveltime prediction equation and used to develop a specific traveltime prediction equation for Arkansas streams. In general, the national traveltime prediction equation yielded results that over-predicted the velocity of the streams for 29 of the 33 sites measured. The standard error for the national traveltime prediction equation was 105 percent. The coefficient of determination was 0.78. The Arkansas prediction equation developed from a regression analysis of dye-tracing results was a significant improvement over the national prediction equation. This regression analysis yielded a standard error of 46 percent and a coefficient of determination of 0.74. The predicted velocities using this equation compared better to measured velocities. Using the variables in a regression analysis, the Arkansas prediction equation derived for the peak velocity in feet per second was: (Actual Equation Shown in report) In addition to knowing when the peak concentration will arrive at a site, it is of great interest to know when the leading edge of a contaminant plume will arrive. The traveltime of the leading edge of a contaminant plume indicates when a potential problem might first develop and also defines the overall shape of the concentration response function. Previous USGS reports have shown no significant relation between any of the variables and the time from injection to the arrival of the leading edge of the dye plume. For this report, the analysis of the dye-tracing data yielded a significant correlation between traveltime of the leading edge and traveltime of the peak concentration with an R2 value of 0.99. These data indicate that the traveltime of the leading edge can be estimated from: (Actual Equation Shown in Report)

Half-cell potentials of semiconductive simple binary sulphides in aqueous solution

USGS Publications Warehouse

Sato, M.

1966-01-01

Theoretical consideration of the charge-transfer mechanism operative in cells with an electrode of a semiconductive binary compound leads to the conclusion that the half-cell potential of such a compound is not only a function of ionic activities in the electrolytic solution, but also a function of the activities of the component elements in the compound phase. The most general form of the electrode equation derived for such a compound with a formula MiXj which dissociates into Mj+ and Xi- ions in aqueous solution is. EMiXj = EMiXj0 + R T 2 ij ln [ (sua Mj+)aqi ?? (suaX)jMiXj/ (suaXi-)aqj ?? (suaM)iMiXj],. where. EMiXj0 = 1 2(EM,Mj+0 + EXi-,X). The equation can be modified to other forms. When applied to semiconductive simple binary sulphides, these equations appear to give better descriptions of the observed electrode potentials of such sulphides than any other proposed equations. ?? 1966.

Helmholtz-Smoluchowski velocity for viscoelastic electroosmotic flows.

PubMed

Park, H M; Lee, W M

2008-01-15

Many biofluids such as blood and DNA solutions are viscoelastic and exhibit extraordinary flow behaviors, not existing in Newtonian fluids. Adopting appropriate constitutive equations these exotic flow behaviors can be modeled and predicted reasonably using various numerical methods. However, the governing equations for viscoelastic flows are not easily solvable, especially for electroosmotic flows where the streamwise velocity varies rapidly from zero at the wall to a nearly uniform velocity at the outside of the very thin electric double layer. In the present investigation, we have devised a simple method to find the volumetric flow rate of viscoelastic electroosmotic flows through microchannels. It is based on the concept of the Helmholtz-Smoluchowski velocity which is widely adopted in the electroosmotic flows of Newtonian fluids. It is shown that the Helmholtz-Smoluchowski velocity for viscoelastic fluids can be found by solving a simple cubic algebraic equation. The volumetric flow rate obtained using this Helmholtz-Smoluchowski velocity is found to be almost the same as that obtained by solving the governing partial differential equations for various viscoelastic fluids.

[Aboveground biomass of three conifers in Qianyanzhou plantation].

PubMed

Li, Xuanran; Liu, Qijing; Chen, Yongrui; Hu, Lile; Yang, Fengting

2006-08-01

In this paper, the regressive models of the aboveground biomass of Pinus elliottii, P. massoniana and Cunninghamia lanceolata in Qianyanzhou of subtropical China were established, and the regression analysis on the dry weight of leaf biomass and total biomass against branch diameter (d), branch length (L), d3 and d2L was conducted with linear, power and exponent functions. Power equation with single parameter (d) was proved to be better than the rests for P. massoniana and C. lanceolata, and linear equation with parameter (d3) was better for P. elliottii. The canopy biomass was derived by the regression equations for all branches. These equations were also used to fit the relationships of total tree biomass, branch biomass and foliage biomass with tree diameter at breast height (D), tree height (H), D3 and D2H, respectively. D2H was found to be the best parameter for estimating total biomass. For foliage-and branch biomass, both parameters and equation forms showed some differences among species. Correlations were highly significant (P <0.001) for foliage-, branch-and total biomass, with the highest for total biomass. By these equations, the aboveground biomass and its allocation were estimated, with the aboveground biomass of P. massoniana, P. elliottii, and C. lanceolata forests being 83.6, 72. 1 and 59 t x hm(-2), respectively, and more stem biomass than foliage-and branch biomass. According to the previous studies, the underground biomass of these three forests was estimated to be 10.44, 9.42 and 11.48 t x hm(-2), and the amount of fixed carbon was 47.94, 45.14 and 37.52 t x hm(-2), respectively.

Mental chronometry with simple linear regression.

PubMed

Chen, J Y

1997-10-01

Typically, mental chronometry is performed by means of introducing an independent variable postulated to affect selectively some stage of a presumed multistage process. However, the effect could be a global one that spreads proportionally over all stages of the process. Currently, there is no method to test this possibility although simple linear regression might serve the purpose. In the present study, the regression approach was tested with tasks (memory scanning and mental rotation) that involved a selective effect and with a task (word superiority effect) that involved a global effect, by the dominant theories. The results indicate (1) the manipulation of the size of a memory set or of angular disparity affects the intercept of the regression function that relates the times for memory scanning with different set sizes or for mental rotation with different angular disparities and (2) the manipulation of context affects the slope of the regression function that relates the times for detecting a target character under word and nonword conditions. These ratify the regression approach as a useful method for doing mental chronometry.

Prediction of maximal surface electromyographically based voluntary contractions of erector spinae muscles from sonographic measurements during isometric contractions.

PubMed

Cuesta-Vargas, Antonio I; González-Sánchez, Manuel

2014-03-01

Currently, there are no studies combining electromyography (EMG) and sonography to estimate the absolute and relative strength values of erector spinae (ES) muscles in healthy individuals. The purpose of this study was to establish whether the maximum voluntary contraction (MVC) of the ES during isometric contractions could be predicted from the changes in surface EMG as well as in fiber pennation and thickness as measured by sonography. Thirty healthy adults performed 3 isometric extensions at 45° from the vertical to calculate the MVC force. Contractions at 33% and 100% of the MVC force were then used during sonographic and EMG recordings. These measurements were used to observe the architecture and function of the muscles during contraction. Statistical analysis was performed using bivariate regression and regression equations. The slope for each regression equation was statistically significant (P < .001) with R(2) values of 0.837 and 0.986 for the right and left ES, respectively. The standard error estimate between the sonographic measurements and the regression-estimated pennation angles for the right and left ES were 0.10 and 0.02, respectively. Erector spinae muscle activation can be predicted from the changes in fiber pennation during isometric contractions at 33% and 100% of the MVC force. These findings could be essential for developing a regression equation that could estimate the level of muscle activation from changes in the muscle architecture.

Beyond logistic regression: structural equations modelling for binary variables and its application to investigating unobserved confounders.

PubMed

Kupek, Emil

2006-03-15

Structural equation modelling (SEM) has been increasingly used in medical statistics for solving a system of related regression equations. However, a great obstacle for its wider use has been its difficulty in handling categorical variables within the framework of generalised linear models. A large data set with a known structure among two related outcomes and three independent variables was generated to investigate the use of Yule's transformation of odds ratio (OR) into Q-metric by (OR-1)/(OR+1) to approximate Pearson's correlation coefficients between binary variables whose covariance structure can be further analysed by SEM. Percent of correctly classified events and non-events was compared with the classification obtained by logistic regression. The performance of SEM based on Q-metric was also checked on a small (N = 100) random sample of the data generated and on a real data set. SEM successfully recovered the generated model structure. SEM of real data suggested a significant influence of a latent confounding variable which would have not been detectable by standard logistic regression. SEM classification performance was broadly similar to that of the logistic regression. The analysis of binary data can be greatly enhanced by Yule's transformation of odds ratios into estimated correlation matrix that can be further analysed by SEM. The interpretation of results is aided by expressing them as odds ratios which are the most frequently used measure of effect in medical statistics.